Grade 6

Module 1: Ratios and Unit Rates

Eureka MathDesmos Math 6–A1
Topic A Representing and Reasoning About Ratios 
Lesson 1: Ratios
Lesson 2: Ratios
Unit 2
Lesson 1: Pizza Maker [Free lesson]
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Equivalent Ratios
Lesson 4: Equivalent Ratios
Unit 2
Lesson 3: Rice Ratios
Lesson 4: Fruit Lab [Free lesson]
Lesson 5: Balancing Act
Lesson 7: Mixing Paint, Part 1
Lesson 8 World Records (Print available)
Lesson 11 Community Life (Print available)
Practice Day 1 (Print available)
Lesson 5: Solving Problems by Finding Equivalent Ratios
Lesson 6: Solving Problems by Finding Equivalent Ratios
Unit 2
Lesson 5 Balancing Act
 
Lesson 7: Associated Ratios and the Value of a Ratio
Lesson 8: Equivalent Ratios Defined Through the Value of a Ratio
Unit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Topic B Collections of Equivalent Ratios 
Lesson 9: Tables of Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 10: The Structure of Ratio Tables-Additive and MultiplicativeUnit 2
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 11: Comparing Ratios Using Ratio TablesUnit 2
Lesson 10: Balloons
Lesson 12: From Ratio Tables to Double Number Line DiagramsUnit 2
Lesson 6: Product Prices (Print available)
Lesson 8: World Records (Print available)
Lesson 12: Mixing Paint, Part 2
Lesson 14: Lunch Waste (Print available)
Practice Day 2 (Print available)
Lesson 13: From Ratio Tables to Equations Using the Value of a Ratio 
Lesson 14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane 
Lesson 15: A Synthesis of Representations of Equivalent Ratio Collections 
Topic C Unit Rates 
Lesson 16: From Ratio to RatesUnit 2
Lesson 8: World Records (Print available)
 
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 17: From Rates to Ratios 
Lesson 18: Finding a Rate by Dividing Two QuantitiesUnit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 7: More Soft Serve
Lesson 19: Comparison Shopping-Unit Price and Related Measurement Conversions
Lesson 20: Comparison Shopping-Unit Price and Related Measurement Conversions
Lesson 21: Getting the Job Done—Speed, Work, and Measurement Units
Lesson 22: Getting the Job Done—Speed, Work, and Measurement Units
Unit 3
Lesson 2: Counting Classrooms
Lesson 3: Pen Pals
Lesson 23: Problem-Solving Using Rates, Unit Rates, and Conversions.Unit 3
Lesson 13: A Country as a Village
Topic D Percent 
Lesson 24: Percent and Rates per 100Unit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 25: A Fraction as a Percent 
Lesson 26: Percent of a Quantity.Unit 3
Lesson 10: What´s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 27: Solving Percent Problems
Lesson 28: Solving Percent Problems
Lesson 29: Solving Percent Problems
Unit 3
Lesson 10: What´s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Practice Day 2 (Print available)

Module 2: Arithmetic Operations Including Division of Fractions

Lesson 1: Interpreting Division of a Fraction by a Whole Number—Visual Models.Unit 4
Lesson 2: Making Connections (Print available)
Lesson 2: Interpreting Division of a Whole Number by a Fraction —Visual Models.Unit 4
Lesson 1: Cookie Cutter
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Lesson 5: Garden Bricks (Print available)
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Unit 4
Lesson 5: Garden Bricks
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 5: Creating Division Stories. 
Lesson 6: More Division Stories. 
Lesson 7: The Relationship Between Visual Fraction Models and Equations 
Lesson 8: Dividing Fractions and Mixed NumbersUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 6: Fill the Gap [Free lesson]
Topic B Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
Lesson 9: Sums and Differences of DecimalsUnit 5
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 10: The Distributive Property and the Products of DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 11: Fraction Multiplication and the Products of DecimalsUnit 5
Lesson 7: Multiplication Methods (Print available)
Topic C Dividing Whole Numbers and Decimals
Lesson 12: Estimating Digits in a Quotient 
Lesson 13: Dividing Multi-Digit Numbers Using the AlgorithmUnit 5
Lesson 9: Long Division Launch
Practice Day 1 (Print available)
Practice Day 2 (Print available)
Lesson 14: The Division Algorithm—Converting Decimal Division into Whole Number Division Using Fractions. 
Lesson 15: The Division Algorithm—Converting Decimal Division into Whole Number Division Using Mental Math 
Topic D Number Theory—Thinking Logically About Multiplicative Arithmetic 
Lesson 16: Even and Odd Numbers 
Lesson 17: Divisibility Tests for 3 and 9 
Lesson 18: Least Common Multiple and Greatest Common FactorUnit 5
Lesson 14: Common Multiples
Lesson 15: Common Factors
Practice Day 2 (Print available)
Lesson 19: The Euclidean Algorithm as an Application of the Long Division Algorithm 

Module 3: Rational Numbers

Lesson 1: Positive and Negative Numbers on the Number Line—Opposite Direction and ValueUnit 7Lesson 2: Digging Deeper
Lesson 2: Real-World Positive and Negative Numbers and Zero.
Lesson 3: Real-World Positive and Negative Numbers and Zero.
Unit 7 Lesson 4: Sub-Zero
Lesson 4: The Opposite of a Number
Lesson 5: The Opposite of a Number’s Opposite
Lesson 6: Rational Numbers on the Number Line
Unit 7Lesson 2: Digging Deeper
Topic B Order and Absolute Value
Lesson 7: Ordering Integers and Other Rational Numbers
Lesson 8: Ordering Integers and Other Rational Numbers
Lesson 9: Comparing Integers and Other Rational Numbers
Unit 7Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 10: Writing and Interpreting Inequality Statements Involving Rational Numbers 
Lesson 11: Absolute Value—Magnitude and Distance
Lesson 12: The Relationship Between Absolute Value and Order
Unit 7Lesson 5: Distance on the Number Line
Lesson 13: Statements of Order in the Real World. 
Topic C Rational Numbers and the Coordinate Plane 
Lesson 14: Ordered Pairs
Lesson 15: Locating Ordered Pairs on the Coordinate Plane
Unit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate PlaneLesson 11: Polygon Maker
Lesson 16: Symmetry in the Coordinate Plane. 
Lesson 17: Drawing the Coordinate Plane and Points on the PlaneLesson 10: The A-maze-ing Coordinate Plane
Lesson 18: Distance on the Coordinate PlaneUnit 7Lesson 11: Polygon Maker
Lesson 19: Problem Solving and the Coordinate PlaneUnit 7Lesson 12: Graph Telephone (Print available)Practice Day 2 (Print available)

Module 4: Expressions and Equations

Topic A Relationships of the Operations 
Lesson 1: The Relationship of Addition and Subtraction 
Lesson 2: The Relationship of Multiplication and Division 
Lesson 3: The Relationship of Multiplication and Addition. 
Lesson 4: The Relationship of Division and Subtraction 
Topic B Special Notations of Operations 
Lesson 5: ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)Practice Day 2 (Print available)
Lesson 6: The Order of Operations 
Topic C Replacing Letters and Numbers 
Lesson 7: Replacing Letters with Numbers
Lesson 8: Replacing Numbers with Letters
Unit 6Lesson 7: Border TilesLesson 12: Squares and Cubes
Topic D Expanding, Factoring, and Distributing Expressions 
Lesson 9: Writing Addition and Subtraction ExpressionsUnit 6Lesson 6: Vari-applesLesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 11: Factoring Expressions
Lesson 12: Distributing Expressions
Unit 6Lesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences
Lesson 13: Writing Division Expressions 
Lesson 14: Writing Division Expressions 
Topic E Expressing Operations in Algebraic Form 
Lesson 15: Read Expressions in Which Letters Stand for Numbers
Lesson 16: Write Expressions in Which Letters Stand for Numbers
Lesson 17: Write Expressions in Which Letters Stand for Numbers
Unit 6Lesson 6: Vari-applesLesson 7: Border Tiles
Topic F Writing and Evaluating Expressions and Formulas 
Lesson 18: Writing and Evaluating Expressions—Addition and Subtraction
Lesson 19: Substituting to Evaluate Addition and Subtraction Expressions
Lesson 20: Writing and Evaluating Expressions—Multiplication and Division
Lesson 21: Writing and Evaluating Expressions—Multiplication and Addition
Unit 6Lesson 7: Border TilesLesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and DifferencesLesson 12: Squares and Cubes
Lesson 22: Writing and Evaluating Expressions—ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)Lesson 12: Squares and CubesPractice Day 2 (Print available)
Topic G Solving Equations 
Lesson 23: True and False Number Sentences
Lesson 24: True and False Number Sentences
Unit 6Lesson 1: Weight for It [Free lesson]
Lesson 25: Finding Solutions to Make Equations TrueUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations
Lesson 26: One-Step Equations—Addition and SubtractionUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five EquationsLesson 3: Hanging Around
Lesson 27: One-Step Equations—Multiplication and Division
Lesson 28: Two-Step Problems—All Operations
Lesson 29: Multi-Step Problems—All Operations
Unit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and Solve
Topic H Applications of Equations 
Lesson 30: One-Step Problems in the Real World
Lesson 31: Problems in Mathematical TermsLesson Lesson 32: Multi-Step Problems in the Real World
Unit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and SolvePractice Day 1 (Print available)
Lesson 33: From Equations to Inequalities
Lesson 34: Writing and Graphing Inequalities in Real-World Problems
Unit 7Lesson 6: Tunnel Travel [Free lesson]Lesson 7: Comparing WeightsLesson 8: Shira´s Solutions

Module 5: Area, Surface Area, and Volume Problems

Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 1: The Area of Parallelograms Through Rectangle FactsUnit 1Lesson 3: Exploring Parallelograms (Print available) [Free lesson]Lesson 4: Off the Grid
Lesson 2: The Area of Right Triangles
Lesson 3: The Area of Acute Triangles Using Height and Base
Unit 1Lesson 5: Exploring Triangles (Print available)Lesson 6: Triangles and ParallelogramsLesson 7: Off the Grid, Part 2
Lesson 4: The Area of All Triangles Using Height and BaseUnit 1Lesson 6: Triangles and ParallelogramsLesson 7: Off the Grid, Part 2
Lesson 5: The Area of Polygons Through Composition and DecompositionUnit 1Lesson 2: LettersLesson 8: Pile of PolygonsPractice Day 1 (Print available)
Lesson 6: Area in the Real World 
Topic B Polygons on the Coordinate Plane 
Lesson 7: Distance on the Coordinate PlaneUnit 1Lesson 8: Pile of Polygons
Lesson 8: Drawing Polygons in the Coordinate PlaneUnit 7Lesson 11: Polygon Maker
Lesson 9: Determining Perimeter and Area of Polygons on the Coordinate PlaneUnit 1Lesson 8: Pile of Polygons
Lesson 10: Distance, Perimeter, and Area in the Real World 
Topic C Volume of Right Rectangular Prisms 
Lesson 11: Volume with Fractional Edge Lengths and Unit CubesUnit 4Lesson 11: Classroom ComparisonsLesson 12: Puzzling Areas (Print available) [Free lesson]Lesson 13: Volume ChallengesLesson 14: Planter Planner (Print available)
Lesson 12: From Unit Cubes to the Formulas for Volume  
Lesson 13: The Formulas for Volume 
Lesson 14: Volume in the Real WorldUnit 4Lesson 14: Planter Planner (Print available)
Topic D Nets and Surface Area 
Lesson 15: Representing Three-Dimensional Figures Using Nets
Lesson 16: Constructing Nets
Lesson 17: From Nets to Surface Area
Unit 1Lesson 10: Plenty of PolyhedraLesson 11: Nothing But Nets (Print available)Lesson 13: Take It To Go (Print available)
Lesson 18: Determining Surface Area of Three-Dimensional FiguresUnit 1Lesson 9: Renata´s Stickers [Free lesson]Lesson 10: Plenty of PolyhedraLesson 11: Nothing But Nets (Print available)Lesson 13: Take It To Go (Print available)Practice Day 2 (Print available)
Lesson 19: Surface Area and Volume in the Real World 
Lesson 19a: Addendum Lesson for Modeling―Applying Surface Area and Volume to Aquariums 
Lesson 3: The Area of Acute Triangles Using Height and BaseUnit 1Lesson 5 Exploring TrianglesLesson 6 Triangles and ParallelogramsLesson 7 Off the Grid, Part 2

Module 6: Statistics

Topic A Understanding Distributions 
Lesson 1: Posing Statistical QuestionsUnit 8 Lesson 1: Screen TimeLesson 2: Dot Plots
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Unit 8 Lesson 2: Dot PlotsLesson 3: Minimum Wage (Print available) [Free lesson]Lesson 4: Lots More Dots
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Unit 8Lesson 5: The Plot Thickens [Free lesson]Lesson 6: DIY Histograms (Print available)
Topic B Summarizing a Distribution That Is Approximately Symmetric Using the Mean and Mean Absolute Deviation 
Lesson 6: Describing the Center of a Distribution Using the Mean
Lesson 7: The Mean as a Balance Point
Unit 8Lesson 7: Snack Time
Lesson 8: Variability in a Data DistributionUnit 8Lesson 8: Pop It!
Topic 9: The Mean Absolute Deviation (MAD).Unit 8Lesson 9: Hoops
Lesson 10: Describing Distributions Using the Mean and MAD
Lesson 11: Describing Distributions Using the Mean and MAD
Unit 8Lesson 10 Hollywood Part 1Practice Day 1 (Print available)
Topic C Summarizing a Distribution That Is Skewed Using the Median and the Interquartile Range 
Lesson 12: Describing the Center of a Distribution Using the MedianUnit 8Lesson 11: Toy Cars [Free lesson]Lesson 12: In the News
Lesson 13: Describing Variability Using the Interquartile Range (IQR)Unit 8Lesson 13: Pumpkin Patch
Lesson 14: Summarizing a Distribution Using a Box Plot
Lesson 15: More Practice with Box Plots
Unit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 16: Understanding Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)Lesson 15: Hollywood Part 2Lesson 16: Hollywood Part 3 (Print available)Practice Day 2 (Print available)
Topic D Summarizing and Describing Distributions 
Lesson 17: Developing a Statistical Project 
Lesson 18: Connecting Graphical Representations and Numerical SummariesUnit 8Lesson 5: The Plot Thickens [Free lesson]
Lesson 19: Comparing Data DistributionsUnit 8Lesson 15: Hollywood Part 2
Lesson 20: Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation
Lesson 21: Summarizing a Data Distribution by Describing Center, Variability, and Shape
Unit 8Lesson 16: Hollywood Part 3 (Print available)
Lesson 22: Presenting a Summary of a Statistical Project 
Lesson 3: Creating a Dot PlotUnit 8Lesson 2 Dot PlotsLesson 3 Minimum Wage [Free lesson]Lesson 4 Lots More Dots

Grade 7

Module 1: Ratios and Proportional Relationships

Eureka MathDesmos Math 6–A1
Topic A Proportional Relationships 
Lesson 1: An Experience in Relationships as Measuring RateUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
 
Unit 4
Lesson 1: Mosaics [Free lesson]
Lesson 2: Peach Cobbler (Print available)
Lesson 2: Proportional RelationshipsUnit 2  
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
 
Unit 4
Lesson 3: Sticker Sizes
Lesson 3: Identifying Proportional and Non-Proportional Relationships in Tables
Lesson 4: Identifying Proportional and Non-Proportional Relationships in Tables
Unit 2
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs
Lesson 6: Identifying Proportional and Non-Proportional Relationships in Graphs
Unit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Topic B Unit Rate and the Constant of Proportionality 
Lesson 7: Unit Rate as the Constant of ProportionalityUnit 2
Lesson 2: Balloon Float
Lesson 8: Representing Proportional Relationships with Equations
Lesson 9: Representing Proportional Relationships with Equations
Unit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 10: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Topic C Ratios and Rates Involving Fractions 
Lesson 11: Ratios of Fractions and Their Unit Rates
Lesson 12: Ratios of Fractions and Their Unit Rates
Unit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two [Free lesson]
Lesson 13: Finding Equivalent Ratios Given the Total QuantityUnit 2  
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 14: Multi-Step Ratio Problems 
Lesson 15: Equations of Graphs of Proportional Relationships Involving FractionsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Topic D Ratios of Scale Drawings 
Lesson 16: Relating Scale Drawings to Ratios and RatesUnit 1
Lesson 1: Scaling Machines [Free lesson]
Lesson 17: The Unit Rate as the Scale FactorUnit 1
Lesson 2: Scaling Robots
Lesson 3: Make It Scale
Lesson 4: Scale Factor Challenges
Practice Day 1 (Print available)
Lesson 18: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 19: Computing Actual Areas from a Scale DrawingUnit 1
Lesson 5: Tiles
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 20: An Exercise in Creating a Scale Drawing
Lesson 21: An Exercise in Changing Scales
Lesson 22: An Exercise in Changing Scales
Unit 1
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Practice Day 2 (Print available)

Module 2: Rational Numbers

Topic A Addition and Subtraction of Integers and Rational Numbers 
Lesson 1: Opposite Quantities Combine to Make ZeroUnit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: Using the Number Line to Model the Addition of Integers
Lesson 3: Understanding Addition of Integers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 6: The Distance Between Two Rational Numbers 
Lesson 7: Addition and Subtraction of Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10; Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Practice Day 1 (Print available)
Lesson 8: Applying the Properties of Operations to Add and Subtract Rational Numbers 
Lesson 9: Applying the Properties of Operations to Add and Subtract Rational Numbers 
Topic B Multiplication and Division of Integers and Rational Numbers 
Lesson 10: Understanding Multiplication of Integers
Lesson 11: Develop Rules for Multiplying Signed Numbers
Unit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 12: Division of IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 13: Converting Between Fractions and Decimals Using Equivalent Fractions 
Lesson 14: Converting Rational Numbers to Decimals Using Long DivisionUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 15: Multiplication and Division of Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers 
Topic C Applying Operations with Rational Numbers to Expressions and Equations 
Lesson 17: Comparing Tape Diagram Solutions to Algebraic SolutionsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 18: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
Lesson 19: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers
Unit 5
Lesson 9 Expressions
Lesson 20: Investments—Performing Operations with Rational Numbers
Lesson 21: If-Then Moves with Integer Number Cards
Lesson 22: Solving Equations Using Algebra
Lesson 23: Solving Equations Using Algebra
Unit 6
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 6: Balancing Equations
Lesson 7: Keeping It True (Print available)
Lesson 12: Community Day (Print available)
 
Unit 5
Lesson 3: Bumpers

Module 3: Expressions and Equations

Topic A Use Properties of Operations to Generate Equivalent Expressions 
Lesson 1: Generating Equivalent Expressions
Lesson 2: Generating Equivalent Expressions
Unit 5 Lesson 9: Expressions (Print available)Unit 6Lesson 9: Always-Equal MachinesLesson 11: Equation Roundtable (Print available)
Lesson 3: Writing Products as Sums and Sums as Products
Lesson 4: Writing Products as Sums and Sums as Products
Unit 6 Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 8: Factoring and ExpandingLesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Lesson 12: Community Day (Print available)
Lesson 5: Using the Identity and Inverse to Write Equivalent Expressions 
Lesson 6: Collecting Rational Number Like Terms 
Topic B Solve Problems Using Expressions, Equations, and Inequalities 
Lesson 7: Understanding EquationsUnit 6Lesson 2: Smudged ReceiptsLesson 5: Balancing MovesLesson 6: Balancing Equations
Lesson 8: Using If-Then Moves in Solving Equations
Lesson 9: Using If-Then Moves in Solving Equations
Unit 6Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 8: Factoring and Expanding (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Lesson 12: Community Day (Print available)Practice Day 1 (Print available)
Lesson 10: Angle Problems and Solving EquationsUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Lesson 11: Angle Problems and Solving Equations 
Lesson 12: Properties of Inequalities
Lesson 13: Inequalities
Lesson 14: Solving Inequalities
Unit 6Lesson 14: Unbalanced HangersLesson 15: Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 15: Graphing Solutions to InequalitiesUnit 6Lesson 13: I Saw the SignsPractice Day 2 (Print available)
Topic C Use Equations and Inequalities to Solve Geometry Problems 
Lesson 16: The Most Famous Ratio of AllUnit 3Lesson 2: Is It a Circle?Lesson 3: Measuring Around [Free lesson]
Lesson 17: The Area of a CircleUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi? (Print available)Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. SquarePractice Day 2 (Print available)
Lesson 18: More Problems on Area and CircumferenceUnit 3Lesson 4: Perimeter ChallengesLesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi? (Print available)Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. Square
Lesson 19: Unknown Area Problems on the Coordinate Plane
Lesson 20: Composite Area Problems
Unit 3Lesson 4: Perimeter ChallengesPractice Day 2 (Print available)
Lesson 21: Surface Area
Lesson 22: Surface Area
Lesson 23: The Volume of a Right Prism
Lesson 24: The Volume of a Right Prism
Unit 7Lesson 10: Simple PrismsLesson 11: More Complicated Prisms Lesson 12: Surface Area Strategies (Print Available)Lesson 13: Popcorn PossibilitiesPractice Day 2 (Print available)
Lesson 25: Volume and Surface Area
Lesson 26: Volume and Surface Area
Unit 7Lesson 13: Popcorn PossibilitiesPractice Day 2

Module 4: Percent and Proportional Relationships

Topic A Finding the Whole 
Lesson 1: PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 2: Part of a Whole as a PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)
Lesson 3: Comparing Quantities with PercentUnit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 4: Percent Increase and DecreaseUnit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 5: Finding One Hundred Percent Given Another Percent 
Lesson 6: Fluency with PercentsUnit 4Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Topic B Percent Problems Including More Than One Whole 
Lesson 7: Markup and Markdown ProblemsUnit 4Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 8: Percent Error Problems
Lesson 9: Problem Solving When the Percent Changes
Unit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 10: Simple Interest 
Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent ApplicationsUnit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]Practice Day (Print available)
Topic C Scale Drawings 
Lesson 12: The Scale Factor as a Percent for a Scale Drawing 
Lesson 13: Changing ScalesUnit 1Lesson 1: Scaling Machines [Free lesson]Lesson 2: Scaling RobotsLesson 3: Make It ScaleLesson 4: Scale Factor ChallengesLesson 5: TilesLesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]Lesson 8: Scaling States (Print available)Lesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)Practice Day 1 (Print available)Practice Day 2 (Print available) Unit 3Lesson 1 Toothpicks
Lesson 14: Computing Actual Lengths from a Scale DrawingUnit 1Lesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]Lesson 8: Scaling States (Print available)Lesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available) Unit 3Lesson 1: Toothpicks
Lesson 15: Solving Area Problems Using Scale DrawingsUnit 1Lesson 5: Tiles
Topic D Population, Mixture, and Counting Problems Involving Percents 
Lesson 16: Population ProblemsUnit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Lesson 17: Mixture Problems 
Lesson 18: Counting Problems 

Module 5: Statistics and Probability

Topic A Calculating and Interpreting Probabilities 
Lesson 1: Chance ExperimentsUnit 8Lesson 1: How Likely? (Print available) [Free lesson]Lesson 2: Prob-bear-bilities [Free lesson]Lesson 3: Mystery Bag
Lesson 2: Estimating Probabilities by Collecting Data
Lesson 3: Chance Experiments with Equally Likely Outcomes
Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes
Unit 8Lesson 3: Mystery BagLesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Lesson 5: Chance Experiments with Outcomes That Are Not Equally LikelyUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair GamesLesson 7: Weather or Not
Lesson 6: Using Tree Diagrams to Represent a Sample Space and to Calculate ProbabilitiesUnit 8Lesson 6: Fair GamesLesson 7: Weather or Not
Lesson 7: Calculating Probabilities of Compound EventsUnit 8Lesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)Practice Day 1 (Print available)
Topic B Estimating Probabilities 
Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities
Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model
Unit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)
Lesson 10: Conducting a Simulation to Estimate the Probability of an EventUnit 8Lesson 7: Weather or NotLesson 8: Simulate It! (Print available)Lesson 9: Car, Bike, or Train? (Print available)
Lesson 11: Conducting a Simulation to Estimate the Probability of an Event
Lesson 12: Applying Probability to Make Informed Decisions
Unit 8Lesson 7: Weather or NotLesson 8: Simulate It! (Print available)
Topic C Random Sampling and Estimating Population Characteristics 
Lesson 13: Populations, Samples, and Generalizing from a Sample to a PopulationUnit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 11: HeadlinesLesson 12: Flower Power
Lesson 14: Selecting a Sample
Lesson 15: Random Sampling
Lesson 16: Methods for Selecting a Random Sample
Unit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Lesson 17: Sampling VariabilityUnit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and Samples
Lesson 18: Sampling Variability and the Effect of Sample Size
Lesson 19: Understanding Variability When Estimating a Population Proportion
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)
Lesson 20: Estimating a Population Proportion 
Topic D Comparing Populations 
Lesson 21: Why Worry About Sampling Variability?Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)
Lesson 22: Using Sample Data to Compare the Means of Two or More Populations
Lesson 23: Using Sample Data to Compare the Means of Two or More Populations
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)

Module 6: Geometry

Topic A Unknown Angles 
Lesson 1: Complementary and Supplementary AnglesUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle Diagrams
Lesson 2: Solving for Unknown Angles Using Equations
Lesson 3: Solving for Unknown Angles Using Equations
Lesson 4: Solving for Unknown Angles Using Equations
Unit 7Lesson 1: PinwheelsLesson 2: Friendly AnglesLesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Topic B Constructing Triangles 
Lesson 5: Identical TrianglesUnit 7Lesson 6: Is It Enough?Lesson 7: More Than One
Lesson 6: Drawing Geometric ShapesUnit 7Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)
Lesson 7: Drawing Parallelograms 
Lesson 8: Drawing TrianglesUnit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Lesson 9: Conditions for a Unique Triangle―Three Sides and Two Sides and the Included
Lesson 10: Conditions for a Unique Triangle—Two Angles and a Given Side Angle
Unit 7Lesson 8: Can You Draw It? (Print available)
Lesson 11: Conditions on Measurements That Determine a TriangleUnit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Lesson 12: Unique Triangles―Two Sides and a Non-Included Angle 
Lesson 13: Checking for Identical Triangles
Lesson 14: Checking for Identical Triangles
Unit 7Lesson 6: Is It Enough?Lesson 7: More Than OnePractice Day 1
Lesson 15: Using Unique Triangles to Solve Real-World and Mathematical Problems 
Topic C Slicing Solids 
Lesson 16: Slicing a Right Rectangular Prism with a Plane
Lesson 17: Slicing a Right Rectangular Pyramid with a Plane
Lesson 18: Slicing on an Angle
Unit 7Lesson 9: Slicing Solids
Lesson 19: Understanding Three-Dimensional Figures 
Topic D Problems Involving Area and Surface Area 
Lesson 20: Real-World Area ProblemsUnit 3Lesson 5: Area Strategies
Lesson 21: Mathematical Area ProblemsUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)
Lesson 22: Area Problems with Circular RegionsUnit 3Lesson 5: Area StrategiesLesson 8: Area Challenges [Free lesson]
Lesson 23: Surface Area
Lesson 24: Surface Area
Unit 7Lesson 12: Surface Area Strategies (Print available)Lesson 13: Popcorn Possibilities
Topic E Problems Involving Volume 
Lesson 25: Volume of Right PrismsUnit 7Lesson 10: Simple PrismsLesson 11: More Complicated PrismsLesson 13: Popcorn Possibilities
Lesson 26: Volume of Composite Three-Dimensional ObjectsUnit 7Lesson 11: More Complicated Prisms
Lesson 27: Real-World Volume ProblemsUnit 7Lesson 13: Popcorn Possibilities

Grade 8

Module 1: Integer Exponents and Scientific Notation

Eureka MathDesmos Math 6–A1
Topic A Exponential Notation and Properties of Integer Exponents 
Lesson 1: Exponential NotationUnit 7 Lesson 1 Circles [Free lesson]Lesson 2 Combining Exponents
Lesson 2: Multiplication of Numbers in Exponential Form
Lesson 3: Numbers in Exponential Form Raised to a Power
Unit 7 Lesson 2 Combining ExponentsLesson 3 Power Pairs (Print available) [Free lesson]Lesson 4 Rewriting Powers
Lesson 4: Numbers Raised to the Zeroth Power
Lesson 5: Negative Exponents and the Laws of Exponents
Unit 7 Lesson 5 Zero and Negative ExponentsLesson 6 Write a Rule (Print available)Practice Day 1 (Print available)
Lesson 6: Proofs of Laws of Exponents 
Topic B Magnitude and Scientific Notation 
Lesson 7: MagnitudeUnit 7 Lesson 7 Scales and Weights
Lesson 8: Estimating QuantitiesUnit 7 Lesson 7: Scales and WeightsLesson 8: Point ZapperLesson 9: Use Your Powers
Lesson 9: Scientific Notation
Lesson 10: Operations with Numbers in Scientific Notation
Unit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 13: Star Power
Lesson 11: Efficacy of Scientific NotationUnit 7 Lesson 13: Star Power
Lesson 12: Choice of Unit 
Lesson 13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using TechnologyUnit 7  Lesson 13: Star Power Practice Day 2 (Print available)

Module 2: The Concept of Congruence

Topic A Definitions and Properties of the Basic Rigid Motions 
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Unit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Translating LinesUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson] Unit 3Lesson 6: Translations
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Unit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Topic B Sequencing the Basic Rigid Motions 
Lesson 7: Sequencing Translations
Lesson 8: Sequencing Reflections and Translations
Unit 1Lesson 3: Transformation GolfLesson 6: Connecting the Dots [Free lesson]
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Unit 1Lesson 3: Transformation GolfLesson 6: Connecting the Dots [Free lesson]Lesson 13: Tessellate [Free lesson]Practice Day
Topic C Congruence and Angle Relationships 
Lesson 11: Definition of Congruence and Some Basic PropertiesUnit 1 Lesson 7: Are They the Same?Lesson 8: No Bending, No StretchingLesson 9: Are They Congruent?Practice Day
Lesson 12: Angles Associated with Parallel LinesUnit 1 Lesson 10: Transforming Angles  
Lesson 13: Angle Sum of a TriangleUnit 1 Lesson 11: Tearing It Up (Print available)
Lesson 14: More on the Angles of a TriangleUnit 1 Lesson 11: Tearing It Up (Print available)Lesson 12: Puzzling It Out [Free lesson]
Topic D: The Pythagorean Theorem 
Lesson 15: Informal Proof of the Pythagorean TheoremUnit 8Lesson 7: Pictures to Prove It
Lesson 16: Applications of the Pythagorean TheoremUnit 8Lesson 10: Taco TruckPractice Day 2 (Print available)

Module 3: Similarity

Topic A Dilation 
Lesson 1: What Lies Behind “Same Shape”?Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf [Free lesson]
Lesson 2: Properties of Dilations
Lesson 3: Examples of Dilations
Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf [Free lesson]Lesson 3: Match My DilationLesson 4: Dilations on a Plane (Print available)
Lesson 4: Fundamental Theorem of Similarity
Lesson 5: First Consequences of FTS
Unit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 6: Dilations on the Coordinate PlaneUnit 8Lesson 4: Dilations on a Plane (Print available)
Lesson 7: Informal Proofs of Properties of Dilations 
Topic B Similar Figures 
Lesson 8: Similarity
Lesson 9: Basic Properties of Similarity
Unit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 10: Informal Proof of AA Criterion for SimilarityUnit 2Lesson 7: Are Angles Enough?
Lesson 11: More About Similar TrianglesUnit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Lesson 12: Modeling Using SimilarityUnit 2Lesson 8: ShadowsLesson 9: Water SlideLesson 10: Points on a PlanePractice Day 
Topic C The Pythagorean Theorem 
Lesson 13: Proof of the Pythagorean TheoremUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove ItLesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 14: The Converse of the Pythagorean TheoremUnit 8 Lesson 9: Make It Right

Module 4: Linear Equations

Topic A Writing and Solving Linear Equations 
Lesson 1: Writing Equations Using Symbols 
Lesson 2: Linear and Nonlinear Expressions in x 
Lesson 3: Linear Equations in xUnit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 4: Solving a Linear EquationUnit 4Lesson 3: Balanced MovesLesson 4: More Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 5: Writing and Solving Linear EquationsUnit 3Lesson 1: Turtle Time Trials Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 6: Solutions of a Linear EquationUnit 3Lesson 10: Solutions Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 7: Classification of SolutionsUnit 4Lesson 7: All, Some, or None?
Lesson 8: Linear Equations in Disguise 
Lesson 9: An Application of Linear Equations 
Topic B Linear Equations in Two Variables and Their GraphsUnit 3Lesson 2: Water TankLesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 10: A Critical Look at Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 7: Water CoolerLesson 8: Landing PlanesLesson 9: Coin Capture
Lesson 11: Constant RateUnit 2Lesson 9: Water SlideLesson 10: Points on a PlanePractice Day  Unit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations Unit 4Lesson 8: When Are They the Same?
Lesson 12: Linear Equations in Two VariablesUnit 3Lesson 3: PostersLesson 6: Translations Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 13: The Graph of a Linear Equation in Two VariablesUnit 3 Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 10: SolutionsLesson 11: Pennies and Quarters
Lesson 14: The Graph of a Linear Equation―Horizontal and Vertical LinesUnit 3 Lesson 9: Coin CapturePractice Day  [Free lesson]
Topic C Slope and Equations of Lines 
Lesson 15: The Slope of a Non-Vertical LineUnit 3Lesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 8: Landing Planes
Lesson 16: The Computation of the Slope of a Non-Vertical LineUnit 3Lesson 7: Water CoolerLesson 8: Landing Planes
Lesson 17: The Line Joining Two Distinct Points of the Graph 𝑦 = 𝑚x + 𝑏 Has Slope mUnit 3Lesson 7: Water Cooler
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given SlopeUnit 3Lesson 5: Flags [Free lesson]Lesson 7: Water Cooler
Lesson 19: The Graph of a Linear Equation in Two Variables Is a LineUnit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 20: Every Line Is a Graph of a Linear EquationUnit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 21: Some Facts About Graphs of Linear Equations in Two VariablesUnit 3Lesson 3: PostersLesson 6: TranslationsPractice Day 
Lesson 22: Constant Rates RevisitedUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 3: Posters
Lesson 23: The Defining Equation of a LineUnit 3Lesson 10: SolutionsLesson 11: Pennies and Quarters
Topic D Systems of Linear Equations and Their Solutions 
Lesson 24: Introduction to Simultaneous EquationsUnit 4Lesson 7: All, Some, or None?Lesson 8: When Are They the Same?Lesson 13: All, Some, or None? Part 2
Lesson 25: Geometric Interpretation of the Solutions of a Linear SystemUnit 4  Lesson 9: On or Off the Line?Lesson 10: On Both LinesLesson 11: Make Them Balance [Free lesson]Lesson 12: Line Zapper [Free lesson]Lesson 13: All, Some, or None? Part 2Practice Day 2 (Print available)
Lesson 26: Characterization of Parallel LinesUnit 3 Lesson 6: Translations
Lesson 27: Nature of Solutions of a System of Linear EquationsUnit 4  Lesson 9: On or Off the Line?
Lesson 28: Another Computational Method of Solving a Linear System 
Lesson 29: Word Problems 
Lesson 30: Conversion Between Celsius and Fahrenheit 
Topic E Pythagorean Theorem 
Lesson 31: System of Equations Leading to Pythagorean Triples 

Module 5: Examples of Functions from Geometry

Topic A Functions 
Lesson 1: The Concept of a FunctionUnit 5 Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Formal Definition of a FunctionUnit 5 Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson] Lesson 3: Function or Not?
Lesson 3: Linear Functions and ProportionalityUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 4: Window Frames
Lesson 4: More Examples of FunctionsUnit 5Lesson 3: Function or Not?Lesson 4: Window Frames
Lesson 5: Graphs of Functions and EquationsUnit 5Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: Graphs of Linear Functions and Rate of ChangeUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 7: Comparing Linear Functions and GraphsUnit 5Lesson 3: PostersLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Graphs of Simple Nonlinear Functions 
Topic B Volume 
Lesson 9: Examples of Functions from GeometryUnit 8Lesson 1: Tilted SquaresLesson 2: From Squares to Roots
Lesson 10: Volumes of Familiar Solids—Cones and CylindersUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling CylindersLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 11: Volume of a SphereUnit 5 Lesson 15: Spheres Practice Day 2 (Print available)

Module 6: Linear Functions

Topic A Linear Functions 
Lesson 1: Modeling Linear RelationshipsUnit 5 Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 2: Interpreting Rate of Change and Initial ValueUnit 2Lesson 9: Water SlideLesson 10: Points on a Plane Unit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water TankLesson 3: PostersLesson 4: Stacking Cups
Lesson 3: Representations of a LineUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 4: Increasing and Decreasing Functions
Lesson 5: Increasing and Decreasing Functions
Unit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing Stories
Topic B Bivariate Numerical Data 
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Unit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Practice Day 1 (Print available) [Free lesson]
Lesson 8: Informally Fitting a LineUnit 6 Lesson 4: Dapper Cats [Free lesson]Lesson 5: Fit Fights [Free lesson]Lesson 6: Interpreting SlopesLesson 7: Scatter Plot CityLesson 8: Animal BrainsPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 9: Determining the Equation of a Line Fit to Data 
Topic C Linear and Nonlinear Models 
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Unit 5 Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesUnit 6 Lesson 6: Interpreting SlopesLesson 8: Animal BrainsPractice Day 2 (Print available)
Lesson 12: Nonlinear Models in a Data Context 
Topic D Bivariate Categorical Data 
Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way TableUnit 6 Lesson 9: Tasty Fruit
Lesson 14: Association Between Categorical VariablesUnit 6 Lesson 10: Finding Associations [Free lesson] Lesson 11: Federal Budgets Practice Day 3

Module 7: Introduction to Irrational Numbers Using Geometry

Topic A Square and Cube Roots 
Lesson 1: The Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 2: Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 3: Existence and Uniqueness of Square Roots and Cube RootsUnit 8
Lesson 5: Filling Cubes
Lesson 4: Simplifying Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Practice Day 1 (Print available)
Lesson 5: Solving Equations with Radicals 
Topic B Decimal Expansions of Numbers 
Lesson 6: Finite and Infinite Decimals
Lesson 7: Infinite Decimals
Lesson 8: The Long Division Algorithm
Lesson 9: Decimal Expansions of Fractions, Part 1
Lesson 10: Converting Repeating Decimals to Fractions
Unit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 11: The Decimal Expansion of Some Irrational Numbers 
Lesson 12: Decimal Expansions of Fractions, Part 2 
Lesson 13: Comparing Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 14: Decimal Expansion of π 
Topic C The Pythagorean Theorem 
Lesson 15: Pythagorean Theorem, RevisitedUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 16: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 17: Distance on the Coordinate PlaneUnit 8
Lesson 11: Pond Hopper
Lesson 18: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck [Free lesson]
Practice Day 2 (Print available)
Topic D Applications of Radicals and Roots 
Lesson 19: Cones and Spheres 
Lesson 20: Truncated Cones 
Lesson 21: Volume of Composite Solids 
Lesson 22: Average Rate of Change 
Lesson 23: Nonlinear Motion 

Grade 6

Unit 1: Area and Surface Area

Illustrative MathematicsDesmos Math 6–A1
Topic A: Reasoning to Find Area 
Lesson 1: Tiling the PlaneUnit 1
Lesson 1: Shapes on a Plane [Free lesson]
Lesson 2: Finding Area by Decomposing and Rearranging
Lesson 3: Reasoning to Find Area
Unit 1
Lesson 2: Letters
Topic 2: Parallelograms
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Unit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Topic 3: Triangles
Lesson 7: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 8: Area of TrianglesUnit 1
Lesson 5: Exploring Triangles (Print available)
Lesson 9: Formula for the Area of a Triangle
Lesson 10: Bases and Heights of Triangles
Unit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Topic 4: Polygons
Lesson 11: PolygonsUnit 1
Lesson 2: Letters
Lesson 8: Pile of Polygons
Practice Day 1 (Print available)
Unit 7
Lesson 11: Polygon Maker
Topic 5: Surface Area
Lesson 12: What is Surface Area?Unit 1
Lesson 9: Renata´s Stickers [Free lesson]
Lesson 13: PolyhedraUnit 1Lesson 10: Plenty of Polyhedra
Lesson 14: Nets and Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 13: Take It To Go
Lesson 15: More Nets, More Surface AreaUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11: Nothing But Nets (Print available)
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Practice Day 2 (Print available)
Lesson 16: Distinguishing Between Surface Area and Volume
Topic 6: Squares and Cubes 
Lesson 17: Squares and CubesUnit 6
Lesson 12: Squares and Cubes
Lesson 18: Surface Area of a Cube 
Topic 7: Let’s Put It to Work 
Lesson 19: Designing a TentUnit 1
Lesson 13: Take It To Go (Print available)

Unit 2: Introducing Ratios

Topic 1: Introducing Ratios
Lesson 1: Introducing Ratios and Ratio LanguageUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)
Lesson 2: Representing Ratios with DiagramsUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 2: Ratio Rounds (Print available)Lesson 3: Rice Ratios (Print available)
Topic 2: Equivalent Ratios
Lesson 3: RecipesUnit 2Lesson 1: Pizza Maker [Free lesson]Lesson 3: Rice Ratios (Print available)
Lesson 4: Color MixturesUnit 2Lesson 7: Mixing Paint, Part 1Lesson 12: Mixing paint, Part 2
Lesson 5: Defining Equivalent RatiosUnit 2Lesson 3: Rice Ratios (Print available)Lesson 4: Fruit Lab [Free lesson]Lesson 11: Community LifePractice Day 1 (Print available)
Topic 3: Representing Equivalent ratios
Lesson 6: Introducing Double Number Line DiagramsUnit 2Lesson 5: Balancing Act
Lesson 7: Creating Double Line DiagramsUnit 2Lesson 5: Balancing ActLesson 6: Product prices (Print available)
Lesson 8: How Much for One?Unit 2Lesson 6: Product prices (Print available)
Lesson 9: Constant SpeedUnit 2Lesson 8: World Records (Print available)
Lesson 10: Comparing Situations by Examining RatiosUnit 2Lesson 7: Mixing Paint, Part 1 
Topic 4: Solving Ratio and Rate Problems
Lesson 11: Representing Ratios with TablesUnit 2Lesson 9: Disaster Preparation [Free lesson]
Lesson 12: Navigating a Table of Equivalent Ratios
Lesson 13: Tables and Double Line Diagrams
Unit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1
Lesson 14: Solving Equivalent Ratio ProblemsUnit 2Lesson 6: Product prices (Print available)Lesson 7: Mixing Paint, Part 1Lesson 10: BalloonsLesson 11: Community Life (Print available)
Topic 5: Part-Part-Whole Ratios
Lesson 15: Part-Part-Whole RatiosUnit 2Lesson 12: Mixing paint, Part 2Lesson 13: City Planning
Lesson 16: Solving More Ratio ProblemsUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Topic 6: Let’s Put It to Work 
Lesson 17: A Fermi ProblemUnit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)Practice Day 2 (Print available)

Unit 3: Rates and Percentages

Topic 1: Units of Measurement 
Lesson 1: The Burj KhalifaUnit 3
Lesson 4: Model Trains
Topic 2: Unit Conversion
Lesson 2: Anchoring Units of MeasurementUnit 3
Lesson 1: Many Measurements (Print available) [Free lesson]
Lesson 3: Measuring with Different-Sized Units
Lesson 4: Converting Units
Unit 3
Lesson 2: Counting Classrooms
Lesson 3: Pen Pals
Topic 3: Rates
Lesson 5: Comparing Speeds and PricesUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 6: Interpreting Rates
Lesson 7: Equivalent Ratios Have the Same Unit Rates
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 8: More About Constant SpeedUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 9: Solving Rate ProblemsUnit 3
Lesson 7: More Soft Serve
Topic 4: Percentages
Lesson 10: What Are percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 11: Percentages and Double Number LinesUnit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing? (Print available)
Lesson 12: Percentages and Tape DiagramsUnit 3
Lesson 10: What’s Missing? (Print available)
Lesson 13: Benchmark percentagesUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 14: Solving Percentage Problems
Lesson 15: Finding This Percent of That
Lesson 16: Finding the Percentage
Unit 3
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Topic 5: Let’s Put It to Work 
Lesson 17: Painting a RoomUnit 3
Lesson 13: A Country as a Village
Lesson 7: Equivalent Ratios Have the Same Unit RatesUnit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]

Unit 4: Dividing Fractions

Topic 1: Making Sense of Division 
Lesson 1: Size of Divisor and Size of Quotient
Lesson 2: Meanings of Division
Unit 4Lesson 1: Cookie Cutter
Lesson 3: Interpreting Division SituationsUnit 4Lesson 2: Making Connections (Print available)
Topic 2: Meanings of Fraction Division
Lesson 4: How Many Groups (Part 1)Unit 4Lesson 3: Flour Planner [Free lesson]Lesson 4: Flower Planters 
Lesson 5: How Many Groups (Part 2)Unit 4Lesson 5: Garden Bricks (Print available)
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4Lesson 5: Garden Bricks (Print available)Lesson 6: Fill the Gap [Free lesson]
Lesson 7: What Fraction of a Group?
Lesson 8: How Much in Each Group? (Part 1)
Lesson 9: How Much in Each Group? (Part 2)
Unit 4Lesson 8: Potting Soil
Topic 3: Algorithm for Fraction Division
Lesson 10: Dividing by Unit and Non-Unit FractionsUnit 4Lesson 7: Break It DownLesson 8: Potting SoilLesson 9: Division Challenges 
Lesson 11: Using an Algorithm to Divide FractionsUnit 4Lesson 9: Division ChallengesPractice Day
Topic 4: Fractions in Lengths, Areas, and Volumes
Lesson 12: Fractional LengthsUnit 4Lesson 11: Classroom Comparisons
Lesson 13: Rectangles with Fractional Side LengthsUnit 4Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 14: Fractional Lengths in Triangles and Prisms
Lesson 15: Volume of PrismsUnit 4Lesson 13: Volume Challenges
Topic 5: Let’s Put It to Work
Lesson 16: Solving Problems with FractionsUnit 4Lesson 10: Swap Meet (Print available)
Lesson 17: Fitting Boxes into BoxesUnit 4Lesson 14: Planter Planner (Print available)

Unit 5: Arithmetic in Base Ten

Topic 1: Warming Up to Decimals 
Lesson 1: Using Decimals in a Shopping ContextUnit 5Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Topic 2: Adding and Subtracting Decimals
Lesson 2: Using Decimals to Represent Addition and SubtractionUnit 5Lesson 3: Fruit by the PoundLesson 4: Missing Digits
Lesson 3: Adding and Subtracting Decimals with Few Non-Zero DigitsUnit 5Lesson 4: Missing Digits
Lesson 4: Adding and Subtracting Decimals with Many Non-Zero Digits 
Topic 3: Multiplying Decimals
Lesson 5: Decimal Points in ProductsUnit 5Lesson 5: Decimal Multiplication
Lesson 6: Methods for Multiplying DecimalsUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with AreasLesson 7: Multiplication methods (Print available)
Lesson 7: Using Diagrams to Represent MultiplicationUnit 5Lesson 5: Decimal MultiplicationLesson 6: Multiplying with Areas
Lesson 8: Calculating Products of DecimalsUnit 5Lesson 6: Multiplying with Areas
Topic 4: Dividing Decimals
Lesson 9: Using the Partial Quotients MethodUnit 5Lesson 8: Division Diagrams
Lesson 10: Using Long DivisionUnit 5Lesson 8: Division DiagramsLesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Lesson 11: Dividing Numbers That Result in Decimals
Lesson 12: Dividing Decimals by Whole Numbers
Lesson 13: Dividing Decimals by Decimals
Unit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)
Topic 5: Let’s Put It to Work
Lesson 14: Using Operations on Decimals to Solve ProblemsUnit 5Lesson 11: Movie Time [Free lesson]
Lesson 15: Making and Measuring Boxes
Lesson 12: Dividing Decimals by Whole Numbers 
Lesson 13: Dividing Decimals by DecimalsUnit 5Lesson 9: Long Division Launch (Print available)Lesson 10: Return of the Long Division (Print available)

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and Equations
Lesson 2: Truth and Equations
Unit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)
Lesson 3: Staying in BalanceUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging Around
Lesson 4: Practice Solving Equations and Representing Situations with EquationsUnit 6Lesson 3: Hanging AroundLesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Lesson 5: A New Way to Interpret a and bUnit 6Lesson 4: Hanging It UpLesson 5: Swap and Solve (Print available)
Topic 2: Equal and Equivalent
Lesson 6: Write Expressions Where Letters Stand for NumbersUnit 6Lesson 6: Vari-applesLesson 7: Border Tiles
Lesson 7: Revisit PercentagesUnit 3Lesson 10: What’s Missing?Lesson 11: Cost BreakdownLesson 12: More Bicycle Goals
Lesson 8: Equal and EquivalentUnit 6Lesson 1: Weight for It [Free lesson]Lesson 2: Five Equations (Print available)Lesson 3: Hanging AroundLesson 6: Vari-apples
Topic 9: The Distributive Property, Part 1Unit 6Lesson 8: Products and Sums [Free lesson]
Lesson 10: The Distributive Property, Part 2
Lesson 11: The Distributive Property, Part 3
Unit 6Lesson 8: Products and Sums [Free lesson]Lesson 9: Products, Sums, and Differences (Print available)
Topic 3: Expressions with Exponents
Lesson 12: Meaning of ExponentsUnit 6Lesson 10: PowersLesson 11: Exponent Expressions (Print available)
Lesson 13: Expressions with Exponents
Lesson 14: Evaluating Expressions with Exponents
Lesson 15: Equivalent Exponential Expressions
Unit 6Lesson 11: Exponent Expressions (Print available)Lesson 12: Squares and Cubes
Topic 4: Relationships Between Quantities 
Lesson 16: Two Related Quantities, Part 1
Lesson 17: Two Related Quantities, Part 2
Lesson 18: More Relationships
Unit 6Lesson 13: Turtles All the WayLesson 14: Representing RelationshipsLesson 15: Connecting Representations (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Tables, Equations, and Graphs, Oh My!Unit 6Lesson 16: Subway fares (Print available) [Free lesson]

Unit 7: Rational Numbers

Topic 1: Positive and Negative Numbers
Lesson 1: Positive and Negative NumbersUnit 7Lesson 1: Can You Dig In [Free lesson]Lesson 2: Digging Deeper
Lesson 2: Points on the Number LineUnit 7Lesson 2: Digging Deeper
Lesson 3: Comparing Positive and Negative Numbers
Lesson 4: Ordering Rational Numbers
Unit 7Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 5: Using Negative Numbers to make Sense of ContextsUnit 7 Lesson 4: Sub-Zero
Lesson 6: Absolute Value of Numbers
Lesson 7: Comparing Numbers and Distance from Zero
Unit 7Lesson 5: Distance on the Number Line
Topic 2: Inequalities
Lesson 8: Writing and Graphing InequalitiesUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Solutions of Inequalities
Lesson 10: Interpreting Inequalities
Unit 7Lesson 6: Tunnel Travel [Free lesson]Lesson 7: Comparing WeightsLesson 8: Shira´s Solutions
Topic 3: The Coordinate Plane
Lesson 11: Points on the Coordinate Plane
Lesson 12: Constructing the Coordinate Plane
Unit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate Plane
Lesson 13: Interpreting Points on a Coordinate PlaneUnit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate PlaneLesson 11: Polygon Maker
Lesson 14: Distances on a Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Lesson 15: Shapes on the Coordinate PlaneUnit 1Lesson 1: Shapes on a Plane [Free lesson]Lesson 2: LettersLesson 5: Exploring Triangles (Print available)Lesson 6: Triangles and ParallelogramsUnit 7Lesson 3: Exploring Parallelograms (Print available)Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)
Topic 4: Common Factors and Common Multiples
Lesson 16: Common FactorsUnit 5Lesson 15: Common factors
Lesson 17: Common MultiplesUnit 5Lesson 14: Common Multiples
Lesson 18: Using Common Multiples and Common FactorsUnit 5Lesson 14: Common MultiplesLesson 15: Common factorsPractice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 19: Drawing on the Coordinate PlaneUnit 7Lesson 11: Polygon MakerLesson 12: Graph Telephone (Print available)

Unit 8: Data Sets and Distributions

Topic 1: Data, Variability, and Statistical Questions
Lesson 1: Got Data?
Lesson 2: Statistical Questions
Unit 8Lesson 1: Screen TimeLesson 2: Dot Plots
Topic 2: Dot Plots and Distributions
Lesson 3: Representing Data Graphically
Lesson 4: Dot Plots
Lesson 5: Using Dot Plots to Answer Statistical Questions
Unit 8Lesson 2: Dot PlotsLesson 3: Minimum Wage (Print available) [Free lesson]Lesson 4: Lots More Dots
Lesson 6: Interpreting Histograms
Lesson 7: Using Histograms to Answer Statistical Questions
Lesson 8: Describing Distributions on Histograms
Unit 8Lesson 5: The Plot Thickens [Free lesson]Lesson 6: DIY Histograms (Print available)
Topic 3: Measures of Center and Variability
Lesson 9: Mean
Lesson 10: Finding and Interpreting the Mean as a Balance Point
Unit 8Lesson 7: Snack Time
Lesson 11: Variability and MADUnit 8Lesson 8: Pop It!
Lesson 12: Using Mean and MAD to Make ComparisonsUnit 8Lesson 9: Hoops
Topic 4: Median and IQR
Lesson 13: MedianUnit 8Lesson 11: Toy Cars [Free lesson]Lesson 12: In the News
Lesson 14: Comparing Mean and MedianUnit 8Lesson 12: In the News
Lesson 15: Quartiles and Interquartile RangeUnit 8Lesson 13: Pumpkin Patch
Lesson 16: Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 17: Using Box PlotsUnit 8Lesson 14: Car, Plane, Bus, or Train? (Print available)Lesson 15: Hollywood Part 2Lesson 16: Hollywood Part 3 (Print available)Practice Day 2 (Print available)
Topic 5: Let’s Put It to Work
Lesson 18: Using Data to Solve ProblemsUnit 8Lesson 16: Hollywood Part 3 (Print available)

Unit 9: Putting It All Together

Topic 1: Making Connections
Lesson 1: Fermi Problems
Lesson 2: In Our Class Were the World
Unit 3Lesson 13: A Country as a Village
Lesson 3: Rectangle MadnessUnit 5Lesson 14: Common MultiplesLesson 15: Common factors
Topic 2: Voting
Lesson 4: How Do We Choose?Unit 2Lesson 13: City PlanningLesson 14: Lunch Waste (Print available)
Lesson 5: More than Two ChoicesUnit 3Lesson 13: A Country as a Village
Lesson 6: Picking RepresentativesUnit 8Lesson 16: Hollywood Part 3 (Print available)

Grade 7

Unit 1: Scale Drawings

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Scaled Copies 
Lesson 1: What are Scaled Copies?Unit 1Lesson 1: Scaling Machines [Free lesson]
Lesson 2: Corresponding Parts and Scale FactorsUnit 1Lesson 2: Scaling Robots Unit 3Lesson 1: Toothpicks
Lesson 3: Making Scaled Copies
Lesson 4: Scaled Relationship
Unit 1Lesson 3: Make It Scale Unit 4Lesson 3: Sticker Sizes
Lesson 5: The Size and the Scale FactorUnit 1Lesson 4: Scale Factor Challenges
Lesson 6: Scaling and AreaUnit 1Lesson 5: TilesPractice Day 1 (Print available)
Topic 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1Lesson 6: Introducing ScaleLesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scale Drawings and Maps 
Lesson 9: Creating Scale Drawings
Lesson 10: Changing Scales in Scale Drawings
Unit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)
Lesson 11: Scales without Units 
Lesson 12: Units in Scale DrawingsUnit 1Lesson 8: Scaling StatesLesson 9: Scaling BuildingsLesson 10: Room Redesign (Print available)Practice Day 2 (Print available)
Topic 3: Let’s Put It to Work
Lesson 13: Draw It to ScaleUnit 1Lesson 10: Room Redesign (Print available)

Unit 2: Introducing Proportional Relationships

Topic 1: Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the OthersUnit 2Lesson 1: Paint [Free lesson] 
Lesson 2: Introducing Proportional Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 3: More About Constant of ProportionalityUnit 2Lesson 3: Sugary Drinks (Print available)Unit 4Lesson 3: Sticker Sizes
Topic 2: Representing Proportional Relationships with Equations 
Lesson 4: Proportional Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of Equations
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Unit 2Lesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsPractice Day
Topic 3: Comparing Proportional and Nonproportional Relationships 
Lesson 7: Comparing Relationships with TablesUnit 2Lesson 2: Balloon FloatLesson 3: Sugary Drinks (Print available)Lesson 4: Robot Factory
Lesson 8: Comparing Relationships with EquationsUnit 2Lesson 4: Robot FactoryLesson 5: SnapshotsLesson 6: Two and Two (Print available) [Free lesson]Lesson 7: All Kinds of EquationsLesson 11: Four RepresentationsLesson 12: Water Efficiency
Lesson 9: Solving Problems About Proportional RelationshipsUnit 2Lesson 12: Water Efficiency
Topic 4: Representing Proportional Relationships with Graphs
Lesson 10: Introducing Graphs of Proportional Relationships
Lesson 11: Interpreting Graphs of Proportional Relationships
Lesson 12: Using Graphs to Compare Relationships
Lesson 13: Two Graphs for Each Relationship
Unit 2Lesson 8: Dino Pops [Free lesson]Lesson 9: Gallon ChallengeLesson 10: Three TurtlesLesson 11: Four RepresentationsLesson 12: Water Efficiency
Topic 5: Let’s Put It to Work
Lesson 14: For RepresentationsUnit 2Lesson 11: Four Representations (Print available)
Lesson 15: Using Water EfficiencyUnit 2Lesson 12: Water Efficiency

Unit 3: Measuring Circles

Topic 1: Circumference of a Circle 
Lesson 1: How Well Can You Measure?Unit 3Lesson 1: Toothpicks
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Unit 3Lesson 2: Is It a Circle?Lesson 3: Measuring Around [Free lesson]
Lesson 5: Circumference and Wheels 
Topic 2: Area of a Circle
Lesson 6: Estimating AreasUnit 3Lesson 5: Area Strategies
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Unit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)Lesson 7: Why Pi?Lesson 8: Area Challenges [Free lesson]Lesson 9: Circle vs. SquarePractice Day 2 (Print available)
Lesson 9: Applying Area of CirclesUnit 3Lesson 6: Radius Squares (Print available)
Topic 3: Let’s Put It to Work
Lesson 10: Distinguishing Circumference and AreaUnit 3Lesson 7: Why Pi?
Lesson 11: Stained-Glass WindowsUnit 3Lesson 5: Area StrategiesLesson 6: Radius Squares (Print available)

Unit 4: Proportional Relationships and Percentages

Topic 1: Proportional Relationships with Fractions 
Lesson 1: Lots of Flags
Lesson 2: Ratios and Rates with Fractions
Lesson 3: Revisiting Proportional Relationships
Lesson 4: Half as Much Again
Unit 4Lesson 1: Mosaics [Free lesson]Lesson 2: Peach Cobbler (Print available)Lesson 3: Sticker Sizes
Lesson 5: Say It with Decimals 
Topic 2: Percent Increase and Decrease 
Lesson 6: Increasing and DecreasingUnit 4Lesson 4: More and LessLesson 5: All the EquationsLesson 6: 100% (Print available)Lesson 7: Percent machines [Free lesson]Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 7: One Hundred percentUnit 4Lesson 6: 100% (Print available)
Lesson 8: Percent Increase and Decrease with EquationsUnit 4Lesson 5: All the Equations
Lesson 9: More and Less than 1% 
Topic 3: Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Unit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]
Lesson 12: Finding the PercentagesUnit 4Lesson 4: More and Less
Lesson 13: Measurement Error
Lesson 14: Percent Error
Lesson 15: Error Intervals
Unit 4Lesson 11: Bookcase Builder
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Percent ProblemsUnit 4Lesson 8: Tax and TipLesson 9: Minimum Wage (Print available)Lesson 10: Cost of College (Print available)Lesson 11: Bookcase BuilderLesson 12: Posing Percent Problems [Free lesson]Practice Day

Unit 5: Rational Number Arithmetic

Topic 1: Interpreting Negative Numbers 
Lesson 1: Interpreting Negative NumbersUnit 5Lesson 1: Floats and Anchors [Free lesson]
Topic 2: Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Unit 5Lesson 2: More Floats and AnchorsLesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 4: Money and Debts 
Lesson 5: Representing SubtractionUnit 5Lesson 5: Number Puzzles
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Unit 5Lesson 3: BumpersLesson 4: Draw Your Own (Print available) [Free lesson]Lesson 5: Number PuzzlesLesson 10: Integer Puzzles [Free lesson]Lesson 11: Changing TemperaturesLesson 13: Solar Panels and More (Print available)Practice Day 1 (Print available)
Topic 3: Multiplying and Dividing Rational Numbers
Lesson 8: Position, Speed, and Direction
Lesson 9: Multiplying Rational Numbers
Lesson 10: Multiply!
Unit 5Lesson 7: Back in Time
Lesson 11: Dividing Rational NumbersUnit 5Lesson 8: Speeding Turtles
Lesson 12: Negative Rates 
Topic 4: Four Operations with Rational Numbers 
Lesson 13: Expressions with Rational NumbersUnit 5Lesson 9: Expressions (Print available)
Lesson 14: Solving Problems with Rational NumbersLesson 11: Changing Temperatures
Lesson 12: Arctic Ice Sea (Print available)
Lesson 13: Solar Panels and More (Print available)
Topic 5: Solving Equations When There Are Negative Numbers 
Lesson 15: Making and Measuring Boxes 
Lesson 16: Representing Contexts with Equations 
Topic 6: Let’s Put It to Work 
Lesson 17: The Stock market

Unit 6: Expressions, Equations, and Inequalities

Topic 1: Representing Situations of the Form px + q and p(+ q) = r
Lesson 1: Relationships Between Quantities
Unit 2 Lesson 1: Paint [Free lesson] Lesson 2: Balloon Float
Unit 4 Lesson 1: Mosaics [Free lesson] Lesson 2: Peach Cobbler (Print available)
Unit 6 Lesson 1: Toothpicks and Tiles
Lesson 2: Reasoning about Contexts with Tape Diagrams
Lesson 3: Reasoning about Equations with Tape Diagrams
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
Unit 6Lesson 2: Smudged ReceiptsLesson 3: EquationsLesson 4: Seeing Structure (Print available)
Lesson 6: Distinguishing between Two Types of SituationsUnit 6Lesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)
Topic 2: Solving Equations of the Form px + q and p(+ q) = and Problems That lead to Those Equations 
Lesson 7: Reasoning about Solving Equations (Part 1)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available) 
Lesson 8: Reasoning about Solving Equations (Part 2)Unit 6Lesson 5: Balancing MovesLesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 9: Always-Equal Machines
Topic 9 Dealing with Negative Numbers 
Lesson 10: Different Options for Solving One EquationUnit 6Lesson 7: Keeping It True (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)
Lesson 11: Using Equations to Solve ProblemsUnit 6Lesson 12: Community Day (Print available)
Lesson 12: Solving Problems about Percent Increase or DecreaseUnit 4Lesson 10: Cost of College (Print available)
Topic 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6Lesson 13: I Saw the SignsLesson 15: BudgetingLesson 16: Shira the Sheep [Free lesson]
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiency Solving Inequalities
Unit 6Lesson 14: Unbalanced HangersLesson 15 Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Unit 6Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)Practice Day 2 (Print available)
Topic 4: Writing Equivalent Expressions 
Lesson 18: Subtraction in Equivalent ExpressionsUnit 6Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available) 
Lesson 19: Expanding and FactoringUnit 6Lesson 8: Factoring and Expanding (Print available)Lesson 11: Equation Roundtable (Print available)
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Unit 6Lesson 2: Smudged ReceiptsLesson 6: Balancing EquationsLesson 8: Factoring and Expanding (Print available)Lesson 9: Always-Equal MachinesLesson 10: Collect the Squares [Free lesson]Lesson 11: Equation Roundtable (Print available)Practice Day 1 (Print available)
Topic 5: Let’s Put It to Work
Lesson 23: Applications of ExpressionsUnit 6Lesson 12: Community Day (Print available)

Unit 7: Angles, Triangles, and Prisms

Topic 1: Angle Relationships
Lesson 1:Relationships of Angles
Unit 7 Lesson 1: Pinwheels Lesson 2: Friendly Angles [Free lesson] Lesson 3: Angle Diagrams
Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Unit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle Diagrams
Lesson 4: Solving for Unknown AnglesUnit 7Lesson 2: Friendly Angles [Free lesson]Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available)
Lesson 5: Using Equations to Solve for Unknown AnglesUnit 7Lesson 3: Angle DiagramsLesson 4: Missing Measures (Print available) [Free lesson]
Topic 2: Drawing Polygons with Given Conditions 
Lesson 6: Building Polygons (Part 1)
Lesson 7: Building Polygons (Part 2)
Unit 7Lesson 6: Is It Enough?
Lesson 8: Triangles with 3 Common MeasuresUnit 7Lesson 13: Popcorn Possibilities
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Unit 7Lesson 5: Can You Build It? [Free lesson]Lesson 6: Is It Enough?Lesson 7: More Than OneLesson 8: Can You Draw It? (Print available)Practice Day 1 (Print available)
Topic 3: Solid Geometry
Lesson 11: Slicing SolidsUnit 7Lesson 9: Slicing Solids
Lesson 12: Volume of Right PrismsUnit 7Lesson 10: Simple Prisms
Lesson 13: Decomposing Bases for AreasUnit 7Lesson 11: More Complicated Prisms
Lesson 14: Surface Area of Right PrismsUnit 7Lesson 10: Simple PrismsLesson 11: More Complicated PrismsLesson 12: Surface Area Strategies (Print available)
Lesson 15: Distinguishing Volume and Surface Area
Lesson 16: Applying Volume and Surface AreaUnit 7Lesson 13: Popcorn Possibilities
Topic 4: Let’s Put It to Work
Lesson 17: Building Prisms

Unit 8: Probability and Sampling

Topic 1: Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Unit 8 Lesson 1: How Likely? (Print available) [Free lesson] Lesson 2: Prob-bear-bilities [Free lesson] Lesson 3: Mystery Bag
Lesson 4: Estimating Probabilities Through Repeated ExperimentsUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Lesson 5: More Estimating ProbabilitiesUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 9: Car, Bike, or Train? (Print available)
Lesson 6: Estimating Probabilities Using SimulationUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 2: Probabilities of Multi-step Events
Lesson 7: Simulating Multi-step EventsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Lesson 8: Keeping Track of All Possible OutcomesUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?Lesson 6: Fair Games
Topic 9: Multi-step experiments
Lesson 10: Designing SimulationsUnit 8Lesson 7: Weather or NotLesson 8: Simulate ItLesson 9: Car, Bike, or Train? (Print available)
Topic 3: Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Unit 8Lesson 10: Crab Island [Free lesson]Lesson 11: Headlines
Topic 4: Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Unit 8 Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 11: HeadlinesLesson 12: Flower Power
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations with Friends
Unit 8Lesson 9: Car, Bike, or Train? (Print available)Lesson 10: Crab Island [Free lesson]Lesson 13: Plots and SamplesLesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)
Topic 5: Let’s Put It to Work
Lesson 20: Memory TestUnit 8Lesson 14: School Newspaper (Print available)Lesson 15: Asthma Rates (Print available)

Grade 8

Unit 1: Rigid Transformations and Congruence

Illustrative MathematicsDesmos Math 6–A1
Topic 1: Rigid Transformations 
Lesson 1: Moving in the PlaneUnit 1Lesson 1: Transformers [Free lesson]
Lesson 2: Naming the MovesUnit 1Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Grid MovesUnit 1Lesson 3: Transformation GolfLesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting CoordinatedUnit 3Lesson 6: Translations
Lesson 4: Making the MovesUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 5: Coordinate MovesUnit 1Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 6: Describing TransformationsUnit 1Lesson 5: Getting CoordinatedLesson 6: Connecting the Dots [Free lesson]
Topic 2: Properties of Rigid Transformations 
Lesson 7: No Bending or StretchingUnit 1Lesson 7: No Bending, No Stretching
Lesson 8: Rotation PatternsUnit 1Lesson 1: Transformers [Free lesson]Lesson 2: Spinning, Flipping, Sliding [Free lesson]Lesson 4: Moving Day (Print available) [Free lesson]Lesson 5: Getting Coordinated
Lesson 9: Moves in Parallel
Lesson 10: Composing Figures
Unit 1 Lesson 10: Transforming Angles
Topic 3: Congruence 
Lesson 11: What is the Same?
Lesson 12: Congruent Polygons
Lesson 13: Congruence
Unit 1 Lesson 7: Are They the Same?Lesson 9: Are They Congruent?Practice Day (Print available)
Topic 4: Angles in a Triangle
Lesson 14: Alternate Interior Angles
Lesson 15: Adding the Angles in a Triangle
Unit 1 Lesson 11: Tearing It Up (Print available)
Lesson 16: Parallel Lines and the Angles in a TriangleUnit 1 Lesson 10: Transforming Angles
Topic 5: Let’s Put It to Work
Lesson 17: Rotate and TessellateLesson 13: Tessellate [Free lesson]

Unit 2: Dilations, Similarity, and Introducing Slope

Topic 1: Dilations
Lesson 1: Projecting and ScalingUnit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]
Lesson 2: Circular Grid
Lesson 3: Dilations with No Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Unit 2Lesson 1: Sketchy Dilations [Free lesson]Lesson 2: Dilation Mini Golf (Print available) [Free lesson]Lesson 3: Match My DilationLesson 4: Dilations on a Plane
Topic 2: Similarity 
Lesson 6: SimilarityUnit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 7: Similar Polygons 
Lesson 8: Similar Triangles
Lesson 9: Side Length Quotients in Similar Triangles
Unit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Topic 3: Slope
Lesson 10: Meet SlopeUnit 2Lesson 9: Water SlideLesson 10: Points on a PlanePractice Day (Print available)Unit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations Unit 4Lesson 8: When Are They the Same?
Lesson 11: Writing Equations of LinesUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: SolutionsLesson 11: Pennies and Quarters Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 12: Using Equations of LinesUnit 3Lesson 9: Coin Capture
Topic 4: Let’s Put It to Work
Lesson 13: The Shadow KnowsUnit 2Lesson 8: Shadows

Unit 3: Linear Relationships

Topic 1: Proportional Relationships 
Lesson 1: Understanding Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Graphs of Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 2: Water Tank Unit 5Lesson 4: Window Frames
Lesson 3: Representing Proportional RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 4: Window FramesLesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 4: Comparing Proportional RelationshipsUnit 3Lesson 3: Posters
Topic 2: Representing Linear Relationships
Lesson 5: Introduction to Linear RelationshipsUnit 3Lesson 1: Turtle Time Trials [Free lesson]Lesson 4: Stacking CupsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: More Linear RelationshipsUnit 5Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 7: Representations of Linear RelationshipsUnit 3Lesson 5: Flags [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 8: Translating mx + bUnit 3Lesson 3: PostersLesson 6: Translations
Topic 3: Finding Slopes 
Lesson 9: Slopes Don’t Have to be PositiveUnit 3Lesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 8: Landing Planes
Lesson 10: Calculating SlopeUnit 3Lesson 7: Water CoolerLesson 8: Landing Planes
Lesson 11: Equations of All Kinds of LinesUnit 3Lesson 3: PostersLesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Topic 4: Linear Equations 
Lesson 12: Solutions to Linear EquationsUnit 3Lesson 3: PostersLesson 6: TranslationsLesson 10: Solutions Unit 4Lesson 3: Balanced MovesLesson 4: More Balanced Moves (Print available)
Lesson 13: More Solutions to Linear EquationsUnit 3 Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: TranslationsLesson 7: Water CoolerLesson 10: Solutions
Topic 5: Let’s Put It to Work 
Lesson 14: Using Linear Relations to Solve ProblemsUnit 3 Lesson 11: Pennies and Quarters

Unit 4: Linear Equations and Linear Systems

Topic 1: Puzzle Problems 
Lesson 1: Number PuzzlesUnit 4Lesson 1: Number machines
Topic 2: Linear Equation in One Variable 
Lesson 2: Keeping the Equation BalancedUnit 4Lesson 2: Keep It Balanced
Lesson 3: Balanced MovesUnit 4Lesson 3: Balanced Moves
Lesson 4: More Balanced MovesUnit 4Lesson 4: More Balanced Moves (Print available)
Lesson 5: Solving Any Linear EquationUnit 4Lesson 4: More Balanced Moves (Print available)Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 6: Strategic SolvingUnit 4Lesson 5: Equation Roundtable (Print available) [Free lesson]Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or No Solutions
Lesson 8: How many Solutions?
Unit 4Lesson 7: All, Some, or None?
Lesson 9: When Are They the SameUnit 4Lesson 8: When Are They the Same?
Topic 3: Systems of Linear Equations
Lesson 10: On or Off the Line?Unit 4Lesson 7: All, Some, or None?Lesson 8: When Are They the Same?Lesson 13: All, Some, or None? Part 2
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Unit 4 Lesson 9: On or Off the Line?Lesson 10: On Both LinesLesson 11: Make Them Balance [Free lesson]Lesson 12: Line Zapper [Free lesson]Lesson 13: All, Some, or None? Part 2Practice Day 2 (Print available)
Lesson 14: Solving More Systems 
Lesson 15: Writing Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Problems with Systems of EquationsUnit 4 Lesson 14: Strategic Solving, Part 2 (Print available)

Unit 5: Functions and Volume

Topic 1: Inputs and Outputs 
Lesson 1: Inputs and OutputsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Introduction to FunctionsUnit 5Lesson 1: Turtle Crossing [Free lesson]Lesson 2: Guess My Rule [Free lesson]Lesson 3: Function or Not?
Topic 2: Representing and Interpreting Functions 
Lesson 3: Equations of FunctionsUnit 3Lesson 1: Turtle Time Trials [Free lesson] Unit 5Lesson 3: Function or Not?Lesson 4: Window Frames
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Unit 5Lesson 4: Window FramesLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: Charge! (Print available)
Lesson 6: Even More Graphs of Functions 
Lesson 7: Connecting Representations of FunctionsUnit 5Lesson 7: Feel the Burn (Print available) [Free lesson]Lesson 8: (Print available)Charge!
Topic 3: Linear Functions and Rates of Change
Lesson 8: Linear FunctionsUnit 2Lesson 9: Water SlideLesson 10: Points on a PlaneUnit 3Lesson 4: Stacking CupsLesson 5: Flags [Free lesson]Lesson 6: Translations
Lesson 9: Linear ModelsUnit 5Lesson 3: PostersLesson 5: The Tortoise and the Hare [Free lesson]Lesson 6: Graphing StoriesLesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 10: Piecewise Linear FunctionsUnit 5Lesson 9: Piecing It Together
Topic 4: Cylinder and Cones 
Lesson 11: Filling Containers 
Lesson 12: How Much Will Fit? 
Lesson 13: The Volume of a CylinderUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling Cylinders
Lesson 14: Finding Cylinder DimensionsUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling CylindersLesson 14: Missing Dimensions (Print available)
Lesson 15: The Volume of a ConeUnit 5Lesson 10: Volume LabLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 16: Finding Cone DimensionsUnit 5Lesson 12: Scaling CylindersLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Topic 5: Dimensions and Spheres 
Lesson 17: Scaling One DimensionUnit 5Lesson 12: Scaling Cylinders
Lesson 18: Scaling Two Dimensions 
Lesson 19: Estimating a Hemisphere 
Lesson 20: The Volume of a Sphere
Lesson 21: Cylinders, Cones, and Spheres
Unit 5Lesson 15: SpheresPractice Day 2 (Print available)
Topic 6: Let’s Put It to Work 
Lesson 22: Volume As a Function of …Unit 5Lesson 15: Spheres

Unit 6: Associations in Data

Topic 1: Does This Predict That? 
Lesson 1: Organizing DataUnit 6 Lesson 1: Click Battle
Lesson 2: Plotting DataUnit 6 Lesson 2: Wing Span
Topic 2: Associations in Numerical Data 
Lesson 3: What a Point in a Scatter Plot MeansUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 4: Fitting a LineUnit 6 Lesson 4: Dapper Cats [Free lesson]Lesson 5: Fit Fights [Free lesson]Lesson 6: Interpreting SlopesLesson 8: Animal BrainsPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 5: Describing Trends in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City(Print available)Practice Day 1 [Free lesson]
Lesson 6: The Slope of a Fitted LineUnit 6 Lesson 6: Interpreting SlopesLesson 7: Scatter Plot CityPractice Day 1 (Print available) [Free lesson]Practice Day 2 (Print available)
Lesson 7: Observing More patterns in Scatter PlotsUnit 6 Lesson 1: Click BattleLesson 2: Wing SpanLesson 3: Robots [Free lesson]Lesson 7: Scatter Plot City
Lesson 8: Analyzing Bivariate DataUnit 6Lesson 9: Tasty Fruit
Topic 3: Associations in Categorical data 
Lesson 9: Looking for AssociationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 11: Federal BudgetsPractice Day 3 (Print available)
Lesson 10: Using Data Displays to Find associationsUnit 6Lesson 10: Finding Associations [Free lesson]Lesson 9: Tasty Fruit
Topic 4: Let’s Put It to Work
Lesson 11: Gone in 30 SecondsUnit 6Lesson 11: Federal Budgets

Unit 7: Exponents and Scientific Notation

Topic 1: Exponent Review 
Lesson 1: Exponent ReviewUnit 7 Lesson 1: Circles [Free lesson]Lesson 2: Combining Exponents
Topic 2: Exponent Rules 
Lesson 2: Multiplying Powers of 10
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Unit 7 Lesson 3: Power Pairs (Print available) [Free lesson]Lesson 4: Rewriting Powers  
Lesson 5: Negative Exponents with Powers of 10Unit 7 Lesson 5: Zero and Negative ExponentsLesson 6: Write a Rule (Print available)Practice Day 1 (Print available)
Lesson 6: What about Other Bases? 
Lesson 7: Practice with Rational Bases
Lesson 8: Combining Bases 
Topic 3: Scientific Notation 
Lesson 9: Describing Large and Small Numbers using Powers of 10Unit 7 Lesson 7: Scales and Weights
Lesson 10: Representing Large Numbers on the Number Line
Lesson 11: Representing Small Numbers on the Number Line
Unit 7 Lesson 8: Point Zapper
Lesson 12: Applications of Arithmetic with Powers of 10Unit 7  Lesson 8: Point ZapperLesson 9: Use Your Powers
Lesson 13: Defining Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Unit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 13: Star Power
Lesson 15: Adding and Subtracting with Scientific NotationUnit 7 Lesson 10: Solar System [Free lesson]Lesson 11: Balance the Scales [Free lesson]Lesson 12: City LightsLesson 13: Star Power
Topic 4: Let’s Put It to Work
Lesson 16: Is a Smartphone Smart Enough to Go to the Moon?Lesson 13: Star Power Practice Day 2 (Print available)

Unit 8: Pythagorean Theorem and Irrational Numbers

Topic 1: Side Lengths and Areas of Squares
Lesson 1: The Areas of Squares and Their Side LengthsUnit 8Lesson 1: Tilted Squares
Lesson 2: Side Lengths and AreasUnit 8Lesson 2: From Squares to RootsLesson 3: Between Squares
Lesson 3: Rational and Irrational Numbers
Lesson 4: Square Roots on the Number Line
Lesson 5: Reasoning about Square RootsUnit 8Lesson 2: From Squares to RootsLesson 3: Between SquaresLesson 4: Root Down [Free lesson]Practice Day 1 (Print available)
Topic 2: The Pythagorean Theorem
Lesson 6: Finding Side Lengths of TrianglesUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove ItLesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 7: A Proof of the Pythagorean TheoremUnit 8Lesson 7: Pictures to Prove It
Lesson 8: Finding Unknown Side LengthsUnit 8Lesson 11: Pond Hopper
Lesson 9: The ConverseUnit 8Lesson 9: Make It Right
Lesson 10: Applications of the Pythagorean TheoremUnit 8Lesson 10: Taco Truck [Free lesson]
Lesson 11: Finding Distances in the Coordinate PlaneUnit 8Lesson 11: Pond Hopper
Topic 3: Side Lengths and Volumes of Cubes
Lesson 12: Edge Lengths and Volumes
Lesson 13: Cube Roots
Unit 8Lesson 5: Filling Cubes
Topic 4: Decimal Representation of Rational and Irrational Numbers
Lesson 14: Decimal Representation of Rational and Numbers
Lesson 15: Infinite Decimal expansions
Unit 8Lesson 12: Fractions to DecimalsLesson 13: Decimals to Fractions
Topic 5: Let’s Put It to Work
Lesson 16: When Is the Same Size Not the Same Size?Unit 8Lesson 10: Taco Truck [Free lesson]

Unit 9: Putting It All Together

Topic 1: Tessellations
Lesson 1: Tessellations of the Plane
Lesson 2: Regular Tessellations
Lesson 3: Tessellating Polygons
Topic 2: The Weather
Lesson 4: What Influences Temperature?
Lesson 5: Plotting the Weather
Lesson 6: Using and Interpreting a Mathematical Model

Families and caregivers, welcome to Amplify Desmos Math K–5!

Welcome to the Amplify Desmos Math K–5 Caregiver Hub. We hope your student enjoys exploring math, working with friends to solve problems, and learning new and interesting concepts. And we hope you enjoy the math journey with them! Below are some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math.

Para la versión en español, haga clic aquí.

Three children are engaging in a math activity with a grid and orange markers. One child holds a "9-3" card. The background includes beach elements and abstract math symbols.

Caregiver Unit Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of key concepts, plus a problem from the lesson practice set you can work through with your student. You’ll find a Caregiver Resource for each unit, in both English and Spanish.

Unit 1: Math in Our World

Unit 2: Numbers 1–10

Unit 3: Flat Shapes All Around Us

Unit 4: Understanding Addition and Subtraction

Unit 5: Make and Break Apart Numbers Within 10

Unit 6: Numbers 0–20

Unit 7: Solid Shapes All Around Us

Unit 1: Adding, Subtracting, and Working With Data

Unit 2: Addition and Subtraction Story Problems

Unit 3: Adding and Subtracting Within 20

Unit 4: Numbers to 99

Unit 5: Adding Within 100

Unit 6: Measuring Lengths of Up to 120 Length Units

Unit 7: Geometry and Time

Unit 1: Working With Data and Solving Comparison Problems

Unit 2: Adding and Subtracting Within 100

Unit 3: Measuring Length

Unit 4: Addition and Subtraction on the Number Line

Unit 5: Numbers to 1,000

Unit 6: Geometry and Time

Unit 7: Adding and Subtracting Within 1,000

Unit 8: Equal Groups

Unit 1: Introducing Multiplication

Unit 2: Area and Multiplication

Unit 3: Wrapping Up Addition and Subtraction Within 1,000

Unit 4: Relating Multiplication to Division

Unit 5: Fractions as Numbers

Unit 6: Measuring Length, Time, Liquid Volume, and Weight

Unit 7: Two-Dimensional Shapes and Perimeter

Unit 1: Factors and Multiples

Unit 2: Fraction Equivalence and Comparison

Unit 3: Extending Operations to Fractions

Unit 4: From Hundredths to Hundred Thousands

Unit 5: Multiplicative Comparison and Measurement

Unit 6: Multiplying and Dividing Multi-Digit Numbers

Unit 7: Angles and Properties of Shapes

Unit 1: Volume

Unit 2: Fractions as Quotients and Fraction Multiplication

Unit 3: Multiplying and Dividing Fractions

Unit 4: Multiplication and Division With Multi-Digit Whole Numbers

Unit 5: Place Value Patterns and Decimal Operations

Unit 6: More Decimal and Fraction Operations

Unit 7: Shapes on the Coordinate Plane

Unit refresh videos

Unit 1

  • Sub-Unit 2 – Answering the Question “Are There Enough?”
  • Sub-Unit 3 – Counting and Cardinality

Unit 2

  • Sub-Unit 1 – Comparing 2 Groups Using the Terms More, Fewer, and Same
  • Sub-Unit 2 – Counting Objects in Different Orders
  • Sub-Unit 3 – Making Groups to Represent Numerals
  • Sub-Unit 4 – Comparing Written Numbers

Unit 3

  • Sub-Unit 1 – Identifying Circles and Triangles in Different Sizes and Orientations
  • Sub-Unit 2 – Using Positional Words to Describe the Location of Shapes

Unit 4

  • Sub-Unit 1 – Adding and Subtracting Within 10
  • Sub-Unit 2 – Representing Addition and Subtraction Story Problems
  • Sub-Unit 3 – Finding the Values of Expressions

Unit 5

Unit 1

  • Sub-Unit 1 – Organizing Data to Count How Many in Each Category
  • Sub-Unit 2 – Counting on to Add and Counting Back to Subtract
  • Sub-Unit 3 – Representing 2 Categories of Data With Addition Equations

Unit 2

  • Sub-Unit 1 – Representing and Solving Add To, Change Unknown Story Problems
  • Sub-Unit 2 – Using Addition or Subtraction to Find an Unknown Part of a Total Amount
  • Sub-Unit 3 – Solving Compare, Difference Unknown Problems
  • Sub-Unit 4 – Making Sense of Story Problems With Different Questions

Unit 3

  • Sub-Unit 1 – Finding a Difference Using the Relationship Between Addition and Subtraction
  • Sub-Unit 2 – Using the Structure of Teen Numbers to Find Missing Addends
  • Sub-Unit 3 – Breaking Apart Addends to Make 10 When Adding
  • Sub-Unit 4 – Subtracting From Teen Numbers in Parts to Get to 10

Unit 4

  • Sub-Unit 1 – Adding a Ten To and Subtracting a Ten From Multiples of 10
  • Sub-Unit 2 – Representing and Writing Two-Digit Numbers
  • Sub-Unit 3 – Comparing Two-Digit Numbers
  • Sub-Unit 4 – Representing the Same Two-Digit Number With Different Amounts of Tens and Ones

Unit 5

  • Sub-Unit 1 – Adding a Number of Tens or Ones to a Two-Digit Number
  • Sub-Unit 2 – Adding a Two-Digit Number and a One-Digit Number When Composing a Ten is Necessary
  • Sub-Unit 3 – Adding a Two-Digit Number and a Two-Digit Number When Composing a Ten is Necessary

Unit 1

  • Sub-Unit 1 – Choosing Strategies to Add Within 20
  • Sub-Unit 2 – Representing Data in a Picture Graph and Bar Graph
  • Sub-Unit 3 – Finding the Difference Between 2 Categories Shown on a Bar Graph

Unit 2

  • Sub-Unit 1 – Strategies to Solve Story Problems Involving Money
  • Sub-Unit 2 – Decomposing a Ten When Subtracting by Place
  • Sub-Unit 3 – Making Sense of Story Problems About Comparing That Use the Word More
  • Sub-Unit 4 – Making Sense of One- and Two-Step Story Problems

Unit 3

  • Sub-Unit 1 – Measuring the Length of an Object in Centimeters Using a Ruler
  • Sub-Unit 2 – Measuring Objects in Inches and Feet
  • Sub-Unit 3 – Representing Measurement Data on a Line Plot

Unit 4

  • Sub-Unit 1 – Locating Numbers on Number Lines
  • Sub-Unit 2 – Representing Addition and Subtraction Strategies on a Number Line

Unit 5

  • Sub-Unit 1 – Composing Hundreds to Represent Three-Digit Numbers
  • Sub-Unit 2 – Comparing Three-Digit Numbers

Unit 1

  • Sub-Unit 1 – Representing Equal-Groups Situations With Equal-Groups Drawings
  • Sub-Unit 2 – Representing Arrays With Multiplication Equations
  • Sub-Unit 3 – Representing Data Using Scaled Bar Graphs

Unit 2

  • Sub-Unit 1 – Determining the Area of a Rectangle Using Counting and Skip Counting
  • Sub-Unit 2 – Determining the Area of a Rectangle Using Multiplication
  • Sub-Unit 3 – Decomposing to Determine the Area of Rectilinear Figures

Unit 3

  • Sub-Unit 1 – Using the Expanded Form and Partial Sums Algorithms to Add
  • Sub-Unit 2 – Using the Expanded Form Algorithm to Subtract
  • Sub-Unit 3 – Rounding Numbers to the Nearest Hundred and Ten Using Number Lines
  • Sub-Unit 4 – Representing and Solving Two-Step Story Problems Involving Multiplication

Unit 4

  • Sub-Unit 1 – Representing Division Situations With Equal-Groups Drawings
  • Sub-Unit 2 – Representing an Equal-Groups Problem With a Division and Multiplication Equation
  • Sub-Unit 3 – Using the Distributive Property of Multiplication to Multiply a One-Digit Number by a Teen Number
  • Sub-Unit 4 – Decomposing Dividends to Divide

Unit 5

  • Sub-Unit 1 – Writing Unit and Non-Unit Fractions
  • Sub-Unit 2 – Locating Non-Unit Fractions on the Number Line
  • Sub-Unit 3 – Identifying Equivalent Fractions
  • Sub-Unit 4 – Comparing Fractions With the Same Denominator or Same Numerator

Unit 1

  • Sub-Unit 1 – Using Factor Pairs to Determine All the Possible Side Lengths of a Rectangle With a Given Area
  • Sub-Unit 2 – Finding Multiples and Common Multiples

Unit 2

  • Sub-Unit 1 – Locating Fractions with Different Denominators On the Same Number Line
  • Sub-Unit 2 – Using Multiples or Factors to Determine Equivalent Fractions
  • Sub-Unit 3 – Comparing Fractions Using Equivalent Fractions With Common Denominators

Unit 3

  • Sub-Unit 1 – Adding and Subtracting Fractions with the Same Denominator
  • Sub-Unit 2 – Multiplying Whole Numbers and Fractions
  • Sub-Unit 3 – Adding Fractions with Denominators of 10 and 100

Unit 4

  • Sub-Unit 1 – Writing Fractions With Denominators of 10 and 100 as Decimals
  • Sub-Unit 2 – Relationships Between Place Values in Multi-Digit Whole Numbers
  • Sub-Unit 3 – Comparing Multi-Digit Numbers
  • Sub-Unit 4 – Using the Standard Algorithm to Subtract When Decomposing is Required

Unit 5

  • Sub-Unit 1 – Representing Multiplicative Comparison Situations
  • Sub-Unit 2 – Converting Measurements in the Metric System
  • Sub-Unit 3 – Comparing Measurements

Unit 1

  • Sub-Unit 1 – Using the Layered Structure of a Rectangular Prism to Determine the Volume
  • Sub-Unit 2 – Determining the Volume of a Rectangular Prism
  • Sub-Unit 3 – Determining the Volume of Figures Composed of Rectangular Prisms

Unit 2

  • Sub-Unit 1 – Representing Equal-Sharing Story Problems with Fractional Quotients
  • Sub-Unit 2 – Representing Fractions with Equivalent Multiplication and Division Expressions
  • Sub-Unit 3 – Determining the Area of a Rectangle With a Fractional Side Length

Unit 3

  • Sub-Unit 1 – Representing Multiplication of 2 Unit Fractions with Diagrams
  • Sub-Unit 2 – Dividing Whole Numbers by Unit Fractions

Unit 4

  • Sub-Unit 1 – Multiplying Multi-digit Whole Numbers Using the Partial Products and Standard Algorithms
  • Sub-Unit 2 – Dividing Multi-Digit Whole Numbers Using Partial Quotients
  • Sub-Unit 3 – Representing Multi-Step Story Problems with Equations

Unit 5

  • Sub-Unit 1 – Comparing Decimals
  • Sub-Unit 2 – Using the Standard Algorithms to Add and Subtract Decimals
  • Sub-Unit 3 – Multiplying a Whole Number and a Decimal Using the Distributive Property
  • Sub-Unit 4 – Dividing Whole Numbers by Decimals Less Than 1

Access Amplify Desmos Math at home.

In addition to a print Student Edition workbook, your student will have digital access to all learning, practice, and assessment materials through the Amplify platform. The digital curriculum can be accessed in school and at home by following these instructions:

  • Click the Amplify Desmos Math button.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, caregivers can view student work by opening previous assignments.

Learn how to navigate the student home page.

Materials overview

Amplify Desmos Math supports blended learning with supporting print materials and a unique digital experience. All K–5 lessons are available in a write-in Student Edition book. Many of the lessons include hands-on activities with manipulatives, tools that help students understand abstract concepts by making them tangible. Your student will also work with digital devices for an age-appropriate number of lessons.

When students use devices, teachers can monitor their work in real time, making sure they get the exact support that they need at every part of the lesson, in and outside of class.

Una interfaz digital que muestra los nombres anónimos de los estudiantes y su estado de participación en diversas actividades. La interfaz incluye opciones para realizar resúmenes, capturas de pantalla y vistas individuales de los estudiantes.

Components of a lesson

Students in an Amplify Desmos Math classroom can be seen (and heard!) asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

A typical Amplify Desmos Math lesson includes:

  • Warm-up: A short, attention-getting problem to pique students’ interest in the lesson.
  • Activities: One to two mini-activities that challenge students’ problem-solving skills.
  • Synthesis: Discussion to review and bring together the important concepts from the lesson.
  • Show What You Know and Reflection: Questions for students to show what they know from the lesson. (Note: The Show What You Know lesson assessment is optional for kindergarten and grade 1.)
  • Centers: Student-led activity stations that reinforce the math learned during lesson activities through interactive and often game-like formats. In kindergarten and grade 1, time for Centers is built into the last 15 minutes of every lesson.

To support, strengthen, and stretch students’ learning after the lesson, Amplify Desmos Math offers options for:

  • Differentiation: Mini-Lessons, Centers, Extensions, Boost Personalized Learning, and Fluency Practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. If your student has already completed the practice problems for the lesson, ask them to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your student follow-up questions to encourage the use of math language as they explain their thinking, such as, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students are stuck, ask support questions, such as, “What information do you know here?” or “How could you represent this problem?”

Your student’s teacher may introduce a Center game with students in the lesson or beyond the lesson. These games are aligned to the math of the unit and can be played with students outside of class. Your student’s teacher may introduce a Center game to students during or after completing a lesson, or you may need to teach the game before you play by using easy-to-follow instructions. Sign up for a free account to explore Centers and additional K–5 content in our Featured Collections.

Each unit in Amplify Desmos Math begins with a read-aloud story to engage students and provide context for the math of the unit. Elements and characters from the Unit Story then appear in lessons throughout the unit.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Relate math to daily activities at home, whether grocery shopping, preparing a meal, or planning for a trip to the store. Your student can help you figure out how many more apples there are than oranges in the grocery cart, show how to split a sandwich into fourths, or figure out how much change you’ll receive in exchange for a $10 bill. Encourage your student to point out ways that you use math in your daily tasks.

Remind your student that getting stuck is part of the process and a necessary—beneficial, even!—part of learning. Many students (and adults) fear making mistakes. But research shows that making mistakes helps our brains grow. When your student gets stuck on a problem, encourage them to keep trying different strategies, even if they’re not sure if they are right.

Get more information.

Have a question about Amplify Desmos Math? Visit our help library to search for articles with answers to your program questions. For additional support, please contact your student’s teacher.

Grade K

Unit 1: Position, Length, Height, and Sorting

Lesson 2: Describe and Compare Length and Height, Session 3Connecting Cubes

Unit 2: Numbers to 5, Shapes and Weight

Lesson 4: Count, Show and Write Numbers to 5, Session 2Skye’s Style
Lesson 5: Compare Numbers to 5, Session 4Matching Groups
Lesson 5: Compare Numbers to 5, Session 5Designing Shoes With Skye
Lesson 6: Three-Dimensional Shapes and Weight, Session 1What’s That Shape?
Lesson 6: Three-Dimensional Shapes and Weight, Session 2Building Solid Shapes
Lesson 6: Three-Dimensional Shapes and Weight, Session 5Putting Solid Shapes Together

Unit 3: Addition and Subtractions with 5 and Shapes,

Lesson 8: Two-Dimensional Shapes,
Session 1
So Much Sorting
Lesson 8: Two-Dimensional Shapes,
Session 2
What’s That Shape Called?
Another Shape

Unit 4: Numbers to 10 and Shapes

Lesson 11: Count, Show, and Write Numbers to 10, Session 1Investigate: Cafeteria Math
Fingers as Math Tools
Lesson 12: Compare Numbers to 10, Session 1Moving and Grooving
Fingers and Counters
Lesson 12: Compare Numbers to 10, Session 2More, Fewer, or the Same
Comparing Words
Lesson 12: Compare Numbers to 10, Session 5Forest Friends
Lesson 14: Compose and Decompose 10, Session 2Harry’s Hamster Wheel
Lesson 14: Compose and Decompose 10, Session 3Harry Explores Space
Lesson 14: Compose and Decompose 10, Session 4Showing What We Know About 10
Lesson 14: Compose and Decompose 10, Session 5Harry Explores the Ocean

Unit 6: Addition and Subtraction Within 10

Lesson 20: Add Within 10, Session 1Investigate: Casey’s Town
What Does It Mean to Add?
Lesson 20: Add Within 10, Session 2How Many Objects?
Lesson 20: Add Within 10, Session 3How Many Objects in Pictures?
How Will You Count?
Lesson 21: Subtract Within 10, Session 1What Does It Mean to Subtract?
Lesson 22: Add and Subtract to Solve Wold Problems, Session 1The Bus Depot

Unit 7: Teen Numbers and Shapes

Lesson 23: Compose and Decompose Teen Numbers with Tools and Drawings, Session 2Investigate: Packing Snacks
Getting Ready for the Game
Pass, Shoot, Score
Lesson 23: Compose and Decompose Teen Numbers with Tools and Drawings, Session 3How Many on the Field?
Lesson 25: Compose and Decompose Teen Numbers with Symbols, Session 2Jersey Jam!
People at the Park

Grade 1

Unit 1: Relating Addition and Subtraction

Lesson 2: Add and Subtract Within 10, Session 1What’s the Difference?
Leaping Lily Pads!
Investigate: Let’s Grow!
Lesson 2: Add and Subtract Within 10, Session 3Packing a Picnic
Lesson 5: Solve Word Problems to 10, Session 2Tutu’s Garden in Maui
Lesson 5: Solve Word Problems to 10, Session 2Replanting Huli
Lesson 5: Solve Word Problems to 10, Session 3The Kalo Plants
Lesson 5: Solve Word Problems to 10, Session 4A Community Working Together
Lesson 5: Solve Word Problems to 10, Session 5Helping Others

Unit 2: Addition and Subtraction Within 20

Lesson 6: Teen Numbers, Session 2Same Number, Different Ways
Lesson 7: Add Three Numbers, Session 2Making 10
Kitten Coaster

Unit 4: Using Tens and Ones to Organize and Count

Lesson 15: Tens and Ones, Session 1Investigate: Game Points
Lesson 15: Tens and Ones, Session 3Meeting Yara
It’s a Match
Lesson 16: Numbers to 120, Session 1How Many Cubes?
Boris’s Thimbles
Lesson 21: Add Two-Digit Numbers, Session 1How Many Tens?
Investigate: Squashes at the Playground
Lesson 21: Add Two-Digit Numbers,
Session 2
Town Helpers
Lesson 21: Add Two-Digit Numbers,
Session 3
Making Squash Butter

Unit 5: Operations with Tens and Ones

Lesson 19: Addition with Two-Digit Numbers, Session 2From Park to Table

Unit 6: Geometry and Measurement

Lesson 22: Shapes, Session 1Shapes Ying Saw
Lesson 23: Break Shapes Into Equal Parts, Session 2Fair and Square
One of the Parts, All of the Parts
Lesson 23: Break Shapes Into Equal Parts, Session 5A Bigger Part

Grade 1 (ADM G2)

Unit 1: Relating Addition and Subtraction

Lesson 1: Partner Pairs for 10, Session 3Ways to Make 10
Lesson 2: Add and Subtract Within 10, Session 3Exploring Within 10

Grade 2

Unit 1: Numbers Within 20

Lesson 2: Using Mental Math Strategies to Subtract, Session 1Awesome Aquariums

Unit 2: Numbers Within 100

Lesson 10: Solve Word Problems Involving Money, Session 1Investigate
Lesson 10: Solve Word Problems Involving Money, Session 2Discovering Coins (Part 1)
The Toy Stand
Lesson 10: Solve Word Problems Involving Money, Session 3How Much Money?
Discovering Coins (Part 2)
Lesson 10: Solve Word Problems Involving Money, Session 4The Craft Stand at the Block Party

Unit 3: Numbers Within 1000

Lesson 12: Three-Digit Numbers, Session 1Investigate: A Mistake in Mom’s Office
What Makes a Hundred?
Lesson 12: Three-Digit Numbers, Session 2Looking for Patterns
Lesson 13: Read and Write Three-Digit Numbers, Session 1What’s the Value?
Lesson 13: Read and Write Three-Digit Numbers, Session 2Mail Call!
Lesson 13: Read and Write Three-Digit Numbers, Session 3A New Representation
What’s Your Name?
All the Ways!
Lesson 15: Mental Addition and Subtraction, Session 2Turtle Hurdle
Lesson 16: Add Three-Digit Numbers, Session 2There’s Something About Berries
Lesson 18: Using Addition and Subtraction Strategies with Three-Digit Numbers, Session 2Baking With Skunk

Unit 4: Length

Lesson 25: Solving Problems About Length, Session 2Lengths of Jungle Animals
Lesson 27: Sorting and Organizing Data, Session 1Messy Measurements
Lesson 27: Sorting and Organizing Data, Session 3Bracelets and Wristbands
Lesson 26: Add and Subtract on the Number Line, Session 1Investigate
Time to Line Up!
In Full Bloom
Lesson 26: Add and Subtract on the Number Line, Session 2What’s That Number?
Lesson 26: Add and Subtract on the Number Line, Session 3Greater Than, Less Than, or Equal to

Unit 5: Shapes and Arrays

Lesson 28: Recognize and Draw Shapes, Session 2Frame It!
Lesson 28: Recognize and Draw Shapes, Session 3Measure It, Draw It
Lesson 32: Even and Odd Numbers,
Session 1
Can You Share?
Lesson 32: Even and Odd Numbers,
Session 2
Everybody, Find A Partner!
Lesson 32: Even and Odd Numbers,
Session 3
Is It Even or Odd?

Grade 2 (ADM G3)

Unit 2: Numbers Within 100

Lesson 6: Adding Two-Digit Numbers, Session 1Panda Patterns
Lesson 12: Understand Three-Digit Numbers, Session 2Investigate: Creating a Photo Gallery
Lesson 16: Add Three-Digit Numbers, Session 2How Would You Solve It?
Adding Your Way
What Is an Algorithm?
Lesson 16: Add Three-Digit Numbers, Session 3Using Fewer Digits
Determining Sums of 2 or More Addends
Lesson 16: Add Three-Digit Numbers, Session 3Adding Strategically

Unit 4: Length

Lesson 27: Read and Make Line Plots, Session 2The Plot Chickens
Let’s Make a Line Plot

Grade 3

Unit 2: Multiplication and Division

Lesson 4: Understand the Meaning of Multiplication, Session 1Equal Groups
Lesson 6: Multiply with 3, 4, and 6, Session 2Rectangles and Arrays
Lesson 8: Use Order and Grouping to Multiply, Session 2Arrays of Flavor
Lesson 11: Understand How Multiplication and Division Are Connected, Session 1It’s Chili in Here!
Lesson 12: Multiplication and Division Facts, Session 3Relating Quotients to Familiar Products

Unit 3: Multiplication

Lesson 19: Scaled Graphs, Session 1Puppy Pile
Lesson 19: Scaled Graphs, Session 42, 5, or 10?
Lesson 14: Understand Area, Session 1Tiling Figures
Lesson 14: Understand Area, Session 2Which Covers More Space?
Lesson 15: Multiply to Find Area, Session 3Area Hunt
Lesson 17: Solve One-Step Word Problems Using Multiplication and Division, Session 2Division and Multiplication Equations

Unit 4: Fractions

Lesson 21: Understand Fractions on a Number Line, Session 1Cat Crossing
Lesson 21: Understand Fractions on a Number Line, Session 2Fractions on the Number Line
Lesson 21: Understand Fractions on a Number Line, Session 3Location, Location, Location

Unit 6: Shapes

Performance TaskInvestigate: Comparing Rugs
Lesson 30: Understand Categories of Shapes, Session 1Piho’s Shapes
Lesson 31: Classify Quadrilaterals, Session 1Rectangles, Squares, and Rhombuses
Lesson 31: Classify Quadrilaterals, Session 3More Quadrilaterals

Grade 4

Unit 2: Operations

Lesson 6: Understand Multiplication as a Comparison, Session 1Sticker Mania
Lesson 6: Understand Multiplication as a Comparison, Session 2Representing “Times as Many”
Going Swimming
Lesson 8: Multiples and Factors, Session 1Hamster Homes
Lesson 8: Multiples and Factors, Session 3Factor or Multiple?
Lesson 8: Multiples and Factors, Session 4A Number Game
Lesson 9: Number and Shape Patterns, Session 1How Does It Grow?

Unit 3: Multi-Digit Operations and Measurement

Lesson 11: Multiply by One-Digit Numbers, Session 1Investigate: Packing Lei
Counting Flowers for Lei
Lesson 11: Multiply by One-Digit Numbers, Session 3A Lei Making Workshop
A Reasonable Answer
Three of a Kind
Lesson 12: Multiply by Two-Digit Numbers, Session 2Growing Flowers for the Lei
Double Decomposition
Lesson 12: Multiply by Two-Digit Numbers, Session 3Revisiting Strategies
How Many Supplies?

Unit 4: Fractions, Decimals, and Measurement

Lesson 17: Understand Equivalent Fractions, Session 1Investigate: Building Your Own Number Line
Fraction Strips
Lesson 18: Understand Equivalent Fractions, Session 3Chop It
All Kinds of Fractions
Lesson 19: Fraction Addition and Subtraction, Session 1Pizza Problems
Lesson 20: Add and Subtract Fractions, Session 4Math Pizzeria
Lesson 24: Multiply Fractions by Whole Numbers, Session 2Equal Groups of Fractions
Lesson 25: Fractions as Tenths and Hundredths, Session 3Investigate: Different Units
Lesson 26: Relate Decimals and Fractions, Session 2A New Way to Write Tenths
A New Way to Write Hundredths
Lesson 26: Relate Decimals and Fractions, Session 4Are They Equivalent?
Lesson 27: Compare Decimals, Session 2How Can You Compare?
Lesson 27: Compare Decimals, Session 3Robot Factory
Lesson 27: Compare Decimals, Session 4What’s the Order

Unit 5: Geometry and Measurement

Lesson 30: Points, Lines, Rays, and Angles, Session 3Angle Adventures
Lesson 31: Angles, Session 1The Spin on Angles
Lesson 32: Add and Subtract with Angles, Session 3Angles in Motion

Grade 5

Unit 1: Whole Number Operations and Applications

Lesson 2: Find Volume Using Unit Cubes, Session 1Which is Largest
Lesson 2: Find Volume Using Unit Cubes, Session 2Packing the Barge
Lesson 3: Find Volume Using Formulas, Session 3Putting it Together
Figures Made of Prisms
Lesson 4: Multiply Multi-Digit Numbers, Session 1Partial Products Everywhere
Lesson 4: Multiply Multi-Digit Numbers, Session 4How Do They Compare?
Lesson 5: Divide Multi-Digit Numbers, Session 4Emptying the Water Tank

Unit 2: Decimals and Fractions

Lesson 6: Understand Decimal Place Value, Session 1Investigate: Numbers Between Numbers
Lesson 6: Understand Decimal Place Value, Session 2What Is One Thousandth?
Lesson 8: Read and Write Decimals,
Session 1
Say What?
Place Value Patterns
Lesson 9: Compare and Round Decimals, Session 2Selling Collectibles
Lesson 9: Compare and Round Decimals, Session 3The Claw
Which Way Down the Mountain?
Lesson 9: Compare and Round Decimals, Session 4Rounding Races
Lesson 7: Understand Powers of 10, Session 1Monarch Butterflies
All About That Base
Powers of 10 Parade

Unit 3: More Decimals & Fractions

Lesson 18: Fractions as Division, Session 1Investigate: Sharing Sandwiches
Division Story Problems
Making Generalizations
Investigate: Folding Paper
Lesson 18: Fractions as Division, Session 2Sharing More Sandwiches
Dance Breaks
Lesson 19: Multiplication by a Fraction, Session 2Parts of Parts
Lesson 20: Multiply Fractions to Find Area, Session 2One Part of One Part
Lesson 20: Multiply Fractions to Find Area, Session 3Making Food
Lesson 22: Multiply Fractions in Word Problems, Session 3Installing Turf
Rows and Columns
Lesson 22: Multiply Fractions in Word Problems, Session 4Messy Multiplication
Applying Fraction Multiplication
Lesson 21: Exploring Multiplication as Scaling, Session 1Chores at Animal Haven
The Re-size-inator

Unit 5: Algebraic Thinking and the Coordinate Plane

Lesson 31: Understand the Coordinate Plane, Session 1Bullseye!
Lesson 31: Understand the Coordinate Plane, Session 2Creating a Coordinate System
Coordinating Satellite Repairs

Grade 6

Unit 1: Expressions and Equations: Area, Algebraic Expressions, and Exponents

iReady ClassroomAmplify Classroom
Lesson 1: Find the Area of a ParallelogramUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2

Unit 2: Decimals and Fractions: Base-Ten Operations, Division with Fractions, and Volume

Lesson 7: Add, Subtract, and Multiply Multi-Digit DecimalsUnit 4
Lesson 1: Dishing Out Decimals
Lesson 8: Divide Whole Numbers and Multi-Digit DecimalsUnit 5
Lesson 13: Movie Time
Lesson 9: Understand Division with FractionsUnit 4
Lesson 3: Flour Planner
Lesson 10: Divide FractionsUnit 4
Lesson 6: Fill the Gap

Unit 3: Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Lesson 12: Understand Ratio ConceptsUnit 2
Lesson 1: Pizza Maker
Lesson 13: Find Equivalent RatiosUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation

Unit 4: Ratio Reasoning: Unit Rates and Percent

Lesson 15: Understand Rate ConceptsUnit 3
Lesson 1: Many Measurements
Lesson 16: Use Unit Rates to Solve ProblemsUnit 3
Lesson 6: Soft Serve
Lesson 17: Understand PercentsUnit 3
Lesson 9: Lucky Duckies

Unit 5: Algebraic Thinking: Equivalent Expressions and Equations with Variables

Lesson 19: Write and Identify Equivalent ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 22: Analyze Two-Variable RelationshipsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 6: Positive and Negative Numbers: Absolute Value, Inequalities, and the Coordinate Plane

Lesson 23: Understand Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It?
Lesson 24: Order Positive and Negative NumbersUnit 7
Lesson 4: Order in the Class
Lesson 26: Write and Graph One-Variable InequalitiesUnit 7
Lesson 7: Tunnel Travels

Unit 7: Statistical Thinking: Data Distributions and Measures of Center and Variability

Lesson 30: Use Dot Plots and Histograms to Describe Data DistributionsUnit 8
Lesson 3: Minimum Wage
Lesson 5: The Plot Thickens
Lesson 31: Interpret Median and Interquartile Range in Box PlotsUnit 8
Lesson 11: Toy Cars

Grade 7

Unit 1: Proportional Relationships: Ratios, Rates, and Circles

iReady ClassroomAmplify Classroom
Lesson 2: Find Unit Rates Involving Ratios and FractionsUnit 2
Lesson 1: Paint
Lesson 4: Represent Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 5: Solve Proportional Relationship Problems
Lesson 6: Solve Area and Circumference Problems Involving CirclesUnit 3
Lesson 3: Measuring Around
Lesson 9: Area Challenges

Unit 2: Numbers and Operations: Add and Subtract Rational Numbers

Lesson 7: Understand Addition with Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 8: Add with Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 9: Understand Subtraction with Negative IntegersUnit 5
Lesson 1: Floats and Anchors
Lesson 10: Add and Subtract Positive and Negative NumbersUnit 5
Lesson 1: Floats and Anchors

Unit 3: Numbers and Operations: Multiply and Divide Rational Numbers

Lesson 14: Use the Four Operations with Negative NumbersUnit 5
Lesson 10: Integer Puzzles

Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities

Lesson 19: Write and Solve InequalitiesUnit 6
Lesson 16: Shira the Sheep

Unit 5: Proportional Reasoning: Percents and Statistical Samples

Lesson 20: Solve Problems Involving Percents Unit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 22: Understand Random SamplingUnit 8
Lesson 2: Prob-bear-bilities
Lesson 24: Compare PopulationsUnit 8
Lesson 10: Crab Island

Unit 6: Geometry: Solids, Triangles, and Angles

Lesson 28: Find Unknown Angle MeasuresUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures

Unit 7: Probability: Theoretical Probability, Experimental Probability, and Compound Events

Lesson 30: Understand ProbabilityUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Grade 8

Unit 1: Geometric Figures: Rigid Transformations and Congruence

iReady ClassroomAmplify Classroom
Lesson 1: Understand Rigid Transformations and Their PropertiesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 2: Work with Single Rigid Transformations in the Coordinate PlaneUnit 1
Lesson 4: Moving Day

Unit 2: Geometric Figures: Transformations, Similarity, and Angle Relationships

Lesson 4: Understand Dilations and SimilarityUnit 2
Lesson 2: Dilation Mini Golf
Lesson 6: Describe Angle RelationshipsUnit 2
Lesson 6: Social Scavenger Hunt
Lesson 7: Describe Angle Relationships in TrianglesUnit 1
Lesson 12: Puzzling It Out

Unit 3: Linear Relationships: Slope, Linear Equations, and Systems

Lesson 8: Graph Proportional Relationships and Define SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 13: Solve Systems of Linear Equations AlgebraicallyUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 4: Functions: Linear and Nonlinear Relationships

Lesson 15: Understand FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 16: Use Functions to Model Linear RelationshipsUnit 5
Lesson 5: The Tortoise and the Hare

Unit 5: Integer Exponents: Properties and Scientific Notation

Lesson 19: Apply Exponent Properties for Positive Integer ExponentsUnit 7
Lesson 1: Circles
Lesson 3: Power Pairs
Lesson 22: Work with Scientific NotationUnit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 6: Real Numbers: Rational Numbers, Irrational Numbers, and the Pythagorean Theorem

Lesson 23: Find Square Roots and Cube Roots to Solve ProblemsUnit 8
Lesson 4: Root Down
Lesson 25: Find Rational Approximations of Irrational NumbersUnit 8
Lesson 10: Taco Truck
Lesson 27: Apply the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 28: Solve Problems with Volumes of Cylinders, Cones, and SpheresUnit 8
Lesson 11: Cylinders
Lesson 13: Cones

Unit 7: Statistics: Two-Variable Data and Fitting a Linear Model

Lesson 29: Analyze Scatter Plots and Fit a Linear Model to DataUnit 6
Lesson 3: Robots
Lesson 4: Dapper Cats
Lesson 6: Find the Fit

Disclaimer

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Grade K

Unit 1: Count Sequence and Numbers to 5

Module 1: Represent Numbers to 5 with Objects

Lesson 1: Represent 1 and 2Connecting Cubes
Lesson 2: Represent 3 and 4Skye’s Style
Matching Groups
Designing Shoes With Skye

Unit 2: Count Sequence and Numbers to 10

Module 7: Represent Numbers 6 to 10 with Objects

Module 10: Compare Numbers to 10

Lesson 4: Compare Groups Within 10 by CountingMore, Fewer, or the Same
Fingers and Counters
Lesson 5: Compare Groups Within 10 by MatchingComparing Words
Forest Friends

Module 11: Add To and Take From Within 10

Module 12: Put Together and Take Apart Within 10

Lesson 3: Solve Put Together Problems Within 10How Many Objects in Pictures?
How Will You Count?
What Does It Mean to Add?
Lesson 4: Solve Take Apart Problems Within 10What Does It Mean to Subtract?
Lesson 5: Solve Word Problems Within 10The Bus Depot

Module 13: Ways to Make Numbers to 10

Lesson 4: Ways to Make 10Harry’s Hamster Wheel
Harry Explores Space
Lesson 5: Make 10 From a Given NumberShowing What We Know About 10
Lesson 1: Ways to Make 6 and 7Harry Explores the Ocean

Unit 3: Geometry

Module 14: Analyze and Compare Three-Dimensional Shapes

Module OpenerWhat’s That Shape?
Lesson 5: Build ShapesBuilding Solid Shapes

Module 15: Describe Position of Objects

Module 16: Analyze and Compare Two-Dimensional Shapes

Lesson 7: Compare Two-Dimensional and Three-Dimensional ShapesSo Much Sorting
What’s That Shape Called?
Another Shape

Unit 4: Number and Operations in Base Ten

Module 17: Place Value Foundations-Represent Numbers to 20

Lesson 3: Compose Ten Ones and Some More Ones to 19Investigate: Packing Snacks
Lesson 4: Represent Numbers to 20Getting Ready for the Game
How Many on the Field?
Pass, Shoot, Score

Module 18: Place Value Foundations-Represent Number to 20 with a Written Numeral

Lesson 1: Count and Write 11 to 14Jersey Jam!
Lesson 3: Count and Write 16-19People at the Park

Grade 1

Unit 1: Ways to Add and Subtract

Module 2: Subtraction Strategies

Lesson 2.1: Represent SubtractionPacking a Picnic
Lesson 2.2: Count BackWhat’s the Difference?
Lesson 2.3: Count on to SubtractLeaping Lily Pads!

Module 3: Properties of Operations

Lesson 3.6: Determin Equatl and Not EqualReplanting Huli

Module 4: Apply Addition and Subtraction Relationships

Lesson 4.2: Represent Related FactsSame Number, Different Ways
Lesson 4.3: Identify Related FactsKitten Coaster
Lesson 4.6: Solve for Unknow AddendTutu’s Garden in Maui

Module 5: Understand Add to and Take From Problems

Lesson 5.4: Solve Add To and Take From ProblemsA Community Working Together
Helping Others
Making 10

Module 6: Understand Put Together and Take Apart Problems

Lesson 6.3: Represent Addend and Unknown Problems with Objects and DrawingInvestigate: Let’s Grow!

Module 8: Data

Lesson: 8.2 Represent Data with Picture GraphsShapes Ying Saw

Unit 3: Numbers to 120

Module 10: Count and Represent Numbers

Lesson 10.4: Decompose Numbers in Different WaysInvestigate: Game Points
Lesson 10.5: Represent, Read, and Write Numbers from 100 to 110From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans
Lesson 10.5: Represent, Read, and Write Numbers from 110 to 120From Head to Claw
From Wing Tip to Wing Tip
Measuring More Wingspans

Unit 4: Addition and Subtractoin in Base Ten

Module 12: Understand Addition and Subtraction with Tens and Ones

Lesson 12.1: Representing Adding TensMeeting Yara
It’s a Match
From Park to Table
Lesson 12.3: Add and Subtract TensHow Many Cubes?
Boris’s Thimbles
How Many Tens?

Module 13: Two-Digita Addition and Subtraction

Lesson 13.1: Use Hundred Charts to Show Two-Digit Addtion and Subtraction.Investigate: Squashes at the Playground
Lesson 13.2: Understand and Explain Place Value AdditionTown Helpers
Making Squash Butter

Unit 6: Measurment

Module 16: Fraction Foundations

Lesson 16.1: TAke Apart Two-Dimensional ShapesFair and Square
Lesson 16.2: Identify Equal or Unequal PartsOne of the Parts, All of the Parts
Lesson 16.4: Partition Shapes into FourthsA Bigger Part

Grade 2

Unit 1: Numbers and Data

Module 1: Fluency for Addition and Subtraction Within 20

Lesson 1.5: Use the Make a Ten Strategy to AddExploring Within 10
Ways to Make 10

Module 1: Fluency for Addition and Subtraction Within 21

Lesson 1.6: Use a Tens Fact to SubtractExploring Within 10
Ways to Make 10

Module 2: Equal Groups

Lesson 2.1: Identify Even and Odd NumbersCan You Share?
Is It Even or Odd?
Lesson 2.2: Write Equations to Represent Even NumbersEverybody, Find A Partner!

Module 3: Data

Lesson 3.5: Draw bar graphs to Represent DataAwesome Aquariums

Unit 2: Place Value

Module 4: Understand Place Value

Lesson 4.1: Group Tens as HundredsWhat Makes a Hundred?
Lesson 4.2: Understand Three-Digit NumbersWhat’s the Value?
Lesson 4.4: Represent Numbers with Hundreds, Tens, and OnesMail Call!
What’s Your Name?

Module 5: Read, Write, and Show Numbers to 1000

Lesson 5.3: Different Ways to Write NumbersA New Representation
Lesson 5.4: Different Ways to Show NumbersAll the Ways!

Module 6: Use Place Value

Lesson 6.1: Count Within 1000Investigate
Turtle Hurdle
Lesson 6.5: Use Symbols to Compare NumbersTime to Line Up!

Unit 3: Money and Time

Module 7: Coins

Lesson 7.1: Relate Place Value to CoinsInvestigate
Lesson 7.2 Identify and Find Value of CoinsDiscovering Coins (Part 1)
Lesson 7.3: Compute the Value of Coin CombinationsHow Much Money?
Lesson 7.4: Show Amounts in Different WaysDiscovering Coins (Part 2)
The Toy Stand

Module 8: Dollar Amounts

Lesson 8.3: Solve Problems Involving MoneyThe Craft Stand at the Block Party

Unit 5: Three-Digita Addition and Subtraction

Module 16: Three-Digit Addition

Lesson 16.1: Use Drawing to Represent Three-Digit AdditionThere’s Something About Berries
Lesson 16.2: Decomposte Three-Digit AddendsBaking With Skunk

Unit 6: Measurement

Module 18: Lengths in Inches, Feet, and Yards

Lesson 18.4: Make Line Ploits to Show Measurement DataMessy Measurements
Bracelets and Wristbands

Module 20: Relate Addition and Subtraction to Length

Lesson 20.1: Relate Inches to a Number LineInvestigate
Time to Line Up!
What’s That Number?
Lesson 20.2: Add and Subtract Lengths in InchesLengths of Jungle Animals
Lesson 20.3: Relate Centimeters to a Number LineInvestigate
Time to Line Up!
In Full Bloom

Unit 7: Geometry and Fractions

Module 21: Two- and Three- Dimensional Shapes

Lesson 21.2 Identify and Draw Three-Dimensional ShapesMore to Measure
Lesson 21.2: Identify and Draw Two-Dimensional ShapesFrame It!
Measure It, Draw It

Grade 3

Unit 1: Understand Multiplication and Area

Module 1: Understand Multiplication

Lesson 1.1: Count Equal GroupsEqual Groups
Lesson 1.3: Represent Multiplication with ArraysArrays of Flavor
Lesson 1.4: Understand the Commutative Property of MultiplicationArrays of Flavor

Module 2: Relate Multiplication and Area

Lesson 2.1 Understand Area by Counting Unit SquareInvestigate: Comparing Rugs
Which Covers More Space?
Lesson 2.2: Measuring Area by Counting Unit SquaresTiling Figures
Area Hunt
Lesson 2.3: Relate Area to Addition and MultiplicationRectangles and Arrays

Unit 2: Multiplication and Division

Module 7: Relate Multiplication and Division

Lesson 7.7: Build Fluency with Multiplication and DivisionRelating Quotients to Familiar Products

Module 8: Apply Multiplication and Division

Lesson 8.3: Use Multiplication and Division to Solve Problem SituationsIt’s Chili in Here!
Lesson 8.4: Solve Two-Step ProblemsDivision and Multiplication Equations

Unit 3: Addition and Subtraction Strategies

Module 9: Addition and Subtraction Strategies

Lesson 9.3: Use Properties to AddHow Would You Solve It?
Lesson 9.4: Use Mental Math to Assess ReasonablenessAdding Strategically

Module 10: Addition and Subtraction Within 1000

Lesson 10.1: Use Expanded Form to AddWhat Is an Algorithm?
Lesson 10.2: Use Place Value to AddAdding Your Way
Using Fewer Digits
Lesson 10.5: Choose a Strategy to Add or SubtractDetermining Sums of 2 or More Addends

Unit 4: Fractions

Module 13: Understand Fractions as Numbers

Lesson 13.4: Represent and Name Fractions on a Number LineFractions on the Number Line
Lesson 13.5: Express Whole Numbers as FractionsCat Crossing
Lesson 13.6: Represent and Name Fractions Greater Than 1Location, Location, Location

Unit 5: Measurement and Data

Module 18: Represent and Interpret Data

Lesson 18.4: Make a Bar GraphPuppy Pile
2, 5, or 10?
Egg-cellent Pick
Lesson 18.5: Use Line Plots to Display Measurement DataHow Long Is It?
More Precise Measurements
Same Lengths, Different Names
Lesson 18.6: Make Line Plots to Display Measurement DataThe Plot Chickens
Let’s Make a Line Plot

Unit 6: Geometry

Module 19: Define Two-Dimensional Shapes

Lesson 19.1: Describe ShapesPiho’s Shapes
Lesson 19.4: Define QuadrilateralsRectangles, Squares, and Rhombuses

Module 20: Categorize Two-Dimensional Shapes

Lesson 20.1: Draw QuadrilateralsMore Quadrilaterals

Grade 4

Unit 1: Place Value and Whole Number Operations

Module 3: Interpret and Solve Problem Situations

Lesson 3.1: Explore Multiplicative ComparisonsSticker Mania
Lesson 3.4: Use Comparison to Solve Problem SituationsRepresenting “Times as Many”
Going Swimming

Unit 2: Multiplication and Division Problems

Module 4: Mental Math and Estimation Strategies

Lesson 4.3: Estimate Products by 1-Digit NumbersA Reasonable Answer

Module 5: Multiply by 1-Digit Numbers

Lesson 5.1: Represent MultiplicationInvestigate: Packing Lei
Lesson 5.2: Use Area Models and the Distributive Property to MultiplyCounting Flowers for Lei
Lesson 5.4: Multiplying Using Partial ProductsThree of a Kind
Lesson 5.6: Multiplying 3-Digit and 4-Digit NumbersA Lei Making Workshop

Unit 3: Extend and Apply Multiplication

Module 8: Extend and Apply Multiplication

Lesson 8.1: Multiply with TensGrowing Flowers for the Lei
Lesson 8.3: Relate Area Model and Partial ProductsDouble Decomposition
Lesson 8.4: Multiplying Using Partial ProductsRevisiting Strategies
Lesson 8.7: Solve Multi-step Problems and Assess ReasonablenessHow Many Supplies?

Unit 4: Fractions and Decimals

Module 10: Algebraic Thinking and Number Theory

Lesson 10.1: Investigate FactorsHamster Homes
Lesson 10.2: Identify FactorsFactor or Multiple?
Lesson 10.4: Identify Prime and Composite NumbersA Number Game
Lesson 10.5 Generate and Analyze Number PatternsHow Does It Grow?

Module 11: Fraction Equivalence and Comparison

Lesson 11.1: Compare Fractions Using Viaula ModelsInvestigate: Building Your Own Number Line
Lesson 11.2: Compare Fractions Using BenchmarksFraction Strips
Lesson 11.6: Compare Fractions Using Common DenominatorsChop It
Lesson 11.7: Use Comparison to Order FractionsAll Kinds of Fractions

Module 12: Relate Fractions and Decimals

Lesson 12.1: Represent Tenths as Fractions and DecimalsA New Way to Write Tenths
Lesson 12.2 Represent Hundredths as Fractions and DecimalsA New Way to Write Hundredths
Lesson 12.3: Identify Equivalent Fractions and DecimalsAre They Equivalent?
Lesson 12.4: Compare DecimalsHow Can You Compare?
Robot Factory
What’s the Order

Module 13: Use Fractions to Understand Angles

Lesson 13.2: Explore AnglesAngle Adventures
Lesson 13.3: Relate Angles to Fraction Part of a CircleThe Spin on Angles
Lesson 13.6: Join and Separate AnglesAngles in Motion

Module 14: Understand Addition and Subtraction of Fractions with Like Denominators

Lesson 14.2: Joining Parts of the Same WholePizza Problems

Module 15: Add and Subtract Fractions and Mixed Numbers with Like Denominators

Lesson 15.1: Add and Subtract Fractions to Solve ProblemsMath Pizzeria

Unit 6: Two-Dimensional Figures and Symmetry

Module 18: Symmetry and Patterns

Lesson 18.3: Generate and Identify Shape PattersHow Does It Grow?

Grade 5

Unit 1: Whole Numbers, Expressions, and Volume

Module 1: Whole Number Place Value and Multiplication

Lesson 1.3: Use a Pattern to Multiply by Multiplies of 10, 100, and 1000Partial Products Everywhere
Monarch Butterflies
All About That Base
Lesson 1.5: Multiply Multi-Digit NumbersHow Do They Compare?

Module 2: Understand Division of Whole Numbers

Lesson 2.4: Use Partial QuotientsEmptying the Water Tank

Module 5: Volume

Lesson 5.2: Understand VolumeWhich is Largest
Lesson 5.3: Estimate VolumePacking the Barge
Lesson 5.6: Find Volume of Composed FiguresPutting it Together
Figures Made of Prisms

Unit 3: Multiplying Fractions and Mixed Numbers

Module 8: Understand Multiplication of Fractions

Lesson 8.1: Explore Groups of Equal Shares to Show MultiplicationInvestigate: Sharing Sandwiches
Investigate: Folding Paper
Lesson 8.2: Represent Multiplication of Whole Numbers by FractionsSharing More Sandwiches
Lesson 8.3: Represent Multiplication with Unit FractionOne Part of One Part
Lesson 8.4: Represent Multiplication of FractionsDance Breaks
Parts of Parts
Making Food
Lesson 8.5: Use Representations of Area to Develop ProceduresOne Part of One Part
Installing Turf
Rows and Columns
Lesson 8.6: Interpret Fraction Multiplication as ScalingChores at Animal Haven
The Re-size-inator
Lesson 8.7: Multiplying FractionsMessy Multiplication

Module 9: Understand and Apply Multiplication of Mixed Numbers

Lesson 9.3: Practice Multiplication with Fractions and Mixed NumbersMessy Multiplication
Applying Fraction Multiplication

Unit 4: Divide Fractions and Convert Customary Units

Module 10: Understand Division with Whole Numbers and Unit Fractions

Lesson 10.1: Interpret a Fraction as DivisionDivision Story Problems
Making Generalizations

Unit 5: Add and Subtract Decimals

Module 13: Decimal Place Value

Lesson 13.1: Understand ThousandthsWhat Is One Thousandth?
Lesson 13.2: Read and Write Decimals to ThousandthsSay What?
Lesson 13.3: Round DecimalsWhich Way Down the Mountain?
Rounding Races
Lesson 13.4: Compare and Order DecimalsInvestigate: Numbers Between Numbers
The Claw
Selling Collectibles

Unit 6: Multiply Decimals

Module 15: Multiply Decimals and Whole Numbers

Lesson 15.1: Understand Decimal Multiplication PatternsPlace Value Patterns
Powers of 10 Parade

Unit 7: Divide Decimals and Convert Customary Units

Module 17: Understand Decimal Division Patterns

Lesson 17.1: Understand Decimal Division PatternsPowers of 10 Parade

Unit 8: Graphs, Patterns, and Geometry

Module 19: Graphs and Patterns

Lesson 19.1: Describe a Coordinate SystemCreating a Coordinate System
Lesson 19.2: Understand Ordered PairsBullseye!
Lesson19.4: Generate and Identify Numerical PattermsCoordinating Satellite Repairs

Grade 6

Unit 1: Number Systems and Operations

Module 1: Integer Concepts

Lesson 1: Identify and Interpret IntegersCan You Dig It?
Lesson 2: Compare and Order Integers on a Number LineOrder in the Class

Module 3: Fraction Division

Lesson 1: Understand Fraction DivisionFlour Planner
Fill the Gap

Module 4: Fluency with Multi-Digit Decimal Operations

Lesson 1: Add and Subtract Multi-Digit DecimalsDishing Out Decimals
Decimal Diagrams and Algorithms
Lesson 4: Divide Multi-Digit DecimalsMovie Time

Unit 2: Ratio and Rate Reasoning

Module 5: Ratio and Rates

Lesson 1: Understand the Concept and Language of RatiosPizza Maker
Lesson 2: Represent Ratios and Rates with Tables and GraphsFruit Lab
Disaster Preparation
Lesson 3: Compare Ratios and RatesModel Trains
Lesson 4: Find and Apply Unit RatesWorld Records
Lesson 5: Solve Ratio and Rate Problems Using Proportional ReasoningWelcome to the Robot Factory
More Soft Serve

Module 6: Apply Ratios and Rates to Measurement

Lesson 2: Use Rate Reasoning to Convert withing Measurement SystemsSoft Serve
Many Measurements

Module 7: Understand, Express, and Compare Percent Ratios

Lesson 1: Understand, Express, and Compare Percent RatiosLucky Duckies

Unit 3: Expressions, Equations, and Inequalities

Module 8: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions to Model SituationsProducts and Sums

Module 9: Solve Problems Using Equations and Inequalities

Lesson 1: Write Equations to Represent SituationsWeight for It
Five Equations
Lesson 2: USe Additions and Subtraction Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 3: Use Multiplication and Division Equations to Solve ProblemsHanging Around
Hanging It Up
Lesson 4: Use One-Step Equations to Solve a Variety of ProblemsSwap and Solve
Lesson 5: Write and Graph InequalitiesTunnel Travels

Module 10: Real-World Relationships Between Variables

Lesson 1: Represent Equations in Tables and GraphsSubway Fares
Lesson 2: Write Equations from Verbal DescriptionsSubway Fares

Unit 4: Relationships in Geometry

Module 11: Polygons on the Coordinate Plane

Lesson 4: Find the Perimeter and Area on the Coordinate PlaneShapes on a Plane

Module 12: Area of Triangles and Special Quadrilaterals

Lesson 1: Develop and Use the Formula for Area of ParallelogramsExploring Parallelograms, Part 1
Exploring Parallelograms, Part 2
Off the Grid, Part 1
Lesson 2: Develop and Use the Formula for Area of TrianglesExploring Triangles
Triangles and Parallelograms
Off the Grid, Part 2
Lesson 3: Develop and Use the Formula for Area of TrapezoidsPile of Polygons
Lesson 4: Find Area of Composite FiguresPuzzling Areas
Letters

Module 13: Surface Area and Volume

Lesson 1: Explore Nets and Surface AreaRenata’s Stickers

Unit 5: Data Collection and Analysis

Module 14: Data Collection and Displays

Lesson 2: Display Data in Dot PlotsMinimum Wage
Lesson 3: Make Histograms and Frequency TablesThe Plot Thickens

Module 15: Measure of Center

Lesson 2: Find Measures of CenterToy Cars
Lesson 3: Choose a Measure of CenterHoops

Grade 7

Unit 1: Proportional Relationships

Module 1: Identify and Represent Proportional Relationships

Lesson 1: Explore RelationshipsPaint
Lesson 2: Recognize Proportional Relationships in TablesTwo and Two
Lesson 3: Compute Unit Rates Involving FractionsDinoPops
Lesson 4: Recognize Proportional Relationships in GraphsScale Factor Challenges
Lesson 5: Use Proportional Relationships to Solve Rate ProblemsScaling Robots
Lesson 6: Practice Proportional Reasoning with Scale DrawingsScaling Machines
Make it Scale
Tiles
Will It Fit

Module 2: Proportional Reasoning with Percents

Lesson 1: Percent ChangeMosaics
Percent Machines
Lesson 2: Markups and DiscountsMore and Less
All the Equations
Lesson 3: Taxes and Gratuities100%
Lesson 5: Simple InterestBack in My Day

Unit 2: Rational Number Operations

Module 3: Understand Addition and Subtraction of Rational Numbers

Lesson 1: Add or Subtract a Positive Integer on a Number lineFloats and Anchors
Lesson 3: Use a Number Line to Add and Subtract Rational NumbersDraw Your Own

Module 4: Add and Subtract Rational Numbers

Lesson 1: Compute Sums of IntegersMore Floats and Anchors
Lesson 2: Compute Differences of IntegersMore Floats and Anchors
Lesson 4: Apply Properties to Multi-step Addition and Subtraction ProblemsInteger Puzzles

Unit 3: Model with Expressions, Equations, and Inequalities

Module 7: Solve Problems Using Expressions and Equations

Lesson 1: Write Linear Expressions in Different Forms for Different SituationsCollect the Squares
Lesson 3: Write Two-Step Equations for SituationsKeeping it True
Lesson 5: Apply Two-Step Equations fo Find Angle MeasuresFriendly Angles
Missing Measures

Module 8: Solve Problems Using Inequalities

Lesson 1: Understand and Apply Properties to Solve One-Step InequalitiesI Saw the Signs
Lesson 2: Write Two-Step Inequalities for SituationsUnbalanced Hangers
Shira the Sheep
Lesson 3: Apply Two-Step Inequalities to Solve ProblemsBudgeting
Write Them and Solve Them

Unit 4: Geometry

Module 9: Draw and Analyze Two-Dimensional Figures

Lesson 2: Draw Circles and Other FiguresCan You Build It

Module 10: Analyze Figures to Find Circumference and Area

Lesson 1: Derive and Apply Formulas for CircumferenceMeasuring Around
Lesson 2: Derive and Apply a Formula for the Area of a CircleWhy Pi?
Lesson 4: Areas of Composite FiguresArea Challenges

Unit 5: Sampling and Data Analysis

Module 13: Use Statistics and Graphs to Compare Data

Lesson 3: Compare Means Using MAD and Repeated SamplingCrab Island

Module 14: Understand and Apply Experimental Probability

Lesson 1: Understand Probability of an EventHow Likely
Lesson 2: Find Experimental Probability of Simple EventsProb-bear-bilities

Module 15: Find Theoretical Probability of Simple Events

Lesson 1: Find Theoretical Probability of Simple EventsIs It Fair?

Grade 8

Unit 1: Transformational Geometry

Module 1: Transformations and Congruence

Module 2: Transformations and Similarity

Lesson 1: Investigate Reductions and EnlargementsSketchy Dilations
Lesson 2: Explore DilationsDilation Mini Golf
Lesson 3: Understand and Recognize Similar FiguresSocial Scavenger Hunt

Unit 2: Linear Equations and Applications

Module 3: Solve Linear Equations

Lesson 1: Solve Multi-Step Linear EquationsEquation Roundtable
Lesson 3: Apply Linear Equations

Module 4: Angle Relationships

Lesson 1: Develop Angle Relationships for TrianglesPuzzling It Out
Lesson 3: Explore Prarallel Lines Cut by a TransversalPuzzling It Out

Unit 3: Relationships and Functions

Module 5: Proportional Relationships

Lesson 2: Derive y = mxTurtle Time Trials
Lesson 3: Interpret and Graph Proportional RelationshipsTurtle Time Trials
Lesson 4: Compare Proportional RelationshipsTurtle Time Trials

Module 6: Understand and Analyze Functions

Lesson 1: Understand and Graph FunctionsGuess My Rule
Lesson 2: Derive and Interpret y = mx + bFlags
Translations
Lesson 3: Interpret Rat of Change and Initial ValueStacking Cups (Optional)
Lesson 4: Construct FunctionsWater Cooler
Lesson 5: Compare FunctionsUps and Downs
Lesson 6: Describe and Sketch Nonlinear FunctionsTurtle Crossing
The Tortoise and the Hare

Module 7: Systems of Linear Equations

Lesson 1: Represent Systems by GraphingMake Them Balance
Lesson 2: Solve Systems by GraphingLine Zapper

Unit 4: Statistics and Probability

Module 8: Scatter Plots

Lesson 1: Construct Scatter Plots and Examine AssociationRobots
Dapper Cats
Lesson 2: Draw and Analyze Trend LinesInterpreting Scatter Plots
Find the Fit (called Fit Fights in Desmos Math)
Lesson 3: Interpret Linear Data in ContextInterpreting Slopes
Scatter Plot City
Animal Brains

Module 9: Two-Way Tables

Lesson 1: Construct and Interpret Two-Way Frequency TablesFinding Associations
Lesson 3: Interpret Two-Way Relative Freqency TablesFinding Associations

Unit 5: Real Numbers and the Pythagorean Theorem

Module 10: Real Numbers

Lesson 2: Investigate RootsRoot Down

Module 11: The Pythagorean Theorem

Lesson 1: Prove the Pythagorean TheoremTriangle Tracing Turtle
Lesson 3: Apply the Pythagorean TheoremTaco Truck

Unit 6: Exponents, Scientific Notation, and Volume

Module 12: Exponents and Scientific Notation

Lesson 1: Know and Apply Properties of ExponentsCircles
Power Pairs
Lesson 2: Understand Scientific NotationSpecific and Scientific (formerly Solar System)
Lesson 3: Compute with Scientific NotationBalance the Scale

Module 13: Volume

Lesson 1: Find Volume of CylindersCylinders
Lesson 2: Find Volumes of ConesCones

Algebra 1

Intro/Launch

Unit 1: Real Numbers and Connections to Algebra

Module 2: Linear Equations and Inequalities in One Variable

Lesson 2.2: Write and Solve EquationsWorking Backwards
Solving Strategies
Same Position
Lesson 2.3: Rewrite Formulas and Solve Literal EquationsVarious Variables
Lesson 2.4: Write and Solve InequalitiesPizza Delivery

Unit 2: Linear Functions and Equations

Module 3: Linear Equations in Two Variables

Lesson 3.1: Linear Equations in Standard FormShelley the Snail
Five Representations
Lesson 3.2: Slopes of Lines and Rates of ChangePlane, Train, and Automobile

Module 4: Linear Functions and Models

Lesson 4.3: Characteristics of Linear FunctionsCraft-a-Graph

Module 5: Relationships Among Linear Functions

Lesson 5.3: Compare Linear FunctionsSubway Seats
Lesson 5.4: Inverses of Linear FunctionsChip the Robot

Unit 3: Build Linear Functions and Models

Module 6: Fit Linear Functions to Data

Lesson 6.1: Scatter Plots, Correlation, and Fitted LinesCorrelation Coefficient
How Hot Is It?
City Slopes
Behind the Headlines
City Data
Lesson 6.2: Residualts and Best-Fit LinesResidual Fruit
Penguin Populations

Module 7: Discrete Linear Functions

Lesson 7.1: Arithmetic Sequences Defined RecursivelySequence Carnival
Lesson 7.2: Arithmetic Sequences Defined ExplicitlyMore Visual Patterns

Module 8: Piecewise-Defined Functions

Lesson 8.1: Graph Piecewise-Defined FunctionsPumpkin Prices

Unit 4: Linear Systems

Module 9: Systems of Linear Equations

Lesson 9.1: Solve Linear Systems by GraphingLizard Lines
Lesson 9.2: Solve Linear Systems by SubstitutionShape It Up

Module 10: Linear Inequalities

Lesson 10.2: Graph Systems of Linear InequalitiesQuilts
Seeking Solutions

Unit 5: Exponential Functions and Equations

Module 11: Exponential Functions and Models

Lesson 11.1: Exponential Growth FunctionsCarlos’s Fish

Unit 6: Build Exponential Functions and Models

Module 13: Fit Exponential Functions to Data

Lesson 13.1: Scatter Plots and Fitted Exponential CurvesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Module 14: Discrete Exponential Functions

Lesson 14.1: Geometric Sequences Defined RecursivelySequence Carnival
Lesson 14.2: Geometric Sequences Defined ExplicitlyMore Visual Patterns

Unit 8: Quadratic Functions and Equations

Module 17: Use Graphing and Factoring to Solve Quadratic Equations

Lesson 17.1: Solve Quadratic Equations by Graphing Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
On the Fence
Plenty of Parabolas
Lesson 17.3: Solve Quadratic Equations by Factoring ax^2+bx+cStomp Rockets
Two for One
Robot Launch
Lesson 17.4: Use Special Factoring Patterns to Solve Quadratic EquationsParabola Zapper
Shooting Stars

Module 18: Use Square Roots to Solve Quadratic Equations

Lesson 18.2: Solve Quadratic Equations by Completing the SquareSquare Tactic
Lesson 18.3: Use the Quadratic Formula to Solve EquationsStomp Rockets in Space

Unit 9: Function Analysis

Module 20: Function Analysis

Lesson 20.1: Choose Among Linear, Exponential, and Quadratic ModelsSorting Relationships

Unit 10: Data Analysis

Module 22: Numerical Data

Lesson 22.1: Data Distributions and Appropriate StatisticsFinding Desmo

Disclaimer

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Eureka Math²

Level K

Module 1: Counting and Cardinality

Topic A: Classify to Make Categories and Count

Lesson 1: Compare objects based on their attributes.Connecting Cubes
Lesson 3: Classify objects into two categories and count.Skye’s Style

Topic B: Answer How Many Questions with Up to 5 Objects

Lesson 3: Sort by Same ColorMatching Groups

Topic C: Write Numerals and Create Sets of Up to 5 Objects

Lesson 10: Count out a group of objects to match a numeral.Designing Shoes with Skye

Topic E: Answer How Many Questions with Up to 10 Objects

Lesson 19: Organize, count, and represent a collection of objects.Investigate: Cafeteria Math
Lesson 20: Count objects in 5-group and array configurations and match to a numeral.Fingers as Math Tools
Lesson 23: Conserve number regardless of the order in which objects are counted.Moving and Grooving

Module 2: Two- and Three- Dimensional Shapes

Topic A: Analyze and Name Two-Dimensional Shapes

Lesson 1: Find and describe attributes of flat shapes.So Much Sorting
Lesson 2: Classify shapes as triangles or nontriangles.What’s That Shape Called?
Lesson 3: Classify shapes as circles, hexagons, or neither.What’s That Shape Called?
Lesson 4: Classify shapes as rectangles or nonrectangles, with square rectangles as a special case.Another Shape

Module 3: Comparison

Topic C: Compare Sets Within 10

Lesson 12: Relate more and fewer to length.More, Fewer, or the Same
Forest Friends
Lesson 13: Compare sets by using more than, fewer than, and the same number as.Fingers and Counters
Comparing Words

Module 4: Composition and Decomposition

Topic A: Explore Composition and Decomposition

Lesson 1: Compose flat shapes and count the parts.Investigate: Casey’s Town
Lesson 2: Decompose flat shapes and count the parts.How Many Objects?
Lesson 3: Decompose a group to identify parts and total.How Many Objects in Pictures?

Topic B: Record Composition and Decomposition

Lesson 5: Sort to decompose a number in more than one way.How Will You Count?
Lesson 6: Decompose a number in more than one way and record.Harry Explores the Ocean

Module 5: Addition and Subtraction

Topic A: Represent Addition

Lesson 1: Represent add to with result unknown story problems by using drawings and numbers.What Does It Mean to Add?

Topic B: Represent Subtraction

Lesson 8: Understand taking away as a type of subtraction.What Does It Mean to Subtract?

Topic C: Make Sense of Problems

Lesson 15: Identify the action in a problem to represent and solve it.The Bus Depot

Level 1

Module 1: Counting, Comparison, and Addition

Topic A: Count and Compare with Data

Lesson 2: Organize and represent data to compare two categories.Shapes Ying Saw

Module 2: Addition and Subtraction Relationships

Topic A: Reason About Take From Situations

Lesson 1: Represent result unknown problems and record as addition or subtraction number sentences.Packing for a Picnic
Lesson 3: Subtract 1 or subtract 1 less than the total.What’s the Difference?
Leaping Lily Pads!

Topic B: Relate and Distinguish Addition and Subtraction

Lesson 5: Use the Read–Draw–Write process to solve result unknown problems.Investigate: Let’s Grow!
Lesson 6: Represent and solve related addition and subtraction result unknown problems.Tutu’s Garden in Maui
Lesson 7: Count on or count back to solve related addition and subtraction problems.The Kalo Plants

Topic C: Find an Unknown Part in Change Unknown Problems

Lesson 8: Interpret and find an unknown change.Replanting Huli
Lesson 11: Represent and solve take from with change unknown problems.Helping Others
A Community Working Together

Module 3: Properties of Operations to Make Easier Problems

Topic B: Make Easier Problems to Add

Lesson 9: Make ten with either addend.Making 10
Kitten Coaster

Topic D: Reason about Ten as a Unit to Add or Subtract

Lesson 16: Identify ten as a unit.Same Number, Different Ways

Module 5: Place Value Concepts to Compare, Add, and Subtract

Topic A: Grouping Units in Tens and Ones

Lesson 2: Count a collection and record the total in units of tens and ones.Investigate: Game Points
Meeting Yara
Lesson 4: Represent a number in multiple ways by trading 10 ones for a ten.It’s a Match
Lesson 6: Add 10 or take 10 from a two-digit number.How Many Cubes?

Topic D: Addition and Subtraction of Tens

Lesson 15: Count on and back by tens to add and subtract.Boris’s Thimbles
Lesson 16: Use related single-digit facts to add and subtract multiples of ten.How Many Tens?

Level 2

Module 1: Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

Topic A: Representing Data to Solve Problems

Lesson 3: Use information presented in a bar graph to solve put together and take apart problems.Exploring Within 10
Ways to Make 10
Lesson 4: Use information presented in a bar graph to solve compare problems.Awesome Aquariums

Topic C: Estimate, Measure, and Compare Lengths

Lesson 12: Model and reason about the difference in length.Lengths of Jungle Animals

Topic D: Solve Compare Problems by Using the Ruler as a Number Line

Lesson 15: Use a measuring tape as a number line to add efficiently.Investigate: Where Am I?
Time to Line Up!
What’s That Number?
Lesson 17: Represent and solve comparison problems by using measurement contexts.Greater Than, Less Than, or Equal to

Module 2: Addition and Subtraction Within 200

Topic A: Simplifying Strategies for Addition

Lesson 1: Reason about addition with four addends.Investigate: Activities at the Block Party

Module 5: Money, Data, and Customary Measurement

Topic A: Problem Solving with Coins and Bills

Lesson 1: Organize, count, and represent a collection of coins.Discovering Coins (Part 1)
Discovering Coins (Part 2)
Lesson 2: Use the fewest number of coins to make a given value.How Much Money?
Lesson 5: Use different strategies to make 1 dollar or to make change from 1 dollar.The Toy Stand
Lesson 3: Solve one- and two-step word problems to find the total value of a group of coins.The Craft Stand at the Block Party

Topic B: Use Customary Units to Measure and Estimate Length

Lesson 12: Identify unknown numbers on a number line by using the interval as a reference point.In Full Bloom

Topic C: Use Measurement and Data to Solve Problems

Lesson 15: Use measurement data to create a line plot.Messy Measurements
“Lesson 16: Create a line plot to represent data and ask and answer questions.
60 min
Bracelets and Wristbands

Level 3

Module 1: Multiplication and Division with Units of 2, 3, 4, 5, and 10

Topic A: Conceptual Understanding of Multiplication

Lesson 2: Interpret equal groups as multiplication.Equal Groups

Topic C: Properties of Multiplication

Lesson 10: Demonstrate the commutative property of multiplication using a unit of 2 and the array model.Arrays of Flavor

Topic D: Two Interpretations of Division

Lesson 15: Model division as an unknown factor problem.It’s Chili in Here

Module 2: Place Value Concepts Through Metric Measurement

Topic A: Understanding Place Value Concepts Through Metric Measurement

Lesson 1: Connect the composition of 1 kilogram to the composition of 1 thousand.Investigate: Create a Photo Gallery

Topic C: Simplifying Strategies to Find Sums and Differences

Lesson 13: Collect and represent data in a scaled bar graph and solve related problems.Puppy Pile
Lesson 14: Use place value understanding to add and subtract like units.Adding Your Way
Lesson 15: Use the associative property to make the next ten to add.Panda Patterns
Lesson 16: Use compensation to add.How Would You Solve It?

Topic D: Two- and Three-Digit Measurement Addition and Subtraction

Lesson 20: Add measurements using the standard algorithm to compose larger units once.What is an Algorithm?
Using Fewer Digits
Lesson 21: Add measurements using the standard algorithm to compose larger units twice.Determining Sums of 2 or More Addends
Adding Strategically

Module 3: Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

Topic B: Multiplication and Division Concepts with an Emphasis on the Unit of 7

Lesson 11: Use the break apart and distribute strategy to divide with units of 7.Relating Quotients to Familiar Products
Lesson 12: Solve one-step word problems involving multiplication and division.Division and Multiplication Equations

Module 4: Multiplication and Area

Topic A: Foundations for Understanding Area

Lesson 2: Recognize area as an attribute of polygons.Investigate: Comparing Rugs
Which Covers More Space?
Lesson 3: Tile polygons to find their areas.Tiling Figures
Area Hunt

Topic B: Concepts of Area Measurement

Lesson 6: Tile rectangles with squares to make arrays and relate the side lengths to area.Rectangles and Arrays
Lesson 7: Draw rows and columns to complete a rectangular array and determine its area.Area Hunt

Module 6: Geometry, Measurement, and Data

Topic D: Collecting and Displaying Dat

Lesson 23: Solve problems by creating scaled picture graphs and scaled bar graphs.2, 5, or 10?

Level 4

Module 1: Place Value Concepts for Addition and Subtraction

Topic A: Multiplication as Multiplicative Comparison

Lesson 1: Interpret multiplication as multiplicative comparison.How Does It Grow?

Module 2: Place Value Concepts for Multiplication and Division

Topic E: Factors and Multiples

Lesson 24: Recognize that a number is a multiple of each of its factors.Hamster Homes
Factor or Multiple?
Lesson 25: Explore properties of prime and composite numbers up to 100 by using multiples.A Number Game

Module 4: Foundations for Fraction Operations

Lesson 1: Decompose whole numbers into a sum of unit fractions.

Lesson 1: Decompose whole numbers into a sum of unit fractions.Investigate: Building Your Own Number Line
Lesson 3: Decompose fractions into a sum of fractions.Math Pizzeria
Lesson 4: Represent fractions by using various fraction models.Fraction Strips
Chop It
Lesson 5: Rename fractions greater than 1 as mixed numbers.All Kinds of Fractions

Topic D: Add and Subtract Fractions

Lesson 21: Solve addition and subtraction word problems and estimate the reasonableness of the answers.Pizza Problems

Topic F: Repeated Addition of Fractions as Multiplication

Lesson 32: Multiply a fraction by a whole number by using the associative property.Equal Groups of Fractions

Module 5: Place Value Concepts for Decimal Fractions

Topic A: Exploration of Tenths

Lesson 1: Organize, count, and represent a collection of money.Investigate: Different Units
Lesson 3: Represent tenths as a place value unit.A New Way to Write Tenths
Lesson 4: Write mixed numbers in decimal form with tenths.A New Way to Write Tenths

Topic B: Tenths and Hundredths

Lesson 5: Decompose 1 one and express hundredths in fraction form and decimal form.Are They Equivalent?
Lesson 6: Represent hundredths as a place value unit.A New Way to Write Hundredths
Lesson 7: Write mixed numbers in decimal form with hundredths.A New Way to Write Hundredths

Topic C: Comparison of Decimal Numbers

Lesson 10: Use pictorial representations to compare decimal numbers.How Can You Compare?
Lesson 11: Compare and order decimal numbers.Robot Factory
What’s the Order?

Level 5

Module 1: Place Value Concepts for Multiplication and Division with Whole Numbers

Topic B: Multiplication of Whole Numbers

Lesson 8: Multiply two- and three-digit numbers by two-digit numbers by using the distributive property.Partial Products Everywhere
Lesson 9: Multiply two- and three-digit numbers by two-digit numbers by using the standard algorithm.How Do They Compare?

Topic C: Division of Whole Numbers

Lesson 15: Divide three-digit numbers by two-digit numbers in problems that result in two-digit quotients.Emptying the Water Tank

Module 2: Addition and Subtraction with Fractions

Topic A: Fractions and Division

Lesson 1: Interpret a fraction as division.Investigate: Sharing Sandwiches
Sharing More Sandwiches
Dance Breaks
Lesson 3: Represent fractions as division by using models.Making Generalizations
Lesson 4: Solve word problems involving division and fractions.Division Story Problems

Module 3: Multiplication and Division with Fractions

Topic B: Multiplication of Fractions

Lesson 7: Multiply fractions less than 1 by unit fractions pictorially.Investigate: Folding Paper
Lesson 8: Multiply fractions less than 1 pictorially.Parts of Parts
One Part of One Part
Rows and Columns
Lesson 9: Multiply fractions by unit fractions by making simpler problems.Messy Multiplication
Lesson 10: Multiply fractions greater than 1 by fractions.Making Food
Installing Turf
Lesson 11: Multiply fractions.Applying Fraction Multiplication
Chores at Animal Haven
The Re-size-inator

Module 5: Addition and Multiplication with Area and Volume

Topic C: Volume Concepts

Lesson 17: Find the volume of right rectangular prisms by packing with unit cubes and counting.Which is Largest
Lesson 18: Find the volume of right rectangular prisms by packing with improvised units.Packing the Barge

Topic D: Volume and the Operations of Multiplication and Addition

Lesson 25: Find the volumes of solid figures composed of right rectangular prisms.Putting It Together
Figures Made of Prisms

Level 6

Module 1: Ratios, Rates, and Percents

Topic A: Ratios

Lesson 2: Introduction to RatiosPizza Maker

Topic B: Collections of Equivalent Ratios

Lesson 6: Ratios Tables and Double Number LinesFruit Lab
Lesson 9: Multiplication Patterns in Ratio RelationshipsDisaster Preparation

Topic D: Rates

Lesson 16: SpeedWorld Records
Lesson 17: RatesMany Measurements
Soft Serve
Lesson 18: Comparing RatesWelcome to the Robot Factory
Lesson 19: Unit Rates to Convert UnitsModel Trains
More Soft Serve
Lesson 20: Solving Rate ProblemsLucky Duckies

Module 2: Operations with Fractions and Multi-Digit Numbers

Topic B: Dividing Fractions

Lesson 6: Dividing a Whole Number by a FractionFlour Planner
Lesson 8: Dividing Fractions by Making Common DenominatorsFill the Gap

Topic C: Dividing Fractions Fluently

Lesson 9: Dividing Fractions by Using Tape DiagramsPuzzling Areas

Topic D: Decimal Addition, Subtraction, and Multiplication

Lesson 13: Decimal Addition and SubtractionDishing Out Decimals
Lesson 16: Applications of Decimal OperationsDecimal Diagrams and Algorithms

Topic F: Decimal Division

Lesson 21: Dividing a Decimals by a Whole NumberMovie Time
Lesson 22: Dividing a Decimal by a Decimal Greater than 1Movie Time
Lesson 23: Dividing a Decimal by a Decimal Less than 1Movie Time

Module 3: Rational Numbers

Topic A: Integers and Rational Numbers

Lesson 1: Positive and Negative NumbersCan You Dig It?
Lesson 3: Rational NumbersOrder in the Class

Module 4: Expressions and One-Step Equations

Topic B: Expressions and Real-World Problems

Lesson 9: Addition and Subtraction Expressions from the Real-WorldSubway Fares

Topic C: Equivalent Expressions Using the Properties of Operations

Lesson 13: The Distributive PropertyProducts and Sums

Topic D: Equations and Inequalities

Lesson 17: Equations and SolutionsFive Equations
Lesson 18: Inequalities and SolutionsHanging It Up
Tunnel Travels
Lesson 19: Solving Equations with Addition and SubtractionWeight for It
Lesson 20: Solving Equations with Multiplication and DivisionHanging Around
Lesson 21: Solving Problems with EquationsSwap and Solve

Module 5: Area, Surface Area, and Volume

Topic A: Areas of Polygons

Lesson 1: The Area of a ParallelogramExploring Parallelograms, Part 1
Lesson 2: The Area of a Right TriangleOff the Grid, Part 2
Lesson 3: The Area of a TriangleExploring Parallelograms, Part 2
Off the Grid, Part 1
Lesson 4: Areas of Triangles in Real-World SituationsExploring Triangles

Topic B: Problem Solving with Area

Lesson 5: Perimeter and Area in the Coordinate PlaneShapes on a Plane
Lesson 6: Problem Solving with Area in the Coordinate PlaneLetters
Lesson 7: Areas of Trapezoids and Other PolygonsTriangles and Parallelograms
Lesson 8: Areas of Composite Rigures in Real-World SituationsPile of Polygons

Topic C: Nets and Surface Area

Lesson 12: From Nets to Surface AreaRenata’s Stickers

Module 6: Statistics

Topic A: Understanding Distributions

Lesson 2: Describing a Data DistributionHoops
Lesson 3: Creating a Dot PlotMinimum Wage
Lesson 4: Creating a HistogramThe Plot Thickens

Topic B: Mean and Mean Absolute Deviation

Lesson 7: Using the Mean to Describe CenterToy Cars

Level 7

Module 1: Ratios and Proportional Relationships

Topic A: Understanding Proportional Relationships

Lesson 1: An Experiment with Ratios and RatesPaint
Lesson 2: Exploring Tables and Proportional RelationshipsTwo and Two
Lesson 4: Exploring Graphs of Proportional RelationshipsDinoPops

Topic C: Scale Drawing and Proportional Relationships

Lesson 14: Extreme BicyclesScaling Machines
Lesson 15: Scale DrawingScaling Robots
Lesson 16: Using Scale FactorScale Factor Challenges
Lesson 17: Finding Actual Distances from ScaleMake it Scale
Lesson 18: Relating Areas of Scale DrawingTiles
Will It Fit

Module 2: Operations with Rational Numbers

Topic A: Adding Rational Numbers

Lesson 2: Adding IntegersFloats and Anchors

Topic B: Subtracting Rational Numbers

Lesson 8: Subtracting Integers, Part 1More Floats and Anchors
Lesson 10: Subtracting Rational Numbers, Part 1Draw Your Own

Topic E: Numberical Expressions with Rational Numbers

Lesson 25: Writing and Evaluating Expressions with Rational NumbersInteger Puzzles

Module 3: Expressions, Equations, and Inequalities

Topic A: Equivalent Expressions

Lesson 1: Equivalent ExpressionsCollect the Squares

Topic B: Unknown Angle Measurements

Lesson 7: Angle Relationships and Unknown Angle MeasuresFriendly Angles

Topic C: Solving Equations

Lesson 11: Dominoes and DominoesKeeping it True

Topic D: Inequalities

Lesson 18: Understanding Inequalities and Their SolutionsI Saw the Signs
Lesson 19: Using Equations to Solve InequalitiesUnbalanced Hangers
Lesson 20: Preserving and ReversingShira the Sheep
Lesson 21: Solving Two-Step InequalitiesBudgeting
Lesson 22: Solving Problems Involving InequalitiesWrite Them and Solve Them

Module 4: Geometry

Topic A: Constructing Geometric Figures

Lesson 3: Side Lengths of a TriangleCan You Build It
Lesson 4: Angles of a TriangleFriendly Angles

Topic C: Circumference and Areas of Circles

Lesson 10: The Outside of a CicleMeasuring Around
Lesson 11: The Inside of a CircleWhy Pi?
Lesson 14: Composite Figures with Circular RegionsArea Challenges

Module 5: Percent and Applications of Percent

Topic A: Proportion and Percent

Lesson 3: Percent as a Rate per 100Mosaics
Lesson 4: Proportion and PercentMore and Less

Topic C: More of Less Than 100%

Lesson 10: Percent IncreaseAll the Equations

Topic D: Applications of Percent

Lesson 16: Markups and Discount100%
Lesson 18: Simple Interest – Solving for Unknown ValuesPercent Machines

Topic E: Problems Involving Percent

Lesson 20: Making Money, Day 1Back in My Day

Module 6: Probability and Populations

Topic A: Calculating and Interpreting Probabilities

Lesson 2: Empirical ProbabilityHow Likely
Lesson 4: Theoretical ProbabilityProb-bear-bilities

Topic B: Estimating Probabilities

Lesson 7: The Law of Large NumbersIs It Fair?

Topic C: Random Sampling

Lesson 11: Populations and SamplesCrab Island

Level 8

Module 1: Scientific Notation, Exponents, and Irrational Numbers

Topic A: Introduction to Scientific Notation

Lesson 2: Comparing Large NumbersSpecific and Scientific (formerly Solar System)
Lesson 4: Adding and Subtracting Numbers Written in Scientific NotationBalance the Scale

Topic B: Properties and Definitions of Exponents

Lesson 6: More Properties of ExponentsCircles
Lesson 7: Making Sense of the Exponent 0Power Pairs

Topic D: Perfect Squares, Perfect Cubes, and the Pythagorean Theorem

Lesson 18: The Pythagorean TheoremTriangle Tracing Turtle
Lesson 19: Using the Pythagorean TheoremTaco Truck
Lesson 23: Ordering Irrational NumbersRoot Down

Module 2: Rigid Motions and Congruent Figures

Topic A: Rigid Motion and Their Properties

Lesson 1: Motions in the PlaneTransformers
Moving Day
Lesson 2: TranslationsSpinning, Flipping, Sliding
Moving Day
Lesson 4: Translations and Reflections on the Coordinate PlaneGetting Coordinated, Part 1
Lesson 6: Rotations on the Coordinate PlaneGetting Coordinated, Part 2

Topic B: Rigid Motions and Congruent Figures

Lesson 8: Sequencing the Rigid MotionsTransformation Golf

Topic C: Angle Relationships

Lesson 12: Lines Cut by a TransversalPuzzling It Out

Module 3: Dilations and Similar Figures

Topic A: Dilations

Lesson 1: Exploring DilationsSketchy Dilations
Lesson 3: Reductions and More EnlargmentsDilation Mini Golf

Topic B: Properties of Dilations

Lesson 5: Figures and DilationsSocial Scavenger Hunt

Module 4: Linear Equations in One and Two Variables

Topic A: Linear Equations in One Variable

Lesson 3: Solving Linear Equations with Rational CoefficientsEquation Roundtable

Topic D: Slope of a Line

Lesson 16: Proportional Relationships and SlopeTurtle Time Trials
Lesson 17: Slopes of Rising LinesFlags
Ups and Downs
Lesson 18: Slopes of Falling LinesFlags
Water Cooler
Ups and Downs

Topic E: Different Forms of a Linear Equation

Lesson 20: Slope-Intercept form of the Equation of a LineStacking Cups (Optional)
Lesson 21: Slopes and Parallel LinesTranslations

Module 5: Systems of Linear Equations

Topic A: Solving Systems of Linear Equations Graphically

Lesson 1: Solving Problems with Equations and Their GraphsMake Them Balance

Topic B: Solving Systems of Linear Equations Algebraically

Lesson 6: Solving Systems of Linear Equations without GraphingLine Zapper

Module 6: Functions and Bivariate Statistics

Topic A: Functions

Lesson 1: Motion and SpeedTurtle Crossing
Lesson 2: Definition of a FunctionGuess My Rule

Topic B: Linear and Nonlinear Functions

Lesson 9: Increasing and Decreasing FunctionsThe Tortoise and the Hare

Topic C: Bivariate Numerical Data

Lesson 11: Scatter PlotsRobots
Dapper Cats
Lesson 12: Patterns in Scatter PlotsInterpreting Scatter Plots
Lesson 13: Informally Fitting a Line to DataFind the Fit (called Fit Fights in Desmos Math)
Lesson 14: Determining an Equation of a Line Fit to DataInterpreting Slopes
Lesson 15: Linear ModelAnimal Brains
Lesson 16: Using the Investigative ProcessScatter Plot City
Lesson 17: Analyzing the ModleScatter Plot City

Topic D: Bivariate Categorical Data

Lesson 18: Bivariate Categorical DataFinding Associations

Topic E: Volume

Lesson 22: Volume of a CylinderCylinders
Lesson 23: Volume of ConesCones

Algebra 1

Module 1: Expressions, Equations and Inequalities in One Variable

Lesson 1: The Growing Pattern of DucksMore Visual Patterns
Lesson 8: Solution Sets for Equations and Inequalities in One VariableSame Position
Lesson 9: Solving Linear Equations in One VariableWorking Backwards
Solving Strategies
Lesson 12: Rearranging FormulasSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 13: Solving Linear Inequalities in One VariablePizza Delivery
Lesson 21: Describing Variability in a Univariate Distribution with Standard DeviationFinding Desmo

Module 2: Equations and Inequalities in Two Variables

Lesson 1: Solution Sets of Linear Equations in Two VariablesSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 6: Applications of Linear Equations and InequalitiesSubway Seats
Various Variables
Shelley the Snail
Five Representations
Pizza Delivery
Lesson 8: Systems of Linear Equations in Two VariablesShape It Up
Lizard Lines
Lesson 12: Solution Sets of Systems of Linear InequalitiesQuilts
Lesson 13: Graphing Solution Sets of Systems of Linear InequalitiesSeeking Solutions
Lesson 16: Using Lines to Model Bivariate Quantitative DataCity Data
Lesson 17: Modeling Relationships with a LinePenguin Populations
Lesson 18: Calculating and Analyzing ResidualsResidual Fruit
Lesson 20: Interpreting CorrelationCorrelation Coefficient
How Hot Is It?
City Slopes
Lesson 21: Analyzing Bivariate Quantitative DataBehind the Headlines

Module 3: Functions and Their Representations

Lesson 7: Exploring Key Features of a Function and Its GraphCraft-a-Graph
Lesson 17: Piecewise Linear Functions in ContextPumpkin Prices

Module 4: Quadratic Functions

Topic A: Quadratic Functions and Their GraphsRobot Launch
Lesson 1: Falling ObjectsQuadratic Visual Patterns
Lesson 2: Projectile MotionStomp Rockets
Lesson 3: Analyzing Functions That Model Projectile MotionStomp Rockets in Space
Lesson 4: Graphs of Quadratic FunctionsOn the Fence
Plenty of Parabolas
Lesson 5: Solving Equations that Contain Factored ExpressionsShooting Stars
Lesson 11: Graphing Quadratic Functions from Factored FormTwo for One
Parabola Zapper
Lesson 14: Solving Quadratic Equations by Completing the SquareSquare Tactic
Lesson 27: Search and Rescue HelicopterCity Data

Module 5: Linear and Exponential Functions

Topic A: Arithmetic and Geometric SequencesMore Visual Patterns
Sequence Carnival
Lesson 8: Exponential FunctionsCarlos’s Fish
Topic A: Arithmetic and Geometric SequencesSequence Carnival
Topic A: Arithmetic and Geometric SequencesRevisiting Visual Patterns, Part 1
Lesson 18: Modeling PopulationsSorting Relationships
Lesson 20: Comparing Growth of FunctionsPlane, Train, and Automobile
Sorting Relationships

Module 6: Modeling with Functions

Topic A: Modeling Bivariate Quantitative DataCity Data
Topic B: Developing Models for ContextsDetroit’s Population, Part 1
Detroit’s Population, Part 2

Grade 6

Unit 1: Area and Surface Area

Amplify MathDesmos Math 6–A1
Unit 1: Area and Surface AreaUnit 1: Area and Surface Area
Unit 7: Positive and Negative Numbers
Lesson 1: The TangramUnit 1
Lesson 1: Shapes on a Plane
Lesson 2: Exploring the TangramUnit 1
Lesson 2: Letters
Sub-Unit 1 : Area of Special Polygons
Lesson 3: Tilting the PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 4: Compositing and Rearranging to Determine AreaUnit 1
Lesson 2: Letters
Lesson 5: Reasoning to Determine AreaUnit 1
Lesson 2: Letters
Lesson 6: ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 7: Bases and Heights of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 8: Bases and Heights of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 9: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms (Print available)
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 10: Bases and Heights of TrianglesUnit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 11: Formula for the Area of a TriangleUnit 1
Lesson 5: Exploring Triangles (Print available)
Lesson 12: From Triangles to TrapezoidsUnit 1
Lesson 4: Off the Grid
Lesson 6: Triangles and Parallelograms
Lesson 13: PolygonsUnit 1
Lesson 2: Letters
Lesson 8: Pile of Polygons Practice Day 1 (Print available)

Unit 7
Lesson 11: Polygon Maker
Sub-Unit 2: Nets and Surface Area
Lesson 14: What is Surface Area?Unit 1
Lesson 9: Renata’s Stickers
Lesson 15: Nets and Surface Area of Rectangular PrismsUnit 1
Lesson 10: Plenty of Polyhedra
Lesson 11:Nothing but Nets(Print available)
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Lesson 16: Nets and Surface Area of PrismsUnit 1
Lesson 12: Face Value
Lesson 13: Take It To Go (Print available)
Lesson 17: Constructing a RhombicuboctahedronUnit 1
Lesson 13: Take It To Go (Print available)
Lesson 18: Simplifying Expressions for Squares and CubesUnit 1
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 19: Simplifying Expressions Even More Using ExponentsUnit 1
Lesson 11: Exponent Expressions (Print available)
Lesson 20: Designing a Suspended Tent 

Unit 2: Introducing Ratios

Amplify MathDesmos Math 6–A1
Unit 2: Introducing RatiosUnit 2: Introducing Ratios
Lesson 1: Fermi Problems 
Sub-Unit 1: What are Ratios?
Lesson 2: Introducing Ratios and Ratio LanguageUnit 2
Lesson 1: Pizza Maker
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Representing Ratios with DiagramsUnit 2
Lesson 1: Pizza Maker
Lesson 2: Ratio Rounds (Print available)
Lesson 3:Rice Ratios (Print available)
Lesson 4: A Recipe for Purple Oobleck 
Lesson 5: Kapa Dyes 
Sub-Unit 2:Equivalent Ratios
Lesson 6: Defining Equivalent RatiosUnit 2
Lesson 3: Rice Ratios (Print available)
Lesson 4: Fruit Lab (Print available)
Lesson 11: Community Life (Print available)
Practice Day 1 (Print available)
Lesson 7: Representing Equivalent Ratios with Tables 
Lesson 8: Reasoning with Multiplication and Division (optional) 
Lesson 9: Common Factors 
Lesson 10: Common Multiples 
Lesson 11: Navigating a Table of Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 12: Tables and Double Number Line DiagramsUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 13: Tempo and Double Number LinesUnit 2
Lesson 5: Balancing Act
Lesson 6: Product Prices (Print available)
Sub-Unit 3: Solving Ratio Problems 
Lesson 14: Solving Equivalent RatiosUnit 2
Lesson 6: Product Prices (Print available)
Lesson 7: Mixing Paint, Part 1
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 15: Part-Part-Whole RatiosUnit 2
Lesson 12 Mixing Paint, Part 2
Lesson 13: City Planning
Lesson 16: Comparing Ratios 
Lesson 17: More Comparing and Solving 
Lesson 18: Measuring with Different-Sized Units 
Lesson 20: More Fermi Problems 

Unit 3: Rates and Percentages

Amplify MathDesmos Math 6–A1
Unit 3: Rates and PercentagesUnit 2: Introducing Ratios
Unit 3: Unit Rates and percentages
Lesson 1: Choosing Representation for Student CouncilLaunch Lesson
Sub-Unit 1: Rates
Lesson 2: How Much for One?Unit 3
Lesson 4: Model Trains
Lesson 3: Constant Speed  
Lesson 4: Comparing SpeedsUnit 2
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve
Lesson 6: Welcome to the Robot Factory
Lesson 5: Interpreting RatesUnit 3
Lesson 8: World Records (Print available) 

Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve
Lesson 6: Welcome to the Robot Factory
Lesson 6: Comparing Rates 
Lesson 7: Solving Rate ProblemsUnit 3
Lesson 7: More Soft Serve
Sub-Unit 2: Percentages
Lesson 8: What Are percentages?Unit 3
Lesson 8: Lucky Duckies
Lesson 9: Bicycle Goals
Lesson 9: Determining Percentages 
Lesson 10: Benchmark PercentagesUnit 3
Lesson 7: Lucky Duckies
Lesson 11: Finding This Percent of ThatUnit 3
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Lesson 12: This Percent of What 
Lesson 13: Solving Percentage ProblemsUnit 3
Lesson: 10: What’s Missing (Print available)
Lesson: 11: Cost Breakdown
Lesson: 12: More Bicycle Goals
Lesson: 13: A Country as a Village
Lesson 14: If Our Class Were the World 
Lesson 15: Voting for a School Mascot 

Unit 4: Dividing Fractions

Amplify MathDesmos Math 6–A1
Lesson 1: Seeing Fractions
Sub-Unit 1: Interpreting Division Scenarios
Lesson 3: Relating Multiplication and Division 
Lesson 4: Size of Divisor and Size of QuotientUnit 4
Lesson 1: Cookie Cutter
Sub-Unit 2: Division with Fractions
Lesson 5: How Many GroupsUnit 4
Lesson 3: Flour Planner
Lesson 4: Flower Planters
Lesson 4: Garden Bricks (Print available) 
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 6: Fill the Gap
Lesson 7: Dividing with Common DenominatorsUnit 4
Lesson 6: Fill the Gap
Lesson 8: How Much in Each Group? (Part 1)Unit 4
Lesson 8: Potting Soil
Lesson 9: How Much in Each Group? (Part 2)Unit 4
Lesson 8: Potting Soil
Lesson 10: Dividing by Unit and Non-Unit FractionsUnit 4
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 11: Using an Algorithm to Divide FractionsUnit 4
Lesson 9: Division Challenges Practice Day
Lesson 13: Fractional LengthsUnit 4
Lesson 12: Puzzling 
Lesson 14: Area with Fractional LengthsUnit 4
Lesson 9: Puzzling Area (Print available)
Lesson 15: Volume of PrismsUnit 4
Lesson 13: Volume Challenges (Print available)
Lesson 16: Fish Tanks Inside of Fish TanksUnit 4
Lesson 10: Swap Meet
Lesson 17: Now, Where Was That Bus?Unit 4
Lesson 10: Capstone

Unit 5: Arithmetic in Base Ten

Amplify MathDesmos Math 6–A1
Lesson 1: Precision and World Records 
Sub-Unit 1: Adding and Subtracting Decimals 
Lesson 2: Speaking of Decimals…Unit 5
Lesson 1: Dishing Out Decimals (Print available)
Lesson 3: Adding and Subtracting DecimalsUnit 5
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 4: X Games Medal ResultsUnit 5
Lesson 2: Decimal Diagrams
Sub-Unit 2: Multiplying Decimals
Lesson 5: Decimal Points in ProductsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Methods for Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 7: Using Diagrams to Represent MultiplicationUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying with Areas
Lesson 8: Calculating Products of DecimalsUnit 5
Lesson 6: Multiplying with Areas
Sub-Unit 3: Dividing Decimals
Lesson 9: Exploring Division 
Lesson 10: Using Long DivisionUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Dividing Numbers That Result in DecimalsUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 12: Using Related Expressions to Divide with Decimals 
Lesson 13: Dividing Multi-Digit DecimalsUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 14: The So-called World’s Littlest Skyscraper

Unit 6: Expressions and Equations

Amplify MathDesmos Math 6–A1
Unit 6: Expressions and EquationsUnit 6: Expressions and Equations
Lesson 1: Detecting Counterfeit Coins
Sub-Unit 1: Expressions and Equations in One Variable
Lesson 2: Write Expressions Where Letters Stand for Numbers 
Lesson 3: Tape Diagrams and Equations 
Lesson 4: Truth and EquationsUnit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 5: Staying in BalanceUnit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Staying in Balance with Variables 
Lesson 7: Practice Solving EquationsUnit 6
Lesson 3: Hanging Around
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 8: A New Way to Interpret a over bUnit 6
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 9: Revisiting Percentages
Sub-Unit 2: Equivalent Expressions
Lesson 10: Equal and Equivalent (Part 1)Unit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Vari-apples
Lesson 11: Equal and Equivalent (Part 2)Unit 6
Lesson 1: Weight for It
Lesson 2: Five Equations (Print available)
Lesson 3: Hanging Around
Lesson 6: Vari-apples
Lesson 12: The Distributive Property, Part 1Unit 6
Lesson 8: Products and Sums
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 13: The Distributive Property, Part 2Unit 6
Lesson 8: Products and Sums
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 14: Meaning of ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Lesson 15: Evaluating Expressions with ExponentsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 16: Analyzing Exponential Expressions and EquationsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Sub-Unit 3: Relationships Between Quantities
Lesson 17: Two Related Quantities, Part 1Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 18: Two Related Quantitites, Part 2Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 19: Creating a Class Mobile 

Unit 7: Rational Numbers

Amplify MathDesmos Math 6–A1
Unit 7: Rational Numbers
Unit 1: Area and Surface Area
Unit 7: Positive and Negative Numbers
Lesson 1: How Far? Which Way?
Sub-unit 1: Negative Numbers and Absolute Value
Lesson 2: Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig In
Lesson 2: Digging Deeper
Lesson 3: Points on the Number LineUnit 7
Lesson 2: Digging Deeper
Lesson 4: Comparing IntegersUnit 7
Lesson 3: Order in the Class (Print available)
Lesson 5: Comparing and Ordering Rational NumbersUnit 7 
Lesson 3: Order in the Class (Print available)
Lesson 6: Using Negative Numbers to Make Sense of Contexts>Unit 7
Lesson 4: Sub-Zero
Lesson 7: Absolute Value of NumbersUnit 7
Lesson 5: Distance on the Number Line
Lesson 8: Comparing Numbers and Distance from ZeroUnit 7
Lesson 5: Distance on the Number Line
Sub-Unit 2: Inequalities
Lesson 9: Writing Inequalities 
Lesson 10: Graphing Inequalities 
Lesson 11: Solutions to One or More InequalitiesUnit 7
Lesson 6: Tunnel Travel
Lesson 7: Comparing Weights
Lesson 8: Shira´s Solutions
Lesson 12: Interpreting InequalitiesUnit 7
Lesson 6: Tunnel Travel
Lesson 7: Comparing Weights
Lesson 8: Shira´s Solutions
Sub-Unit 3: The Coordinate Plane
Lesson 13: Extending the Coordinate Plane 
Lesson 14: Points on the Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 15: Interpreting Points on a Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 11: Polygon Maker
Lesson 16: Distances on a Coordinate PlaneUnit 7
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)
Lesson 17: Shapes on the Coordinate PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 2: Letters
Lesson 5: Exploring Triangles (Print available)
Lesson 6: Triangles and Parallelograms

Unit 7
Lesson 3: Exploring Parallelograms (Print available)
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)
Lesson 18: Lost and Found Puzzles 
Lesson 19: Drawing on the Coordinate PlaneUnit 7
Lesson 11: Polygon Maker
Lesson 12: Graph Telephone (Print available)

Unit 8: Data Sets and Distributions

Amplify MathDesmos Math 6–A1
Unit 8: Data Sets and DistributionsUnit 8: Describing Data
Lesson 1: Plausible Variation or New Species?
Sub-Unit 1: Statistical Questions and Representing Data
Lesson 2: Statistical QuestionsUnit 8
Lesson 1: Screen Time
Lesson 2: Dot Plots
Lesson 3: Interpreting Dot PlotsUnit 8
Lesson 2: Dot Plots
Lesson 3: Minimum Wage (Print available)
Lesson 4: Lots More Dots
Lesson 4: USing Dot Plots to Answer Statistical QuestionsUnit 8
Lesson 2: Dot Plots
Lesson 3: Minimum Wage (Print available)
Lesson 4: Lots More Dots
Lesson 5: Interpreting HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Lesson 6: Using Histograms to Answer Statistical QuestionsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Lesson 7: Describing Distributions on HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 6: DIY Histograms (Print available)
Sub-Unit 2: Measures of Center
Lesson 8: Mean as a Fair ShareUnit 8
Lesson 7: Snack Time
Lesson 9: Mean as a Balance PointUnit 8
Lesson 7: Snack Time
Lesson 10: MedianUnit 8
Lesson 11: Toy Cars
Lesson 12: In the News
Lesson 11: Comparing Mean and MedianUnit 8
Lesson 12: In the News
Sub-Unit 3: Measures of Variability
Lesson 12: Describing Variability 
Lesson 13: Variability and MAD 
Lesson 14: Variability and IQRUnit 8
Lesson 13: Pumpkin Patch
Lesson 15: Box PlotsUnit 8
Lesson 14: Car, Plane, Bus, or Train? (Print available)
Lesson 16: Comparing MAD and IQR 
Lesson 17: Asian Elephant Populations 

Grade 7

Unit 1: Scale Drawings

Amplify MathDesmos Math 6–A1
Unit 1: Scale DrawingsUnit 1: Scale Drawings
Unit 3: Measuring Circles
Unit 4: Proportional Relationships and Percentages
Lesson 1: Scale-y Shapes 
Sub-Unit 1: Scaled Copies 
Lesson 2: What are Scaled Copies?Unit 1
Lesson 1: Scaling Machines
Lesson 3: Corresponding Parts and Scale FactorsUnit 1
Lesson 2: Scaling Robots 
Unit 3
Lesson 1: Toothpicks
Lesson 4: Making Scaled CopiesUnit 1
Lesson 3: Make It Scale 
Unit 4
Lesson 3: Sticker Sizes
Lesson 5: The Size of the Scale FactorUnit 1
Lesson 4: Tiles
Lesson 6: Scaling and AreaUnit 1
Lesson 5: Tiles Practice Day 1 (Print available)
Sub-Unit 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available)
Lesson 8: Creating Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Lesson 9: Scale Drawings and Maps 
Lesson 10: Changing Scale in Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Lesson 11: Scales without Units 
Lesson 12: Units in Scale DrawingsUnit 1
Lesson 8: Scaling States
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)Practice Day (Print available)
Lesson 13: Build Your Brand 

Unit 2: Introducing Proportional Relationships

Amplify MathDesmos Math 6–A1
Unit 2: Introducing Proportional RelationshipsUnit 2: Introducing Proportional Relationships
Unit 4: Proportional Relationships and Percentages
Lesson 1: Making Music 
Sub-Unit 1: Representing Proportional Relationships with Tables and Equations
Lesson 2: Introducing Proportional Relationships with TablesUnit 2
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 3: More About Constant of ProportionalityUnit 2
Lesson 3: Sugary Drinks (Print available)

Unit 4
Lesson 3: Sticker Sizes
Lesson 4: Comparing Relationships with TablesUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 5: Proportional Relationships and EquationsUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 6: Speed and Equations 
Lesson 7: Two Equations for Each RelationshipUnit 2
Lesson 4: Two and Two (Print available)
Lesson 5: Lesson 7: All Kinds of Equations
Lesson 8: Using Equations to Solve ProblemsUnit 2
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 9: Comparing Relationships with EquationsUnit 2
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available)
Lesson 7: All Kinds of Equations
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Lesson 10: Solving Problems About Proportional RelationshipsUnit 2
Lesson 12: Water Efficiency
Sub-Unit 2: Representing Proportional Relationships with Graphs 
Lesson 11: Introducing Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 12: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 13: Using Graphs to Compare RelationshipsUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 14: Two Graphs for Each RelationshipUnit 2
Lesson 8: Dino Pops
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations
Lesson 12: Water Efficiency
Lesson 15: Four Ways to Tell One Story (Part 1) 
Lesson 16: Four Ways to Tell One Story (Part 2) 
Lesson 17: Welcoming Committee 

Unit 3: Measuring Circles

Amplify MathDesmos Math 6–A1
Unit 3: Measuring CirclesUnit 3: Measuring Circles
Lesson 1: The Wandering Goat 
Sub-unit 1: Circumference of a Circle 
Lesson 2: Exploring CirclesUnit 3
Lesson 2: Is it a Circle?
Lesson 3: Measuring Around
Lesson 3: How Well Can You Measure? 
Lesson 4: Exploring CircumferenceUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around
Lesson 5: Understanding π 
Lesson 6: Applying CircumferenceUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around
Lesson 7: Circumference and Wheels 
Sub-Unit 2: Area of a Circle
Lesson 8: Exploring the Area of a CircleUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges
Lesson 9: Circle vs. Square
Practice Day 2 (Print available)
Lesson 9: Relating Area to CircumferenceUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges
Lesson 9: Circle vs. Square
Practice Day 2 (Print available)
Lesson 10: Applying Area to CirclesUnit 3
Lesson 6:Radius Squares (Print available)
Lesson 11: Distinguishing Circumference and AreaUnit 3
Lesson 7: Why Pi?
Lesson 12: Capturing Space 

Unit 4: Proportional Relationships and Percentages

Amplify MathDesmos Math 6–A1
Unit 4: PercentagesUnit 4: Proportional Relationships and Percentages
Lesson 1: (Re)Presenting the United States 
Lesson 2: Understanding Percentages and Decimals 
Lesson 3: Percent Increase and DecreaseUnit 4Lesson 4: More or Less
Lesson 4: Determining 100%Unit 4Lesson 6: 100% (Print available)
Lesson 5: Determining Percent ChangeUnit 4Lesson 7: Percent Machines
Lesson 6: Percent Increase and Decrease With EquationsUnit 4Lesson 5: All the Equations
Lesson 7: Using Equations to Solve Percent ProblemsUnit 4Lesson 5: All the Equations
Sub-Unit 2: Applying Percentages 
Lesson 8: Tax and TipUnit 4
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems
Lesson 9: Percent ContextsUnit 4
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems
Lesson 10: Determining the PercentageUnit 4
Lesson 4: More and Less
Lesson 11: Measurement ErrorUnit 4
Lesson 11: Bookcase Builder
Lesson 12: Error IntervalsUnit 4
Lesson 11: Bookcase Builder
Lesson 13: Writing Better Headlines 

Unit 5: Rational Number Arithmetic

Amplify MathDesmos Math 6–A1
Unit 5: Rational Number ArithmeticUnit 5: Rational Number Artithmetics
Lesson 1: Target: Zero 
Sub-Unit 1: Adding and Subtracting Rational Numbers 
Lesson 2: Interpreting Negative Numbers
Lesson 3: Changing TemperaturesUnit 5
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 4: Adding Rational Numbers 
Lesson 5: Money and Debts 
Lesson 6: Representing SubtractionUnit 5
Lesson 5: Number Puzzles
Lesson 7: Subtracting Rational Numbers (Part 1)Unit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 8: Subtracting Rational Numbers (Part 2)Unit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 9: Adding and Subtracting Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available)
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)Practice Day 1 (Print available)
Sub-Unit 2: Multiplying and Dividing Rational Numbers 
Lesson 10: Position, Speed, and TimeUnit 5
Lesson 7: Back in Time
Lesson 11: Multiplying Rational NumbersUnit 5
Lesson 7: Back in Time
Lesson 12: Multiply!Unit 5
Lesson 7: Back in Time
Lesson 13: Dividing Rational NumbersUnit 5
Lesson 7: Speeding Turtles
Lesson 14: Negative Rates 
Sub-Unit 3: Four Operations with Rational Numbers 
Lesson 15: Expressions with Rational NumbersUnit 5
Lesson 9: Expressions (Print available)
Lesson 16: Say It With Decimals 
Lesson 17: Solving Problems with Rational NumbersLesson 11: Changing Temperatures
Lesson 12: Arctic Ice Sea (Print available)
Lesson 13: Solar Panels and More (Print available)
Lesson 18: Solving Equations With Rational Numbers 
Lesson 19: Representing Contexts With Equations 
Lesson 20: Summiting Everest 

Unit 6: Expressions, Equations, and Inequalities

Amplify MathDesmos Math 6–A1
Unit 6: Expressions, Equations, and InequalitiesUnit 2: Introducing Proportional Relationships
Unit 4: Proportional Relationships and Percentages
Unit 6: Expressions, Equations, and Inequalities
Lesson 1: Keeping the Balance 
Lesson 2: Balanced and UnbalancedUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 2: Balanced and UnbalancedUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 3: Reasoning About Solving Equations (Part 1)Unit 6
Lesson 2: Smudged Receipts
Lesson 4: Reasoning About Solving Equations (Part 2)Unit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 5: Dealing with Negative NumbersUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Lesson 5: Dealing with Negative NumbersUnit 6
Lesson 8: Factoring and Expanding (Print available)
Lesson 16: Shira the Sheep
Lesson 6: Two Ways to Solve One EquationUnit 6
Lesson 4: Seeing Struction (Print available)
Lesson 7: Practice Solving EquationsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available)
Sub-Unit 2: Solving Real-World Problems Using Two-Step Equations 
Lesson 8: Reasoning With Tape DiagramsUnit 6
Lesson 2: Smudged Receipts
Lesson 9: Reasoning About Equations and Tape Diagrams (Part 1)Unit 6
Lesson 2: Smudged Receipts
Lesson 10: Reasoning About Equations and Tape Diagrams (Part 2)Unit 6
Lesson 2: Smudged Receipts
Lesson 11: Using Equations to Solve ProblemsUnit 6
Lesson 2: Smudged Receipts
Lesson 3: Equations
Lesson 4: Seeing Structure (Print available) 
Lesson 12: Solving Percent Problems in New WaysUnit 6
Lesson 4: Seeing Structure (Print available)

Unit 4
Lesson 7: Percent MachinesPractice Day 1 (Print available)
Practice Day 2 (Print available)
Sub-Unit 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6
Lesson 1: Toothpicks and Tiles
Lesson 14: Solving InequalitiesUnit 6
Lesson 5: Balancing Moves
Lesson 6: Balancing Equations
Lesson 13: I Saw the Signs
Lesson 15: Finding Solutions to Inequalities in ContextUnit 6
Lesson 13: I Saw the Signs
Practice Day 1 (Print available)
Lesson 16: Efficiently Solving InequalitiesUnit 6
Lesson 10: Collect the Squares
Lesson 17: Interpreting InequalitiesUnit 6
Lesson 13: I Saw the Signs
Lesson 14: Unbalanced Hangers
Lesson 15: Budgeting (Print available)
Lesson 18: Modeling With Inequalities 
Sub-Unit 4: Equivalent Expressions 
Lesson 19: Subtraction in Equivalent Expressions 

Unit 7: Angles, Triangles, and Prisms

Amplify MathDesmos Math 6–A1
Unit 7: Angles, Triangles, and PrismsUnit 7: Angles, Triangles, and Prisms
Lesson 1: Shaping Up 
Sub-Unit 1: Angle Relationships 
Lesson 2: Relationships of AnglesUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles
Lesson 3: Angle Diagrams
Lesson 3: Supplementary and Complementary Angles (Part 1) 
Lesson 4: Supplementary and Complementary Angles (Part 2) 
Lesson 5: Vertical AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 6: Using Equations to Solve for Unknown AnglesUnit 7
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 7: Like Clockwork 
Sub-Unit 2: Drawing Polygons with Given Conditions 
Lesson 8: Building Polygons (Part 1)Unit 7
Lesson 6: Is It Enough?
Lesson 9: Building Polygons (Part 2)Unit 7
Lesson 6: Is It Enough?
Lesson 10: Triangles with Three Common MeasuresUnit 7
Lesson 13: Popcorn Possibilities
Lesson 11: Drawing Triangles (Part 1)Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)
Lesson 12: Drawing Triangles (Part 2)Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)
Sub-Unit 3: Solid Geometry
Lesson 13: Slicing SolidsUnit 7
Lesson 9: Slicing Solids
Lesson 14: Volume of Right PrismsUnit 7
Lesson 10: Simple Prisms
Lesson 15: Decomposing Bases for AreasUnit 7
Lesson 11: More Complicated Prisms
Lesson 16: Surface Area of Right PrismsUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies (Print available)
Lesson 17: Distinguishing Volume and Surface Area
Lesson 18: Applying Volume and Surface AreaUnit 7
Lesson 13: Popcorn Possibilities

Unit 8: Probability and Sampling

Amplify MathDesmos Math 6–A1
Unit 8: Probability and SamplingUnit 8: Probability and Sampling
Lesson 1: The Invention of Fairness 
Lesson 2: Chance Experiments 
Lesson 3: What are Probabilities?Unit 8
Lesson 1: How Likely? (Print available)
Lesson 2: Prob-bear-bilities [Free lesson
Lesson 3: Mystery Bag
Lesson 4: Estimating Probabilities Through Repeated ExperimentsUnit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 6: Fair Games
Lesson 5: Code Breaking (Part 1)
Lesson 6: Code Breaking (Part 2)
Sub-Unit 2: Probabilities of Multi-Step Events
Lesson 7: Keeping Track of All Possible OutcomesUnit 8
Lesson 4: Spin Class
Lesson 5: Is it Fair?
Lesson 6: Fair Games
Lesson 8: Experiments With Multi-Step Events  
Lesson 9: Simulating Multi-Step Events 
Lesson 10: Designing Simulations 
Sub-Unit 3:Sampling
Lesson 11: Comparing Two PopulationsUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Larger PopulationsUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 13: What Makes a Good Sample?Unit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 14: Sampling in a Fair WayUnit 8
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 15: Estimating Population Measures of CenterUnit 8
Lesson 9: Car, Bike, or Train?
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 16: Estimating Population ProportionsUnit 8
Lesson 9: Car, Bike, or Train?
Lesson 10: Crab Island
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 17: Presentation of Findings 

Grade 8

Unit 1: Rigid Transformations and Congruence

Amplify MathDesmos Math 6–A1
Unit 1: Rigid Transformations and CongruenceUnit 1: Rigid Transformations and Congruence
Unit 3: Proportional and Linear Relationships
Lesson 1: Tessellations 
Sub-Unit 1: Rigid Transformations 
Lesson 2: Moving in the PlaneUnit 1
Lesson 1: Transformers
Lesson 3: Symmetry and Reflection 
Lesson 4: Grid MovesUnit 1
Lesson 3: Transformation Golf
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated

Unit 3
Lesson 6: Translations
Lesson 5: Making the MovesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 6: Coordinate Moves (Part 1)Unit 1
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 7: Coordinate Moves (Part 2)Unit 1
Lesson 4: Moving Day (Print available)
Lesson 5: Getting Coordinated
Lesson 6: Describing TransformationsUnit 1
Lesson 5: Getting Coordinated
Lesson 6: Connecting the Dots
Sub-Unit 2: Rigid Transformations and Congruence 
Lesson 9: No Bending or StretchingUnit 1
Lesson 7: No Bending, No Stretching
Lesson 10: What is the Same?Unit 1
Lesson 7: Are They the Same?
Lesson 9: Are They Congruent?
Lesson 11: Congruent PolygonsUnit 1
Lesson 7: Are They the Same?
Lesson 9: Are They Congruent?
Sub-Unit 4: Angles in a Triangle 
Lesson 13: Line Moves 
Lesson 14: Rotation Patterns 
Lesson 15: Alternate Interior AnglesUnit 1 
Lesson 11: Tearing It Up (Print available)
Lesson 16: Adding the Angles in a TriangleUnit 1
Lesson 11: Tearing It Up (Print available)
Lesson 17: Parallel Lines and the Angles in a TriangleUnit 1 
Lesson 10: Transforming Angles
Lesson 18: Creating a Border Pattern Using Transformations 

Unit 2: Dilations, Similarity, and Introducing Slope

Amplify MathDesmos Math 6–A1
Unit 2: Dilations and SimilarityUnit 2: Dilations and Similarity
Lesson 1: Projecting and Scaling 
Sub-Unit 1: Dilations
Lesson 2: Circular GridUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 3: Match My Dilation
Lesson 4: Dilations on a Plane
Lesson 3: Dilations on a Plane 
Lesson 4: Dilations on a Square GridUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 3: Match My Dilation
Lesson 4: Dilations on a Plane
Lesson 5: Dilations with CoordinatesUnit 2
Lesson 4: Dilations on a Plane
Sub-Unit 2: Similiarity
Lesson 6: SimilarityUnit 2
Lesson 5: Transformations Golf with Dilations
Lesson 6: Social Scavenger Hunt (Print available)
Lesson 7: Similar PolygonsUnit 2
Lesson 6: Social Scavenger Hunt (Print available)
Lesson 8: Similar TrianglesUnit 2
Lesson 7: Are Angles Enough?
Lesson 8: Shadows
Lesson 9: Ratios of Side Lengths in Similar Triangles
Lesson 12: Optical Illusions 

Unit 3: Linear Relationships

Amplify MathDesmos Math 6–A1
Unit 3: Proportional and Linear RelationshipsUnit 3: Proportional and Linear Relationships
Unit 4: Linear Equations and Linear Systems
Unit 5: Functions and Volume
Lesson 1: Visual Patterns 
Sub-Unit 1: Proportional Relationships 
Lesson 2: Proportional Relationships 
Lesson 3: Understanding Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphs of Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Water Tank 

Unit 5
Lesson 4: Window Frames
Lesson 5: Representing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials 
Unit 5
Lesson 4: Window Frames
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 6: Comparing Proportional RelationshipsUnit 3
Lesson 3: Posters
Sub-Unit 2: Linear Relationships
Lesson 7: Introduction to Linear RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Stacking Cups

Unit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 8: Comparing Linear Relationships 
Lesson 9: More Linear RelationshipsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 10: Representations of Linear RelationshipsUnit 3
Lesson 5: Flags
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available)
Lesson 8: Charge! (Print available)
Lesson 11: Writing Equations for Lines Using Two Points 
Lesson 12: Translating mx + bUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 13: Slopes Don’t Have to be PositiveUnit 3
Lesson 5: Flags
Lesson 6: Translations
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 10: Calculating SlopeUnit 3
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 14: Writing Equations for Lines Using Two Points, Revisited 
Lesson 11: Equations of All Kinds of LinesUnit 3
Lesson 3: Posters
Lesson 4: Stacking Cups
Lesson 5: Flags
Lesson 6: Translations
Sub-Unit 3: Linear Equations 
Lesson 16: Solutions to Linear EquationsUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 10: Solutions

 Unit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 17: More Solutions to Linear EquationsUnit 3 
Lesson 4: Stacking Cups
Lesson 5: Flags
Lesson 6: Translations
Lesson 7: Water Cooler
Lesson 10: Solutions
Lesson 18: Coordinating Linear Relationships 
Lesson 19: Rogue Planes 

Unit 4: Linear Equations and Linear Systems

Amplify MathDesmos Math 6–A1
Unit 4: Linear Equations and Systems of Linear EquationsUnit 4: Linear Equations and Systems of Linear Equations
Lesson 1: Number PuzzlesUnit 4
Lesson 1: Number machines
Sub-Unit 1: Linear Equations in One Variable 
Lesson 2: Writing Expressions and Equations
Lesson 3: Keeping the BalanceUnit 4
Lesson 2: Keep It Balanced
Lesson 4: Balanced Moves (Part 1)Unit 4
Lesson 3: Balanced Moves
Lesson 5: Balanced Moves (Part 2)Unit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 6: Solving Any Linear EquationsUnit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available)
Lesson 6: Strategic Solving (Print available)
Lesson 7: How Many Solutions? (Part 1)Unit 4
Lesson 5: Equation Roundtable (Print available)
Lesson 8: How Many Solutions? (Part 2)Unit 4
Lesson 5: Equation Roundtable (Print available)
Lesson 9: Strategic Solving 
Lesson 10: When Are They the SameUnit 4
Lesson 8: When Are They the Same?
Sub-Unit 2: Systems of Linear Equations
Lesson 11: On or Off the Line?Unit 4
Lesson 9: On or Off the Line?
Lesson 12: On Both of the LinesUnit 4
Lesson 10: On Both Lines
Lesson 13: Systems of Linear EquationsUnit 4
Lesson 11: Make Them Balance
Lesson 14: Solving Systems of Equations (Part 1)Unit 4
Lesson 14: All, Some, or None? Part 2
Lesson 15: Solving Systems of Equations (Part 2)Unit 4
Lesson 12: All, Some, or None? Part 2
Lesson 16: Writing Systems of Linear EquationsUnit 4
Lesson 14: Strategic Solving, Part 2 (Print available)
Lesson 17: Pay Gaps 

Unit 5: Functions and Volume

Amplify MathDesmos Math 6–A1
Unit 5: Functions and VolumeUnit 2: Dilations, Similarity, and Introducing Slope
Unit 3:
Proportional and Linear Relationships
Unit 5:
Functions and Volume
Lesson 1: Pick a Pitch 
Sub-Unit 1: Representing and Interpreting Functions 
Lesson 2: Introduction to FunctionsUnit 5
Lesson 2: Guess My Rule
Lesson 3: Equations of FunctionsUnit 3
Lesson 4: Window Frames
Lesson 4: Graphs of Functions (Part 1)Unit 5
Lesson 3: Function or Not?
Lesson 5: Graphs of Functions (Part 2)Unit 5
Lesson 5: The Tortoise and the Hare
Lesson 6: Graphs of Functions (Part 3)Unit 5
Lesson 6: Graphing Stories
Lesson 7: Connecting Representations of FunctionsUnit 5
Lesson 7: Feel the Burn (Print available)Lesson 8: Charge! (Print available)
Lesson 8: Comparing Linear Functions 
Lesson 9: Modeling with Linear Functions 
Lesson 10: Piecewise Linear FunctionsUnit 5
Lesson 9: Piecing It Together
Sub-Unit 2: Cylinder, Cones, and Spheres 
Lesson 11: Filling Containers 
Lesson 12: The Volume of a CylinderUnit 5
Lesson 10: Volume LabLesson 11: Cylinders
Lesson 12: Scaling Cylinders
Lesson 13: Determining Dimensions of CylindersUnit 5
Lesson 14: Missing Dimensions (Print available)
Lesson 14: The Volume of a ConeUnit 5
Lesson 10: Volume LabLesson 13: Cones
Lesson 15: Determining Dimensions of ConesUnit 5
Lesson 12: Scaling Cylinders
Lesson 13: Cones
Lesson 14: Missing Dimensions (Print available)
Lesson 16: Estimating a Hemisphere 
Lesson 17: The Volume of a SphereUnit 5
Lesson 15: Spheres
Lesson 18: Cylinders, Cones and SpheresUnit 5
Lesson 15: Practice Day 2 (Print available)
Lesson 19: Scaling One Dimension 
Lesson 20: Scaling Two Dimensions 
Lesson 21: Packing Spheres 

Unit 6: Exponents and Scientific Notation

Amplify MathDesmos Math 6–A1
Unit 6: Exponents and Scientific NotationUnit 7: Exponents and Scienctific Notation
Lesson 1: Create a Sierpinski Triangle 
Sub-Unit 1: Exponent Rules 
Lesson 2: Reviewing ExponentsUnit 7
 Lesson 1: Circles
Lesson 2: Combining Exponents
Lesson 3: Multiplying PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 4: Rewriting Powers
Lesson 4: Dividing PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 4: Rewriting Powers
Lesson 5: Negative ExponentsUnit 7 
Lesson 5: Zero and Negative Exponents
Lesson 6: Powers of PowersUnit 7 
Lesson 3: Power Pairs (Print available)
Lesson 7: Different Bases, Same Exponent 
Lesson 8: Practice with Rational BasesUnit 7
Practice Day 1 (Print available)
Sub-Unit 2: Scientific Notation 
Lesson 9: Representing Large Numbers on the Number LineUnit 7
Lesson 8: Point Zapper
Lesson 10: Representing Small Numbers on the Number LineUnit 7
Lesson 8: Point Zapper
Lesson 11: Applications of Arthithmetic with Powers of 10Unit 7
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 12: Definition of Scientific NotationUnit 7
Lesson 10: Solar System
Lesson 11: Balance the Scale
Lesson 13: Star Power
Lesson 13: Multiplying, Dividing, and Estimating with Scientific NotationUnit 7
Lesson 11: Balance the Scale
Lesson 13: Star Power
Lesson 14: Adding and Subtracting with Scientific NotationUnit 7
Lesson 11: Balance the Scale
Lesson 12: City Lights
Lesson 13: Star Power
Lesson 15: Is a Smartphone Smart Enough to Go to the Moon? 

Unit 7: Irrationals and the Pythagorean Theorem

Practice Day 2 (Print available)

Amplify MathDesmos Math 6–A1
Unit 7: Irrationals and the Pythagorean TheoremUnit 8: The Pythagorean Theorem and Irrational Numbers
Lesson 1: Sliced Bread
Sub-Unit 1: Rational and Irrational Numbers
Lesson 2: The Square RootUnit 8
Lesson 2: From Squares to Roots
Lesson 3: The Ares of Squares and Their Side LengthsUnit 8
Lesson 1: Tilted Squares
Lesson 3: Between Squares
Lesson 4: Estimating Square RootsUnit 8
Lesson 3: Between Squares
Lesson 4: Root Down
Lesson 5: The Cube RootUnit 8
Lesson 5: Filling Cubes
Lesson 6: Rational and Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 7: Decimal Representations of Rational NumbersUnit 8
Lesson 12: Fractions to Decimals
Lesson 8: Converting Repeating Decimals Into FractionsUnit 8
Lesson 13: Decimals to Fractions
Sub-Unit 2: The Pythagorean Theorem
Lesson 9: Observing the Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 10: Proving the Pythagorean TheoremUnit 8
Lesson 7: Pictures to Prove It
Lesson 11: Determining Unknown Side LengthsUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 12: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make it Right
Lesson 13: Distances on the Coordinate Plane (Part 1)Unit 8
Lesson 11: Pond Hopper
Lesson 13: Distances on the Coordinate Plane (Part 1)Unit 8
Lesson 11: Pond Hopper
Lesson 14: Distances on the Coordinate Plane (Part 2)Unit 8
Lesson 11: Pond Hopper
Lesson 15: Applications of the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Taco Truck
Lesson 16: Pythagorean Triples

Unit 8: Pythagorean Theorem and Irrational Numbers

Amplify MathDesmos Math 6–A1
Unit 8: Associations in DataUnit 6: Associations in Data
Lesson 1: Creating a Scatter PlotUnit 6
Lesson 1: Click Battle
Sub-Unit 1: Associations in Data
Lesson 2: Interpreting Points on a Scatter PlotUnit 6
Lesson 3: Robots
Lesson 3: Observing Patterns in a Scatter PlotUnit 6
Lesson 7: Scatter Plot City
Lesson 4: Fitting a Line to DataUnit 6
Lesson 4: Dapper Cats
Lesson 5: Fit Fights
Lesson 5: Using a Linear ModelUnit 6
Lesson 6: Interpreting Slopes
Lesson 6: Interpreting Slope and y-interceptUnit 6
Lesson 6: Interpreting Slopes
Lesson 7: Analyzing Bivariate DataUnit 6
Lesson 8: Animal Brains
Lesson 8: Looking for AssociationsUnit 6
Lesson 9: Tasty Fruit
Lesson 9: Using Data Displays to Find AssociationsUnit 6
Lesson 10: Finding Associations
Lesson 11: Federal Budgets

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Grade K

Unit 1: Math Is…

Lesson 1-2: Math is Exploring and ThinkingConnecting Cubes

Unit 4: Sort, Classify and Count Objects

Lesson 4-1: Alike and DifferentSo Much Sorting
Lesson 4-2: Sort Objects into GroupsSo Much Sorting
Lesson 4-3: Count Objects in GroupsWhat’s that Shape called?
Another Shape

Unit 5: 2-Dimensional Shapes

Lesson 5-1: TrianglesWhat’s that Shape called?
Lesson 5-2: Squares and RectanglesAnother Shape
Lesson 5-4: CirclesWhat’s that Shape called?

Unit 6: Understand Addition

Lesson 6-1: Represent and Solve Add To ProblemsHow Many Objects?
Lesson 6-2: Represent and Solve More Add to ProblemsWhat does it mean to add?
Lesson 6-3: Represent and Solve Put Together ProblemsWhat does it mean to add?

Unit 7: Understand Subtraction

Lesson 7-1: Represent Take Apart ProblemsWhat does it mean to subtract?
Lesson 7-2: Represent and Take From ProblemsWhat does it mean to subtract?

Unit 8: Addition and Subtraction Strategies

Lesson 8-4: Ways to Decompose 6 and 7Harry Explores the Ocean
Lesson 8-6: Ways to Decompose 8 and 9Harry Explores the Ocean
Lesson 8-7: Ways to Make 10Harry Explores Space
Lesson 8-8: Ways to Decompose 10Showing What We Know About 10

Unit 13: Analyze, Compare and Compose Shapes

Lesson 13-1: Compare and Contrast 2-Dimensional ShapesWhat’s that Shape called?

Unit 14: Compare Measurable Attributes

Lesson 14-1: Describe Attributes of ObjectsAnother Shape

Grade 1

Unit 2: Number Patterns

Lesson 2-5: Patterns when Representing Objects in a GroupMeeting Yara

Unit 3: Place Value

Lesson 3-1: Numbers 11 to 19Same Number, Different Ways
Lesson 3-2: Understand 10sBoris’s Thimbles
Lesson 3-4: Represent 2-DigitsSame Number, Different Ways
Lesson 3-5: Represent 2-Digits in Different WaysSame Number, Different Ways

Unit 4: Addition within 20: Facts and Strategies

Lesson 4-1: Relate Counting to AdditionInvestigate: Game Points
Meeting Yara
Lesson 4-5: Make a Ten to AddMaking 10
Lesson 4-9: Find an Unknown Number in an Addition EquationA Community Working Together
Lesson 4-10: Understand The Equal SignKitten Coaster
Lesson 4-11: True Addition EquationsKitten Coaster
Replanting Huli

Unit 5: Subtraction within 20: Facts and Strategies

Lesson 5-1: Relate Counting to SubtractionPacking a Picnic

Unit 7: Meanings of Addition

Lesson 7-1: Represent and Solve Add to ProblemsThe Kalo Plants
Tutu’s Garden in Maui
Lesson 7-2: Represent and Solve More Add to ProblemsHelping Others

Unit 8: Meanings of Subtraction

Lesson 8-1: Represent and Solve Take From ProblemsThe Kalo Plants
Tutu’s Garden in Maui
Lesson 8-2: Represent and Solve More Take From ProblemsHelping Others

Unit 13: Equal Shares

Lesson 13-1: Understand Equal SharesA Bigger Part
Lesson 13-2: Partition Shapes into HalvesFair and Square
Lesson 13-3: Partition Shapes into FourthsFair and Square
Lesson 13-4: Describe the WholeOne of the Parts, All of the Parts
Lesson 13-5: Describe the Halves and Fourths of ShapesOne of the Parts, All of the Parts

Grade 2

Unit 2: Place Value to 1,000

Lesson 2-1: Understand HundredsWhat Makes a Hundred?
Lesson 2-2: Understand 3-digit numbersWhat’s the Value?
Lesson 2-3: Read and Write Numbers to 1000All the Ways!
Lesson 2-4: Decompose 3-digit numbersA New Representation

Unit 3: Patterns within Numbers

Lesson 3-1: Counting PatternsInvestigate: A Mistake in Mom’s Office
Lesson 3-2: Patterns when Skip Counting by 5?What’s that Number?
Lesson 3-3: Patterns when Skip Counting by 10s and 100sLooking for Patterns

Unit 4: Meanings of Addition and Subtraction

Lesson 4-7: Represent and Solve Compare ProblemsAwesome Aquariums

Unit 5: Strategies to Add Fluently Within 100

Lesson 5-9: Add More Than Two NumbersHow Much Money?

Unit 7: Measure and Compare Lengths

Lesson 7-10: Solve Problems using LengthLengths of Jungle Animals

Unit 8: Measurement, Time and Money

Lesson 8-1: Understand the Value of CoinsDiscovering Coins (Part I)
Discovering Coins (Part 2)
Lesson 8-2: Solving Money Problems Using CoinsHow Much Money?

Unit 9: Strategies to Add 3-Digit Numbers

9-2: Represent Addition with 3-Digit NumbersThere’s Something About Berries
9-3: Represent Addition with 3-Digit Numbers With RegroupingBaking with Skunk

Unit 11: Data Analysis

Lesson 11-5: Understand Line PlotsMessy Measurements
Lesson 11-6: Show Data on a Line PlotBracelets and Wristbands

Grade 3

Unit 2: Use Place Value Fluently to Add and Subtract within 1001

Lesson 2-3: Estimate Sums and DifferencesAdding Strategically
Lesson 2-6: Use Partial Sums to AddWhat is an Algorithm
Lesson 2-10: Fluently Add Within 1,000How Would You Solve It?
Determining the Sum of 2 or More Addends

Unit 3: Multiplication and Division

Lesson 3-1: Understand Equal GroupsEqual Groups
Lesson 3-3: Understand the Commutative PropertyArrays of Flavor
Lesson 3-7: Find the UnknownIt’s Chilli In Here!

Unit 4: Use Patterns to Multiply by 0,1, 2, 5 and 11

Lesson 4-6: Solve Problems Using Equal GroupsDivision and Multiplication Equations

Unit 6: Connect Area and Multiplication

Lesson 6-1: Understand AreaTiling Figures
Lesson 6-2: Count Unit Squares to Determine AreaRectangles and Arrays
Unit 2: Lesson 4: Area Hunt

Unit 7: Fractions

Lesson 7-5: Represent Whole Numbers as FractionsCat Crossing
Lesson 7-6: Represent a Greater Than One on a Number LineFractions on the Number Line

Unit 9: Use Multiplication to Divide

Lesson 9-1: Use Multiplication to Solve Division ProblemsRelating Quotients to Familar Products

Unit 12: Measurement and Data

Lesson 12-10: Measure to Halves or Fourths of an InchHow Long Is It?
More Precise Measurements
Lesson 12-11: Show Measurement Data on a Line PlotThe Plot Chickens

Unit 13: Describe and Analyze 2-Dimensional Shapes

Lesson 13-1: Describe and Classify PolygonsPiho’s Shapes
Lesson 13-2: Classify QuadrilateralsRectangles, Squares and Rhombuses

Grade 4

Unit 4: Multiplication as Comparison

Lesson 4-1: Understanding Comparing with MultiplicationRepresenting “Times as Many”
Lesson 4-2: Represent Comparison ProblemsSticker Mania
Lesson 4-3: Solve Comparison Problems Using MultiplicationGoing Swimming

Unit 5: Numbers and Number Patterns

Lesson 5-1: Understand Factors of a NumberHamster Homes
Lesson 5-3: Understand MultiplesFactor or Multiple
Lesson 5-4: Number or Shape PatterrnsHow Does it Grow?
Lesson 5-5: Generate a PatternHow Does it Grow?

Unit 6: Multiplication Strategies with Multi-Digit Numbers

Lesson 6-2: Estimate ProductsA Reasonable Answer
Lesson 6-4: Multiply 2-Digit by 1-Digit FactorsCounting Flowers for Lei
Lesson 6-5: Multiply Multi-Digit 1-Digit FactorsA Lei Making Workshop
Lesson 6-7: Multiply 2-Digit FactorsDouble Decomposition

Unit 9: Addition and Subtractions Meanings and Strategies with Fractions

Lesson 9-2: Represent Adding FractionsPizza Problems
Lesson 9-3: Add Fractions with Like DenominatorsPizza Problems
Lesson 9-4: Represent Subtracting FractionsPizza Problems
Lesson 9-5: Subtract Fractions with Like DenominatorsPizza Problems
Lesson 9-6: Solve Problems Using FractionsPizza Problems

Unit 10: Addition and Subtraction Strategies with Mixed Numbers

Lesson 10-1: Understand Decomposing Mixed NumbersMath Pizzeria

Unit 11: Multiply Fractions by Whole Numbers

Lesson 11-1: Represent Multiplication of a Unit Fraction by a Whole NumberEqual Groups of Fractions

Unit 12: Decimal Fractions

Lesson 12-2: Understand Decimal NotationA New Way to Write Tenths
A New Way to Write Hundredths
Lesson 12-3: Compare DecimalsCan You Compare?

Grade 5

Unit 2: Volume

Lesson 2-2: Use Unit Cubes to Determine VolumePutting It Together
Lesson 2-3: Use Formula to Determine VolumePutting It Together
Lesson 2-4: Determine the Volume of Composite FiguresFigures Made of Prisms

Unit 3: Place Value and Number Relationships

Lesson 3-1: Generalize Place ValuePlace Value Patterns
Lesson 3-4: Compare DecimalsSelling Collectibles
Lesson 3-5: Use Place Value to Round DecimalsWhich Way Down the Mountain?

Unit 5: Multiply Multi-Digit Whole Numbers

Lesson 5-1: Understand Powers and ExponentsMonarch Butterflies
Lesson 5-2: Patterns When Multiplying a Whole Number by Powers of 10All About that Base
Lesson 5-5: Use Partial Products to Multiply Multi-Digit FactorsHow Do They Compare?
Lesson 5-6: Relate Partial Products to an AlgorithmPatrial Products Everywhere
Lesson 5-7: Multiply Multi-Digit Factors FluentlyPatrial Products Everywhere

Unit 6: Multiply Decimals

Lesson 6-1: Patterns when Multiplying Decimals by Powers of 10Powers of 10 Parade

Unit 7: Divide Whole Numbers

Lesson 7-5: Use Partial Quotients to DivideEmptying the Water Tank

Unit 8: Divide Decimals

Lesson 8-1: Division Patterns with Decimals and Patterns of 10Powers of 10 Parade

Unit 10: Multiply Fractions

Lesson 10-3: Represent Multiplication of a Fraction By A FractionMaking Food
Lesson 10-4: Multiply a Fraction By A FractionMaking Food
Lesson 10-5: Determine the Area of Rectanges with Fractional Side LengthsInstalling Turf
Lesson 10-6: Represent Multiplication of Mixed NumbersInstalling Turf
Lesson 10-7: Multiply Mixed NumbersInstalling Turf

Unit 13: Geometry

Lesson 13-2: Plot Ordered Pairs on the Coordinate PlaneBullseye!

Grade 6

Module 1: Ratios and Rates

Reveal MathAmplify Classroom
Lesson 1: Understand ratiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Tables of Equivalent RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Compare Ratio RelationshipsUnit 2
Lesson 4: Fruit Lab
Lesson 6: Convert Customary Measurement UnitsUnit 3
Lesson 1: Many Measurements
Lesson 7: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3
Lesson 9: Lucky Duckies
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Compute with Multi-Digit Numbers and Fractions

Lesson 1: Divide Multi-Digit Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 3: Divide Whole Numbers by FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Divide Fractions by FractionsUnit 4
Lesson 6: Fill the Gap
Lesson 5: Divide with Whole and Mixed NumbersUnit 4
Lesson 6: Fill the Gap

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Compare and Order IntegersUnit 7
Lesson 4: Order in the Class

Module 5: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions
Lesson 4: Evaluate Algebraic Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 6: Use the Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 7: Equivalent Algebraic ExpressionsUnit 6
Lesson 1: Weight for It

Module 6: Relationships in Geometry

Lesson 2: One-Step Addition Equations
Lesson 3: One-Step Subtraction Equations
Unit 6
Lesson 1: Weight for It
Lesson 6: InequalitiesUnit 7
Lesson 7: Tunnel Travels

Module 7: Relationships Between Two Variables

Lesson 4: Multiple RepresentationsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Module 8: Area

Module 9: Volume and Surface Area

Lesson 2: Surface Area of Rectangular PrismsUnit 1
Lesson 10: Renata’s Stickers

Module 10: Statistical Measures and Displays

Lesson 1: Statistical QuestionsUnit 8
Lesson 3: Minimum Wage
Lesson 2: Dot Plots and HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 7: Interpret Graphical DisplaysUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Proportional Relationships

Reveal MathAmplify Classroom
Lesson 1: Unit Rates Involving Ratios of FractionsUnit 2
Lesson 1: Paint
Lesson 3: Tables of Proportional ReasoningUnit 2
Lesson 1: Paint
Lesson 4: Graphs of Proportional ReasoningUnit 2
Lesson 8: Dino Pops
Lesson 5: Equations of Proportional ReasoningUnit 2
Lesson 6: Two and Two

Module 2: Solve Percent Problems

Lesson 1: Percent of ChangeUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 3: Tips and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 4: DiscountsUnit 4
Lesson 5: Percent Machines

Module 3: Operations with Integers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 4: Operations with Rational Numbers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 5: Simplify Algebraic Expressions

Lesson 2: Add Linear Expressions
Lesson 3: Subtract Linear Expressions
Unit 6
Lesson 10: Collect the Squares
Lesson 4: Solve Inequalities Using Addition or SubtractionUnit 6
Lesson 16: Shira the Sheep

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6
Lesson 16: Shira the Sheep

Module 7: Write and Solve Inequalities

Lesson 6: Wirte and Solve Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Module 8: Geometric Figures

Lesson 1: Vertical and Adjacent AnglesUnit 7
Lesson 4: Missing Measures
Lesson 2: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 4: Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?

Module 9: Measure Figures

Lesson 1: Circumference of CirclesUnit 3
Lesson 3: Measuring Around
Lesson 2: Area of CirclesUnit 3
Lesson 9: Area Challenges

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Module 11: Sampling and Statistics

Lesson 1: Biased and Unbiased SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Make Predictions
Lesson 3: Generate Multiple Samples
Unit 8 
Lesson 10: Crab Island
Lesson 4: Compare Two PopulationsUnit 8
Lesson 10: Crab Island

Grade 8

Module 1: Exponents and Scientific Notation

Reveal MathAmplify Classroom
Lesson 1: Powers and ExponentsUnit 7 
Lesson 1: Circles
Lesson 2: Multiply and Divide MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 3: Power of MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 5: Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 6: Compute with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: Real Numbers

Lesson 2: RootsUnit 8
Lesson 4: Root Down

Module 3: Solve Equations with Variables on Each Side

Lesson 1: Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 2: Write and Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Determine the Number of Solutions

Module 4: Linear Relationships and Slope

Lesson 1: Proportional Relationships and SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Slope of a LineUnit 3
Lesson 4: Flags
Lesson 5: Slope-Intercept FormUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Graph Linear EquationsUnit 3
Lesson 4: Flags
Unit 5
Lesson 5: The Tortoise and the Hare

Module 5: Functions

Lesson 1: Identify FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 6: Qualitative GraphsUnit 5
Lesson 5: The Tortoise and the Hare

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 11: Make Them Balance

Module 7: Triangles and the Pythagorean Theorem

Lesson 2: Angle Relationships and TrianglesUnit 1 
Lesson 12: Puzzling It Out

Module 8: Transformations

Lesson 1: Translations
Lesson 2: Reflections
Lesson 3: Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 4: DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Module 9: Congruence and Similarity

Lesson 3: Similarity and TransformationsUnit 2
Lesson 6: Social Scavenger Hunt

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volume of ConesUnit 5
Lesson 13: Cones

Module 11: Scatter Plots and Two-Way Tables

Lesson 1: Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 2: Draw Lines of FitUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 4: Two-Way TablesUnit 6
Lesson 11: Finding Associations
Lesson 5: Associations in Two-Way TablesUnit 6
Lesson 11: Finding Associations

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Families and caregivers, welcome to Amplify Desmos Math California K–5!

Welcome to the Amplify Desmos Math California K–5 Caregiver Hub. We hope your student enjoys exploring math, working with friends to solve problems, and learning new and interesting concepts. And we hope you enjoy the math journey with them! Below are some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math California.

Para la versión en español, haga clic aquí.

Three children are engaging in a math activity with a grid and orange markers. One child holds a "9-3" card. The background includes beach elements and abstract math symbols.

Caregiver Unit Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of key concepts, plus a problem from the lesson practice set you can work through with your student. You’ll find a Caregiver Resource for each unit, in both English and Spanish.

Unit 1: Math in Our World

Unit 2: Numbers 1–10

Unit 3: Flat Shapes All Around Us

Unit 4: Understanding Addition and Subtraction

Unit 5: Make and Break Apart Numbers Within 10

Unit 6: Numbers 0–20

Unit 7: Solid Shapes All Around Us

Unit 1: Adding, Subtracting, and Working With Data

Unit 2: Addition and Subtraction Story Problems

Unit 3: Adding and Subtracting Within 20

Unit 4: Numbers to 99

Unit 5: Adding Within 100

Unit 6: Measuring Lengths of Up to 120 Length Units

Unit 7: Geometry and Time

Unit 1: Working With Data and Solving Comparison Problems

Unit 2: Adding and Subtracting Within 100

Unit 3: Measuring Length

Unit 4: Addition and Subtraction on the Number Line

Unit 5: Numbers to 1,000

Unit 6: Geometry and Time

Unit 7: Adding and Subtracting Within 1,000

Unit 8: Equal Groups

Unit 1: Introducing Multiplication

Unit 2: Area and Multiplication

Unit 3: Wrapping Up Addition and Subtraction Within 1,000

Unit 4: Relating Multiplication to Division

Unit 5: Fractions as Numbers

Unit 6: Measuring Length, Time, Liquid Volume, and Weight

Unit 7: Two-Dimensional Shapes and Perimeter

Unit 1: Factors and Multiples

Unit 2: Fraction Equivalence and Comparison

Unit 3: Extending Operations to Fractions

Unit 4: From Hundredths to Hundred Thousands

Unit 5: Multiplicative Comparison and Measurement

Unit 6: Multiplying and Dividing Multi-Digit Numbers

Unit 7: Angles and Properties of Shapes

Unit 1: Volume

Unit 2: Fractions as Quotients and Fraction Multiplication

Unit 3: Multiplying and Dividing Fractions

Unit 4: Multiplication and Division With Multi-Digit Whole Numbers

Unit 5: Place Value Patterns and Decimal Operations

Unit 6: More Decimal and Fraction Operations

Unit 7: Shapes on the Coordinate Plane

Unit refresh videos

Unit 1

  • Sub-Unit 2 – Answering the Question “Are There Enough?”
  • Sub-Unit 3 – Counting and Cardinality

Unit 2

  • Sub-Unit 1 – Comparing 2 Groups Using the Terms More, Fewer, and Same
  • Sub-Unit 2 – Counting Objects in Different Orders
  • Sub-Unit 3 – Making Groups to Represent Numerals
  • Sub-Unit 4 – Comparing Written Numbers

Unit 3

  • Sub-Unit 1 – Identifying Circles and Triangles in Different Sizes and Orientations
  • Sub-Unit 2 – Using Positional Words to Describe the Location of Shapes

Unit 4

  • Sub-Unit 1 – Adding and Subtracting Within 10
  • Sub-Unit 2 – Representing Addition and Subtraction Story Problems
  • Sub-Unit 3 – Finding the Values of Expressions

Unit 5

Unit 1

  • Sub-Unit 1 – Organizing Data to Count How Many in Each Category
  • Sub-Unit 2 – Counting on to Add and Counting Back to Subtract
  • Sub-Unit 3 – Representing 2 Categories of Data With Addition Equations

Unit 2

  • Sub-Unit 1 – Representing and Solving Add To, Change Unknown Story Problems
  • Sub-Unit 2 – Using Addition or Subtraction to Find an Unknown Part of a Total Amount
  • Sub-Unit 3 – Solving Compare, Difference Unknown Problems
  • Sub-Unit 4 – Making Sense of Story Problems With Different Questions

Unit 3

  • Sub-Unit 1 – Finding a Difference Using the Relationship Between Addition and Subtraction
  • Sub-Unit 2 – Using the Structure of Teen Numbers to Find Missing Addends
  • Sub-Unit 3 – Breaking Apart Addends to Make 10 When Adding
  • Sub-Unit 4 – Subtracting From Teen Numbers in Parts to Get to 10

Unit 4

  • Sub-Unit 1 – Adding a Ten To and Subtracting a Ten From Multiples of 10
  • Sub-Unit 2 – Representing and Writing Two-Digit Numbers
  • Sub-Unit 3 – Comparing Two-Digit Numbers
  • Sub-Unit 4 – Representing the Same Two-Digit Number With Different Amounts of Tens and Ones

Unit 5

  • Sub-Unit 1 – Adding a Number of Tens or Ones to a Two-Digit Number
  • Sub-Unit 2 – Adding a Two-Digit Number and a One-Digit Number When Composing a Ten is Necessary
  • Sub-Unit 3 – Adding a Two-Digit Number and a Two-Digit Number When Composing a Ten is Necessary

Unit 1

  • Sub-Unit 1 – Choosing Strategies to Add Within 20
  • Sub-Unit 2 – Representing Data in a Picture Graph and Bar Graph
  • Sub-Unit 3 – Finding the Difference Between 2 Categories Shown on a Bar Graph

Unit 2

  • Sub-Unit 1 – Strategies to Solve Story Problems Involving Money
  • Sub-Unit 2 – Decomposing a Ten When Subtracting by Place
  • Sub-Unit 3 – Making Sense of Story Problems About Comparing That Use the Word More
  • Sub-Unit 4 – Making Sense of One- and Two-Step Story Problems

Unit 3

  • Sub-Unit 1 – Measuring the Length of an Object in Centimeters Using a Ruler
  • Sub-Unit 2 – Measuring Objects in Inches and Feet
  • Sub-Unit 3 – Representing Measurement Data on a Line Plot

Unit 4

  • Sub-Unit 1 – Locating Numbers on Number Lines
  • Sub-Unit 2 – Representing Addition and Subtraction Strategies on a Number Line

Unit 5

  • Sub-Unit 1 – Composing Hundreds to Represent Three-Digit Numbers
  • Sub-Unit 2 – Comparing Three-Digit Numbers

Unit 1

  • Sub-Unit 1 – Representing Equal-Groups Situations With Equal-Groups Drawings
  • Sub-Unit 2 – Representing Arrays With Multiplication Equations
  • Sub-Unit 3 – Representing Data Using Scaled Bar Graphs

Unit 2

  • Sub-Unit 1 – Determining the Area of a Rectangle Using Counting and Skip Counting
  • Sub-Unit 2 – Determining the Area of a Rectangle Using Multiplication
  • Sub-Unit 3 – Decomposing to Determine the Area of Rectilinear Figures

Unit 3

  • Sub-Unit 1 – Using the Expanded Form and Partial Sums Algorithms to Add
  • Sub-Unit 2 – Using the Expanded Form Algorithm to Subtract
  • Sub-Unit 3 – Rounding Numbers to the Nearest Hundred and Ten Using Number Lines
  • Sub-Unit 4 – Representing and Solving Two-Step Story Problems Involving Multiplication

Unit 4

  • Sub-Unit 1 – Representing Division Situations With Equal-Groups Drawings
  • Sub-Unit 2 – Representing an Equal-Groups Problem With a Division and Multiplication Equation
  • Sub-Unit 3 – Using the Distributive Property of Multiplication to Multiply a One-Digit Number by a Teen Number
  • Sub-Unit 4 – Decomposing Dividends to Divide

Unit 5

  • Sub-Unit 1 – Writing Unit and Non-Unit Fractions
  • Sub-Unit 2 – Locating Non-Unit Fractions on the Number Line
  • Sub-Unit 3 – Identifying Equivalent Fractions
  • Sub-Unit 4 – Comparing Fractions With the Same Denominator or Same Numerator

Unit 1

  • Sub-Unit 1 – Using Factor Pairs to Determine All the Possible Side Lengths of a Rectangle With a Given Area
  • Sub-Unit 2 – Finding Multiples and Common Multiples

Unit 2

  • Sub-Unit 1 – Locating Fractions with Different Denominators On the Same Number Line
  • Sub-Unit 2 – Using Multiples or Factors to Determine Equivalent Fractions
  • Sub-Unit 3 – Comparing Fractions Using Equivalent Fractions With Common Denominators

Unit 3

  • Sub-Unit 1 – Adding and Subtracting Fractions with the Same Denominator
  • Sub-Unit 2 – Multiplying Whole Numbers and Fractions
  • Sub-Unit 3 – Adding Fractions with Denominators of 10 and 100

Unit 4

  • Sub-Unit 1 – Writing Fractions With Denominators of 10 and 100 as Decimals
  • Sub-Unit 2 – Relationships Between Place Values in Multi-Digit Whole Numbers
  • Sub-Unit 3 – Comparing Multi-Digit Numbers
  • Sub-Unit 4 – Using the Standard Algorithm to Subtract When Decomposing is Required

Unit 5

  • Sub-Unit 1 – Representing Multiplicative Comparison Situations
  • Sub-Unit 2 – Converting Measurements in the Metric System
  • Sub-Unit 3 – Comparing Measurements

Unit 1

  • Sub-Unit 1 – Using the Layered Structure of a Rectangular Prism to Determine the Volume
  • Sub-Unit 2 – Determining the Volume of a Rectangular Prism
  • Sub-Unit 3 – Determining the Volume of Figures Composed of Rectangular Prisms

Unit 2

  • Sub-Unit 1 – Representing Equal-Sharing Story Problems with Fractional Quotients
  • Sub-Unit 2 – Representing Fractions with Equivalent Multiplication and Division Expressions
  • Sub-Unit 3 – Determining the Area of a Rectangle With a Fractional Side Length

Unit 3

  • Sub-Unit 1 – Representing Multiplication of 2 Unit Fractions with Diagrams
  • Sub-Unit 2 – Dividing Whole Numbers by Unit Fractions

Unit 4

  • Sub-Unit 1 – Multiplying Multi-digit Whole Numbers Using the Partial Products and Standard Algorithms
  • Sub-Unit 2 – Dividing Multi-Digit Whole Numbers Using Partial Quotients
  • Sub-Unit 3 – Representing Multi-Step Story Problems with Equations

Unit 5

  • Sub-Unit 1 – Comparing Decimals
  • Sub-Unit 2 – Using the Standard Algorithms to Add and Subtract Decimals
  • Sub-Unit 3 – Multiplying a Whole Number and a Decimal Using the Distributive Property
  • Sub-Unit 4 – Dividing Whole Numbers by Decimals Less Than 1

Access Amplify Desmos Math California at home.

In addition to a print Student Edition workbook, your student will have digital access to all learning, practice, and assessment materials through the Amplify platform. The digital curriculum can be accessed in school and at home by following these instructions:

  • Click the Amplify Desmos Math California button.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, caregivers can view student work by opening previous assignments.

Learn how to navigate the student home page.

Materials overview

Amplify Desmos Math California address blended learning with supporting print materials and a unique digital experience. All K–5 lessons are available in a write-in Student Edition book. Many of the lessons include hands-on activities with manipulatives, tools that help students understand abstract concepts by making them tangible. Your student will also work with digital devices for an age-appropriate number of lessons.

When students use devices, teachers can monitor their work in real time, making sure they get the exact support that they need at every part of the lesson, in and outside of class.

Una interfaz digital que muestra los nombres anónimos de los estudiantes y su estado de participación en diversas actividades. La interfaz incluye opciones para realizar resúmenes, capturas de pantalla y vistas individuales de los estudiantes.

Components of a lesson

Students in an Amplify Desmos Math California classroom can be seen (and heard!) asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

A typical Amplify Desmos Math California lesson includes:

  • Warm-up: A short, attention-getting problem to pique students’ interest in the lesson.
  • Activities: One to two mini-activities that challenge students’ problem-solving skills.
  • Synthesis: Discussion to review and bring together the important concepts from the lesson.
  • Show What You Know and Reflection: Questions for students to show what they know from the lesson. (Note: The Show What You Know lesson assessment is optional for kindergarten and grade 1.)
  • Centers: Student-led activity stations that reinforce the math learned during lesson activities through interactive and often game-like formats. In kindergarten and grade 1, time for Centers is built into the last 15 minutes of every lesson.

To support, strengthen, and stretch students’ learning after the lesson, Amplify Desmos Math California offers options for:

  • Differentiation: Mini-Lessons, Centers, Extensions, Boost Personalized Learning, and Fluency Practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. If your student has already completed the practice problems for the lesson, ask them to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your student follow-up questions to encourage the use of math language as they explain their thinking, such as, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students are stuck, ask support questions, such as, “What information do you know here?” or “How could you represent this problem?”

Your student’s teacher may introduce a Center game with students in the lesson or beyond the lesson. These games are aligned to the math of the unit and can be played with students outside of class. Your student’s teacher may introduce a Center game to students during or after completing a lesson, or you may need to teach the game before you play by using easy-to-follow instructions. Sign up for a free account to explore Centers and additional K–5 content in our Featured Collections.

Each unit in Amplify Desmos Math begins with a read-aloud story to engage students and provide context for the math of the unit. Elements and characters from the Unit Story then appear in lessons throughout the unit.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Relate math to daily activities at home, whether grocery shopping, preparing a meal, or planning for a trip to the store. Your student can help you figure out how many more apples there are than oranges in the grocery cart, show how to split a sandwich into fourths, or figure out how much change you’ll receive in exchange for a $10 bill. Encourage your student to point out ways that you use math in your daily tasks.

Remind your student that getting stuck is part of the process and a necessary—beneficial, even!—part of learning. Many students (and adults) fear making mistakes. But research shows that making mistakes helps our brains grow. When your student gets stuck on a problem, encourage them to keep trying different strategies, even if they’re not sure if they are right.

Get more information.

Have a question about Amplify Desmos Math California? Visit our help library to search for articles with answers to your program questions. For additional support, please contact your student’s teacher.

Grade K

Topic Opener Numbers 0 to 5

Topic Opener Numbers 0 to 5Connecting Cubes

Topic 1: Numbers 0 to 5

Lesson 1-2 Recognize 1, 2, and 3 in Different ArrangementsSkye’s Style
Lesson 1-5 Recognize 4 and 5 in Different ArrangementsMatching Groups
Designing Shoes with Skye
3-ACT MATH: Set the TableInvestigate: Cafeteria Math

Topic 3: Numbers 6 to 10

Lesson 3-2: Read, Make, and Write 6 and 7Moving and Grooving
Lesson 3-4: Read, Make, and Write 8 and 9Moving and Grooving
Lesson 3-6: Read, Make, and Write 10Moving and Grooving
Lesson 3-7: Count Numbers to 10Fingers as Math Tools

Topic 4: Compare Numbers 0 to 10

Lesson 4-1: Compare Groups to 10 by MatchingMore, Fewer, or the Same
Forest Friends
Lesson 4-2: Compare Numbers Using Numerals to 10Fingers and Counters
Lesson 4-3: Compare Groups to 10 by CountingComparing Words

Topic 6: Understand Addition

Interactive Math StoryInvestigate: Casey’s Town
Lesson 6-1: Explore AdditionHow Many Objects in Pictures?
The Bus Depot
Lesson 6-2: Represent Addition as Adding ToHow Will You Count?
Lesson 6-3: Represent Addition as Putting TogetherHow Many Objects?
Lesson 6-4: Represent and Explain Addition with EquationsWhat Does It Mean to Add?

Topic 7: Understand Subtraction

Lesson 7-1: Explore SubtractionWhat Does It Mean to Subtract?
The Bus Depot

Topic 8: More Addition and Subtraction

Lesson 8-5: Decompose 6 and 7 to Solve ProblemsHarry Explores the Ocean
Lesson 8-6: Decompose 8 and 9 to Solve ProblemsHarry Explores the Ocean
Lesson 8-8: Decompose 10 to Solve ProblemsHarry Explores the Ocean

Topic 12: Identify and Describe Shapes

Lesson 12-2: Circles and TrianglesWhat’s That Shape Called?
Lesson 12-3: Squares and Other RectanglesAnother Shape

Topic 13: Analyze, Compare, and Create Shapes

Lesson 13-1: Analyze and Compare Two-Dimensional (2-D) ShapesAnother Shape
So Much Sorting

Grade 1

Topic 1: Understand Addition and Subtraction

Lesson 1-4: Take FromPacking for a Picnic
What’s the Difference?
Lesson 1-7: Change UnknownReplanting Huli
Lesson 1-8: Practice Adding and SubtractingLeaping Lily Pads!

Topic 2: Fluently Add and Subtract Within 10

enVision STEM ProjectA Community Working Together
Topic 2 Interactive Math StoryInvestigate: Let’s Grow!
Lesson 2-8: Solve Word Problems with Facts to 10Tutu’s Garden in Maui
The Kalo Plants
Helping Others

Topic 3: Addition Facts to 20: Use Strategies

Lesson 3-5: Make 10 to AddMaking 10
Lesson 3-6: Continue to Make 10 to AddKitten Coaster

Topic 6: Represent and Interpret Data

Lesson 6-1: Organize Data into Three CategoriesShapes Ying Saw

Topic 7: Extend the Counting Sequence

Lesson 7-1: Count by 10s to 120Meeting Yara
Grade 1 Lesson 7-5: Count on an Open Number LineTime to Line Up!
Grade 1 Lesson 7-5: Count on an Open Number LineWhat’s That Number?

Topic 8: Understand Place value

Lesson 8-1: Make Numbers 11 to 19Same Number, Different Ways
Lesson 8-2: Numbers Made with TensInvestigate: Game Points
It’s a Match

Topic 9: Compare Two-Digit Numbers

Lesson 9-3: Compare NumbersInvestigate: Where Am I?
Grade 1 Lesson 9-5: Compare Numbers on a Number LineGreater Than, Less Than, or Equal to
Grade 1 Lesson 9-5: Compare Numbers on a Number LineIn Full Bloom

Topic 10: Use Models and Strategies to Add Tens and Ones

Lesson 10-1: Add Tens Using ModelsHow Many Cubes?
Boris’s Thimbles
How Many Tens?

Topic 11: Use Models and Strategies to Subtract Tens

Lesson 11-1: Subtract Tens Using ModelsBoris’s Thimbles
Lesson 11-2: Subtract Tens Using a Hundred ChartHow Many Tens?

Topic 14: Reason with Shapes and Their Attributes

Lesson 14-1: Use Attributes to Define Two-Dimensional (2-D) ShapesShapes Ying Saw

Grade 2

Topic 1: Fluently Add and Subtract Within 20

Lesson 1-1: Addition Fact StrategiesExploring Within 10
Lesson 1-3: Make a 10 to AddWays to Make 10

Topic 8: Work with Time and Money

Lesson 8-1: Solve Problems with CoinsInvestigate: Activities at the Block Party
Discovering Coins (Part 1)
Discovering Coins (Part 2)
Lesson 8-2: Continue to Solve Problems with CoinsHow Much Money?
Discovering Coins (Part 2)
Lesson 8-5: Problem Solving: ReasoningThe Toy Stand
The Craft Stand at the Block Party

Topic 12: Measuring Length

Lesson 12-8: Compare LengthsLengths of Jungle Animals

Topic 15: Graphs and Data

Lesson 15-1: Line PlotsMessy Measurements
Lesson 15-2: More Line PlotsBracelets and Wristbands
Lesson 15-3: Bar GraphsAwesome Aquariums

Grade 3

Topic 1: Understand Multiplication and Division of Whole Numbers

Lesson 1-1: Relate Multiplication and AdditionEqual Groups
Lesson 1-3: Arrays and PropertiesArrays of Flavor

Topic 4: Use Multiplication to Divide: Division Facts

Lesson 4-1: Relate Multiplication and DivisionIt’s Chili in Here
Relating Quotients to Familiar Products
Lesson 4-8: Solve Multiplication and Division EquationsDivision and Multiplication Equations

Topic 6: Connect Area to Multiplication and Addition

Lesson 6-1: Cover RegionsInvestigate: Comparing Rugs
Which Covers More Space?
Lesson 6-2: Area: Nonstandard UnitsTiling Figures
Lesson 6-3: Area: Standard UnitsArea Hunt
Lesson 6-4: Area of Squares and RectanglesRectangles and Arrays

Topic 7: Represent and Interpret Data

Lesson 7-3: Make Bar GraphsPuppy Pile
2, 5, or 10?

Topic 8: Use Strategies and Properties to Add and Subtract

Topic 8 VocabularyInvestigate: Create a Photo Gallery
Lesson 8-2: Algebra: Addition PatternsPanda Patterns
Lesson 8-3: Mental Math: AdditionHow Would You Solve It?

Topic 9: Fluently Add and Subtract within 1,000

Lesson 9-1: Use Partial Sums to AddAdding Your Way
What is an Algorithm?
Lesson 9-2: Use Regrouping to AddUsing Fewer Digits
Lesson 9-3: Add 3 or More NumbersDetermining Sums of 2 or More Addends
Lesson 9-6: Use Strategies to Add and SubtractAdding Strategically

Grade 4

Topic 7: Factors and Multiples

3-ACT MATH: Can-Do AttitudeHamster Homes
Lesson 7-2: FactorsFactor or Multiple?
Lesson 7-4: Prime and Composite NumbersA Number Game
Lesson 7-5: MultiplesFactor or Multiple?
How Does It Grow?

Topic 8: Extend Understanding of Fraction Equivalence and Ordering

Lesson 8-2: Equivalent Fractions: Number LinesInvestigate: Building Your Own Number Line
All Kinds of Fractions
Lesson 8-5: Use Benchmarks to Compare FractionsFraction Strips
Lesson 8-5: Use Benchmarks to Compare FractionsChop It

Topic 9: Understand Addition and Subtraction of Fractions

Lesson 9-1: Model Addition of FractionsPizza Problems
Lesson 9-4: Model Subtraction of FractionsPizza Problems
Lesson 9-2: Decompose FractionsMath Pizzeria

Topic 10: Extend Multiplication Concepts to Fractions

Lesson 10-1: Fractions as Multiples of Unit FractionsEqual Groups of Fractions

Topic 12: Understand and Compare Decimals

Topic 12 Review What You KnowInvestigate: Different Units
Lesson 12-1: Fractions and DecimalsA New Way to Write Tenths
A New Way to Write Hundredths
Lesson 12-2: Fractions and Decimals on the Number LineAre They Equivalent?
What’s the Order?
Lesson 12-3: Compare DecimalsHow Can You Compare?
Robot Factory

Grade 5

Topic 3: Fluently Multiply Multi-Digit Whole Numbers

Lesson 3-5: Multiply 3-Digit by 2-Digit NumbersPartial Products Everywhere
Lesson 3-7: Practice Multiplying Multi-Digit NumbersHow Do They Compare?

Topic 5: Use Models and Strategies to Divide Whole Numbers

Lesson 5-4: Use Partial Quotients to DivideEmptying the Water Tank

Topic 8: Apply Understanding of Multiplication to Multiply Fractions

Lesson 8-3: Multiply Fractions and Whole NumbersMaking Food
Lesson 8-4: Use Models to Multiply Two FractionsInvestigate: Folding Paper
Parts of Parts
One Part of One Part
Lesson 8-5: Multiply Two FractionsMaking Food
Messy Multiplication
Lesson 8-6: Area of a RectangleInstalling Turf
Rows and Columns
Lesson 8-7: Multiply Mixed NumbersApplying Fraction Multiplication
Messy Multiplication
Lesson 8-8: Multiplication as ScalingChores at Animal Haven
The Re-size-inator

Topic 9: Apply Understanding of Division to Divide Fractions

Topic 11: Understand Volume Concepts

Lesson 11-1: Model VolumeWhich is Largest
3-ACT Math: Fill ‘er UpPacking the Barge
Lesson 11-3: Combine Volumes of PrismsPutting It Together
Figures Made of Prisms

Algebra 1

No lessons focused on only shape patterns.

Topic 1: Solving Equations and Inequalities

Lesson 1-2: Solving Linear EquationsWorking Backwards
Solving Strategies
Lesson 1-3: Solving Linear Equations With a Variable on Both SidesSame Position
Lesson 1-4: Literal Equations & FormulasSubway Seats
Various Variables
Lesson 1-5: Solving Inequalities in One VariablePizza Delivery

Topic 2: Linear Equations

Lesson 2-3: Standard FormShelley the Snail
Five Representations

Topic 3: Linear Functions

Lesson 3-4: Arithmetic SequenceMore Visual Patterns
Sequence Carnival
Lesson 3-5: Scatter Plots and Lines of FitCorrelation Coefficient
How Hot Is It?
City Slopes
Lesson 3-6: Analyzing Lines of FitResidual Fruit
Penguin Populations
Behind the Headlines
City Data

Topic 4: Systems of Linear Equations and Inequalities

Lesson 4-1: Solving Systems of Linear Equations by GraphingLizard Lines
Lesson 4-2: Solving Systems of Equations by SubstitutionShape It Up
Lesson 4-5: Systems of Linear InequalitiesQuilts
Seeking Solutions

Topic 5: Piecewise Functions

Lesson 5-2: Piecewise Defined FunctionsCraft-a-Graph
Pumpkin Prices

Topic 6: Exponents and Exponential Functions

Lesson 6-3: Exponential FunctionsCarlos’s Fish
Lesson 6-5: Geometric SequencesRevisiting Visual Patterns, Part 1
Sequence Carnival
More Visual Patterns

Topic 8: Quadratic Functions

Lesson 8-1: Key Features of a Quadratic FunctionRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
On the Fence
Lesson 8-3: Quadratic Functions in Standard FormPlenty of Parabolas
Two for One
Lesson 8-4: Modeling with Quadratic FunctionsStomp Rockets
Robot Launch
Lesson 8-5: Linear, Exponential and Quadratic ModelsSorting Relationships

Topic 9: Solving Quadratic Equations

Lesson 9-1: Solving Quadratics Using Graphs and TablesStomp Rockets
Lesson 9-2: Solving Quadratic Equations by FactoringParabola Zapper
Shooting Stars
Lesson 9-4: Completing the SquareSquare Tactic
Lesson 9-5: The Quadratic Formula and the DiscriminantStomp Rockets in Space

Topic 10: Working with Functions

Lesson 10-1: The Square Root Function ( & average rate of change)Plane, Train, and Automobile
Lesson 10-3: Analyzing Functions Graphically (Abs, Quad, Sq.Root, Exp, Cubic)Craft-a-Graph
Detroit’s Population, Part 1
Detroit’s Population, Part 2
Lesson 10-7: Inverse FunctionsChip the Robot

Topic 11: Statistics

Lesson 11-4: Standard DeviationFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

What’s included in our grades K–2 language arts curriculum

Amplify Core Knowledge Language Arts® (CKLA) is a comprehensive early literacy curriculum, grounded in the Science of Reading. The K–2 curriculum sequences deep content knowledge-building with research-based foundational skills. With Amplify CKLA, you’ll have the instruction and guidance of proven, evidence-based practices to help all of your students become strong readers, writers, and thinkers.

Choose Level

Year at a glance

The Amplify CKLA curriculum is modeled after proven research in early literacy that supports a two-strand approach to literacy instruction in the early years. With this approach, students in Grades K–2 complete one full lesson per day that builds foundational reading skills in the Skills Strand, as well as one full lesson that builds background knowledge in the Knowledge Strand. The deep content knowledge is sequenced together with research-based foundational skills in Grades K–2 so that students develop the early literacy skills necessary to help them become confident readers, as well as build the context to understand what they’re reading. 

In Grades 3–5, lessons combine skills and knowledge with increasingly complex texts, close reading, and a greater emphasis on writing. Students start to use their skills to go on their own independent reading adventures, further opening up their worlds.

Units & domains at a glance

The number of days to complete each Skills Unit and Knowledge Domain varies based on instructional purpose.

Nursery Rhymes and Fables

Well-known fables introduce students to new vocabulary, build phonological awareness, and prompt discussion of character, virtues, and behavior.

Number of Lessons: 12

The Five Senses

Students explore how they learn about the world using their five senses: sight, hearing, smell, taste, and touch.

Number of Lessons: 8

Stories

Students develop an awareness of language and recurring themes in children’s literature, including classic stories, trickster tales, and fiction from other cultures.

Number of Lessons: 10

Plants

Read-aloud texts introduce students to basic knowledge of ecology, parts of plants, how plants grow, and the interdependence of all living things.

Number of Lessons: 11

Farms

Students identify several farm animals and crops and contrast how plants make their food with how animals get their food.

Number of Lessons9

Native Americans

Students explore cultures of three Native American groups, as well as how conditions in different geographical regions influence their ways of life.

Number of Lessons: 8

Kings and Queens

Students listen to read-aloud texts, both fiction and nonfiction, about kings, queens, and royal families, which build students’ understanding of royal customs.

Number of Lessons: 8

Seasons and Weather

This is an introduction to weather and the seasons, where students learn that regions of Earth experience different characteristic weather patterns throughout the year.

Number of Lessons: 8

Columbus and the Pilgrims

A look at the first contact between Europe and the Americas and some of its results.

Number of Lessons: 9

Colonial Towns and Townspeople

Students are introduced to the early history of the United States as they explore what life was like for people in colonial times.

Number of Lessons: 10

Taking Care of the Earth

Students are introduced to the importance of environmental awareness and conservation as they become familiar with the earth’s natural resources.

Number of Lessons: 10

Presidents and American Symbols

Students learn about the legacies of five famous presidents, several national symbols, the branches of government, the role of the president, and elections.

Number of Lessons: 9

Students build phonological awareness through environmental noises, words within sentences, and sounds within words. They learn basic strokes used to form letters.

Students learn how to blend syllables together to form multisyllabic words. They orally produce two- and three-sound words by blending sounds.

Students learn eight new sounds and practice blending them into words. They learn how to write letters that represent the new sounds.

With oral language games, chaining exercises, and shared reading, students practice blending eight new sounds into words and writing the sound-letter correspondences.

Eight new sounds are introduced, including a spelling alternative for /k/. Students continue to practice previously learned sound-letter correspondences.

Students are introduced to consonant clusters, letter names, and rhyming words. Students begin to read text independently using decodable Student Readers.

Students learn about various digraphs. Students practice blending and segmenting the sounds through phonemic awareness and phonics activities, chaining exercises, and reading.

This unit introduces students to double-letter spellings for consonant sounds, as well as seven new high-frequency Tricky Words.

Students practice writing uppercase letters and learn 17 new Tricky Words. Students answer comprehension questions about stories in the Student Reader.

Students learn the basic code spelling for the five long vowel sounds. Students are administered a cumulative end-of-year assessment.

Fables and Stories

Students are introduced to fables and stories, increase vocabulary and reading comprehension skills, and become familiar with the key elements of a story.

Number of Lessons: 10

The Human Body

Students are introduced to the systems of the human body, care of the body, germs and disease, vaccines, and keys to good health.

Number of Lessons: 10

Different Lands, Similar Stories

Students encounter cultures from around the world as they explore the ways in which folktales from different lands treat similar themes or characters.

Number of Lessons: 9

Early World Civilizations

Students explore Mesopotamia and Egypt and learn about the importance of rivers, farming, writing, laws, art, and beliefs.

Number of Lessons: 16

Early American Civilizations

Students compare and contrast key features of the early civilizations of the Maya, Aztec, and Inca, and explore the development of cities.

Number of Lessons: 11

Astronomy

In this introduction to the solar system, students learn about Earth in relation to the moon, other planets, the sun, and the stars.

Number of Lessons: 9

The History of the Earth

Students learn about the geographical features of Earth’s surface, the layers of the earth, rocks and minerals, volcanoes, geysers, fossils, and dinosaurs.

Number of Lessons: 8

Animals and Habitats

Students focus on the interconnectedness of living things as they learn what a habitat is and explore specific types of habitats.

Number of Lessons: 9

Fairy Tales

Students learn about the Brothers Grimm, identify common elements of fairy tales, make interpretations, and compare and contrast different tales.

Number of Lessons: 9

A New Nation: American Independence

Students are introduced to important historical figures and events in the story of how the 13 colonies became an independent nation.

Number of Lessons: 12

Frontier Explorers

Students are introduced to exploration of the American West, its key figures, and how colonists spread westward, including their interactions with native peoples.

Number of Lessons: 11

Unit 1 provides a review of the sounds/spellings taught in the CKLA Kindergarten curriculum. Teachers administer the beginning-of-year assessment.

Students read and write words with long vowel spellings and learn new Tricky Words. The unit also includes grammar lessons on nouns.

Work continues on vowel sounds and their spellings. Grammar focus is on verbs and verb tense. Formal instruction in the writing process begins.

Students work with /r/-controlled vowel sounds. Students practice segmenting two-syllable words. Adjectives are introduced as students practice descriptive writing.

Students work with spelling alternatives for sounds. Students also learn to identify sentence types. They plan, draft, and edit opinion letters.

Students continue to work with several spelling alternatives for sounds. Students review nouns and pronouns. They plan, draft, and edit personal narratives.

Students focus on spelling alternatives for sounds. Students plan, draft, and edit an informative/explanatory text. Students are administered an end-of-year assessment.

Fairy Tales and Tall Tales

Students consider characteristic elements of fairy tales and tall tales and consider problems faced by the characters and lessons each story conveys.

Number of Lessons: 8

Early Asian Civilizations

Students are introduced to Asia, specifically India and China. In addition, students are introduced to related folktales and poetry.

Number of Lessons: 14

Ancient Greek Civilization

Students explore the civilization of ancient Greece, which lives on in many ways—in our language, government, art, architecture, the Olympics, and more.

Number of Lessons: 12

Greek Myths

Building on the Ancient Greek Civilization domain, students explore common characteristics and story elements of several well-known Greek myths and mythical characters.

Number of Lessons: 10

The War of 1812

Students are introduced to major figures and events in the War of 1812, sometimes called America’s “second war for independence.”

Number of Lessons: 8

Cycles in Nature

Students are introduced to natural cycles that make life on Earth possible, such as seasonal cycles, life cycles, and the water cycle.

Number of Lessons: 9

Westward Expansion

Students are introduced to an important period in the history of the United States—the time of westward expansion during the 1800s.

Number of Lessons: 9

Insects

Students learn about the helpful and harmful characteristics of insects, insect life cycles, and social insects such as bees and ants.

Number of Lessons: 8

The U.S. Civil War

Students learn about the controversy between the North and the South over slavery and about key historical figures during that time.

Number of Lessons: 11

Human Body: Building Blocks and Nutrition

Students learn about the human body, including body systems, good nutrition, keys to good health, and the advances in microbiology made by Anton van Leeuwenhoek.

Number of Lessons: 9

Immigration

Students explore the idea of e pluribus unum and the importance of immigration in the history of the United States.

Number of Lessons: 10

Women in early 20th-century clothing march with signs for voting rights and justice in front of a yellow bus labeled "Cleveland Ave.," making history that can inspire lessons in a K–2 language arts curriculum.
Fighting for a Cause

Students explore the connection between ideas and actions, and see how people can do extraordinary things to change the dominant ideas and actions of an entire nation.

Number of Lessons: 9

Un contorno simplificado de un gato saltando para atrapar una mariposa, sobre un fondo verde con varias ilustraciones relacionadas con gatos y palabras como "saltar" y "leche".

Sound-spellings with an emphasis on consonant sounds, one- and two-syllable words, and Tricky Words are reviewed. The beginning-of-year assessment is administered.

Ilustración de un animal verde sobre un fondo verde con varios objetos delineados como una cama, un conejo, una nube y sonidos fonéticos.

The unit focus is on various sound-spellings and words with one- and two-syllables. Students begin the writing process, writing narratives and opinions.

Fondo verde con el contorno blanco de un birrete de graduación en el centro, rodeado de varios garabatos educativos y relacionados con logros, como un trofeo, una cinta y una portería de fútbol.

Practice with spelling alternatives continues. Grammar focuses on capitalization, quotation marks, ending punctuation, and common and proper nouns. Students write personal narratives.

Ilustración de un paisaje urbano con varios símbolos que incluyen un tren subterráneo, una panadería, la Estatua de la Libertad y carteles que dicen "ahora contratando" y "ciudad/ee" sobre un fondo verde.

Students practice a range of spelling alternatives. Students practice persuasive writing as part of a friendly letter. Students learn more about nouns and verbs.

Students practice chunking sounds as they read multisyllabic words. Grammar work includes adjectives, subjects, and predicates. Writing includes rewriting a story ending.

Students review advanced phonics and grammar skills. Students are introduced to expository/report writing. Students take an end-of-year assessment.

Program components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

Knowledge Strand Teacher Guide

Knowledge Strand Teacher Guides contain Amplify CKLA’s cross-curricular read-alouds and application activities, all of which are standards-based to build mastery of content knowledge and literacy skills. There is one Teacher Guide per Knowledge Domain.

Print or digital

Knowledge classroom materials

Amplify CKLA includes oversized Flip Books and smaller Image Cards that bring each topic to life through vivid visuals.

Print or digital

Skills Strand Teacher Guide

Amplify CKLA Skills Strand Teacher Guides include comprehensive research-based instruction in phonological and phonemic awareness, phonics, print concepts, the alphabetic principle, grammar, writing mechanics, comprehension, spelling, and other critical foundational literacy skills.

Print or digital

Hands-on Skills ancillaries

Dynamic classroom materials include student Chaining Folders, Small and Large Letter Cards, Spelling Cards, Sound Cards, Big Books, Vowel and Consonant Code Flip Books, Code Charts, and more.

Print or digital

Assessment and Remediation Guide

The unit-by-unit Assessment and Remediation Guide provides thousands of pages of activities for reteaching, differentiation, and additional practice.

Print or digital

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Component

FORMAT

Knowledge Strand Activity Books

Knowledge Strand Activity Books provide students with the opportunity to deepen world and word knowledge by responding to text in a diversity of ways.

Print

Skills Strand Student Reader

Unique decodable Student Readers provide direct practice with just-learned sound-spelling patterns, using compelling stories and characters to integrate phonics and comprehension.

Print

Skills Strand Activity book

Skills Strand Activity Books support the program’s connected approach to reading and writing, providing ample opportunities to respond to text while building core skills.

Print

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

Grade 6

Unit 1: Numbers

GO Math!Desmos Math 6–A1
Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 4.2: Dividing FractionsUnit 4
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 4.3: Dividing Mixed NumbersUnit 4
Lesson 8: Potting Soil
Lesson 10: Swap Meet
Practice Day
Lesson 4.4: Solving Multistep Problems with Fractions and Mixed NumbersUnit 4
Lesson 11: Classroom Comparisons
Lesson 12: Puzzling Areas [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner
Module 5: Operations with Decimals
Lesson 5.1: Dividing Whole NumbersUnit 5
Lesson 9: Long Division Launch
Lesson 10: Return of Long Division
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5.3: Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying With Areas
Lesson 7: Multiplication Methods
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 10: Return of Long Division
Lesson 11: Movie Time [Free lesson]
Lesson 5.5: Applying Operations with Rational NumbersUnit 5
Practice Day 1
Lesson 12: Budget Vehicles
Lesson 13: Grocery Prices

Unit 2: Number Operations

Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap [Free lesson]
Lesson 7: Break It Down
Lesson 4.2: Dividing FractionsUnit 4
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 10: Swap Meet (Print available)
Practice Day (Print available)
Lesson 4.3: Dividing Mixed NumbersUnit 4
Lesson 8: Potting Soil
Lesson 10: Swap Meet (Print available)
Practice Day
Lesson 4.4: Solving Multistep Problems with Fractions and Mixed NumbersUnit 4
Lesson 11: Classroom Comparisons
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Module 5: Operations with Decimals
Lesson 5.1: Dividing Whole NumbersUnit 5
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of Long Division
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5.3: Multiplying DecimalsUnit 5
Lesson 5: Decimal Multiplication
Lesson 6: Multiplying With Areas
Lesson 7: Multiplication Methods (Print available)
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 10: Return of Long Division (Print available)
Lesson 11: Movie Time [Free lesson]
Lesson 5.5: Applying Operations with Rational NumbersUnit 5
Practice Day 1 (Print available)
Lesson 12: Budget Vehicles (Print available)
Lesson 13: Grocery Prices (Print available)

Unit 3: Proportionality, Ratios, and Rates

Module 6: Representing Ratios and Rates
Lesson 6.1: RatiosUnit 2
Lesson 1: Pizza Maker [Free lesson]
Lesson 2: Ratio Rounds (Print available)
Lesson 3: Rice Ratios (Print available)
Lesson 7:  Mixing Paint, Part 1
Lesson 12: Mixing Paint, Part 2
Lesson 6.2: Rates Unit 2
Lesson 8: World Records (Print available)
Unit 3
Lesson 4: Model Trains
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory (Print available)
Lesson 7: More Soft Serve
Lesson 13: A County as a Village
Lesson 6.3: Using Ratios and Rates to Solve ProblemsUnit 2
Lesson 4: Fruit Lab [Free lesson]
Lesson 5: Balancing Act
Lesson 6: Product Prices (Print available)
Lesson 9: Disaster Preparation [Free lesson]
Lesson 10: Balloons
Lesson 11: Community Life (Print available)
Lesson 13:City Planning
Lesson 14: Lunch Waste (Print available)
Module 7: Applying Ratios and Rates
Lesson 7.1: Ratios, Rates, Tables, and GraphsUnit 2
Lesson 4: Fruit Lab [Free lesson]
Lesson 6: Product Prices (Print available)
Lesson 9: Disaster Preparation [Free lesson]
Unit 3
Lesson 5: Soft Serve [Free lesson]
Lesson 6: Welcome to the Robot Factory
Lesson 7.2: Solving Problems with Proportions
Lesson 7.3: Converting Within Measurement SystemsUnit 3
Lesson 2: Counting Classrooms
Lesson 7.4: Converting Between Measurement SystemsUnit 3
Lesson 3: Pen Pals
Module 8:  Percents
Lesson 8.1 Understanding Percent.Unit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 9: Bicycle Goals
Lesson 8.2: Percents, Fractions, and Decimals.Unit 3
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village
Lesson 8.3: Solving Percent ProblemsUnit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing? (Print available)
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Lesson 13: A Country as a Village

Unit 4: Equivalent Expressions

Module 9: Generating Equivalent Numerical Expressions
Lesson 9.1: ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Lesson 12: Squares and Cubes
Lesson 9.2: Prime Factorization
Lesson 9.3: Order of Operations
Module 10: Generating Equivalent Algebraic Expressions
Lesson 10.1: Modeling and Writing Expressions
Lesson 10.2: Evaluating Expressions
Unit 6
Lesson 6: Vari-apples
Lesson 8: Products and Sums [Free lesson]
Lesson 9: Products, Sums, and Differences (Print available)
Lesson 10.3: Generating Equivalent ExpressionsUnit 6
Lesson 7: Border Tiles
Lesson 8: Products and Sums [Free lesson]
Lesson 9: Products, Sums, and Differences (Print available)

Unit 5: Equations and Inequalities

Unit 6: Relationships in Geometry

Unit 7: Measurement and Data

Grade 7

Unit 1: The Number System

GO Math!Desmos Math 6–A1
Module 1:  Adding and Subtracting Integers
Lesson 1.1: Adding Integers With the Same Sign
Lesson 1.2: Adding Integers With Different Signs
Lesson 1.3: Subtracting Integers
Unit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 9: Expressions (Print available)
Lesson 10: Integer Puzzles [Free lesson]
Lesson 1.4:  Applying Addition and Subtraction of IntegersUnit 5
Lesson 11: Changing Temperatures
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Module 2: Multiplying and Dividing Integers
Lesson 2.1: Multiplying Integers Unit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 10: Integer Puzzles [Free lesson]
Lesson 2.2: Dividing IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 10: Integer Puzzles [Free lesson]
Lesson 2.3: Applying Integer OperationsUnit 5
Lesson 8: Speeding Turtles
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Module 3:  Rational Numbers
Lesson 3.1: Rational Numbers and Decimals
Lesson 3.2: Adding Rational Numbers
Lesson 3.3: Subtracting Rational Numbers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 3.4: Multiplying Rational NumbersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 3.5: Dividing Rational Numbers Unit 5
Lesson 6: Floating in Groups
Lesson 3.6: Applying Rational Number OperationsUnit 5
Lesson 8: Speeding Turtles
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)

Unit 2: Ratios and Proportional Relationships

Module 4:  Rates and Proportionality
Lesson 4.1: Unit RatesUnit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 9: Gallon Challenge
Unit 4
Lesson 2: Peach Cobbler (Print available)
Lesson 3: Sticker Sizes
Lesson 4.2: Constant Rates of ChangeUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4:  Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 4.3:  Proportional Relationships and GraphsUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 8: DinoPops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency
Unit 4
Lesson 3: Sticker Sizes
Module 5:  Proportions and Percent
Lesson 5.1: Percent Increase and DecreaseUnit 4
Lesson 1: Mosaics [Free lesson]
Lesson 4: More and Less
Lesson 5: All the Equations
Lesson 7: Percent Machines [Free lesson]
Lesson 9: Minimum Wage (Print available)
Lesson 13: Decimal Deep Dive (Print available)
Lesson 5.2: Rewriting Percent ExpressionsUnit 4
Lesson 9: Minimum Wage
Lesson 5.3: Applications of PercentUnit 4
Lesson 6: 100% (Print available)
Lesson 8: Tax and Tip
Lesson 9: Minimum Wage (Print available)
Lesson 10: Cost of College (Print available)
Lesson 11: Bookcase Builder
Lesson 12: Posing Percent Problems [Free lesson]

Unit 3: Expressions, Equations, and Inequalities

Unit 4: Geometry

Module 8: Modeling Geometric Figures
Lesson 8.1: Similar Shapes and Scale DrawingsUnit 1
Lesson 1: Scaling Machines [Free lesson]
Lesson 2: Scaling Robots
Lesson 3: Make It Scale
Lesson 4: Scale Factor Challenges
Lesson 5: Tiles
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Unit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One?
Lesson 8.2: Geometric DrawingsUnit 1
Lesson 6: Introducing Scale
Lesson 7: Will It Fit? (Print available) [Free lesson]
Lesson 8: Scaling States (Print available)
Lesson 9: Scaling Buildings
Lesson 10: Room Redesign (Print available)
Unit 7
Lesson 8:  Can You Draw It? (Print available)
Lesson 8.3: Cross SectionsUnit 7
Lesson 9: Slicing Solids
Lesson 8.4Angle RelationshipsUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures (Print available) [Free lesson]
Module 9:  Circumference, Area, and Volume
Lesson 9.1: CircumferenceUnit 3
Lesson 3: Measuring Around [Free lesson]
Lesson 9.2: Area of CirclesUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares (Print available)
Lesson 7: Why Pi?
Lesson 8: Area Challenges [Free lesson]
Lesson 9: Circle vs. Square
Lesson 9.3: Area of Composite FiguresUnit 3
Lesson 5: Area Strategies
Lesson 8: Area Challenges [Free lesson]
Lesson 9.4: Solving Surface Area ProblemsUnit 7
Lesson 12: Surface Area Strategies (Print available)
Lesson 13: Popcorn Possibilities
Lesson 9.5: Solving Volume ProblemsUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities

Unit 5: Statistics

Module 10: Random Samples and
Populations
Lesson 10.1: Populations and SamplesUnit 8
Lesson 10: Crab Island [Free lesson]
Lesson 11: Headlines
Lesson 12: Flower Power
Lesson 13: Plots and Samples
Lesson 14: School Newspaper (Print available)
Lesson 15: Asthma Rates (Print available)
Lesson 10.2: Making Inferences from a Random Sample
Lesson 10.3: Generating Random Samples
Unit 8
Lesson 13: Plots and Samples
Lesson 15: Asthma Rate (Print available)
Module 11: Analyzing and Comparing Data
Lesson 11.1: Comparing Data Displayed in Dot PlotsUnit 8
Lesson 14: School Newspaper (Print available)
Lesson 15: Asthma Rates (Print available)
Lesson 11.2: Comparing Data Displayed in Box PlotsUnit 8
Lesson 13: Plots and Samples
Lesson 15: Asthma Rates (Print available)
Lesson 11.3: Using Statistical Measures to Compare PopulationsUnit 8
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 10: Crab Island [Free lesson]
Lesson 15: Asthma Rates (Print available)

Unit 6: Probability

Module 12: Experimental Probability
Lesson 12.1: ProbabilityUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 12.2: Experimental Probability of Simple EventsUnit 8
Lesson 3: Mystery Bag
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 12.3: Experimental Probability of Compound EventsUnit 8
Lesson 7: Weather or Not
Lesson 12.4: Making Predictions with Experimental ProbabilityUnit 8
Lesson 3: Mystery Bag
Lesson 5: Is It Fair?
Module 13: Theoretical Probability and
Simulations
Lesson 13.1: Theoretical Probability of Simple EventsUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 13.2: Theoretical Probability of Compound EventsUnit 8
Lesson 6: Fair Games
Lesson 13.3: Making Predictions with Theoretical ProbabilityUnit 8
Lesson 8: Simulate It! (Print available)
Lesson 13.4: Using Technology to Conduct a SimulationUnit 8
Lesson 7: Weather or Not
Lesson 8: Simulate It! (Print available)

Grade 8

Unit 1: Real Numbers, Exponents, and Scientific Notation

GO Math!Desmos Math 6–A1
Module 1: Real Numbers
Lesson 1.1: Rational and Irrational Numbers
Lesson 1.2: Sets of Real Numbers
Unit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 14: Hit the Target
Lesson 1.3: Ordering Real NumbersUnit 8
Lesson 4: Root Down [Free lesson]
Module 2: Exponents and Scientific
Notation
Lesson 2.1: Integer ExponentsUnit 7
Lesson 1: Circles [Free lesson]
Lesson 2: Combining Exponents
Lesson 3: Power Pairs (Print available) [Free lesson]
Lesson 4: Rewriting Powers
Lesson 5: Zero and Negative Exponents
Lesson 6: Write a Rule (Print available)
Lesson 2.2: Scientific Notation with Positive Powers of 10Unit 7
Lesson 7: Scales and Weights
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 2.3: Scientific Notation with Negative Powers of 10Unit 7
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 2.4: Operations with Scientific NotationUnit 7
Lesson 10: Solar System [Free lesson]
Lesson 11: Balance the Scale [Free lesson]
Lesson 12: City Lights
Lesson 13: Star Power 

Unit 2: Proportional and Nonproportional Relationships and Functions

Module 3: Proportional Relationships
Lesson 3.1: Representing Proportional Relationships.Unit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 3.2: Rate of Change and SlopeUnit 2
Lesson 9: Water Slide
Lesson 10: Points on a Line
Unit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Coin Capture
Unit 5
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3.3: Interpreting the Unit Rate as SlopeUnit 3
Lesson 2: Water Tank
Lesson 3: Posters
Module 4: Nonproportional Relationships
Lesson 4.1: Representing Linear Nonproportional RelationshipsUnit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 4.2: Determining Slope and y-interceptUnit 3
Lesson 5: Flags [Free lesson]
Lesson 4.3: Graphing Linear Nonproportional Relationships using Slope and y-intercept.Unit 3
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 6: Translations
Lesson 9: Coin Capture
Lesson 4.4: Proportional and Nonproportional SituationsUnit 3
Lesson 1: Turtle Time Trials [Free lesson]
Module 5: Writing Linear Equations
Lesson 5.1: Writing Linear Equations from Situations and GraphsUnit 3
Lesson 5: Flags [Free lesson]Lesson 9: Coin Capture
Lesson 5.2: Writing Linear Equations from a Table
Lesson 5.3: Linear Relationships and Bivariate DataUnit 6
Lesson 1: Click Bait
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot City
Lesson 8: Animal Brains
Module 6: Functions
Lesson 6.1: Identifying and Representing FunctionsUnit 5
Lesson 2: Guess My Rule [Free lesson]
Lesson 3: Function or Not?
Lesson 4: Window Frames
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6.2: Describing FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 6.3: Comparing FunctionsUnit 5
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 6.4: Analyzing GraphsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 9: Piecing It Together

Unit 3: Solving Equations and Systems of Equations

Module 7:  Solving Linear Equations
Lesson 7.1: Equations with the Variable on Both SidesUnit 4
Lesson 2: Keep It Balanced
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or None?
Lesson 8: When Are They the Same?
Lesson 7.2: Equations with Rational NumbersUnit 4
Lesson 6: Strategic Solving (Print available)
Lesson 7.3: Equations with the Distributive PropertyUnit 4
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 7: All, Some, or None?
Lesson 7.4: Equations with Many Solutions or No SolutionUnit 4
Lesson 7:  All, Some, or None?
Module 8:  Solving Systems of Linear Equations
Lesson 8.1: Solving Systems of Linear Equations by Graphing.Unit 4
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Lesson 8.2: Solving Systems by SubstitutionUnit 4
Lesson 13: All, Some, or None? Part 2
Lesson 14: Strategic Solving, Part 2 (Print available)
Lesson 8.3: Solving Systems by Elimination
Lesson 8.4: Solving Systems by Elimination with Multiplication
Lesson 8.5: Solving Special SystemsUnit 4
Lesson 13: All, Some, or None? Part 2

Unit 4: Transformational Geometry

Unit 5: Measurement Geometry

Module 11: Angle Relationships in Parallel Lines and Triangles
Lesson 11.1: Parallel Lines Cut by a Transversal.Unit 1
Lesson 10: Transforming Angles
Lesson 12: Puzzling It Out [Free lesson]
Lesson 11.2: Angle Theorems for TrianglesUnit 1
Lesson 11: Tearing It Up (Print available)
Lesson 12: Puzzling It Out [Free lesson]
Lesson 11.3: Angle-Angle SimilarityUnit 2
Lesson 3: Match My Dilation
Lesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 7: Are Angles Enough?
Module 12: Pythagorean Theorem
Lesson 12.1: The Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 10: Taco Truck [Free lesson]
Lesson 12.2: Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 12.3: Distance Between Two PointsUnit 8
Lesson 11: Pond Hopper
Module 13: Volume
Lesson 13.1: Volume of CylindersUnit 5
Lesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 12: Scaling Cylinders
Lesson 14: Missing Dimensions (Print available)
Lesson 13.2: Volume of ConesUnit 5
Lesson 10: Volume Lab
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 13.3: Volume of SpheresUnit 5
Lesson 10: Volume Lab
Lesson 15: Spheres

Unit 6: Statistics

Module 14: Scatter Plots
Lesson 14.1: Scatter Plots and AssociationUnit 6
Lesson 1: Click Battle
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot City
Lesson 8: Animal Brains
Lesson 14.2: Trend Lines and PredictionsUnit 6
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 8: Animal Brains
Module 15: Two-Way Tables
Lesson 15.1: Two-Way Frequency TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 15.2: Two-Way Relative Frequency TablesUnit 6
Lesson 10: Finding Associations [Free lesson]
Lesson 11: Federal Budgets

What’s included in our Grades 3–5 language arts curriculum

Grounded in the science of reading, Amplify CKLA for grades 3–5 integrates foundational skills students have learned in grades K–2 while continuing to build rich content knowledge. With Amplify CKLA, you’ll have the instruction and guidance of proven, evidence-based practices to help all of your students become strong readers, writers, and thinkers.

Year at a glance

The Amplify CKLA curriculum is modeled after proven research in early literacy that supports a two-strand approach to literacy instruction in the early years. With this approach, students in Grades K–2 complete one full lesson per day that builds foundational reading skills in the Skills Strand, as well as one full lesson that builds background knowledge in the Knowledge Strand. The deep content knowledge is sequenced together with research-based foundational skills in Grades K–2 so that students develop the early literacy skills necessary to help them become confident readers, as well as build the context to understand what they’re reading. 

In Grades 3–5, lessons combine skills and knowledge with increasingly complex texts, close reading, and a greater emphasis on writing. Students start to use their skills to go on their own independent reading adventures, further opening up their worlds.

Diagram illustrating how language comprehension and word recognition components integrate to lead to skilled reading, as described in the Simple View of Reading model, aligned with the 3-5 CKLA curriculum and Amplify CKLA digital experience.

Units at a glance

Students move fluidly between reading, writing, speaking and listening, and language activities, with increasingly complex texts, close reading, and a greater writing emphasis.

Classic Tales: The Wind in the Willows

Students explore international classic tales, including The Wind in the WillowsAlice in Wonderland, and “Aladdin and the Wonderful Lamp.”

Number of Lessons: 15

Animal Classification

Students learn how scientists use animals’ characteristics to classify and study them; students apply knowledge through text-based discussions and writing exercises.

Number of Lessons: 15

The Human Body: Systems and Senses

This unit involves the study of the human body, building students’ understanding of its senses and skeletal, muscular, and nervous systems.

Number of Lessons: 14

The Ancient Roman Civilization

Students dive into ancient Rome, studying its history, culture, and myths about Roman gods and goddesses.

Number of Lessons: 15

Light and Sound

Students learn the science behind light and sound, read biographies of Alexander Graham Bell and Thomas Edison, and write newspaper articles.

Number of Lessons: 17

The Viking Age (with Core Quest)

This unit’s informational and literary texts convey information about the Vikings, their culture, and their exploration.

Number of Lessons: 11

Astronomy: Our Solar System and Beyond

Students learn about astronomy, the universe, and important figures in the history of space exploration, including Nicolaus Copernicus and Mae Jemison.

Number of Lessons: 20

Native Americans: Regions and Cultures

Students compare, contrast, assemble information, and reflect on what they have learned about Native Americans and their ways of life.

Number of Lessons: 13

Early Explorations of North America

Students explore reasons for European exploration, what exploration was like, and who went exploring; then students write opinion pieces using this information.

Number of Lessons: 14

Colonial America

Students learn about colonies in early America, including how colonies were started and the progress colonists made after settling.

Number of Lessons: 16

Ecology

Students learn about different aspects of ecology, including food chains, the balance of nature, changes to the environment, and protecting the environment.

Number of Lessons: 12

Personal Narratives

This unit examines the genre of personal narratives, including nonfiction works written by a first-person narrator involved in the events being described.

Number of Lessons: 15

Empires in the Middle Ages

This unit covers the history of various empires and geographical regions throughout the Middle Ages.

Number of Lessons: 25

Poetry

Students explore poetry, training in methods and devices poets use and learning to read, write, and interpret formal and free verse poems.

Number of Lessons: 15

Eureka! Student Inventor

This Core Quest, a narrative-driven unit, immerses students in close-reading adventures and scientific and historical content about inventions. Students write and read opinion, informational, and narrative texts.

Number of Lessons: 10

Geology

This unit focuses on the composition of Earth and the forces that change its surface.

Number of Lessons: 15

Contemporary Fiction with excerpts from The House on Mango Street

This unit explores narrative literature and writing, using excerpts from The House on Mango Street as its anchor text.

Number of Lessons: 13

American Revolution

Students learn that disagreements about principles of government led colonists in North America to seek independence from Great Britain.

Number of Lessons: 17

Treasure Island

Students focus on character development, setting, plot, and literary devices while reading an abridged version of a classic novel, Treasure Island.

Number of Lessons: 19

Writing Quest (supplemental): The Contraption

In this supplemental Quest, students interact with a mysterious machine fueled by their writing and solve the machine’s puzzles. This Quest features a digital environment controlled by the teacher.

Personal Narratives

This unit examines the genre of personal narratives, including nonfiction works written by a first-person narrator involved in the events being described.

Number of Lessons: 15

Early American Civilizations

Students study the geography, climate, flora, and fauna of the Americas and the rise and fall of the Maya, Aztec, and Inca civilizations.

Number of Lessons: 15

Poetry

Students explore poetry, training in methods and devices poets use and learning to read, write, and interpret formal and free verse poems.

Number of Lessons: 13

Adventures of Don Quixote

In this unit students trace the development of plot, characters, and literary elements while reading a full-length, adapted version of Don Quixote.

Number of Lessons: 15

The Renaissance

This unit provides students with a broad exposure to the art and literature of the Renaissance through the works of renowned masters.

Number of Lessons: 19

The Reformation

This unit teaches students about the Reformation, a movement involving religious and political upheaval that shifted the political power in Europe.

Number of Lessons: 10

A Midsummer Night’s Dream (Core Quest)

This unit is an immersive Quest that treats Shakespeare’s comedy as both literature and a living text for interpretation and performance.

Number of Lessons: 15

Native Americans

Students learn how settlers, explorers, and the American government in the 1800s affected Native American cultures and their relationship with the land.

Number of Lessons: 15

Chemical Matter

Students learn about chemistry and close-reading through a literary and informational work, The Badlands Sleuth, in which the protagonist uses chemistry to solve mysteries.

Number of Lessons: 15

Writing Quest (supplemental): The Robot

Students interact with a classroom pet that learns and grows with their writing. This Quest features a digital environment controlled by the teacher.

Program components

The program includes instructional guidance and student materials for a year of instruction, with lessons and activities that keep students engaged every day.

Component

FORMAT

Teacher Guides

Teacher Guides for each unit provide engaging lessons with standards-based objectives and formative assessments that empower teachers with proven strategies and research-based tools.

Print or digital

Differentiation resources

The online Assessment and Remediation Guide (Grade 3) and the Decoding and Encoding Supplement (Grades 4–5) provide thousands of pages of targeted activities in decoding, spelling, and other core literacy skills. Supplemental Guides provide opportunities for enrichment.

Digital

Writing Studio

A riveting connected writing program for more time, practice, and challenge in writing, with a focus on informative, narrative, and opinion modes of writing.

Print or digital

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Component

FORMAT

Student Readers

Amplify CKLA’s Student Readers anchor each of the content-based units, providing a close-reading experience fueled by rich background knowledge that inspires students to dig deeper.

Print

Activity Books

In addition to providing daily opportunities for students to respond to text and apply skills and knowledge, Activity Books feature formative assessments for each day’s objectives.

Print

Digital experience

The Amplify CKLA digital experience delivers ready-made, customizable, slides-based lesson presentations to enhance instruction and save time. Everything needed to plan and present high-quality, engaging early literacy instruction is in one convenient place.

Digital

Explore more programs

Our programs are designed to support and complement one another. Learn more about our related programs.

Grade 6

Chapter 1: Use Positive Rational Numbers

enVision MathDesmos Math 6–A1
Lesson 1: Fluently Add, Subtract, and Multiply DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Practice Day 1 (Print available)
Lesson 2: Fluently Divide Whole Numbers and DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch (Print available)
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson]
Lesson 12: Budget Vehicles (Print available)
Practice Day 2
Lesson 3: Multiply FractionsUnit 4
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Lesson 4: Understand Division with FractionsUnit 4
Lesson 1: Cookie Cutter
Lesson 2: Making Connections (Print available)
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Practice Day (Print available)
Lesson 5: Divide Fractions by fractionsUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 14: Planter planner (Print available)
Practice Day (Print available)
Lesson 6: Divide Mixed NumbersUnit 4
Lesson 5 Garden Bricks (Print available)
Lesson 6 Fill the Gap [Free lesson]
Lesson 11 Classroom Comparisons
Lesson 7: Solve Problems with Rational NumbersLesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Lesson 5: Garden Bricks (Print available)
Lesson 10: Swap Meet (Print available)

Chapter 2: Integers and Rational Numbers

Lesson 1: Understand IntegersUnit 7
Lesson 1: Can You Dig it In [Free lesson]
Lesson 4 Sub-Zero
Lesson 2: Represent Rational Numbers on the Number LineUnit 7
Lesson 2: Digging Deeper
Lesson 3: Order in the Class (Print available) [Free lesson]
Practice Day 1
Lesson 3: Absolute Values of Rational NumbersUnit 7
Lesson 5: Distance on the Number Line
Practice Day 1 (Print available)
Lesson 4: Represent Rational Numbers on the Coordinate Plane 
Lesson 5: Find Distances on the Coordinate Plane
Lesson 6: Represent Polygons on the Coordinate Plane
Unit 7
Lesson 11: Polygon Maker

Chapter 3: Numeric and Algebraic Expressions

Chapter 4: Represent and Solve Equations and Inequalities

Lesson 1: Understand Equations and SolutionsUnit 6
Lesson 1: Weight for It [Free lesson]
Lesson 3: Hanging Around
Lesson 13: Turtles All the Way
Lesson 2: Apply Properties of Equality
Lesson 3: Write and Solve Addition and Subtraction Equations
Lesson 4: Write and Solve Multiplication and Division Equations
Unit 6
Lesson 3: Hanging Around
Lesson 4: Hanging It Up
Lesson 5: Swap and Solve (Print available)
Practice Day 1 (Print Available)
Lesson 5: Write and Solve Equations with Rational NumbersUnit 6
Lesson 4; Hanging It Up
Lesson 5: Swap and Solve (Print available)
Lesson 6: Understand and Write InequalitiesUnit 7
Lesson 6: Tunnel Travel [Free lesson]
Lesson 7: Comparing Weights
Lesson 7: Solve InequalitiesUnit 7
Lesson 8: Shira’s Solutions
Lesson 8: Understand Dependent and Independent VariablesUnit 6
Lesson 13: Turtles All the Way
Lesson 9: Use Patterns to Write and Solve Equations
Lesson 10: Relate Tables, Graphs, and Equations
Unit 6
Lesson 13: Turtles All the Way
Lesson 14: Representing Relationships
Lesson 15: Connecting Representations (Print available)
Lesson 16: Subway Fares (Print available) [Free lesson]
Practice Day 2 (Print available)

Chapter 5: Understand and Use Ratio and Rate

Chapter 6: Understand and Use Percent

Lesson 1: Understand PercentUnit 3
Lesson 8: Lucky Duckies [Free lesson]
Lesson 2: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 13: Grocery Prices (Print available)
Lesson 3: Represent Percents Greater Than 100 or Less than 1 
Lesson 4: Estimate to Find Percent 
Lesson 5: Find the Percent of a Number
Lesson 6: Find the Whole Given a Part and the Percent
Unit 3
Lesson 9: Bicycle Goals
Lesson 10: What’s Missing?
Lesson 11: Cost Breakdown
Lesson 12: More Bicycle Goals
Practice Day 2 (Print Available)

Chapter 7: Solve Area, Surface Area, and Volume Problems

Chapter 8: Display, Describe, and Summarize data

Grade 7

Chapter 1: Rational Number Operations

enVision MathDesmos Math 6–A1
Lesson 1: Relate Integers and Their OppositesUnit 5
Lesson 1: Floats and Anchors [Free lesson]
Lesson 2: Understand Rational NumbersUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 3: Add Integers
Lesson 4: Subtract Integers
Unit 5
Lesson 2: More Floats and Anchors
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Lesson 5: Add and Subtract Rational NumbersUnit 5
Lesson 3: Bumpers
Lesson 4: Draw Your Own (Print available) [Free lesson]
Lesson 5: Number Puzzles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 11: Changing Temperatures
Lesson 13: Solar Panels and More (Print available)
Practice Day 1 (Print available)
Lesson 6: Multiply IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 7: Multiply Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 8: Divide IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 9: Divide Rational NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)
Practice Day 2 (Print available)
Lesson 10 Solve Problems with Rational NumbersUnit 5
Lesson 11: Changing Temperatures
Lesson 12: Arctic Sea Ice (Print available)
Lesson 13: Solar Panels and More (Print available)

Chapter 2: Analyze and Use Proportional Relationships

Lesson 1: Connect Ratios, Rates, and Unit Rates 
Lesson 2: Determine Unit Rates with Ratios of Fractions 
Lesson 3: Understand Proportional Relationships: Equivalent RatiosUnit 2
Lesson 1: Paint [Free lesson]
Lesson 2: Balloon Float
Lesson 4: Describe Proportional Relationships: Constant of ProportionalityUnit 2
Lesson 3: Sugary Drinks (Print available)
Lesson 4: Robot Factory
Lesson 5: Snapshots
Lesson 6: Two and Two (Print available) [Free lesson]
Lesson 7: All Kinds of Equations
Lesson 10: Three Turtles
Practice Day (Print available)
Unit 3
Lesson 1 Circumference of a Circle
Lesson 5: Graph Proportional RelationshipsUnit 2
Lesson 8: Dino Pops [Free lesson]
Lesson 9: Gallon Challenge
Lesson 10: Three Turtles
Lesson 11: Four Representations (Print available)
Lesson 6: Apply Proportional Reasoning to Solve ProblemsUnit 2
Lesson 11: Four Representations (Print available)
Lesson 12: Water Efficiency

Chapter 3: Analyze and Solve Percent Problems

Chapter 4: Generate Equivalent Expressions

Chapter 5: Solve Problems Using Equations and Inequalities

Chapter 6: Use Sampling to Draw Inferences About Populations

Chapter 7: Probability

Lesson 1: Understand Likelihood and ProbabilityUnit 8
Lesson 1 How Likely? (Print available) [Free lesson]
Lesson 2 Prob-bear-bilities [Free lesson]
Lesson 3 Mystery Bag
Lesson 2: Understand Theoretical Probability
Lesson 3: Understand Experimental Probability
Unit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 6: Fair Games
Lesson 4: Use Probability ModelsUnit 8
Lesson 6: Fair Games
Lesson 7: Weather or Not
Lesson 8: Simulate It
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 5: Determine Outcomes of Compound EventsUnit 8
Lesson 9: Car, Bike, or Train? (Print available)
Lesson 6: Find Probabilities of Compound Events
Lesson 7: Simulate Compound Events
Unit 8
Lesson 8: Simulate It
Lesson 9: Car, Bike, or Train? (Print available)
Practice Day 1 (Print Available)

Chapter 8: Solve Problems Involving Geometry

Lesson 1: Solve Problems Involving Scale DrawingsUnit 1 Lesson 1: Scaling Machines [Free lesson] Lesson 2: Scaling Robots Lesson 3: Make It Scale Lesson 4: Scale Factor Challenges Lesson 5: Tiles Lesson 6: Introducing Scale Lesson 7: Will It Fit? [Free lesson] Lesson 8: Scaling States Lesson 9: Scaling Buildings Lesson 10: Room Redesign Practice Day 1 Practice Day 2   Unit 3 Lesson 1: Toothpicks   Unit 4 Lesson 3: Sticker Sizes
Lesson 2: Draw Geometric FiguresUnit 7
Lesson 6: Is It Enough?
Lesson 3: Draw Triangles with Given ConditionsUnit 7
Lesson 5: Can You Build It? [Free lesson]
Lesson 6: Is It Enough?
Lesson 7: More Than One
Lesson 8: Can You Draw It?
Practice Day 1
Lesson 4: Solve Problems Using Angle RelationshipsUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 3: Angle Diagrams
Lesson 4: Missing Measures [Free lesson]
Lesson 5: Solve Problems Involving Circumference of a CircleUnit 3
Lesson 2: Is It a Circle?
Lesson 3: Measuring Around [Free lesson]
Lesson 4: Perimeter Challenges
Practice Day 1 (Print available) [Free lesson]
Lesson 6: Solve Problems Involving Area of a CircleUnit 3
Lesson 5: Area Strategies
Lesson 6: Radius Squares
Lesson 7: Why Pi?
Lesson 8: Area Challenges [Free lesson]
Lesson 9: Circle vs. Square
Practice Day 2
Lesson 7: Describe Cross SectionsUnit 7
Lesson 9: Slicing Solids
Lesson 8: Solve Problems Involving Surface AreaUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies
Lesson 13: Popcorn Possibilities
Lesson 9: Solve Problems Involving VolumeUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities
Practice Day 2

Grade 8

Chapter 1: Real Numbers

enVision MathDesmos Math 6–A1
Lesson 1: Rational Numbers as DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 2: Understand Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 3: Compare and Order Real Numbers 
Lesson 4: Evaluate Square Roots and Cube RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 5: Solve Equations Using Square Roots and Cube RootsUnit 8
Lesson 5: Filling Cubes
Practice Day 1 (Print available)
Lesson 6: Use Properties of Integer ExponentsUnit 7  
Lesson 2: Combining Exponents
Lesson 3: Power Pairs (Print available) [Free lesson]
Lesson 4: Rewriting Powers
Practice Day 1 (Print available)
Lesson 7: More Properties of Integer ExponentsUnit 7  
Lesson 5: Zero and Negative Exponents
Lesson 6: Write a Rule (Print available)
Lesson 8: Use Powers of 10 to Estimate QuotientsUnit 7  
Lesson 7: Scales and Weights
Lesson 8: Point Zapper
Lesson 9: Use Your Powers
Lesson 9: Understand Scientific NotationUnit 7  
Lesson 10: Solar System [Free lesson]
Lesson 11: Balance the Scales [Free lesson]
Lesson 13: Star Power
Practice Day 2 (Print available)

Chapter 2: Analyze and Solve Linear Equations

Lesson 1: Combine Like Terms to Solve EquationsUnit 4
Lesson 2: Keep It Balanced
Lesson 2: Solve Equations with Variables on Both SidesUnit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 3: Solve Multi-Step EquationsUnit 4
Lesson 3: Balanced Moves
Lesson 4: More Balanced Moves (Print available)
Lesson 5: Equation Roundtable (Print available) [Free lesson]
Lesson 6: Strategic Solving (Print available)
Lesson 4: Equations with No Solutions or Infinitely Many SolutionsUnit 4
Lesson 7: All, Some, or None?
Lesson 5: Compare Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 6: Connect proportional Relationships and SlopeUnit 2
Lesson 9: Water Slide
Lesson 10: Points on a Plane
Practice Day 
 
Unit 3
Lesson 2: Water Tank
Lesson 4: Stacking Cups
Lesson 5: Flags [Free lesson]
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Coin Capture
Lesson 7: Analyze Linear Equations: y = mxUnit 3
Lesson 3: Posters
Lesson 6: Translations
Lesson 8: Understand the y-intercept of a LineUnit 3
Lesson 5: Flags [Free lesson]
Lesson 6: Translations
Lesson 9: Analyze Linear Equations: y = mx + bUnit 3  
Lesson 6: Translations
Lesson 7: Water Cooler
Practice Day 

Chapter 3: Use Functions to Model Relationships

Lesson 1: Understand Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Connect Representations of FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3: Compare Linear and Nonlinear FunctionsUnit 5
Lesson 4: Window Frames
Lesson 4: Construct Functions to Model Linear RelationshipsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 5: Intervals of Increase and DecreaseUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 6: Graphing Stories
Lesson 6: Sketch Functions from Verbal DescriptionsUnit 5  
Lesson 6: Graphing Stories

Chapter 4: Investigate Bivariate Data

Lesson 1: Construct and Interpret Scatter PlotsUnit 6  
Lesson 1: Click Battle
Lesson 2: Wing Span
Lesson 3: Robots [Free lesson]
Practice Day 1 (Print available) [Free lesson]
Lesson 2: Analyze Linear AssociationUnit 6  
Lesson 4: Dapper Cats [Free lesson]
Lesson 5: Fit Fights [Free lesson]
Lesson 7: Scatter Plot City
Lesson 3: Use Linear Models to Make PredictionsUnit 6  
Lesson 6: Interpreting Slopes
Lesson 8: Animal Brains
Practice Day 2 (Print available)
Lesson 4: Interpret Two-Way Frequency TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 5: Interpret Two-Way Relative Frequency TablesUnit 6
Lesson 10: Finding Associations [Free lesson]
Lesson 11: Federal Budgets
Practice Day 3

Chapter 5: Analyze and Solve Systems of Linear Equations

Chapter 6: Congruence and Similarity

Chapter 7: Understand and Apply the Pythagorean Theorem

Lesson 1: Understand the Pythagorean TheoremUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 2: Understand the Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right
Lesson 3: Apply the Pythagorean Theorem to Solve ProblemsUnit 8
Lesson 10: Taco Truck [Free lesson]
Practice Day 2 (Print available)
Lesson 4: Find Distance in the Coordinate PlaneUnit 8
Lesson 11: Pond Hopper

Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 1: Find Surface Area of Three-Dimensional Figures 
Lesson 2: Find Volume of CylindersUnit 5
Lesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 3: Find Volume of ConesUnit 5
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 4: Find Volume of SpheresUnit 5
Lesson 15: Spheres
Practice Day 2 (Print available)

Grade 6

Unit 1: Expressions and Equations: Area, Algebraic Expressions, and Exponents

iReady ClassroomDesmos Math 6–A1
Lesson 1: Find the Area of a ParallelogramUnit 1
Lesson 3: Exploring Parallelograms (Print available) [Free lesson]
Lesson 4: Off the Grid
Lesson 2: Find the Area of Triangles and Other PolygonsUnit 1
Lesson 7: Off the Grid, Part 2
Practice Day 1 (Print available)
Lesson 3: Use Nets to Find Surface AreaUnit 1
Lesson 11: Nothing But Nets (Print available)
Practice Day 2 (Print available)
Lesson 4: Work with Algebraic ExpressionsUnit 6
Lesson 6: Vari-apples
Lesson 5: Write and Evaluate Expressions with ExponentsUnit 6
Lesson 4: Hanging it Up
Lesson 5: Swap and Solve (Print available)
Practice Day 2 (Print available)
Lesson 6: Find Greatest Common Factor and Least Common MultipleUnit 5
Lesson 14: Common Multiples
Lesson 15: Common Factors
Practice Day 2 (Print available)

Unit 2: Decimals and Fractions: Base-Ten Operations, Division with Fractions, and Volume

Unit 3: Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Unit 4: Ratio Reasoning: Unit Rates and Percent

Unit 5: Algebraic Thinking: Equivalent Expressions and Equations with Variables

Unit 6: Positive and Negative Numbers: Absolute Value, Inequalities, and the Coordinate Plane

Lesson 23: Understand Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It [Free lesson]
Lesson 4: Sub-Zero
Lesson 24: Order Positive and Negative NumbersUnit 7
Lesson 2: Digging Deeper
Lesson 3: Order in the Class (Print available) [Free lesson]
Lesson 25: Understand Absolute ValueUnit 7
Lesson 5: Distance on the Number Line
Practice Day 1 (Print available)
Lesson 26: Write and Graph One-Variable InequalitiesUnit 7
Lesson 6: Tunnel Travels [Free lesson]
Lesson 7: Comparing Weights
Lesson 8: Shira’s Solutions
Lesson 27: Understand the Four-Quadrant Coordinate PlaneUnit 7
Lesson 9: Sand Dollar Search
Lesson 10: The A-maze-ing Coordinate Plane
Lesson 11: Polygon Maker
Practice Day 2 (Print available)
Lesson 28: Solve Problems in the Coordinate PlaneUnit 7
Lesson 12: Graph Telephone
Practice Day 2 (Print available)

Unit 7: Statistical Thinking: Data Distributions and Measures of Center and Variability

Grade 7

Unit 1: Proportional Relationships: Ratios, Rates, and Circles

Unit 2: Numbers and Operations: Add and Subtract Rational Numbers

Unit 3: Numbers and Operations: Multiply and Divide Rational Numbers

Lesson 11: Understand Multiplication with Negative IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 12: Multiply and Divide with Negative NumbersUnit 5
Lesson 8: Speeding Turtles
Lesson 13: Express Rational Numbers as Terminating or Repeating DecimalsUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 14: Use the Four Operations with Negative NumbersUnit 5
Lesson 10: Integer Puzzles [Free lesson]
Lesson 13: Solar Panels and More (Print available)
Practice Day 2  (Print available)

Unit 4: Algebraic Thinking: Expressions, Equations, and Inequalities

Unit 5: Proportional Reasoning: Percents and Statistical Samples

Unit 6: Geometry: Solids, Triangles, and Angles

Lesson 25: Solve Problems Involving Area and Surface AreaUnit 7
Lesson 12: Surface Area Strategies (Print available)
Lesson 26: Solve Problems Involving VolumeUnit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Practice Day 2 (Print available)
Lesson 27: Describe Plane Sections of Three-Dimensional FiguresUnit 7
Lesson 9: Slicing Solids
Lesson 28: Find Unknown Angle MeasuresUnit 7
Lesson 1: Pinwheels
Lesson 2: Friendly Angles [Free lesson]
Lesson 4: Missing Measures (Print available) [Free lesson]
Lesson 29: Draw Plane Figures with Given ConditionsUnit 7
Lesson 6: Is It Enough
Lesson 7: More Than One?
Lesson 8: Can You Draw It? (Print available)
Practice Day 1 (Print available)

Unit 7: Probability: Theoretical Probability, Experimental Probability, and Compound Events

Lesson 30: Understand ProbabilityUnit 8
Lesson 1: How Likely? (Print available) [Free lesson]
Lesson 2: Prob-bear-bilities [Free lesson]
Lesson 31: Solve Problems Involving Experimental ProbabilityUnit 8
Lesson 4: Spin Class
Lesson 5: Is It Fair?
Lesson 32: Solve Problems Involving Probability ModelsUnit 8
Lesson 6: Fair Games
Lesson 33: Solve Problems Involving Compound EventsUnit 8
Lesson 7: Weather or Not
Lesson 8: Simulate It! (Print available)
Practice Day 1 (Print available)

Grade 8

Unit 1: Geometric Figures: Rigid Transformations and Congruence

iReady ClassroomDesmos Math 6–A1
Lesson 1: Understand Rigid Transformations and Their PropertiesUnit 1
Lesson 1: Transformers [Free lesson]
Lesson 2: Spinning, Flipping, Sliding [Free lesson]
Lesson 3: Transformation Golf
Lesson 2: Work with Single Rigid Transformations in the Coordinate PlaneUnit 1
Lesson 4: Moving Day (Print available) [Free lesson]
Lesson 8: No Bending, No Stretching
Lesson 9: Are They Congruent?
Practice Day (Print available)
Lesson 3: Work with Sequences of Transformations and CongruenceUnit 1
Lesson 3: Transformation Golf

Unit 2: Geometric Figures: Transformations, Similarity, and Angle Relationships

Unit 3: Linear Relationships: Slope, Linear Equations, and Systems

Lesson 8: Graph Proportional Relationships and Define SlopeUnit 2
Lesson 9: Water Slide

Unit 3
Lesson 1: Turtle Time Trials [Free lesson]
Lesson 2: Water Tank
Lesson 3: Posters
Lesson 7: Water Cooler
Lesson 8: Landing Planes
Lesson 9: Derive and Graph Linear Equations of the Form y = mx + bUnit 3
Lesson 6: Translations
Lesson 9: Coin Capture
Lesson 10: Solve Linear Equations in One VariableUnit 4
Lesson 1: Number Machines
Lesson 2: Keep It Balanced
Lesson 11: Determine the Number of Solutions to One-Variable EquationsUnit 4
Lesson 7: All, Some, or None
Lesson 8: When Are They the Same?
Lesson 12: Understand Systems of Linear Equations in Two VariablesUnit 4
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 13: Solve Systems of Linear Equations AlgebraicallyUnit 4
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Lesson 14: Represent and Solve Problems with Systems of Linear EquationsUnit 4
Lesson 13: All, Some, or None? Part 2
Lesson 14: Strategic Solving, Part 2 (Print available)
Practice Day 2 (Print available)

Unit 4: Functions: Linear and Nonlinear Relationships

Lesson 15: Understand FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 3: Function or Not?
Lesson 16: Use Functions to Model Linear RelationshipsUnit 5
Lesson 4: Window Frames
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 6: Graphing Stories
Lesson 17: Compare Different Representations of Functions
Lesson 18: Analyze Functional Relationships Qualitatively
Unit 5
Lesson 7: Feel the Burn (Print available) [Free lesson]

Unit 5: Integer Exponents: Properties and Scientific Notation

Unit 6: Real Numbers: Rational Numbers, Irrational Numbers, and the Pythagorean Theorem

Lesson 23: Find Square Roots and Cube Roots to Solve ProblemsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 5: Filling Cubes
Lesson 24: Express Rational Numbers as Fractions and DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 25: Find Rational Approximations of Irrational NumbersUnit 8
Lesson 10: Taco Truck [Free lesson]
Lesson 26: Understand the Pythagorean Theorem and its ConverseUnit 8
Lesson 6: The Pythagorean Theorem
Lesson 27: Apply the Pythagorean TheoremUnit 8
Lesson 7: Pictures to Prove It
Lesson 8: Triangle-Tracing Turtle [Free lesson]
Lesson 9: Make It Right
Lesson 11: Pond Hopper
Practice Day 2 (Print available)
Lesson 28: Solve Problems with Volumes of Cylinders, Cones, and SpheresLesson 10: Volume Lab
Lesson 11: Cylinders [Free lesson]
Lesson 12: Scaling Cylinders
Lesson 13: Cones [Free lesson]
Lesson 14: Missing Dimensions (Print available)
Lesson 15: Spheres

Unit 7: Statistics: Two-Variable Data and Fitting a Linear Model

Lesson 29: Analyze Scatter Plots and Fit a Linear Model to DataUnit 6
Lesson 3: Robots [Free lesson]
Lesson 4: Dapper Cats [Free lesson]
Practice Day 1 (Print available) [Free lesson]
Lesson 5: Fit Fight [Free lesson]
Lesson 30: Write and Analyze an Equation for Fitting a Linear Model to DataUnit 6
Lesson 6: Interpreting Slopes
Lesson 7: Scatter Plot CityLesson 8: Animal Brains
Practice Day 2 (Print available)
Lesson 31: Understand Two-Way TablesUnit 6
Lesson 9: Tasty Fruit
Lesson 10: Finding Associations [Free lesson]
Lesson 32: Construct and Interpret Two-Way TablesUnit 6
Lesson 11: Federal Budgets
Practice Day 3

Grade 6

Module 1: Ratios and Rates

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3Lesson 8: Lucky Duckies [Free lesson]Lesson 9: Bicycle Goals
Lesson 2: Percents Greater Than 100% and Less Than 1% 
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5Lesson 2: Decimal Diagrams [Free lesson]Lesson 13: Grocery Prices (Print available)
Lesson 4: Find the Percent of a NumberUnit 3Lesson 10: What’s Missing? (Print available)Lesson 11: Cost Breakdown
Lesson 5: Estimate the Percent of a Number 
Lesson 6: Find the WholeUnit 3Lesson 10: What’s Missing? (Print available)

Module 3: Compute with Multi-Digit Numbers and Fractions

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7Lesson 1: Can You Dig It [Free lesson]Lesson 4: Sub-Zero
Lesson 2: Opposites and Absolute ValueUnit 7Lesson 5: Distance on the Number Line
Lesson 3: Compare and Order IntegersUnit 7Lesson 2: Digging DeeperLesson 3: Order in the Class (Print available) [Free lesson]
Lesson 4: Rational NumbersUnit 7Lesson 2: Digging Deeper
Lesson 5: The Coordinate PlaneUnit 7Lesson 9: Sand Dollar SearchLesson 10: The A-maze-ing Coordinate Plane
Lesson 6: Graph Reflections of Points
Lesson 7: Absolute Value and DistanceUnit 7Lesson 5: Distance on the Number Line

Module 5: Numerical and Algebraic Expressions

Module 6: Relationships in Geometry

Module 7: Relationships Between Two Variables

Module 8: Area

Module 9: Volume and Surface Area

Module 10: Statistical Measures and Displays

Grade 7

Module 1: Proportional Relationships

Module 2: Solve Percent Problems

Module 3: Operations with Integers

Module 4: Operations with Rational Numbers

Module 5: Simplify Algebraic Expressions

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6Lesson 3: EquationsLesson 4: Seeing Structure (Print available)Lesson 14: Unbalanced HangersLesson 15: BudgetingLesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)
Lesson 2: Solve Two-Step Equations: px + q = r
Lesson 3: Write and Solve Two-Step Equations: px + q = r
Lesson 4: Solve Two-Step Equations: p(x + q) = r
Lesson 5: Write and Solve Two-Step Equations: p(x + q) = r
Unit 6Lesson 4: Seeing Structure (Print available)Lesson 6: Balancing EquationsLesson 7: Keeping It True (Print available)Lesson 12: Community Day (Print available)Practice Day 1 (Print available)

Module 7: Write and Solve Inequalities

Lesson 1: Solve One-Step Addition and Subtraction Inequalities
Lesson 2: Write and Solve One-Step Addition and Subtraction Inequalities
Lesson 3: Solve One-Step Multiplication and Division Inequalities
Lesson 4: Solve One-Step Multiplication and Division Inequalities with Negative Coefficients
Unit 6Lesson 14: Unbalanced HangersLesson 15: Budgeting (Print available)Lesson 16: Shira the SheepLesson 17: Write Them and Solve Them (Print available)
Lesson 5: Write and Solve One-Step Multiplication and Division InequalitiesUnit 6Lesson 15: Budgeting (Print available)
Lesson 6: Write and Solve Two-Step InequalitiesUnit 6Lesson 15: Budgeting (Print available)Lesson 16: Shira the Sheep [Free lesson]Lesson 17: Write Them and Solve Them (Print available)Practice Day 2 (Print available)

Module 8: Geometric Figures

Module 9: Measure Figures

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8Lesson 1: How Likely? (Print available) [Free lesson]Lesson 2: Prob-bear-bilities [Free lesson]Lesson 3: Mystery Bag
Lesson 4: Compare Probabilities of Simple EventsUnit 8Lesson 4: Spin ClassLesson 5: Is It Fair?
Lesson 5: Probability of Compound EventsUnit 8Lesson 6: Fair GamesLesson 7: Weather or NotLesson 8: Simulate It
Lesson 6: Simulate Chance EventsUnit 8Lesson 8: Simulate ItPractice Day 1 (Print available)

Module 11: Sampling and Statistics

Grade 8

Module 1: Exponents and Scientific Notation

Module 2: Real Numbers

Lesson 1: Terminating and Repeating DecimalsUnit 8
Lesson 12: Fractions to Decimals
Lesson 13: Decimals to Fractions
Lesson 2: RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Practice Day 1 (Print available)
Lesson 3: Real NumbersUnit 8
Lesson 14: Hit the Target
Lesson 4: Estimate Irrational NumbersUnit 8
Lesson 3: Between Squares
Lesson 5: Compare and Order Real NumbersUnit 8
Lesson 14: Hit the Target

Module 3: Solve Equations with Variables on Each Side

Module 4: Linear Relationships and Slope

Module 5: Functions

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper
Lesson 13: All, Some, or None? Part 2
(Print available)Practice Day 2 
Lesson 2: Determine Number of SolutionsUnit 4 
Lesson 13: All, Some, or None? Part 2
Lesson 3: Solve Systems of Equations by Substitution
Lesson 4: Solve Systems of Equations by Elimination
Lesson 5: Write and Solve Systems of EquationsUnit 4 
Lesson 14: Strategic Solving, Part 2 (Print available)

Module 7: Triangles and the Pythagorean Theorem

Lesson 1: Angle Relationships and Parallel LinesUnit 1 Lesson 10: Transforming Angles
Lesson 2: Angle Relationships and TrianglesUnit 1 Lesson 10: Transforming Angles Lesson 11: Tearing It Up (Print available)Lesson 12: Puzzling It Out [Free lesson]
Lesson 3: The Pythagorean TheoremUnit 8Lesson 6: The Pythagorean TheoremLesson 7: Pictures to Prove It
Lesson 4: Converse of the Pythagorean TheoremUnit 8Lesson 9: Make It Right
Lesson 5: Distance on the Coordinate PlaneUnit 8Lesson 11: Pond HopperPractice day 2 (Print available)

Module 8: Transformations

Module 9: Congruence and Similarity

Lesson 1: Congruence and Transformations
Lesson 2: Congruence and Corresponding Parts
Unit 1 Lesson 7: Are They the Same?Lesson 9: Are They Congruent?
Lesson 3: Similarity and TransformationsUnit 2Lesson 5: Transformations Golf with DilationsLesson 6: Social Scavenger Hunt (Print available) [Free lesson]
Lesson 4: Similarity and Corresponding PartsUnit 2Lesson 7: Are Angles Enough?Lesson 8: Shadows
Lesson 5: Indirect MeasurementUnit 2Lesson 8: Shadows

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5Lesson 10: Volume LabLesson 11: Cylinders [Free lesson]Lesson 12: Scaling Cylinders
Lesson 2: Volume of ConesUnit 5Lesson 10: Volume LabLesson 13: Cones [Free lesson]Lesson 14: Missing Dimensions (Print available)
Lesson 3: Volume of SpheresUnit 5Lesson 15: Spheres
Lesson 4: Finding Missing DimensionsUnit 5Lesson 14: Missing Dimensions (Print available)
Lesson 5: Volume of Composite SolidsUnit 5Lesson 15: Spheres

Module 11: Scatter Plots and Two-Way Tables

Grade 6

Unit 1: Numbers

GO Math!Amplify Classroom
Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap
Module 5: Operations with Decimals
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Unit 2: Number Operations

Module 4: Operations with Fractions
Lesson 4.1: Applying GCF and LCM to Fraction OperationsUnit 4
Lesson 6: Fill the Gap
Module 5: Operations with Decimals
Lesson 5.2: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5.4: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Unit 3: Proportionality, Ratios, and Rates

Module 6: Representing Ratios and Rates
Lesson 6.1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 6.2: Rates Unit 3
Lesson 6: Soft Serve
Lesson 6.3: Using Ratios and Rates to Solve ProblemsUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation
Module 7: Applying Ratios and Rates
Lesson 7.1: Ratios, Rates, Tables, and GraphsUnit 2
Lesson 4: Fruit Lab
Lesson 10: Disaster Preparation
Unit 3
Lesson 6: Soft Serve
Module 8:  Percents
Lesson 8.1 Understanding Percent.Unit 3
Lesson 9: Lucky Duckies

Unit 4: Equivalent Expressions

Module 10: Generating Equivalent Algebraic Expressions
Lesson 10.1: Modeling and Writing Expressions
Lesson 10.2: Evaluating Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10.3: Generating Equivalent ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)

Unit 5: Equations and Inequalities

Module 11:  Equations and Relationships
Lesson 11.1:  Writing Equations to Represent Situations
Lesson 11.2:  Addition and Subtraction Equations
Lesson 11.3:  Multiplication and Division Equations
Unit 6
Lesson 1:  Weight For It
Lesson 11.4: Writing InequalitiesUnit 7
Lesson 7:  Tunnel Travels
Module 12:  Relationships in Two Variables
Lesson 12.2:  Independent and Dependent Variables in Tables and GraphsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)
Lesson 12.3:  Writing Equations from Tables.Unit 6
Lesson 16: Subway Fares
Take Away (coming soon!)
Lesson 12.4:  Representing Algebraic Relationships in Tables and GraphsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 6: Relationships in Geometry

GO Math!Amplify Classroom
Module 13: Area and Polygons
Lesson 13.1: Area of QuadrilateralsUnit 1
Lesson 1: Shapes on a Plane
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 13.2: Area of TrianglesUnit 1
Lesson 1: Shapes on a Plane
Lesson 13.4: Area of PolygonsUnit 1
Lesson 1: Shapes on a Plane
Module 14:  Distance and Area in the Coordinate Plane
Lesson 14.1: Distance in the Coordinate Plane
Lesson 14.2: Polygons in the Coordinate Plane
Unit 1
Lesson 1: Shapes on a Plane

Unit 7: Measurement and Data

Module 16: Displaying, Analyzing, and
Summarizing Data
Lesson 16.1: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 16.4: Dot Plots and Data DistributionUnit 8
Lesson 3: Minimum Wage
Lesson 16.5: HistogramsUnit 8
Lesson 5: The Plot Thickens

Grade 7

Unit 1: The Number System

GO Math!Amplify Classroom
Module 1:  Adding and Subtracting Integers
Lesson 1.2: Adding Integers With Different Signs
Lesson 1.3: Subtracting Integers
Unit 5
Lesson 1: Floats and Anchors
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Module 2: Multiplying and Dividing Integers
Lesson 2.1: Multiplying Integers Unit 5
Lesson 10: Integer Puzzles
Lesson 2.2: Dividing IntegersUnit 5
Lesson 10: Integer Puzzles
Module 3:  Rational Numbers
Lesson 3.2: Adding Rational Numbers
Lesson 3.3: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own

Unit 2: Ratios and Proportional Relationships

Module 4:  Rates and Proportionality
Lesson 4.1: Unit RatesUnit 2
Lesson 6: Two and Two
Lesson 4.2: Constant Rates of ChangeUnit 2
Lesson 1: Paint
Lesson 6: Two and Two
Lesson 4.3:  Proportional Relationships and GraphsUnit 2
Lesson 1: Paint
Lesson 6: Two and Two
Module 5:  Proportions and Percent
Lesson 5.1: Percent Increase and DecreaseUnit 4
Lesson 1: Mosaics
Lesson 5: Percent Machines
Lesson 5.3: Applications of PercentUnit 4
Lesson 12: Posing Percent Problems(coming soon!)

Unit 3: Expressions, Equations, and Inequalities

Module 6: Expressions and Equations
Lesson 6.3: Writing Two-Step EquationsUnit 6
Lesson 10: Collect the Squares
Module 6: Expressions and Equations
Lesson 7.2: Writing Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 7.3: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Unit 4: Geometry

Module 8: Modeling Geometric Figures
Lesson 8.1: Similar Shapes and Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?
Unit 7
Lesson 5: Can You Build It?
Lesson 8.2: Geometric DrawingsUnit 1
Lesson 7: Will It Fit?
Lesson 8.4: Angle RelationshipsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Module 9:  Circumference, Area, and Volume
Lesson 9.1: CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 9.2: Area of CirclesUnit 3
Lesson 8: Area Challenges
Lesson 9.3: Area of Composite FiguresUnit 3
Lesson 8: Area Challenges

Unit 5: Statistics

Module 10: Random Samples and
Populations
Lesson 10.1: Populations and SamplesUnit 8
Lesson 10: Crab Island
Module 11: Analyzing and Comparing Data
Lesson 11.3: Using Statistical Measures to Compare PopulationsUnit 8
Lesson 10: Crab Island

Unit 6: Probability

Module 13: Theoretical Probability and
Simulations
Lesson 13.1: Theoretical Probability of Simple EventsUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Grade 8

Unit 1: Real Numbers, Exponents, and Scientific Notation

GO Math!Amplify Classroom
Module 1: Real Numbers
Lesson 1.3: Ordering Real NumbersUnit 8
Lesson 4: Root Down
Module 2: Exponents and Scientific
Notation
Lesson 2.1: Integer ExponentsUnit 7
Lesson 1: Circles
Lesson 3: Power Pairs
Lesson 2.4: Operations with Scientific NotationUnit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 2: Proportional and Nonproportional Relationships and Functions

Module 3: Proportional Relationships
Lesson 3.1: Representing Proportional Relationships.Unit 3
Lesson 1: Turtle Time Trials
Lesson 3.2: Rate of Change and SlopeUnit 3
Lesson 4: Flags
Lesson 5: The Tortoise and the Hare
Module 4: Nonproportional Relationships
Lesson 4.1: Representing Linear Nonproportional RelationshipsUnit 3
Lesson 4: Flags
Lesson 4.2: Determining Slope and y-interceptUnit 3
Lesson 4: Flags
Lesson 4.3: Graphing Linear Nonproportional Relationships using Slope and y-intercept.Unit 3
Lesson 4: Flags
Lesson 4.4: Proportional and Nonproportional SituationsUnit 3
Lesson 1: Turtle Time Trials
Module 5: Writing Linear Equations
Lesson 5.1: Writing Linear Equations from Situations and GraphsUnit 3
Lesson 4: Flags
Lesson 5.3: Linear Relationships and Bivariate DataUnit 6
Lesson 3: Robots
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Module 6: Functions
Lesson 6.1: Identifying and Representing FunctionsUnit 5
Lesson 2: Guess My Rule
Lesson 5: The Tortoise and the Hare
Lesson 6.3: Comparing FunctionsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 6.4: Analyzing GraphsUnit 5
Lesson 1: Turtle Crossing
Lesson 5: The Tortoise and the Hare

Unit 3: Solving Equations and Systems of Equations

Module 7:  Solving Linear Equations
Lesson 7.1: Equations with the Variable on Both SidesUnit 4
Lesson 5: Equation Roundtable
Lesson 7.2: Equations with Rational Numbers
Lesson 7.3: Equations with the Distributive PropertyUnit 4
Lesson 5: Equation Roundtable
Module 8:  Solving Systems of Linear Equations
Lesson 8.1: Solving Systems of Linear Equations by Graphing.Unit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 4: Transformational Geometry

Module 9:  Transformations and Congruence
Lesson 9.1: Properties of Translations
Lesson 9.2: Properties of Reflections
Lesson 9.3:  Properties of Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Module 10: Transformations and Similarity
Lesson 10.1: Properties of DilationsUnit 2
Lesson 2: Dilation Mini Golf
Lesson 6: Social Scavenger Hunt
Lesson 10.3: Similar FiguresUnit 2
Lesson 1: Sketchy Dilations
Lesson 6: Social Scavenger Hunt

Unit 5: Measurement Geometry

Module 11: Angle Relationships in Parallel Lines and Triangles
Lesson 11.1: Parallel Lines Cut by a Transversal.Unit 1
Lesson 12: Puzzling It Out
Lesson 11.2: Angle Theorems for TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 11.3: Angle-Angle SimilarityUnit 2
Lesson 6: Social Scavenger Hunt
Module 12: Pythagorean Theorem
Lesson 12.1: The Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Taco Truck
Module 13: Volume
Lesson 13.1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 13.2: Volume of ConesUnit 5
Lesson 13: Cones

Unit 6: Statistics

Module 14: Scatter Plots
Lesson 14.1: Scatter Plots and AssociationUnit 6
Lesson 3: Robots
Lesson 14.2: Trend Lines and PredictionsUnit 6
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Module 15: Two-Way Tables
Lesson 15.2: Two-Way Relative Frequency TablesUnit 6
Lesson 11: Finding Associations

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Families and caregivers, welcome to Amplify Desmos Math Texas K–5!

Welcome to the Amplify Desmos Math Texas K–5 Caregiver Hub. We’re here to support your student as they explore math, work with friends to solve problems, and learn new and interesting concepts—and to support you as you go on this math journey with them! Below are some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math Texas.

Para la versión en español, haga clic aquí.

Three children are engaging in a math activity with a grid and orange markers. One child holds a "9-3" card. The background includes beach elements and abstract math symbols.

Unit Caregiver Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of key concepts. You’ll find a Caregiver Resource for each unit, in both English and Spanish.

Unit 1: Beginning Number Concepts

Unit 2: Numbers 1–10

Unit 3: Shapes, Coins, and Financial Literacy

Unit 4: Understanding Addition and Subtraction

Unit 5: Make and Break Apart Numbers Within 10

Unit 6: Numbers 0–20

Unit 7: Solid Shapes All Around Us

Unit 1: Adding, Subtracting, and Working With Data

Unit 2: Story Problems Within 10

Unit 3: Adding and Subtracting Within 20

Unit 4: Numbers to 99 and Financial Literacy

Unit 5: Adding Within 120

Unit 6: Length Measurement Within 120 Units

Unit 7: Geometry and Time

Unit 1: Working With Data and Developing Financial Literacy

Unit 2: Adding and Subtracting Within 100

Unit 3: Measuring and Solving Problems Using Length

Unit 4: Numbers to 1,200

Unit 5: Geometry and Time

Unit 6: Adding and Subracting Within 1,000

Unit 7: Equal Groups and Area

Unit 1: Introducing Multiplication

Unit 2: Adding, Subtracting, and Rounding Larger Numbers

Unit 3: Relating Multiplication to Division

Unit 4: Fractions as Numbers

Unit 5: Measurement and Financial Literacy

Unit 6: Sorting and Classifying Shapes

Unit 1: Fraction Equivalence and Comparison

Unit 2: Extending Operations to Fractions

Unit 3: From Hundredths to One Billion

Unit 4: Mathematical Relationships and Financial Literacy

Unit 5: Multiplying and Dividing Multi-Digit Numbers

Unit 6: Angles and Properties of Shapes

Unit 1: Volume, Factors, and Expresssions

Unit 2: Multiplying and Dividing Fractions

Unit 3: Multi-Digit Multiplication and Division and Financial Literacy

Unit 4: Place Value Patterns and Decimal Operations

Unit 5: Measurement, Fraction Operations, and Data

Unit 6: Geometry and Algebraic Reasoning

Sub-Unit Summaries

Access Amplify Desmos Math at home.

In addition to a print Student Edition workbook, your student will have digital access to all learning, practice, and assessment materials through the Amplify platform. The digital curriculum can be accessed in school and at home by following these instructions:

  • Select the Amplify Desmos Math button.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, caregivers can view student work by opening previous assignments.

Learn how to navigate the student home page.

Materials overview

Amplify Desmos Math Texas supports blended learning with supporting print materials and a unique digital experience. All K–5 lessons are available in a write-in Student Edition book. Many of the lessons include hands-on activities with manipulatives, tools that help students understand abstract concepts by making them tangible. Your student will also work with digital devices for an age-appropriate number of lessons.

When students use devices, teachers can monitor their work in real time, making sure they get the exact support that they need at every part of the lesson, in and outside of class.

Una interfaz digital que muestra los nombres anónimos de los estudiantes y su estado de participación en diversas actividades. La interfaz incluye opciones para realizar resúmenes, capturas de pantalla y vistas individuales de los estudiantes.

Components of a lesson

Students in an Amplify Desmos Math Texas classroom can be seen (and heard!) asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

A typical Amplify Desmos Math Texas lesson includes:

  • Warm-up: A short, attention-getting problem to pique students’ interest in the lesson.
  • Activities: One to two mini-activities that challenge students’ problem-solving skills.
  • Synthesis: Discussion to review and bring together the important concepts from the lesson.
  • Show What You Know and Reflection: Questions for students to show what they know from the lesson. (Note: The Show What You Know lesson assessment is optional for kindergarten and grade 1.)
  • Centers: Student-led activity stations that reinforce the math learned during lesson activities through interactive and often game-like formats. In kindergarten and grade 1, time for Centers is built into the last 15 minutes of every lesson.

To support, strengthen, and stretch students’ learning after the lesson, Amplify Desmos Math Texas offers options for:

  • Differentiation: Mini-Lessons, Centers, Extensions, Boost Personalized Learning, and Fluency Practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. If your student has already completed the practice problems for the lesson, ask them to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your student follow-up questions to encourage the use of math language as they explain their thinking, such as, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students are stuck, ask support questions, such as, “What information do you know here?” or “How could you represent this problem?”

Your student’s teacher may introduce a Center game with students in the lesson or beyond the lesson. These games are aligned to the math of the unit and can be played with students outside of class. Your student’s teacher may introduce a Center game to students during or after completing a lesson, or you may need to teach the game before you play by using easy-to-follow instructions. Try out the following Center games with your student!

Each unit in Amplify Desmos Math begins with a Read-Aloud to engage students and provide context for the math of the unit. Elements and characters from the Unit Story then appear in lessons throughout the unit.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Relate math to daily activities at home, whether grocery shopping, preparing a meal, or planning for a trip to the store. Your student can help you figure out how many more apples there are than oranges in the grocery cart, show how to split a sandwich into fourths, or figure out how much change you’ll receive in exchange for a $10 bill. Encourage your student to point out ways that you use math in your daily tasks.

Remind your student that getting stuck is part of the process—a necessary and beneficial part of learning. Many students (and adults) fear making mistakes, but research shows that mistakes help our brains grow! When your student gets stuck on a problem, encourage them to keep trying different strategies even if they’re not sure they’re right.

Eureka Math-NEW

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Eureka Math® crosswalk to Amplify Desmos Math free lessons

Grade 6

Module 1: Ratios and Unit Rates

Eureka MathAmplify Classroom
Topic A Representing and Reasoning About Ratios 
Lesson 3: Equivalent Ratios
Lesson 4: Equivalent Ratios
Unit 2
Lesson 4: Fruit Lab
Topic C Unit Rates 
Lesson 16: From Ratio to RatesUnit 3
Lesson 6: Soft Serve
Lesson 18: Finding a Rate by Dividing Two QuantitiesUnit 3
Lesson 6: Soft Serve
Lesson 24: Percent and Rates per 100Unit 3
Lesson 9: Lucky Duckies

Module 2: Arithmetic Operations Including Division of Fractions

Topic A Dividing Fractions by Fractions
Lesson 2: Interpreting Division of a Whole Number by a Fraction —Visual Models.Unit 4
Lesson 3: Flour Planner
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Unit 4
Lesson 6: Fill the Gap
Lesson 8: Dividing Fractions and Mixed NumbersUnit 4
Lesson 6: Fill the Gap
Topic B Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
Lesson 9: Sums and Differences of DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Rational Numbers

Topic B Order and Absolute Value
Lesson 7: Ordering Integers and Other Rational Numbers
Lesson 8: Ordering Integers and Other Rational Numbers
Lesson 9: Comparing Integers and Other Rational Numbers
Unit 7Lesson 4: Order in the Class

Module 4: Expressions and Equations

Topic D Expanding, Factoring, and Distributing Expressions 
Lesson 9: The Relationship of Addition and SubtractionUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 11: Factoring Expressions
Lesson 12: Distributing Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic F Writing and Evaluating Expressions and Formulas 
Lesson 18: Writing and Evaluating Expressions—Addition and Subtraction
Lesson 19: Substituting to Evaluate Addition and Subtraction Expressions
Lesson 20: Writing and Evaluating Expressions—Multiplication and Division
Lesson 21: Writing and Evaluating Expressions—Multiplication and Addition
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic G Solving Equations 
Lesson 23: True and False Number Sentences
Lesson 24: True and False Number Sentences
Unit 6
Lesson 1: Weight for It
Lesson 25: Finding Solutions to Make Equations TrueUnit 6
Lesson 1: Weight for It
Lesson 26: One-Step Equations—Addition and SubtractionUnit 6
Lesson 1: Weight for It
Topic H Applications of Equations 
Lesson 33: From Equations to Inequalities
Lesson 34: Writing and Graphing Inequalities in Real-World Problems
Unit 7
Lesson 7: Tunnel Travels

Module 5: Area, Surface Area, and Volume Problems

Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 1: The Area of Parallelograms Through Rectangle FactsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Topic D Nets and Surface Area 
Lesson 18: Determining Surface Area of Three-Dimensional FiguresUnit 1
Lesson 10: Renata’s Stickers

Module 6: Statistics

Topic A Understanding Distributions 
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Unit 8
Lesson 3: Minimum Wage
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Unit 8
Lesson 5: The Plot Thickens
Topic C Summarizing a Distribution That Is Skewed Using the Median and the Interquartile Range 
Lesson 12: Describing the Center of a Distribution Using the MedianUnit 8
Lesson 11: Toy Cars
Topic D Summarizing and Describing Distributions 
Lesson 18: Connecting Graphical Representations and Numerical SummariesUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Creating a Dot PlotUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Ratios and Proportional Relationships

Eureka MathAmplify Classroom
Topic A Proportional Relationships 
Lesson 1: An Experience in Relationships as Measuring RateUnit 2
Lesson 1: Paint
 
Unit 4
Lesson 1: Mosaics
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs
Lesson 6: Identifying Proportional and Non-Proportional Relationships in Graphs
Unit 2
Lesson 8: Dino Pops
Topic B Unit Rate and the Constant of Proportionality 
Lesson 8: Representing Proportional Relationships with Equations
Lesson 9: Representing Proportional Relationships with Equations
Unit 2
Lesson 6: Two and Two
Lesson 10: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Topic C Ratios and Rates Involving Fractions 
Lesson 11: Ratios of Fractions and Their Unit Rates
Lesson 12: Ratios of Fractions and Their Unit Rates
Unit 2
Lesson 6: Two and Two
Lesson 15: Equations of Graphs of Proportional Relationships Involving FractionsUnit 2
Lesson 8: Dino Pops
Topic D Ratios of Scale Drawings 
Lesson 16: Relating Scale Drawings to Ratios and RatesUnit 1
Lesson 1: Scaling Machines
Lesson 18: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Lesson 19: Computing Actual Areas from a Scale DrawingUnit 1
Lesson 7: Will It Fit?

Module 2: Rational Numbers

Topic A Addition and Subtraction of Integers and Rational Numbers 
Lesson 1: Opposite Quantities Combine to Make ZeroUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Using the Number Line to Model the Addition of Integers
Lesson 3: Understanding Addition of Integers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 7: Addition and Subtraction of Rational NumbersUnit 5
Lesson 4: Draw Your Own
Lesson 10; Integer Puzzles
Topic B Multiplication and Division of Integers and Rational Numbers 
Lesson 10: Understanding Multiplication of Integers
Lesson 11: Develop Rules for Multiplying Signed Numbers
Unit 5
Lesson 10: Integer Puzzles
Lesson 15: Multiplication and Division of Rational NumbersUnit 5
Lesson 10: Integer Puzzles

Module 3: Expressions and Equations

Topic A Use Properties of Operations to Generate Equivalent Expressions 
Lesson 3: Writing Products as Sums and Sums as Products
Lesson 4: Writing Products as Sums and Sums as Products
Unit 6
Lesson 10: Collect the Squares
Topic B Solve Problems Using Expressions, Equations, and Inequalities 
Lesson 8: Using If-Then Moves in Solving Equations
Lesson 9: Using If-Then Moves in Solving Equations
Unit 6Lesson 10: Collect the Squares
Lesson 10: Angle Problems and Solving EquationsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Lesson 12: Properties of Inequalities
Lesson 13: Inequalities
Lesson 14: Solving Inequalities
Unit 6
Lesson 16: Shira the Sheep
Topic C Use Equations and Inequalities to Solve Geometry Problems 
Lesson 16: The Most Famous Ratio of AllUnit 3
Lesson 3: Measuring Around
Lesson 17: The Area of a CircleUnit 3
Lesson 9: Area Challenges
Lesson 18: More Problems on Area and CircumferenceUnit 3
Lesson 9: Area Challenges

Module 4: Percent and Proportional Relationships

Topic A Finding the Whole 
Lesson 1: PercentUnit 4
Lesson 1: Mosaics
Lesson 2: Part of a Whole as a PercentUnit 4
Lesson 1: Mosaics
Lesson 3: Comparing Quantities with PercentUnit 4
Lesson 1: Mosaics
Lesson 4: Percent Increase and DecreaseUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 5: Finding One Hundred Percent Given Another Percent 
Lesson 6: Fluency with PercentsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Topic B Percent Problems Including More Than One Whole 
Lesson 7: Markup and Markdown ProblemsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 8: Percent Error Problems
Lesson 9: Problem Solving When the Percent Changes
Unit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 10: Simple Interest 
Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent ApplicationsUnit 4
Lesson 12: Posing Percent Problems
(coming soon!)
Topic C Scale Drawings 
Lesson 13: Changing ScalesUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?
Lesson 14: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Topic D Population, Mixture, and Counting Problems Involving Percents 
Lesson 16: Population ProblemsUnit 8
Lesson 10: Crab Island

Module 5: Statistics and Probability

Topic A Calculating and Interpreting Probabilities 
Lesson 1: Chance ExperimentsUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities
Topic C Random Sampling and Estimating Population Characteristics 
Lesson 13: Populations, Samples, and Generalizing from a Sample to a PopulationUnit 8
Lesson 10: Crab Island
Lesson 14: Selecting a Sample
Lesson 15: Random Sampling
Lesson 16: Methods for Selecting a Random Sample
Unit 8
Lesson 10: Crab Island
Topic D Comparing Populations 
Lesson 22: Using Sample Data to Compare the Means of Two or More Populations
Lesson 23: Using Sample Data to Compare the Means of Two or More Populations
Unit 8
Lesson 10: Crab Island

Module 6: Geometry

Topic A Unknown Angles 
Lesson 1: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 2: Solving for Unknown Angles Using Equations
Lesson 3: Solving for Unknown Angles Using Equations
Lesson 4: Solving for Unknown Angles Using Equations
Unit 7
Lesson 4: Missing Measures
Topic B Constructing Triangles 
Lesson 8: Drawing TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 11: Conditions on Measurements That Determine a TriangleUnit 7
Lesson 5: Can You Build It?
Topic D Problems Involving Area and Surface Area 
Lesson 22: Area Problems with Circular RegionsUnit 3
Lesson 9: Area Challenges

Grade 8

Module 1: Integer Exponents and Scientific Notation

Eureka MathAmplify Classroom
Topic A Exponential Notation and Properties of Integer Exponents 
Lesson 1: Exponential NotationUnit 7 
Lesson 1: Circles
Lesson 2: Multiplication of Numbers in Exponential Form
Lesson 3: Numbers in Exponential Form Raised to a Power
Unit 7 
Lesson 3: Power Pairs
Topic B Magnitude and Scientific Notation 
Lesson 9: Scientific Notation
Lesson 10: Operations with Numbers in Scientific Notation
Unit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: The Concept of Congruence

Topic A Definitions and Properties of the Basic Rigid Motions 
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 3: Translating LinesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Topic B Sequencing the Basic Rigid Motions 
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Unit 1
Lesson 13: Tessellate
Lesson 14: More on the Angles of a TriangleUnit 1 
Lesson 12: Puzzling It Out

Module 3: Similarity

Topic A Dilation 
Lesson 1: What Lies Behind “Same Shape”?Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 2: Properties of Dilations
Lesson 3: Examples of Dilations
Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 4: Fundamental Theorem of Similarity
Lesson 5: First Consequences of FTS
Unit 2
Lesson 6: Social Scavenger Hunt
Topic B Similar Figures 
Lesson 8: Similarity
Lesson 9: Basic Properties of Similarity
Unit 2
Lesson 6: Social Scavenger Hunt
Topic C The Pythagorean Theorem 
Lesson 13: Proof of the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle

Module 4: Linear Equations

Topic A Writing and Solving Linear Equations 
Lesson 4: Solving a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Writing and Solving Linear EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Solutions of a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Topic B Linear Equations in Two Variables and Their GraphsUnit 3
Lesson 4: Flags
Lesson 10: A Critical Look at Proportional RelationshipsUnit 3
Lesson 1: Turtle Time TrialsLesson 4: Flags
Lesson 11: Constant RateUnit 3
Lesson 4: Flags
Lesson 13: The Graph of a Linear Equation in Two VariablesUnit 3 
Lesson 4: Flags
Topic C Slope and Equations of Lines 
Lesson 15: The Slope of a Non-Vertical LineUnit 3
Lesson 4: Flags
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given SlopeUnit 3
Lesson 4: Flags
Lesson 19: The Graph of a Linear Equation in Two Variables Is a LineUnit 3
Lesson 4: Flags
Lesson 20: Every Line Is a Graph of a Linear EquationUnit 3
Lesson 4: Flags
Lesson 22: Constant Rates RevisitedUnit 3
Lesson 1: Turtle Time Trials
Topic D Systems of Linear Equations and Their Solutions 
Lesson 25: Geometric Interpretation of the Solutions of a Linear SystemUnit 4  
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Module 5: Examples of Functions from Geometry

Topic A Functions 
Lesson 1: The Concept of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Formal Definition of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 3: Linear Functions and ProportionalityUnit 3
Lesson 1: Turtle Time Trials
Lesson 5: Graphs of Functions and EquationsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 6: Graphs of Linear Functions and Rate of ChangeUnit 3
Lesson 4: Flags
Lesson 7: Comparing Linear Functions and GraphsUnit 5
Lesson 5: The Tortoise and the Hare
Topic B Volume 
Lesson 10: Volumes of Familiar Solids—Cones and CylindersUnit 5
Lesson 11: Cylinders

Module 6: Linear Functions

Topic A Linear Functions 
Lesson 2: Interpreting Rate of Change and Initial ValueUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Increasing and Decreasing Functions
Lesson 5: Increasing and Decreasing Functions
Unit 5
Lesson 1: Turtle CrossingLesson 5: The Tortoise and the Hare
Topic B Bivariate Numerical Data 
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Unit 6 
Lesson 3: Robots
Lesson 8: Informally Fitting a LineUnit 6
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Unit 5
Lesson 5: The Tortoise and the Hare
Topic D Bivariate Categorical Data 
Lesson 14: Association Between Categorical VariablesUnit 6
Lesson 11: Finding Associations

Module 7: Introduction to Irrational Numbers Using Geometry

Topic A Square and Cube Roots 
Lesson 2: Square RootsUnit 8
Lesson 4: Root Down
Lesson 4: Simplifying Square RootsUnit 8
Lesson 4: Root Down
Topic C The Pythagorean Theorem 
Lesson 18: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck

Algebra 1

Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs

Topic A: Introduction to Functions Studied this Year—Graphing Stories

Lesson 1: Graphs of Piecewise FunctionsPumpkin Prices
Lesson 2: Graphs of Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns

Topic C: Solving Equations and Inequalities

Lesson 10: True and False EquationsSame Position
Lesson 11: Solution Sets for Equations and InequalitiesWorking Backwards
Solving Strategies
Shelley the Snail
Lesson 19: Rearranging FormulasSubway Seats
Various Variables
Lesson 21: Solution Sets to Inequalities with Two VariablesPizza Delivery
Lesson 22 & Lesson 23: Solution Sets to Simultaneous Equations (and Inequalities)Shape It Up
Lizard Lines
Quilts
Seeking Solutions

Module 2: Descriptive Statistics

Topic D: Numerical Data on Two Variables

Lesson 14: Modeling Relationships with a LineCity Slopes
Residual Fruit
Penguin Populations
Lesson 19: Interpreting CorrelationCorrelation Coefficient
How Hot Is It?
Behind the Headlines
City Data

Module 3: Linear and Exponential Functions

Topic A: Linear and Exponential Sequences

Lesson 3: Arithmetic and Geometric SequencesSequence Carnival
More Visual Patterns
Lesson 5: The Power of Exponential GrowthCarlos’s Fish

Topic B: Describing Variability and Comparing Distributions

Lesson 4: Summarizing Deviations from the MeanFinding Desmo
Lesson 13: Interpreting the Graph of a FunctionCraft-a-Graph
Lesson 14: Linear and Exponential Models – Comparing Growth RatesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Topic D: Using Functions and Graphs to Solve Problems

Lesson 21: Comparing Linear and Exponential Models AgainPlane, Train, and Automobile
Lesson 21: Comparing Linear and Exponential Models AgainCarlos’s Fish

Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

Topic A: Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles

Lesson 8: Exploring the Symmetry in Graphs of Quadratic FunctionsOn the Fence
Plenty of Parabolas
Robot Launch
Lesson 9: Graphing Quadratic Functions from Factored Form, 𝑓(𝑥)=𝑎(𝑥−𝑚)(𝑥−𝑛)Two for One
Parabola Zapper
Shooting Stars
Lesson 10: Interpreting Quadratic Functions from Graphs and TablesStomp Rockets

Topic B: Using Different Forms for Quadratic Functions

Lessons 11–12: Completing the SquareSquare Tactic
Lesson 15: Using the Quadratic FormulaStomp Rockets in Space

Topic C: Function Transformations and Modeling

Lesson 18: Graphing Cubic, Square Root, and Cube Root FunctionsSorting Relationships
Lesson 22: Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different WaysSorting Relationships

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Chapter 2: Fractions and Decimals

Big IdeasAmplify Classroom
Lesson 2: Dividing FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 7: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Chapter 3: Ratios and Rates

Lesson 1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 4: Fruit Lab
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 3: Using Ratio TablesUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Graphing Ratio RelationshipsUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Converting MeasuresUnit 3
Lesson 1: Many Measurements

Chapter 4: Percents

Lesson 1: Percent and FractionsUnit 3
Lesson 9: Lucky Duckies
Lesson 2: Percent and DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Chapter 5: Algebraic Expressions and Properties

Lesson 2: Writing ExpressionsUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 3: Properties of Addition and MultiplicationUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 4: The Distributive PropertyUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)

Chapter 6: Equations

Lesson 1: Writing Equations in One VariableUnit 6
Lesson 1: Weight for It

Chapter 7: Area, Surface Area, and Volume

Lesson 1: Areas of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 5: Surface Area of prismsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Lesson 1: IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Comparing and Ordering IntegersUnit 7
Lesson 4: Order in the Class
Lesson 3: Rational NumbersUnit 7
Lesson 4: Order in the Class
Lesson 7: Writing and Graphing InequalitiesUnit 7
Lesson 7: Tunnel Travels

Chapter 9: Statistical Measures

Lesson 1: Introduction to StatisticsUnit 8
Lesson 3: Minimum Wage
Lesson 2: MeanUnit 8
Lesson 11: Toy Cars
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 4: Measures of VariationUnit 8
Lesson 11: Toy Cars

Chapter 10: Data Displays

Lesson 2: HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 4: Choosing Appropriate MeasuresUnit 8
Lesson 3: Minimum Wage
Lesson 11: Toy Cars

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Big IdeasAmplify Classroom
Lesson 1: Rational NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Adding Integers
Lesson 4: Subtracting Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Adding Rational Numbers
Lesson 5: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 10: Integer Puzzles

Chapter 3: Expressions

Lesson 1: Algebraic ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 2: Adding and Subtracting Linear ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 3: The Distributive PropertyUnit 6
Lesson 10: Collect the Squares

Chapter 4: Equations and Inequalities

Lesson 1: Solving Equations Using Addition or Subtraction
Lesson 2: Solving Equations Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 4: Writing and Graphing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 5: Solving Inequalities Using Addition or Subtraction
Lesson 6: Solving Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 7: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Chapter 5: Ratios and Proportions

Lesson 1: Ratio and Ratio TablesUnit 2
Lesson 1: Paint
Lesson 3: Identifying Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 3: Measuring Around
Lesson 5: Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 6: Percents

Lesson 1: Fraction, Decimals, and PercentsUnit 4
Lesson 1: Mosaics
 
Lesson 4: Percents of Increase and DecreaseUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Discounts and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 7: Probability

Chapter 8: Statistics

Lesson 1: Samples and PopulationsUnit 8
Lesson 10: Crab Island
Lesson 2: Using Random Samples to Describe populationsUnit 8 
Lesson 10: Crab Island
Lesson 3: Comparing Populations
Lesson 4: Using Random Samples to Compare Populations
Unit 8
Lesson 10: Crab Island

Chapter 9: Geometric Shapes and Angles

Lesson 1: Circle and CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 2: Areas of CirclesUnit 3
Lesson 9: Area Challenges
Lesson 5: Finding Unknown Angle MeasuresUnit 7
Lesson 4: Missing Measures

Grade 8

Chapter 1: Equations

Big ideasAmplify Classroom
Lesson 2: Solving Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 3: Solving Equations with Variables on Both SidesUnit 4
Lesson 5: Equation Roundtable

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Lesson 2: Angles and TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 4: Using Similar TrianglesUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Chapter 4: Graphing and Writing Linear Equations

Lesson 1: Graphing Linear EquationsUnit 3 Lesson 4: Flags
Lesson 2: Slope of a LineUnit 3 Lesson 4: Flags
Lesson 3: Graphing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphing Linear Equations in Slope-Intercept FormUnit 3
Lesson 4: Flags

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Data Analysis and Displays

Lesson 1: Scatter PlotsUnit 6
Lesson 3: Robots
Lesson 2: Lines of FitUnit 6
Lesson 4: Dapper Cats
Lesson 3: Two-Way TablesUnit 6
Lesson 11: Finding Associations

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare

Chapter 8: Exponents and Scientific Notation

Lesson 1: ExponentsUnit 7
Lesson 3: Power Pairs
Lesson 2: Products of Powers PropertyUnit 7
Lesson 3: Power Pairs
Lesson 6: Scientific Notation
Lesson 7: Operations in Scientific Notation
Unit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 4: Root Down
Lesson 3: Finding Cube RootsUnit 8
Lesson 4: Root Down

Chapter 10: Volume and Similar Solids

Lesson 1: Volumes of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volumes of ConesUnit 5
Lesson 13: Cones

Algebra 1

Chapter 1: Solving Linear Equations

Lesson 1.1: Solving Simple EquationsWorking Backwards
Lesson 1.3: Solving Equations with Variables on Both SidesSolving Strategies
Same Position
Lesson 1.5: Rewriting Equations and FormulasSubway Seats
Various Variables

Chapter 2: Solving Linear Inequalities

Lesson 2.4: Solving Multi-Step InequalitiesPizza Delivery

Chapter 3: Graphing Linear Functions

Lesson 3.2: Linear FunctionsShelley the Snail
Lesson 3.5: Graphing Linear Equations in Slope Intercept FormFive Representations

Chapter 4: Writing Linear Functions

Lesson 4.4: Scatter Plots and Lines of FitCorrelation Coefficient
How Hot Is It?
City Slopes
Lesson 4.5: Analyzing Lines of FitPenguin Populations
Behind the Headlines
City Data
Residual Fruit
Lesson 4.6: Arithmetic SequencesMore Visual Patterns
Sequence Carnival
Lesson 4.7: Piecewise FunctionsPumpkin Prices

Chapter 5: Solving Systems of Linear Equations

Lesson 5.2: Solving Systems of Linear Equations by SubstitutionShape It Up
Lesson 5.4: Solving Special Systems of Linear EquationsLizard Lines
Lesson 5.7: Systems of Linear InequalitiesQuilts
Seeking Solutions

Chapter 6: Exponential Functions and Sequences

Lesson 6.3: Exponential FunctionsCarlos’s Fish
Lesson 6.6: Geometric SequencesMore Visual Patterns
Sequence Carnival

Chapter 8: Graphing Quadratic Functions

Lesson 8.1: Solving Systems of Linear Equations by SubstitutionCraft-a-Graph
Quadratic Visual Patterns
Lesson 8.4: Solving Special Systems of Linear EquationsOn the Fence
Stomp Rockets
Plenty of Parabolas
Robot Launch
Lesson 8.5: Systems of Linear InequalitiesParabola Zapper
Two for One
Shooting Stars
Lesson 8.6: Systems of Linear InequalitiesPlane, Train, and Automobile
Detroit’s Population, Part 1
Detroit’s Population, Part 2
Revisiting Visual Patterns, Part 1
Sorting Relationships

Chapter 9: Solving Quadratic Equations

Lesson 9.4: Solving Quadratic Equations by Completing the SquareSquare Tactic
Lesson 9.5: Solving Quadratic Equations Using the Quadratic FormulaStomp Rockets in Space

Chapter 10: Radical Functions and Equations

Lesson 10.4: Inverse of a FunctionChip the Robot

Chapter 11: Data Analysis and Displays

Lesson 11.1: Measures of Center and VariationFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Chapter 1: Use Positive Rational Numbers

enVision MathDesmos Classroom
Lesson 1: Fluently Add, Subtract, and Multiply DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 2: Fluently Divide Whole Numbers and DecimalsUnit 5
Lesson 13: Movie Time
Lesson 4: Understand Division with FractionsUnit 4
Lesson 13: Movie Time
Lesson 6: Divide Mixed NumbersUnit 4
Lesson 6 Fill the Gap
Lesson 7: Solve Problems with Rational NumbersUnit 4
Lesson 3: Flour Planner

Chapter 2: Integers and Rational Numbers

Lesson 1: Understand IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Represent Rational Numbers on the Number LineUnit 7
Lesson 4: Order in the Class

Chapter 3: Numeric and Algebraic Expressions

Lesson 4: Write Algebraic ExpressionsUnit 6
Lesson 8: Products and SumsTake Away (coming soon!)
Lesson 6: Generate Equivalent Expressions Unit 6
Lesson 8: Products and SumsTake Away (coming soon!)

Chapter 4: Represent and Solve Equations and Inequalities

Lesson 1: Understand Equations and SolutionsUnit 6
Lesson 1: Weight for It
Lesson 6: Understand and Write InequalitiesUnit 7
Lesson 7: Tunnel Travels
Lesson 9: Use Patterns to Write and Solve Equations
Lesson 10: Relate Tables, Graphs, and Equations
Unit 6
Lesson 16: Subway FaresTake Away (coming soon!)

Chapter 5: Understand and Use Ratio and Rate

Lesson 1: Understand RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Generate Equivalent RatiosUnit 2
Lesson 4: Fruit Lab
Lesson 4: Represent and Graph RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Compare Unit RatesUnit 3
Lesson 6: Soft Serve

Chapter 6: Understand and Use Percent

Lesson 1: Understand PercentUnit 3
Lesson 9: Lucky Duckies

Chapter 7: Solve Area, Surface Area, and Volume Problems

Lesson 1: Find Areas of Parallelograms and RhombusesUnit 1
Lesson 3: Exploring Parallelograms, Part 1
Exploring Parallelograms, Part 2
Lesson 5: Represent Solid Figures Using NetsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Display, Describe, and Summarize data

Lesson 2: Summarize data Using Mean, Median, and ModeUnit 8 
Lesson 11: Toy Cars
Lesson 4: Display Data in Frequency Tables and HistogramsUnit 8 
Lesson 5: The Plot Thickens
Lesson 7: Summarize Data DistributionsUnit 8 
Lesson 3: Minimum Wage

Grade 7

Chapter 1: Rational Number Operations

enVision MathDesmos Classroom
Lesson 1: Relate Integers and Their OppositesUnit 5
Lesson 1: Floats and Anchors
Lesson 3: Add Integers
Lesson 4: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 5: Add and Subtract Rational NumbersUnit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 6: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 7: Multiply Rational NumbersUnit 5
Lesson 10: Integer Puzzles
Lesson 9: Divide Rational NumbersUnit 5
Lesson 10: Integer Puzzles

Chapter 2: Analyze and Use Proportional Relationships

Lesson 3: Understand Proportional Relationships: Equivalent RatiosUnit 2
Lesson 1: Paint
Lesson 4: Describe Proportional Relationships: Constant of ProportionalityUnit 2
Lesson 6: Two and Two
Lesson 5: Graph Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 3: Analyze and Solve Percent Problems

Lesson 1: Analyze Percents of Numbers
Lesson 2: Connect Percent and Proportion
Unit 4
Lesson 1: Mosaics
Lesson 4: Solve Percent Change and Percent Error ProblemsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Solve Markup and Markdown ProblemsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 4: Generate Equivalent Expressions

Lesson 3: Simplify ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 4: Expand ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 6: Add Expressions
Lesson 7: Subtract Expressions
Unit 6
Lesson 10: Collect the Squares

Chapter 5: Solve Problems Using Equations and Inequalities

Lesson 4: Solve Inequalities Using Addition or Subtraction
Lesson 5: Solve Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 6: Solve Two-Step Inequalities
Lesson 7: Solve Multi-Step Problems
Unit 6
Lesson 16: Shira the Sheep

Chapter 6: Use Sampling to Draw Inferences About Populations

Lesson 1: Populations and SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Draw Inferences from DataUnit 8 
Lesson 10: Crab Island
Lesson 3: Make Comparative Inferences About Populations
Lesson 4: Make More Comparative Inferences About Populations
Unit 8
Lesson 10: Crab Island

Chapter 7: Probability

Lesson 1: Understand Likelihood and ProbabilityUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Chapter 8: Solve Problems Involving Geometry

Lesson 1: Solve Problems Involving Scale DrawingsUnit 1 Lesson 1: Scaling Machines Lesson 7: Will It Fit?
Lesson 3: Draw Triangles with Given ConditionsUnit 7
Lesson 5: Can You Build It?
Lesson 4: Solve Problems Using Angle RelationshipsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Lesson 5: Solve Problems Involving Circumference of a CircleUnit 7
Lesson 3: Measuring Around
Lesson 6: Solve Problems Involving Area of a CircleUnit 3
Lesson 9: Area Challenges

Grade 8

Chapter 1: Real Numbers

enVision MathDesmos Classroom
Lesson 4: Evaluate Square Roots and Cube RootsUnit 8
Lesson 4: Root Down
Lesson 6: Use Properties of Integer ExponentsUnit 7  
Lesson 3: Power Pairs
Lesson 9: Understand Scientific NotationUnit 7  
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 2: Analyze and Solve Linear Equations

Lesson 3: Solve Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Compare Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 6: Connect proportional Relationships and SlopeUnit 3
Lesson 4: Flags
Lesson 8: Understand the y-intercept of a LineUnit 3
Lesson 4: Flags

Chapter 3: Use Functions to Model Relationships

Lesson 1: Understand Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Connect Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 5: Intervals of Increase and DecreaseUnit 5
Lesson 1: Turtle Crossing

Chapter 4: Investigate Bivariate Data

Lesson 1: Construct and Interpret Scatter PlotsUnit 6  
Lesson 3: Robots
Lesson 2: Analyze Linear AssociationUnit 6  
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 5: Interpret Two-Way Relative Frequency TablesUnit 6  
Lesson 11: Finding Associations

Chapter 5: Analyze and Solve Systems of Linear Equations

Lesson 2: Solve Systems by GraphingUnit 4  
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Congruence and Similarity

Lesson 1: Analyze TranslationsUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 2: Analyze Reflections
Lesson 3: Analyze Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 6: Describe DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 7: Understand Similar FiguresUnit 2
Lesson 6: Social Scavenger Hunt
Lesson 9: Interior and Exterior Angles of TrianglesUnit 1
Lesson 12: Puzzling It Out

Chapter 7: Understand and Apply the Pythagorean Theorem

Lesson 1: Understand the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 3: Apply the Pythagorean Theorem to Solve ProblemsUnit 8
Lesson 10: Taco Truck

Chapter 8: Solve Problems Involving Surface Area and Volume

Lesson 2: Find Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 3: Find Volume of ConesUnit 5
Lesson 13: Cones

Algebra 1

Topic 1: Solving Equations and Inequalities

Lesson 1-2: Solving Linear EquationsWorking Backwards
Lesson 1-3: Solving Equations with Variables on Both SidesSolving Strategies
Same Position
Lesson 1-4: Literal Equations and FormulasSubway Seats
Various Variables
Lesson 1-5: Solving Inequalities in One VariablePizza Delivery

Topic 2: Linear Functions

Lessons 2-1 to 2-3 Forms of Linear EquationsSubway Seats
Five Representations

Topic 3: Linear Functions

Topic 4: Systems of Linear Equations and Inequalities

Lesson 4-1: Solving Systems of Equations by GraphingLizard Lines
Lesson 4-2: Solving Systems of Equations by SubstitutionShape It Up
Lesson 4-5: Systems of Linear InequalitiesQuilts
Seeking Solutions

Topic 5: Piecewise Functions

Lesson 5-2: Piecewise-Defined FunctionsPumpkin Prices

Topic 6: Exponents and Exponential Functions

Lesson 6-2: Exponential FunctionsCarlos’s Fish
Revisiting Visual Patterns, Part 1
Lesson 6-4: Geometric SequencesSequence Carnival
More Visual Patterns

Topic 8: Quadratic Functions

Lesson 8-1: Key Features of a Quadratic FunctionQuadratic Visual Patterns
Lesson 8-2: Quadratic Functions in Vertex FormOn the Fence
Plenty of Parabolas
Lesson 8-5: Linear, Exponential and Quadratic ModelsDetroit’s Population, Part 1
Detroit’s Population, Part 2
Sorting Relationships
Lesson 8-3: Quadratic Functions in Standard FormRobot Launch
Lesson 8-4: Modeling with Quadratic FunctionsStomp Rockets

Topic 9: Solving Quadratic Equations

Lesson 9-2: Solving Quadratic Equations by FactoringTwo for One
Parabola Zapper
Shooting Stars
Lesson 9-5: Completing the SquareSquare Tactic
Lesson 9-6: The Quadratic Formula and the DiscriminantStomp Rockets in Space

Topic 10: Working with Functions

Lesson 10-1: The Square Root functionPlane, Train, and Automobile
Lesson 10-3: Analyzing Functions GraphicallyCraft-a-Graph
Lesson 10-7: Inverse FunctionsChip the Robot

Topic 11: Statistics

Lesson 11-4: Standard DeviationFinding Desmo

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Module 1: Composing and Decomposing

Topic 1: Factors and Multiples

MATHbookLesson 1: Taking Apart Numbers and ShapesProducts and Sums
MATHbookLesson 5: Yours IS to Reason Why!Fill the Gap

Topic 2: Area, Volume, and Surface Area

MATHbookLesson 1: All About That Base….and HeightExploring Triangles
Triangles and Parallelograms
MATHbookLesson 2: Slicing and Dicing: Composit FigureShapes on a Plane
Letters

Topic 3: Decimals

MATHbookLesson 1: You Have a PointDishing Out Decimals
MATHbookLesson 2: Get In LineDecimal Diagrams and Algorithms
MATHbookLesson 4: Dividend In the HouseMovie Time

Topic 4: Fraction by Fraction Division

MATHiaLesson 1: Representing Fraction DivisionFlour Planner

Topic 5: Area of Triangles and Quadrilaterals

MATHiaLesson 2: Developing Area FormulasExploring Parallelograms,
Part 1
MATHiaLesson 3: Calculating Areas of Various FiguresExploring Parallelograms,
Part 2

Off the Grid, Part 1
Off the Grid, Part 2

Topic 6: Composite Figures

MATHiaLesson 2: Calculating Area of Composite FiguresPile of Polygons

Topic 8: Surface Area of Regulat Prisms and Pyramids

MATHiaLesson 1: Determing Surface Area Using NetsRenata’s Stickers

Module 2: Relating Quantitites

Topic 1: Ratios

MATHbookLesson 2: Going StrongPizza Maker
MATHbookLesson 3: Different but the SamePizza Maker
MATHbookLesson 4: A trip to the MoonFruit Lab

Topic 2: Percents

MATHbookLesson 2: Warming the BenchLucky Duckies

Topic 3: Using Tables to Represent Equivalent Ratios

MATHbookLesson 1: Many ways to MeasureMany Measurements
Model Trains
MATHbookLesson 2: What is the Best Buy?World Records
MATHbookLesson 3: A Trip to the MoonWelcome to the Robot Factory
MATHiaLesson 2: Using Tables to Determine Equivalent RatiosDisaster Preparation
MATHiaLesson 3: Problem Solving with Equivalent Rations and Rates using TablesDisaster Preparation

Topic 9: Introduction to Unit Rate

MATHiaLesson 2: Determining and Comparing RatesSoft Serve
More Soft Serve

Module 3: Determining Unknown Values

Topic 2: Equations

MATHbookLesson 2: Double TalkWeight for It
MATHbookLesson 3: Play It in ReverseWeight for It
MATHbookLesson 4: One, None, or a TonTunnel Travels
MATHbookLesson 5: Getting RealFive Equations
Swap and Solve

Topic 3: Graphing Quantitative Relationships

MATHbookLesson 3: Planes, Trains, and PaychecksSubway Fares

Topic 6: Solving One-Step Addition and Subtraction Equations

MATHiaLesson 1: Exploring One-Step Equations with Double-Number LinesHanging Around

Topic 7: Solving One-Step Multiplication and Division Equations

MATHiaLesson 1: Using Double Number Lines to Solve One-Step Multiplicaiton EquationsHanging Around

Topic 8: Solving One-Step Equations with Decimals and Fractions

MATHiaLessons 1-4:Hanging Around

Module 4: Moving Beyond Positive Quantities

Topic 1: Signed Numbers

MATHbookLesson 1: Signed NumbersCan You Dig It?

Topic 1: Introduction to Negative Numbers

MATHiaLesson 2: Representing Integers on Number LinesOrder in the Class

Module 5: Describing Variability of Quantities

Topic 1: The Statical Process

MATHbookLesson 3: SkyscrapersThe Plot Thickens

Topic 2: Numerical Summaries of Data

MATHbookLesson 1: In the MiddleToy Cars
MATHbookLesson 3: March MADnessHoops

Topic 2: Analyzing Numeric Data Displays

MATHiaLesson 1: Creating Dot PlotsMinimum Wage

Grade 7

Module 1: Thinking Proportionally

Topic 1: Circles and Ratios

MATHbookLesson 1: Pi: The Ultimate RatioMeasuring Around
MATHbookLesson 2: That’s a Spicy Pizza!Why Pi?
MATHbookLesson 2: Circular ReasoningArea Challenges
MATHbook
Lesson 4: Pound for Pount, Inch for Inch
Scaling Machines
Tiles
Scaling Robots

Topic 2: Proportionality

MATHbookLesson 1: Poultry in MotionPaint
MATHbookLesson 6: Minding Your Ps and QsTwo and Two

Topic 3: Proportional Relationships

MATHbookLesson 1: Markups and MarkdownsAll the Equations
100%
MATHbookLesson 4: More Ups and DownsMosaics
More and Less

Topic 3: Scale and Scale Drawing

MATHiaLesson 1: Critical Attributes of Similar FiguresScale Factor Challenges
MATHiaLesson 3: Calculating Measurements Using ScaleMake it Scale
Will It Fit

Topic 4: Ratio Representations

MATHiaLesson 2: Determining Characteristics of Graphs of Proportional RelationshipsDinoPops

Topic 11: Introducing Proportions to Solve Percent Problems

MATHiaLesson 2: Solving Simple Percent ProblemsBack in My Day

Topic 13: Percent Increase and Percent Decrease

MATHiaLesson 1: Calculating Percent Change and Final AmountsPercent Machines

Module 2: Operating with Signed Numbers

Topic 1: Adding and Subtracting Rational Numbers

MATHbookLesson 1: Math FootballFloats and Anchors
MATHbookLesson 2: Walk the LineMore Floats and Anchors
MATHbookLesson 4: What’s the Difference?More Floats and Anchors

Topic 5: Rewriting Expressions

MATHiaLesson 2: Evaluating Simple Numberic Expressions with IntegersInteger Puzzles

Topic 6: Using Number Properties to Interpret Expressions with Signed Numbers

MATHiaLesson 2: Operating with Signed DecimalsDraw Your Own

Module 3: Reasoning Algebraically

Topic 1: Two-Step Expressions and Equations

MATHbookLesson 4: Formally YoursKeeping it True

Topic 2: Multiple Representations of Equations and Inequalities

MATHbookLesson 3: Solving Inequalities with Inverse OperationsUnbalanced Hangers
MATHbook
Lesson 4: Deep Dive
Budgeting
Write Them and Solve Them

Topic 1: Rewriting Algebraic Expressions

MATHiaLesson 2: Rewriting Algebraic Expressions Involving Integer CoefficientsCollect the Squares

Topic 8: Solving Inequalities with Inverse Operations

MATHiaLesson 3: Solving Two-Step InequalitiesI Saw the Signs
Shira the Sheep

Module 4: Analyzing Populations and Probabilities

Topic 1: Introduction to Probability

MATHbookLesson 1: Rolling, Rolling, Rolling…How Likely
Prob-bear-bilities
MATHbookLesson 2: Give the Model a ChanceIs It Fair?

Topic 3: Drawing Inferences

MATHbookLesson 2: Tiles, Gumballs, and PumpkinsCrab Island

Module 5: Constructing and Measuring

Topic 1: Angles and Triangles

MATHbookLesson 2: Special DeliveryFriendly Angles
MATHbookLesson 3: Consider Every SideCan You Build It

Topic 1: Special Angle Relationships

MATHiaLesson 2: Exploring Angle RelationshipsMissing Measures
MATHiaLesson 3: Solving for Angle MeasuresMissing Measures

Grade 8

Module 1: Transforming Geometric Objects

Topic 1: Rigit Motion Transformaitons

MATHbookLesson 1: Patty Paper, Patty PaperTransformers
MATHbookLesson 2: Slides, Flips, and SpinsSpinning, Flipping, Sliding
MATHbookLesson 3: Lateral MovesGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 4: Mirror, MirrorGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLasson 5: Half Turnsa and Quarter TurnsGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 6: Every Which WayTransformation Golf

Topic 2: Dilations

MATHbookLesson 1: Pinch-Zoom GeometrySketchy Dilations
MATHbookLesson 2: Rising, Running, Stepping, ScalingDilation Mini Golf
MATHbookLesson 3: From Here to ThereSocial Scavenger Hunt

Topic 3: Line and Angle Relationships

MATHbookLesson 2: Crisscrsoss ApplesaucePuzzling It Out

Topic 1: Rigid Motion in the Coordinate Plane

MATHiaLesson 1: Experimenting with Rigid MotionMoving Day

Module 2: Modeling Linear Relationships

Topic 1: From Proportions to Linear Relationships

MATHbookLesson 2: Jack and Jill Went Up the HillTurtle Time Trials
MATHbookLesson 4: Up, Down, and All AroundTranslations

Topic 2: Modeling Linear Relationships

MATHbookLesson 2: Been There, Done That, Got the T-shirtWater Cooler
MATHbookLesson 3: Dining, Dancing, DrivingFlags
Ups and Downs
MATHbookLesson 4: Derby DayStacking Cups (Optional)

Topic 3: Systems of Linear Equations

MATHbookLesson 1: Crossing PathsMake Them Balance
MATHbookLesson 2: The Road Less TraveledLine Zapper

Topic 11: Solving Linear Equations with Variables on Both Sides

MATHiaLesson 3: Solving with Variables on Both Sides with RationalsEquation Roundtable

Module 3: Developing Function Foundations

Topic 1: Introduction to Functions

MATHbookLesson 1: Patterns, Sequences, Rules…Guess My Rule
MATHbookLesson 2: Once Upon a GraphTurtle Crossing
MATHbookLesson 4: Over the River and Through the WoodsThe Tortoise and the Hare
Scatter Plot City
Interpreting Slopes

Topic 2: Patterns in Bivariate Data

MATHbookLesson 1: Pass the SqueezeRobots
MATHbookLesson 2: Off the ChainDapper Cats
MATHbookLesson 3: Mia is Growing Like a WeedFind the FIt (called Fit Fights in Desmos Math)
MATHbookLesson 4: The Stroop TestInterpreting Scatter Plots
MATHbookLesson 5: Would You Rather…?Finding Associations

Topic 4: Drawing Lines of Best Fit

MATHiaLesson 1: Estimating Lines of Best FitInterpreting Slopes
MATHiaLesson 2: Using Lines of Best FitAnimal Brains

Module 4: Expanding Number Systems

Topic 2: Pythagorean Theorem

MATHbookLesson 1: The Right ConnectionTriangle Tracing Turtle
MATHbookLesson 4: Catty CornerTaco Truck

Topic 1: The Real Number System

MATHiaLesson 2: Graphing Real Numbers on the Number LineRoot Down

Module 5: Applying Powers

Topic 1: Exponents and Scientific Notation

MATHbookLesson 1: It’s a Generational ThingCircles
MATHbookLesson 2: Show What You KnowPower Pairs
MATHbookLesson 3: The Big and Small of ItSpecific and Scientific (formerly Solar System)
MATHbook
Lesson 4: How Much Larger?
Balance the Scale

Topic 2: Volume of Curved Figures

MATHbookLesson 1: Drum Roll, Please!Cylinders
MATHbookLesson 2: Conse of SilenceCones

Algebra 1

Module 1: Searching for Patterns

Topic 1: Quantities and Relationships

Lesson 3: f of x, Recognizing Functions and Function FamiliesCraft-a-Graph
Pumpkin Prices

Topic 2: Sequences

Lesson 1: Is there a Pattern Here?Visual Patterns
Revisiting Visual Patterns, Part 1
Lesson 2: The Password is Operations!Sequence Carnival
Revisiting Visual Patterns, Part 2
Lesson 3: Did You Mean: Recursion?More Visual Patterns

Topic 3: Linear Regressions

Lesson 1: Like a GlovePenguin Populations
Lesson 2: Gotta Keep It Correlatin’Correlation Coefficient
How Hot Is It?
Behind the Headlines
City Data
Lesson 3: The Residual EffectResidual Fruit
Lesson 4: To Fit or Not To Fit? That Is the Question!City Slopes

Module 2: Exploring Constant Change

Topic 1: Linear Functions

Lesson 1: Connecting the DotsPlane, Train, and Automobile

Topic 2: Solving Linear Equations and Inequalities

Lesson 1: Strike a BalanceWorking Backwards
Solving Strategies
Same Position
Lesson 2: It’s Literally About Literal EquationsSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 3: Not All Statements Are Made EqualPizza Delivery

Topic 3: Systems of Equations and Inequalities

Lesson 1: Double the FunShape It Up
Lizard Lines
Lesson 3: Throwing ShadeSeeking Solutions
Lesson 4: Working with ConstraintsQuilts

Module 3: Investigating Growth and Decay

Topic 1: Introduction to Exponential Functions

Lesson 2: The Power WithinCarlos’s Fish

Topic 2: Using Exponential Equations

Module 4: Describing Distributions

Topic 1: One-Variable Statistics

Lesson 2: A Skewed RealityFinding Desmo

Module 5: Maximizing and Minimizing

Topic 1: Introduction to Quadratic Functions

Lesson 1: Up and Down or Down and UpQuadratic Visual Patterns
On the Fence
Stomp Rockets
Plenty of Parabolas
Robot Launch
Lesson 2: Endless Forms Most BeautifulParabola Zapper
Two for One
Shooting Stars
Lesson 4: You Lose Some, You Lose SomeSorting Relationships

Topic 2: Solving Quadratic Equations

Lesson 4: The Missing LinkSquare Tactic
Lesson 5: The Quadratic FormulaStomp Rockets in Space

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Grade 6

Chapter 1: Numerical Expressions and Factors

Big IdeasDesmos Math 6–A1
Lesson 1: Powers and ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Practice Day 2 (Print available)
Lesson 2: Order of OperationsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 3: Prime Factorization
Lesson 4: Greatest Common FactorUnit 5
Lesson 15: Common factors
Lesson 5: Least Common MultipleUnit 5
Lesson 14: Common Multiples
Practice Day 2 (Print available)

Chapter 2: Fractions and Decimals

Lesson 1: Multiplying FractionsUnit 4
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Lesson 2: Dividing FractionsUnit 4
Lesson 1: Cookie Cutter
Lesson 2: Making Connections (Print available)
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Practice Day (Print available)
Lesson 3: Dividing Mixed NumbersUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 14: Planter Planner (Print available)
Practice Day
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams 
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Practice Day 1 (Print available)
Practice Day 2 (Print available)
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12: Budget Vehicles (Print available)
Lesson 7: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12:(Print available) Budget Vehicles 
Practice Day 1 (Print available)
Practice Day 2 (Print available)

Chapter 3: Ratios and Rates

Chapter 4: Percents

Chapter 5: Algebraic Expressions and Properties

Chapter 6: Equations

Chapter 7: Area, Surface Area, and Volume

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Chapter 9: Statistical Measures

Chapter 10: Data Displays

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Dividing IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 3: Converting Between Fractions and DecimalsUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 4: Multiplying Rational NumbersUnit 5
Lesson 7: Back in Time
Lesson 5: Dividing Rational NumbersUnit 5
Lesson 8: Speeding Turtles

Chapter 3: Expressions

Chapter 4: Equations and Inequalities

Chapter 5: Ratios and Proportions

Chapter 6: Percents

Chapter 7: Probability

Chapter 8: Statistics

Chapter 9: Geometric Shapes and Angles

Chapter 10: Surface Area and Volume

Lesson 1: Surface Area of Prisms
Lesson 2: Surface Area of Cylinders
Lesson 3: Surface Area of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies (Print available)
Lesson 13: Popcorn Possibilities
Lesson 4: Volumes of Prisms
Lesson 5: Volumes of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities
Practice Day 2 (Print available)
Lesson 6: Cross Sections of Three-Dimensional FiguresUnit 7
Lesson 9: Slicing Solids

Grade 8

Chapter 1: Equations

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Chapter 4: Graphing and Writing Linear Equations

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 8: When Are They the Same?
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Solving Systems of Linear Equations by Substitution
Lesson 3: Solving Systems of Linear Equations by Elimination 
Lesson 4: Solving Special Systems of Linear Equations 
Lesson 6: Scale Drawings

Chapter 6: Data Analysis and Displays

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Representations of FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3: Linear FunctionsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 4: Comparing Linear and Nonlinear FunctionsUnit 5
Lesson 4: Window Frames
Lesson 5: Analyzing and Sketching GraphsUnit 5  
Lesson 6: Graphing Stories

Chapter 8: Exponents and Scientific Notation

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 2: The Pythagorean Theorem
Lesson 3: Finding Cube RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 4: Rational Numbers 
Lesson 5: Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 6: The Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right

Chapter 10: Volume and Similar Solids

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Welcome, K–8 Reviewers!

We’re honored to introduce you to Amplify Desmos Math California. We’re confident you’ll find this comprehensive program to be a powerful tool for bringing the vision of the California Math Framework to life in classrooms across the state.

Please start with the video on the right to learn how to navigate the program and access key features referenced within our submission. Below you’ll find additional resources to support your review.

Your Review Samples

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Print Samples

Your print samples should have arrived in grade-specific tubs with a copy of two Reviewer binders. The K-5 Reviewer binder is contained within the Grade K shipping box and the Grade 6-8 Reviewer binder can be located in the Grade 6 shipping box. As you begin the process of organizing your materials, please refer to the inventory checklist found inside each tub as well as within your Reviewer Binder.

Digital Samples

In order to access your digital samples, you’ll need to log into our platform using your unique login credentials found on a Digital Access Flyer inside of your Reviewer Binder. Once you have located the flyer:

  • Click the orange button below to access the platform.
  • Click “Log in with Amplify.”
  • Enter the username and password provided on your Digital Access Flyer.

Navigation Tips

Below you will find helpful tips for navigating Amplify Desmos Math California. We recommend reading these pages alongside the program’s print materials and digital experience to gain a deeper understanding of the program. 

Click the links below to read about navigating program features including:

Built for California

The Amplify Desmos Math California program is designed around the vision articulated in the California Mathematics Framework to enable all California students to become powerful users of mathematics. Our program incorporates the latest research in student learning, meaning that we:

  • Focus on the Big Ideas: Amplify Desmos Math California’s courses, units, and lessons are centered around the Big Ideas. Big Ideas, like standards, are not considered in isolation. In addition to each unit and lesson’s focal Big Ideas, Amplify Desmos Math California also provides connections among the Big Ideas across units and lessons.
  • Center on open and engaging tasks: Amplify Desmos Math California is grounded in engaging tasks meant to address students’ often-asked question: “Why am I learning this?”  Students are invited into learning with low-floor, high-ceiling tasks that provide an entry point for all. Open tasks in Amplify Desmos Math California provide the space for students to try on multiple strategies and represent their thinking in different ways, and allow student explanation and discussion to serve as the center of the classroom. All lessons offer both print and digital representations of lessons.
  • Provide enhanced digital experiences: Amplify Desmos Math California includes digitally-enhanced lesson activities, incorporating interactive digital tools alongside print materials. These purposefully-placed resources allow students to visualize mathematical concepts, receive actionable feedback while practicing, encounter personalized learning support from an onscreen tutor, and engage in discussions about their thinking and approaches.
  • Treat core instruction and differentiation as integral partners: The Amplify Desmos Math California curriculum provides teachers with lessons, strategies, and resources to eliminate barriers and increase access to grade-level content without reducing the mathematical demand of tasks. Every activity has multiple entry points to ensure that all students are supported and challenged. Intervention and personalized learning activities are directly connected to lesson content and offer students the individualized support as they dive into the mathematics.

Category 1: Mathematics Content/Alignment with the Standards

Standards Maps

The links below provide the Standards Maps for Amplify Desmos Math California for each grade level.

Evaluation Criteria Map

Linked here is the Evaluation Criteria Map for grades K–8. Please note that you will need to be logged into the digital platform to access the links in the Evaluation Criteria Map.

Standards for Mathematical Practice

The links below provide the alignment of Amplify Desmos Math California to the Standards for Mathematical Practice at each grade level.

Drivers of Investigation and Content Connections

Amplify Desmos Math California incorporates the Drivers of Investigation (DIs) and Content Connection (CCs) throughout the program. Throughout the year, students engage with open and authentic tasks of varying durations — from lesson activities to unit-level Explore lessons and longer course-level Investigations. Every lesson and investigation opportunity is grounded around the why, how, and what of the learning experience, and helps teachers bring mathematical concepts to life. 

A three-column chart details: Drivers of Investigation, Standards for Mathematical Practice, and Content Connections, each with their respective codes and brief descriptions.

California English Language Development Standards

The links below provide the alignment of Amplify Desmos Math California to the California English Language Development Standards at each grade level.

California Environmental Principles and Concepts

Select lessons, performance tasks, and investigations across grade levels in Amplify Desmos Math California are aligned to one or more of the California Environmental Principles and Concepts. Click the links below to view how the California Environmental Principles and Concepts are represented in each grade level.

Category 2: Program Organization

Amplify Desmos Math California thoughtfully combines conceptual understanding, procedural fluency, and application. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

Big Ideas

Amplify Desmos Math California’s courses, units, and lessons are centered around the Big Ideas. In addition to each unit and lesson’s focal Big Ideas, Amplify Desmos Math California also provides connections among the Big Ideas across units and lessons. Please refer to Keeping the Big Ideas at the Center (linked below) for specific lesson designs and alignment with the Big Ideas for each grade level.

Program Structure

Amplify Desmos Math California combines the best of problem-based lessons, intervention, personalized practice, and assessments into a coherent and engaging experience for both students and teachers.

A diagram showing three stages: Core instruction, Integrated personalized learning, and Embedded intervention, under Screening and progress monitoring with daily tiered support.

Lessons and units in Amplify Desmos Math California are designed around a Proficiency Progression, a model that steps out problem-based learning by systematically building students’ curiosity into lasting grade-level understanding.

Five steps for learning: 1. Activate prior knowledge, 2. Collaborate, 3. Refine ideas, 4. Guide to understanding, 5. Practice and extend for lasting understanding.

In the Proficiency Progression, lessons begin by activating students’ natural curiosity and offering opportunities to generate new ideas through collaboration. Teachers are then able to refine ideas through intentional facilitation and guide students to grade-level understanding, while students retain the ability to use different strategies and methods to show their comprehension of the content. Students are provided ample opportunities to develop lasting understanding.

Scope and Sequence

Below you can view the scope and sequence for each grade level. 

A chart displaying seven kindergarten math units with themes, number of instructional days, and assessment days, totaling 136 suggested instructional days.
Grade 1 instructional units overview showing 7 units on math topics, total suggested days is 153, with each unit listing instructional and assessment days.
Grade 2 math curriculum map showing 8 units with topics, number of instructional and assessment days, and total days; suggested instructional days: 156.
Seven instructional units are shown, each with a title, icon, number of instructional and assessment days, and total days; a note suggests 150 instructional days in total.
A Grade 4 math curriculum overview showing seven units with titles, number of instructional days, and assessment days; the suggested total instructional days is 152.
A curriculum map displays seven math units with icons, titles, instructional days, and assessment days, totaling 149 suggested instructional days.
A chart showing Grade 6 math units, each with instructional days, assessment days, and optional days. Total suggested instructional days is 142, plus 19 optional days.
Overview of Grade 7 math curriculum units, showing unit titles, number of instructional, assessment, and optional days for each, with a total of 125 instructional days plus 22 optional days.
Eight illustrated cards display Grade 8 math units, each with the unit title, topics covered, number of instructional and assessment days, and a total of 131 suggested instructional days.
Curriculum chart showing eight units split into two volumes, with topics, instructional days, assessment days, and optional days listed for each unit over an accelerated 6th-grade year.
A chart displays the breakdown of Accelerated 7 math units, indicating topics, number of instructional days, assessment days, and optional days for each of the nine units across two volumes.

Lesson Design and Structure

A four-part diagram shows: Warm-Up, Activities with a graph of student ideas to grade-level understanding, Synthesis with notes, and Practice and differentiation with students building a structure.

Amplify Desmos Math California is designed with a structured approach to problem-based learning that systematically builds on students’ curiosity and allows students to grapple with the Big Ideas of the California Framework. Every lesson activity is organized into a Launch, Monitor, Connect format.

  • Launch: The launch is a short, whole-class conversation that creates a need or excitement, provides clarity, or helps students connect their prior knowledge or personal experience, which ensures that everyone has access to the upcoming work.  
  • Monitor: As students work individually, in pairs, or in groups, teachers explore student thinking, ask questions, and provide support to help move the conversations closer to the intended math learning goal. 
  • Connect: Teachers connect students’ ideas to the key learning goals of the lesson, facilitating class discussions that help synthesize and solidify the Big Ideas 

Each lesson within Amplify Desmos Math California follows the same structure. 

  • Warm-Up: Every Amplify Desmos Math California lesson begins with a whole class Warm-Up. Warm-Ups are an invitational Instructional Routine intended to provide a social moment at the start of the lesson in which every student has an opportunity to contribute. Warm-Ups may build fluency or highlight a strategy that may be helpful in the current lesson or act as an invitation into the math of the lesson.
  • Lesson Activities: Each lesson includes one or two activities. These activities are the heart of each lesson. Students notice, wonder, explore, calculate, predict, measure, explain their thinking, use math to settle disputes, create challenges for their classmates, and more. Guidance is provided to help teachers launch, monitor, and connect student thinking over the course of the activity.
  • Synthesis and Show What You Know: The Synthesis is an opportunity for the teacher and students to pull all the learning of the lesson together into a lesson takeaway. Students engage in a facilitated discussion to consolidate and refine their ideas about the learning goals, and the teacher synthesizes students’ learning. Show What You Know is a daily assessment opportunity for students to show what they know about the learning goals and what they are still learning.
  • Centers (K–5): Centers are hands-on activities for students in grades K–5 to play collaboratively to strengthen their understanding of key skills and concepts. In grades K–1, students have Daily Center Time built into every lesson. 
  • Practice and Differentiation: Daily practice problems for the day’s lesson are included both online and in the print Student Edition, including fluency, test practice, and spiral review.

Kindergarten–Grade 1

A lesson plan timeline showing phases: Warm-Up (5–10 min, whole class), Lesson Activities (25–30 min), Synthesis (10 min), Centers (15 min), and Practice (time varies).

Grades 2–5

A horizontal flowchart shows a classroom lesson sequence: Warm-Up (5–10 min), Lesson Activities (35 min), Synthesis (10 min), and Practice (time varies); groupings vary.

Grades 6–8

A horizontal timeline shows four lesson segments: Warm-Up (5 min), Lesson Activities (30 min), Synthesis (10 min), and Practice (time varies).

Routines

Amplify Desmos Math California features a variety of lesson routines. Instructional routines and Math Language Routines (MLRs) are used within lessons to highlight student-developed language and ideas, cultivate conversation, support mathematical sense-making, and promote meta-cognition. Both are called out at point-of-use within the Teacher Edition and Teacher Presentation Screens. Below are the types of routines used throughout the Amplify Desmos Math California curriculum:

  • MLR1: Stronger and Clearer Each Time
  • MLR2: Collect and Display
  • MLR3: Critique, Correct, Clarify
  • MLR5: Co-Craft Questions
  • MLR6: Three Reads
  • MLR7: Compare and Connect
  • MLR 8: Discussion Supports
  • Decide and Defend
  • Notice and Wonder
  • Number Talk
  • Tell a Story
  • Think-Pair-Share
  • Which One Doesn’t Belong?

Category 3: Assessments

A variety of performance data in Amplify Desmos Math California provides evidence of student learning, while helping students bolster their skills and understanding.

Unit-Level Assessment

Amplify Desmos Math California has embedded unit assessments that offer key insights into students’ conceptual understanding of math. These assessments provide regular, actionable information about how students are thinking about and processing math, with both auto-scoring and in-depth rubrics that help teachers anticipate and respond to students’ learning needs.

  • Pre-Unit Check: Each unit in grades 2–8 begins with a formative assessment designed to identify the student skills that will be particularly relevant to the upcoming unit. This check is agnostic to the standards covered in the following unit and serves not as a deficit-based acknowledgment of what students do not know, but rather as an affirmation of the knowledge and skills with which students come in.
  • End-of-Unit Assessment: Students engage with rigorous grade-level mathematics through a variety of formats and tasks in the summative End-of-Unit Assessment. A combination of auto-scored (when completed digitally) and rubric-scored items provides deep insights into student thinking. All Amplify Desmos Math California End-of-Unit Assessments include two forms.
  • Sub-Unit Quizzes: Sub-Unit Quizzes are formative assessments embedded regularly in Grades Kindergarten through Algebra 1. In these checks, students are assessed on a subset of conceptual understandings from the unit, with rubrics that help illuminate students’ current understanding and provide guidance for responding to student thinking.
  • Sub-Unit Checklists: These checklists enable teachers to observe key skills and concepts that cannot be assessed on a pencil-and-paper assessment in Kindergarten–Grade 1. The checklists outline the supports students need to achieve mathematical growth and success.
  • Performance Tasks: At the end of each unit in grades 3–8, there is a summative assessment performance task provided to evaluate students’ proficiency with the concepts and skills addressed in the unit. 

Lesson-Level Assessments

Amplify Desmos Math California lessons include daily moments of assessment to provide valuable evidence of learning for both the teacher and student. Beyond formative, summative, and benchmark assessments, students also have opportunities for self-reflection with Watch Your Knowledge Grow. Students take ownership of their learning by reflecting and tracking their progress before and after each unit.

  • Show What You Know: Each lesson has a daily formative assessment focused on one of the key concepts in the lesson. Show What You Know moments are carefully designed to minimize completion time for students while maximizing daily teacher insights to attend to student needs during the following class. 
  • Responsive Feedback™: Teachers have the ability to see and provide in-the-moment feedback as students progress through a digital lesson. Responsive Feedback motivates students and engages them in the learning process.

Diagnostic Assessment

Every grade level features an asset-based diagnostic assessment designed to be administered at the beginning of the year.  Delivered digitally and to the whole class, our diagnostic assessment is uniquely designed to reveal underlying math thinking and identify what students know about grade-level math. With data beyond just right and wrong, teachers have the type of deeper level of insights need to take the right next step.

CAASPP-Aligned Assessment Preparation

Amplify Desmos Math is designed to support students’ mathematical development through problem-based learning, differentiation, and embedded assessments. The program’s emphasis on conceptual understanding, procedural fluency, and application aligns with the mathematical practices and content standards assessed by the CAASPP.

Amplify Desmos Math California includes a CAASPP-aligned Item Bank. This standards-aligned bank of questions allows teachers to filter and search by grade and standard to find items. Once assigned on the digital platform, students will experience CAASPP-like practice with the online digital tools.

Data and Reporting

Amplify Desmos Math California provides teachers and administrators with unified reporting and insights so that educators have visibility into what students know about grade-level math—and can plan instruction accordingly for the whole class, small groups, and individual students. Reporting functionality integrates unit assessments, lesson assessments, diagnostic data, and progress monitoring for a comprehensive look at student learning. Program reports show proficiency and growth by domain, cluster, standard, and priority concept using performance data from unit assessments, then highlight areas of potential student need to allow teachers to modify their instruction and target differentiated support.

Administrator reporting provides a complete picture of student, class, and district performance, allowing administrators to implement instructional and intervention plans.

Category 4: Access and Equity

The Amplify Desmos Math California curriculum provides teachers with lessons, strategies, and resources to eliminate barriers and increase access to grade-level content without reducing the mathematical demand of tasks. Our lessons are developed using the Universal Design for Learning (UDL) framework to proactively ensure that all learners can access and participate in meaningful, challenging learning opportunities.

Every activity has multiple entry points to ensure that all students are supported and challenged. Intervention and personalized learning activities are directly connected to the day’s content and offer students the individualized supports they need to be successful.

Each lesson and unit contains guidance for teachers on how to identify students who may need support, students who need to keep strengthening their understanding, and students who may be ready to stretch their learning. In addition, teachers are provided with recommendations for resources to use with each group of students.

Universal Design for Learning

Each lesson in the program incorporates opportunities for engagement, representation, action, and expression based on the guidelines of Universal Design for Learning (UDL).

  • Multiple Means of Engagement: Students engage in both print and digital learning, and are regularly participating in discussions and hands-on activities. Students are invited to build their own challenge for other students to solve, which provides opportunities for choice and
    autonomy, as well as joy and play.
  • Multiple Means of Representation: Students are encouraged to demonstrate their learning using mathematical representations, both print and digital, and regularly engage with their peers in analyzing multiple possible solutions. Classes engage in open-ended discussions about what individual students notice and wonder about mathematical concepts.
  • Multiple Means of Action and Expression: Learners differ in how they navigate learning environments and express what they know. Students can communicate their ideas in multiple ways, including in print, sketching, uploading photos, or recording an audio response.

Accessibility

Lesson facilitation supports

Every lesson includes at least one specific suggestion the teacher can use to increase access to the lesson without reducing the mathematical demand of the tasks. These suggestions address the following areas:

  • Visual-spatial processing
  • Conceptual processing
  • Executive functioning
  • Memory and attention
  • Fine motor skills

Accessibility tools

Students have the ability to control accessibility tools so that each learning experience is customized to their individual needs. In many instances, these tools can be turned on or off at any point of instruction.

  • Text to speech: Reads text instructions to students in multiple languages
  • Enlarged font: Increases the size of all text on screen
  • Braille mode: Includes narration of digital interactions
  • Language selection: Toggles between languages

Differentiation: In-Lesson Teacher Moves

Within every lesson activity, teachers can use the suggestions in the Differentiation Teacher Moves table to provide in-the-moment instructional support while students are engaged in the work of the lesson. This table can help teachers anticipate the ways students may approach the activity, and provides prompts that they can use during the lesson to Support, Strengthen, and Stretch individual students in their thinking. Teachers are provided with clear student actions and understanding to look for, each matched with immediately usable suggestions for how to respond to the student thinking illustrated in each row of the table. In addition to using these suggestions in the moment as teachers monitor student work, teachers can review the Differentiation table in advance to help them anticipate how students are likely to approach the activity.

A table showing differentiation teacher moves with examples of representing groups in different ways, support prompts, and a stretch question about patterns with more teams.

Differentiation: Beyond the Lesson

Teachers are provided with recommendations for resources to use with each group of students needing support, strengthening, and stretching after each lesson. Support, Strengthen, and Stretch resources include:

  • Mini-Lessons: 15-minute, small-group direct instruction lessons targeted to a specific concept or skill
  • Item Banks: Space for teachers to create practice and assessments by using filters and searching for standards, summative-style items, and more
  • Fluency Practice: Adaptive, personalized practice built out for basic operations and more
  • Centers (K–5): Lesson-embedded routines and practice for students that are vertically aligned across grade levels
  • Extensions: Lesson-embedded Teacher Moves including possible stretch questions and activities for students
  • Lesson Practice: Additional practice problems support every lesson
  • Math Adventures: Strategy-based math games where students engage with math concepts and practice skills in a fun digital environment
  • Lesson Summary Support: Support for students and caregivers that provides efficient explanation of the learning goal with clear examples

Math Identity and Community

The Math Identity and Community feature supports teachers in helping students build confidence in their own mathematical thinking, develop skills to work with and learn from others when doing math, and learn how math is an interwoven part of their broader community. The embedded prompts throughout the lessons are designed to highlight what it means to be good at math, the value of sharing ideas, and the power of flexible and creating thinking. Here are some examples of the Math Identity and Community supports embedded in each lesson:

  • I can be all of me in math class. You will work with partners every day in math class. What do you want your partners to know about you? 
  • We are a math community. What does good listening look like and sound like in a math community? 
  • I am a doer of math. What math strengths did you use today?

Unit Stories

Every unit in grades K–5 contains a Unit Story. These Unit Stories are brief fiction stories read aloud by the teacher at the beginning of each unit that connect to the math of the unit and introduce characters that students will get to know as they engage in the unit. Teachers read the story aloud from their Teacher Edition while projecting illustrations for students from the story, found in the Teacher Presentation Screens for the story. Across the unit, the Unit Story context and characters are used at appropriate points to inspire and engage students in the math as well as in reflections about their math identity and community.

Math Language Development

Every lesson in Amplify Desmos Math California includes opportunities for all students to develop mathematical language as they experience the content. Amplify Desmos Math California purposefully progresses language development from lesson to lesson and across units by supporting students in making their arguments and explanations stronger, clearer, and more precise. This systematic approach to the development of math language can be broken down into the following four categories of support:

  • Vocabulary: Units and lessons start by surfacing students’ language for new concepts, then building connections between their language and the new vocabulary for that unit. This honors the language assets that students bring into their learning.
  • Language goals: Language goals attend to the mathematics students are learning, and are written through the lens of one or more of four language modalities: reading, writing, speaking, and listening.
  • Math Language Routines: Math Language Routines are used within lessons to highlight student-developed language and ideas, cultivate conversation, support mathematical sense-making, and promote meta-cognition.
  • Multilingual/English learner supports: Supports for multilingual/English learners (ML/ELs) are called out at intentional points within each lesson. These specific, targeted suggestions support ML/ELs with modifications that increase access to a task, or through development of contextual or mathematical language (both of which can be supportive of all learners). 

Multilingual and English Learner Supports

Amplify partnered with the English Learner Success Forum (ELSF), a national nonprofit organization that advocates for high-quality instructional materials that are inclusive of multilingual learners. ELSF reviewed Amplify Desmos Math California, and provided directional guidance and feedback to ensure that the program reflects their research-based instructional strategies for multilingual/English learners.

Our Math Language Development Resources book contains lesson-specific strategies and activities for all levels of English Learners (i.e., Emerging, Expanding, Bridging). With support for every lesson, teachers are empowered to help all students, regardless of their language skills, to participate fully, grasp the material, and excel in their mathematical journey.

Amplify Desmos Math California includes a digital glossary for languages other than Spanish. Translations will be provided for up to nine languages.

Amplify Desmos Math California will include Spanish student-facing materials beginning in the 2026–27 school year.

Category 5: Instructional Planning and Support

Amplify Desmos Math California includes a variety of embedded instructional supports to empower teachers to lead effectively and gain actionable insights into student growth and progress. Teachers are equipped with a comprehensive set of resources designed to fulfill the requirements of Category 5.

Within the Teacher Edition front matter:

  • Scope and sequence
  • Big Ideas, Drivers of Investigation, and Content Connections
  • Grade level standards
  • Standards for Mathematical Practice
  • English Language Development Standards
  • Environmental Principals and Concepts

Within each Unit and Sub-Unit Overview:

  • Big Ideas, Drivers of Investigation, and Content Connections
  • Math that Matters Most
  • Grade level standards
  • Standards for Mathematical Practice
  • English Language Development Standards
  • Environmental Principals and Concepts

Within each Lesson:

  • Big Ideas, Drivers of Investigation, and Content Connections
  • Grade level standards
  • Standards for Mathematical Practice
  • English Language Development Standards
  • Environmental Principals and Concepts

At the course level (within the Teacher Edition front matter):

  • Navigating the Program (both print and digital)
  • Facilitating Lesson Activities with Launch, Monitor and Connect
  • Overview of the Digital Facilitation Tools

At the lesson level:

  • Suggestions for timing
  • What materials to prep
  • How to organize and group students 
  • Key lesson takeaways with the Synthesis
  • Recommendations for Differentiation
  • Strategies for intervention and extensions (in the Intervention, Extensions, and Investigation Resources book)

At the activity level:

  • Differentiation recommendations
  • Accessibility tips
  • ML / EL tips
  • Teacher look-fors
  • Recommended Teacher Moves
  • Prompts for guiding student thinking 
  • Sample student responses

A variety of language development supports are provided within the Student and Teacher Editions and Math Language Development Resources book. 

At the lesson level:

  • Diagrams and visuals
  • Sentence frames and word banks
  • Graphic organizers, including Frayer models
  • Vocabulary routines
  • Embedded language supports aligned to the CA ELDs
  • Lesson-specific strategies for Emerging, Expanding, and Bridging

At the unit level: 

  • Words With Multiple Meanings
  • Contextual vocabulary

At the course level:

  • English/Spanish cognates
  • Multilingual Glossary 
  • Additional Practice Resources book
  • Assessment Resources book 
  • Assess and Respond guidance paired with each assessment opportunity
  • Show-What-You-Know activities
  • Answer keys and rubrics 
  • Performance tasks

S3-01: Science as the underdog, and the research behind it

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

Get ready for season 3 of Science Connections: The Podcast!

In our first episode, we unpack the research around our season theme of science as the underdog with Horizon Research, Inc. Vice President Eric R. Banilower and  Senior Researcher Courtney Plumley. Eric and Courtney dive into the research they’ve found and their experiences as former educators to show how science is often overlooked in K–12 classrooms. We discuss how the science classroom compares to other subjects in terms of time and resources, how schools are a reflection of society, and what’s needed to change science and its impact on a larger scale.

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Courtney Plumley (00:00):

We asked teachers how much science, professional development, they’ve had in the last three years, and nearly half of elementary teachers said none.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. I am super-excited to be kicking off the third season with the show. This entire season will be exploring the theme of science as the underdog. And we’re gonna make the case for science, by showing how and why it can be used more effectively. In the coming episodes, we’re gonna talk about how science can be better integrated into other content areas like literacy and math, and explore some of the benefits that you might not be thinking about good science instruction. But first, science as the underdog. I bet some of you out there feel like science is the underdog in your community at school. I know I have at times. To kick off this season, I’m gonna talk to two people who really studied this question by looking at the state of science instruction across the US. Eric Banilower is Vice President of Horizon Research and Courtney Plumley is Senior Researcher at Horizon Research. Eric was the principal investigator and Courtney an author of the latest in a series of studies called “The National Survey of Science and Mathematics Education.” We’re gonna dive into the findings of their most recent report to see what the data’s showing us. Please enjoy my discussion with Eric Banilower and Courtney Plumley. Courtney, hello. And thank you so much for joining us.

Courtney Plumley (01:25):

Hi Eric. It’s nice to be here.

Eric Cross (01:26):

And Eric, welcome.

Eric R. Banilower (01:27):

We’re thrilled to be here, so thank you for having us.

Eric Cross (01:30):

I was reading through the report. Four hundred…a very thorough report, 471 pages, I think, as I got it?

Eric R. Banilower (01:37):

And that’s only one of the many reports from that study.

Eric Cross (01:40):

Yeah. You all have done your work, so I’m really excited to to talk to you about this. And on this season of the show, we’re exploring the theme of science as the underdog. And I think a lot of our listeners, we feel like science is an underdog either in their school or in their district. But you’ve actually done some research on this, in a 2018 study, “The National Survey of Science and Mathematics Education.” So I wanna talk about this report. But first I was hoping you can kind of set the stage. How did you come to work on this report, and then, big picture, what were you hoping to find out?

Eric R. Banilower (02:10):

So the 2018 study that you just mentioned was actually the sixth iteration of a series of studies dating back to 1977. And we collect data every decade or so—you know, plus or minus a few years. And really, what we’re trying to do is get a snapshot of what the science and math education system looks like in in the nation. So my role grew. I started working at Horizon in about 1998, after teaching high school for five years in California. And then going to graduate school. And right about that time, the company was doing the 2000 iteration of the survey. And I worked on it with the team here at Horizon. And then we did it again in 2012. And I had a much more prominent role in that study, and became the kind of leader of the study. And in 2018, the most recent version, we just did it again. So the goal of this study is really to kind of examine key aspects of the K–12 STEM education system. And the main audience of the work has traditionally been policy makers, researchers, and practitioners who work at the federal, state, and district level.

Eric Cross (03:30):

So this study, you took kind of a sample size, but it’s reflective of trends that we tend to see across the nation as a whole. Would that be fair to say?

Eric R. Banilower (03:38):

Yes, definitely it is. It is a random sample of schools in the country. So we start with a list of all the public and private schools in the nation, and then do a random sample of those schools, and then work really, really hard to recruit schools to agree to be in the study. And that has gotten harder every time we’ve done the study, for many understandable reasons. And then once we have schools on board, we sample teachers within schools. So we don’t even survey every teacher in a school. It’s really a sub-sample. So that we can make inferences about the nation as a whole.

Eric Cross (04:14):

Makes sense. And so Courtney, what did you find out about the time spent on science instruction in US schools?

Courtney Plumley (04:22):

So, I’m gonna talk about elementary teachers to begin with.

Eric Cross (04:26):

Because that was your past life, right?

Courtney Plumley (04:28):

I am a former elementary teacher, yeah. So that’s kind of where my head is. And that’s relatable for me. Right? So we asked teachers, like, how many days of the week or weeks of the year that they teach elementary school. And fewer than 20% teach science every day of the school year. They kind of do one or two things, for the most part. They teach a couple days a week or they teach every day of the week, but only for, like, maybe six weeks, and then they swap with social studies and they kind of do that across the school year. Which is really different from, like, math, right? We also asked elementary teachers, how often do they teach math, and it’s every day of the year. Then we also asked them how many minutes they teach when they’re teaching, and we kind of did the math to figure out, all right, if they taught science every day of the school year, how many minutes would it be in a single day, so that we could make a more comparable comparison with math and ELA. If you were to work it out, how many minutes of science an elementary teacher teaches across the year, and break it down to per day, it’s like 18 minutes for the lower elementary grades, 27 for the upper elementary grades. Which is not a lot. But it’s pretty much an hour a day in math, and 80 plus minutes in ELA. So, a lot less. And then, you know, when I was teaching, the first thing to go was always science, right? If there was an assembly, if there was early release or whatever, that was the first thing to go. So those numbers might even be higher. Just because they aren’t factoring that kind of thing in, too.

Eric Cross (06:05):

So, now I’m curious. That is something that I’ve seen just anecdotally, science being the first thing to go. I feel like I’ve seen that almost…it’s almost become a meme, that I’ve heard that so often. Just in your experience, why do you think that is that huge disparity between the two?

Courtney Plumley (06:26):

Well, I mean, when I was teaching, I was teaching third grade. I had an end-of-grade test in math and ELA for my kids. I didn’t have one in science. So the administration said, “Hey, if you’re gonna drop something, drop something that’s not tested.”

Eric Cross (06:41):

Simple as that. And Eric, you, past life: physics teacher. High school. What did you see? ‘Cause our listeners run the gamut from elementary all the way up to high school. What did you see, as far as relative science instruction in the secondary level?

Eric R. Banilower (07:00):

Sure. You know, secondary is just a whole different situation than elementary. Rght? Because you have departmentalization. I taught science. I didn’t have to teach other subjects. And students had periods, and they still do, sorry, they still have periods, even though it’s been a long time since I taught. And you know, they rotate from one class to another. So all the classes were essentially the same length. So, you know, when I was teaching, it was about 50-minute periods. So in terms of minutes of a class or minutes on a subject, it’s not really different. But what is different is what students are required to take in order to graduate high school. One of the things we asked schools about in this study was how many years of a subject do students have to take in order to graduate? And what we saw was in mathematics, over half the schools in the nation require students to take four years of mathematics to graduate. OK? And the vast majority of the rest, about 44%, require three years in science. Most schools require three years. Very few require four years. And many, or a fair number, still only require two years to graduate. So the expectation of what students are taking is lower in science than it is in mathematics.

Eric Cross (08:20):

So you were seeing the same trend in secondary, essentially.

Eric R. Banilower (08:24):

Yes.

Eric Cross (08:24):

The amount of time devoted to the instruction of science…we’re kind of seeing it mirrored just across K–12 across the board.

Eric R. Banilower (08:33):

That’s correct.

Eric Cross (08:34):

And that’s across the country. ‘Cause the sample size represents teachers from Alaska, Hawaii, the South, SoCal, everywhere. So what’s been the reaction to that number? Like 18 to 20 minutes is…I mean, it’s, it’s half of my lunch at our school. What’s been the reaction to that number since this data has been published?

Eric R. Banilower (08:58):

I don’t know, Courtney, if you want to take that…

Courtney Plumley (09:00):

It’s a lot of what you just did. Like, what??? Like, how is it possible to teach all the things you need to teach in such a little amount of time?

Eric R. Banilower (09:08):

What’s really kind of surprising to me, though — though now that I’ve worked on three iterations of the study, it no longer surprises me, but it did at first — is that these numbers really aren’t changing since we’ve started doing this study. You know, people thought maybe with No Child Left Behind and the increase in accountability, time on science might actually go down, because there was more testing in math and English Language Arts. It didn’t happen. It was pretty much constant, that this has been kind of the state of science education for a long time.

Eric Cross (09:44):

So Eric, if I’m hearing you right: The past studies, we’re not seeing an increase or a decline. This has been this way for how many years, roughly, would you say? Since it’s been studied?

Eric R. Banilower (09:54):

You know, I’d have to go back to the 1977 report to get the numbers, but I’m gonna say since then, it has not changed much, if at all.

Eric Cross (10:03):

So this has kind of been entrenched. This has been the norm for almost for the career of a teacher, almost generationally. We’re looking at anyone who’s been in the highest levels of leadership to someone just entering the classroom, this has been the way it’s always been. This is kind of for many people what they’ve only known.

Eric R. Banilower (10:20):

Right.

Eric Cross (10:21):

Kind of become the norm.

Courtney Plumley (10:21):

We didn’t even have science when I was in elementary school. We had science on a cart that came by, you know, every other week.

Eric Cross (10:28):

Was that like a food truck, but like the science version of it? It shows up and does quick science and takes off?

Courtney Plumley (10:35):

And New York was, I mean — we always watched Voyage of the Mimi. I don’t know if you ever watched that. But that’s what we watched every single time the Science on the Cart came. So it’s like a marine biology show. Ben Affleck was on it when he was a kid.

Eric Cross (10:48):

<laugh> Really? For me it was, Mr. Wizard. For some of my students, even now, Bill Nye. You know, the Bill Nye show or something would come on. So what happens when you look at less wealthy districts? Is there a relationship between community resources and science instruction, or is it pretty much equal no matter what the district resources are, the school’s resources are? Did you see any data there?

Eric R. Banilower (11:12):

Yes. We actually did a lot of disaggregating the data by community type, student demographics in the schools, to look to see whether there were areas of inequities across the country. And, you know, one of the factors we looked at was kind of a measure of socioeconomic status. You know, wealth in the community. By looking at percentage of students eligible for free or reduced-price lunch. And interestingly, in terms of time on science instruction, there is actually not a relationship between income level and how much time is spent at the elementary level on science, which actually surprised us.

Eric Cross (11:54):

Because you might have expected it to be the other way now. And granted, it’s 18 to 20 minutes, there isn’t much more to shave off off of that. But were there other differences, like when you compared those communities? Maybe it wasn’t the amount of science instruction, but was there anything else, like teacher preparedness, resources? Were there anything else that you did see discrepancies in? Or was it equal across the board?

Eric R. Banilower (12:13):

No, unfortunately there, there have been, and still are, a number of areas where community resources are related to pretty substantial differences in educational opportunities that students have. So, you know, we’re talking about the high school science requirements. One of the things that we saw was that high schools in less wealthy communities tend to offer less rigorous science courses than high schools in better-off-financially communities. So they may not be AP courses or second year advanced courses to the same extent that there are in the wealthier communities. That’s one big difference that we saw. Another one was what you were just saying about, sort of, the teachers who teach in these communities. You know, I think that for many years people have had a feeling that the best teachers go to the better off schools because it’s easier to teach there. Well, we see that the schools with the most poverty, they tend to have the newer teachers, who are just starting their career. They tend to have teachers who are less well prepared to teach their subject. And there’s a host of other differences we found. And you know, you mentioned the report being 400 pages. This other report that looks at these differences is also quite long, and, you know, identified a number of areas where there are these disparities in the system.

Eric Cross (13:43):

Well, we appreciate you synthesizing this for us, because this is super-important. And you’ve fleshed out a lot of things. And the fact that it’s driven by data, we as science teachers, we as scientists, being objective, really, really value that. Because this is actually validating a lot of the things that our listeners and myself, we experience anecdotally. But you don’t have a lot of things to network you. And sometimes, when you see this, you wonder if it’s just you, or is are other people experiencing this? And so as you start talking about this data, realizing, oh wow, this is not something in isolation. This is systemic. This is something that’s impacted. And then Eric, what you said about schools that were lower-income, that were under-resourced, and didn’t offer those advanced classes, what are some of the impacts of that, maybe downstream, of doing that? Not having those AP classes? I just kind of wanted to put that out there and ask you.

Eric R. Banilower (14:31):

You know, this is a really…this is a current debate right now, about what the goals of schooling K–12 should be. You know, are all kids meant to go to college? Should there be alternative paths? And you know, I know when I was teaching, I would have students say, “Why do I need to know this? I’m not gonna go into science. I’m not gonna study physics. Why do I need to take this?” And, you know, the answer I used to give them was, “You never know where your life is gonna end up and what opportunities you’ll have. And by having these educational experiences, you have more opportunities available to you. Whether or not you choose to go down those paths, you have opportunities. And when you don’t take this kind of coursework, you know, even if you don’t want to go to college, you limit your potential careers. Because so many careers nowadays require some technical knowledge, some knowledge of science, even if it’s not explicitly a science job. It is embedded in our society now. We are a technological and science-based society.”

Eric Cross (15:37):

It reminds me of something that I’ve told my students, that if you become a scientist, that’s awesome. I love that. But if you don’t, and you want to be a dancer or an actor or a lawyer or anything that may not be directly related to STEM, I want you to choose it because it was a choice, and not a lack of options. So as long as you’re choosing not to go in STEM, and you don’t make that decision because you can’t, or because you weren’t given the opportunity. So that’s how I’ve always had this mindset as a teacher. And I’ve explained it to my students. So if you say, “Cross, you know what I want to do, I wanna be an awesome chef,” which, you know, low-key that’s science, right? <laugh> Molecular gastronomy, we know that. But like, you be the best chef. But as long as you’re being a chef because you choose that, and you’re like, “I love science, but I don’t wanna go that direction,” we’re good.

Eric R. Banilower (16:26):

Right. And if you think about, a lot of social justice issues with pollution and climate change, and you look at which communities are more affected by some of these larger environmental problems and challenges, it tends to be the lower socioeconomic communities, the more poverty-stricken communities have worse water, have worse air quality. And so if, if people from these communities are going to make informed decisions about who they’re gonna vote for, about what policies they’re gonna support, those are science topics that you have to have some understanding in order to make informed decisions in your life.

Eric Cross (17:09):

Courtney, you were one of the Swiss Army Knife teachers. This is how I perceive it for elementary. You had to teach everything. And shout out to all of my elementary school teachers that have to be mathematicians and grammar whizzes and scientists and PE instructors and social emotional, all of those different things. you also looked at teacher preparedness. How did teachers feel about teaching science compared to other subjects like language arts and math? Did you see anything there?

Courtney Plumley (17:39):

We did, we did. And I’m glad you said, “How did they feel about it?” Because one thing that, you know, in a survey you can’t really do is capture how someone actually…how good someone actually…the quality of someone’s instruction. But you can ask them how prepared they feel. And you can even ask them like stats, like, “What did you major in in college?” You know. But you really are going on based on what what they say. So we ask them how prepared they feel to teach all the core subjects. And two-thirds of elementary teachers felt very well prepared to teach reading. They felt very well prepared to teach math. But when it comes to science, it’s less than a third felt very well prepared. And you know, like you said, when you’re teaching elementary school, you’re teaching all the subjects. But also in science, there’s usually four main instructional units in a school year. And they’re all from different science disciplines. So not only are you going on, like, “Maybe in college took a lot of bio classes, but I didn’t take any physics classes, and now I have to teach physics to my kids and I have no experience there.” So, you know, we also ask them how well-prepared they felt in these different disciplines. And the numbers are even smaller, you know. Fewer than a quarter felt very well-prepared in life science. And like 13% felt very well-prepared in physical science. So there’s definitely a big difference between how much teachers feel prepared for ELA and math versus science.

Eric Cross (19:08):

And just from a human perspective, when we don’t feel prepared for something, we’re not really gonna probably lean into it as much as we are into our strengths. Like, that’s just kind of how we are across the board.

Courtney Plumley (19:18):

Yeah.

Eric Cross (19:18):

I’m even like that with my own chores in the house. Or when I have things I need to get done, and I might not be as good at doing those things—it’s gonna be a heavy cognitive load; I’m gonna have to do some background research—I tend to find other areas to excel in. Like, I’m gonna be productive in this other area. I’m gonna really crush it here. But this other thing gets put to the back burner.

Courtney Plumley (19:36):

Totally. And the same reason I might skip science today, <laugh> ’cause it’s scary.

Eric Cross (19:41):

Yeah, exactly. But I love this book. <Laugh> Or we could do this math, and let’s really, really dive deep into it. Now, did you also look at professional development and instructional resources that are being provided?

Courtney Plumley (19:53):

We did.

Eric Cross (19:54):

And on the whole, how was the amount—and I’m seeing a trend here, so I’m kind of feeling like I know where this might go—but I wanted to ask it, did the amount of professional development and resources for science, was there much of a difference between that and other subjects?

Eric R. Banilower (20:10):

Well, I’ll start on this, and Courtney, feel free to jump in. You know, one of the things that we asked was how much kind of discretionary funding do schools devote to science and how much to mathematics? So, for consumables or equipment and supplies or computer software for teachers to use in the classroom. And it’s hard to compare, I think, across subjects because the demands for this kind of supplies, et cetera, is very different, I think, in science than it is in mathematics. Right? We have a lot of, you know, equipment for doing investigations, consumable supplies in science. And those things need to be replenished on a regular basis. It turns out, when we look at the data for school discretionary spending on this kind of stuff, the median school spends less than $2 per student at the elementary level on science, compared to over $6 for mathematics. At the high school level, it’s kind of reversed. Schools spend more money on high school science than they do on high school math. but even still, at the high school, it’s less than $7 per student. Which is not a lot of money being devoted to thinking about all the materials, supplies, chemicals, et cetera, that you need to teach science well, at the high school level. More disturbing is the fact that, you know, we were talking about inequities before, schools that serve less well-off communities spend less than schools that serve wealthier communities, by quite a big amount.

Eric Cross (21:46):

So essentially the per-student thing just kind of popped out to me: So, like, an expensive Starbucks drink is what we’re spending on science per student.

Eric R. Banilower (21:57):

At the high school level. Yes.

Eric Cross (21:58):

At the high school level. And I get those catalogs in the mail, from all of those big science companies. You can’t get much for seven bucks. At least, nothing high-level. And I know I do a lot of 99-cent store science. I go down the street, go to the 99-cent store. Thankfully we could do a lot of awesome science with just, you know, cheap things. But a lot of the higher level experiences, they’re pricey. But the experiences are so rich! And $7 at the high school level is nothing. It’s not much at all.

Eric R. Banilower (22:28):

Yeah. It is definitely, you know, kind of shocking to think about what we’re investing in our children’s future.

Eric Cross (22:37):

Now, just to put you both on the spot, ’cause I feel like that we’ve identified some…we’re seeing a trend here, we’re seeing a pattern. We’re talking about, you know, being science teachers. There’s a pattern going on here. Do you think it’s fair to characterize science as the underdog?

Courtney Plumley (22:52):

I think in elementary school, it is a fair statement. Because, like we said before, I mean they’re gonna preference math and ELA almost all the time. I mean, the other thing you’d asked a little bit ago was about professional development, too. And we do have some data on that. And we ask teachers, you know, how much science professional development they’ve had in the last three years. And nearly half of elementary teachers said none. And I know I didn’t have any science professional development. If I was gonna pick from among the catalog, I was picking one that I needed more, like math. Math and ELA. I keep making that statement, but just over and over, it’s the truth.

Eric Cross (23:31):

And going back to what you said earlier, because that’s where the accountability was, right? And that kind of came top-down.

Courtney Plumley (23:38):

Yes.

Eric Cross (23:38):

And influenced everything else.

Eric R. Banilower (23:40):

Yeah. Now, really interesting thing that we did, a year or so ago, ’cause someone asked us, you know, “Hey, could you look at this?” is we compared elementary science instructional time among states where science counted towards accountability versus states where science doesn’t count towards accountability. And at the upper elementary grades, more time was spent on science in schools in states where they had science accountability. Now I’m not arguing for adding science to accountability systems. But that’s a pretty telling piece of data.

Eric Cross (24:19):

What gets measured gets done.

Eric R. Banilower (24:20):

Yeah.

Eric Cross (24:20):

Or what was getting evaluated was getting done. And that raises, that opens up a myriad of other questions about testing, and what that reveals, and all of those different things. But at the end of the day, what you’re finding is that the things that were getting tested were the things that were getting the priority.

Eric R. Banilower (24:36):

That’s right.

Eric Cross (24:37):

How did we get to this point? And Eric, you said it goes back at least to ’77, but we look at society and we’re…I wanna say we’re post-pandemic, but we’re we’re not. but we’re trying to, we’re trying to get past that. But we’re looking at…we had innovations in biology, we have innovations right now in green energy and electric cars and all of these things that are STEM-based. We know that these are things that have moved humanity forward. And we look at the pipeline of people who are in STEM and we, we see the disparities and things like that. Why was science given less of a priority? I’m just curious. Maybe, Courtney, we could start with you, if you have any ideas. Or Eric. Either one. But how did we get here?

Eric R. Banilower (25:22):

<laugh> I think Courtney wants me to take that one. I’m older so I’ve seen more <laugh>. So, you know, I have the gray hair. She doesn’t. I think it’s complicated. And I know this sounds cliche, but but schools are a reflection of society, right? And, and so science education, you know, if you think back when Sputnik was launched, there became this great demand in America to improve and produce more scientists and engineers in response to this Cold War threat. Right? And then in the ’80s there was rising, oh, the gathering storm was an economic argument that we needed to increase science and math, you know, education and people going into those fields in order to compete economically against the global competitors. And I think that America has always produced a fair number, a large number, of high-quality scientists and engineers, you know. And we still lead the world in many ways. But where we’ve identified as a problem is who has those opportunities to go into those fields. You know, it used to be a very select, a very male-dominated, white male-dominated field. Right? And other people didn’t have the opportunity, or they were shown the way out pretty early. And we, I think, have come to realize as a country that, you know, the, the greater the diversity of thought that we can get into these discussions, the more innovative we can be and the more productive as a society we can be. And so I think we’ve had this shift in the country to, instead of thinking about just the quality for the select few, but to be thinking about the quality for everyone. And so that makes it seem like some of these challenges are greater than they used to be. And I think they’re different challenges, right? We’ve evolved as a society and I think schools have evolved.

Eric Cross (27:40):

There is a conversation I was in on a plane with a person who was a materials manager for a company that made the adhesive for sandpaper. And we were flying…I was flying to Denmark and he was flying to some other Scandinavian country. And we were just talking about it. And he came from another industry, and somehow the conversation led to science. I don’t know how that happened. But somehow I just started talking about science and I asked him about, Eric, kind of what you said about the US kind of leading the way in science innovation versus the rest of the world. And I asked him why. And he said one of the reasons why is because the heterogeneous thought. The different groups of people that are coming to a problem actually create more innovative and novel solutions. Versus when it’s more homogeneous. And everyone’s either culturally or just for whatever reason, kind of thinks a certain way. While they might have a more efficient way, the variety of solutions are not as varied and not as novel. I was reminded of that story based on what you just said. So it’s really interesting. So it seems to be that it benefits if we have more heterogeneous groups, more folks who are contributing to STEM, because that’s gonna be solving the next problem more efficiently. Or I guess maybe in my head it seems like the next we need…we do really well when we have a dragon to slay. I mean, it seems like we come together when that’s the case, right? Like, I dunno.

Eric R. Banilower (29:06):

No, I think that’s…I think that’s accurate.

Eric Cross (29:09):

Later on the season of the podcast, we’re gonna explore ways to better integrate science with other subjects like literacy and math. Were you able to study at all any more integrated approaches to science instruction? Does any of your research support that approach?

Courtney Plumley (29:25):

Not on the national survey, we didn’t study that. And it’s something that we’ve talked about before, because it’s difficult to get teachers to…we were talking about instructional time. It’s hard for teachers to put a number on it when they’re integrating, because, you know, it’s not like I have my science block from 3 to 3:30 anymore. Now it’s kind of scattered about. But it’s something that has been in the ether. We’ve been looking at it in a couple of projects. So there’s some evidence that it can be effective, especially for getting more, you know…the idea is you can get more time for science if you are integrating with other subjects. But one thing to kind of caution is like, students need to have opportunities to learn each discipline when they’re doing integrated instruction. So you don’t wanna just have, like, math in your science. Kids already know to just, like, support it. Then it’s hard to take time from math to put it into science when they’re not actually learning anything new. That’s the easy thing to do, though, is say, “Oh, my kids already know how to measure. We did that in a previous unit. So now we’ll we’ll do it as part of our science instruction.” So it’s a lot of work to make it so they’re learning something new, mathematics and science, at the same time. And it’s not really something that we think that teachers should be having to do on their own, with all the other things that teachers have to do. The last thing they need to do is be creating their own, you know, curriculum. Something that’s already…you know, it’s not straightforward. So we’ve been talking about it, we think it’s really something that instructional materials maybe need to be focusing on instead of teachers having to do that on their own,

Eric Cross (31:01):

Teachers would implement it, but asking them to create it is a whole different thing, and it’s a huge ask.

Courtney Plumley (31:08):

Yes.

Eric Cross (31:08):

Yeah. And, did I hear you right? So the ideal situation would’ve been the students learning a newer math concept, but embedded in a science kind of context? Or was that the better way? Versus, “I’m gonna take a math concept they already know and then just put it into the science setting?”

Courtney Plumley (31:26):

Well, if the idea is that you can get more science time if you’re, you know, integrating things, so you can maybe take time away from a specific math block by putting it with science, or whatever, then if the math is something that the kids already know, now you’re just taking away. I think that that has to be new in both cases, in order to justify having more time.

Eric Cross (31:49):

Right. Eric, in the secondary level, any thoughts on that? On integrating these disciplines together?

Eric R. Banilower (31:56):

I think, you know, just like at the elementary level, it can be challenging to do it well. When I taught, I taught my last couple years in a kind of school-within-a-school kind of situation, where our goal was to try to integrate science, mathematics, and language arts. And it’s hard to do that in a meaningful way. And we did not have curriculum materials given to us to help us do this. We were trying to figure out how to do this on our own, while we were teaching 200 kids a day in our subjects. Right? And five preparations. And you know, it’s a big ask of any teacher. And there are teachers who thrive on this and are great at this. And, you know, that’s one thing I wanna, make clear: our data is about the system, and we are former teachers. Almost everyone who works at Horizon is a former teacher. We have the greatest respect for teachers and what they do. And what our data is showing is are kind of like areas where the system isn’t providing teachers and their students the opportunities to do great things. I think at the high school level, there has been this idea of project-based learning where students are bringing together different skills, different ideas from across disciplines. And I think there’s, again, a lot of potential in doing that. But trying to develop those experiences so that they are doing service to the different subjects, so students are learning what they’re supposed to learn in English Language Arts, that they’re learning, important mathematics, and that this is in a science context, where they are getting to do and understand what science is and how science, as a discipline, operates…that’s just a really hard thing to develop.

Eric Cross (33:53):

So what I’m hearing—and I really appreciate the nuance in this, because it’s not a simple “Yes. Integrated is better,”—I’m hearing “Yes. Quality control.” “Yes. It needs to be written not by teachers; they’re the practitioners.” It’s “Yes. And,” not just simply binary. Which…it’s so easy to wanna chunk things and say yes or no on things. But this one seems a much more nuanced approach. And in a future episode, you mentioned project-based learning, we’re gonna try and talk to people who have thoughts on this. And I really appreciate that you talked about project-based learning, because also, how do you evaluate that? How do you evaluate whether or not it is high quality? Is this is something I see? You know, high-quality standards, highest quality science teaching, highly qualified teachers. It’s something that I see often. Now, based on all your research, this is kind of the 30,000-foot view. What advice might you have for people who are thinking about changing the way science is taught in this country? Which hasn’t changed since 1977, at least since we’ve been measuring it. Any advice for people who do want to act? Another way to ask, it might be, if you were given a magic wand, <laugh>, you have all power, what might you do if you can control the entire vertical system?

Eric R. Banilower (35:07):

Yeah, so a clarification, I do think science instruction has changed. It has evolved. I think there’s a lot of really good things going on in different pockets of the country. One of the challenges is bringing those good ideas and good practices to scale. Right? There are approximately 1.2 million teachers of science K–12 in this country. That’s a lot of people. And about 80% of those are elementary teachers who are responsible for teaching other subjects as well. So my thinking is often about, “How do we take what we know and that we’ve learned through decades of research is effective, and impact a large number of teachers, and therefore a large number of students?” And you know, Courtney I think has hinted at this already. And you’ve mentioned it too, Eric, is that teaching is a profession, right? And it’s a craft. But in no other profession do practitioners have the expectation that they’re developing their own tools and methods for their work. I know when I was in my teacher preparation program, and it’s still extremely common, one of the assignments perspective teachers are given is to develop a unit and develop a lesson, right? You don’t have doctors being asked to develop new treatments and new tests to use. Their job is to get to know their patient, assess what’s going on, and then using research-based methods to develop a plan of action, right? And I think that analogy works really well in education and is a way that we could have a scalable approach for kind of raising the floor across the country for the quality of science education. Giving teachers research-based materials, high-quality instructional materials, that they can then use and adapt to meet the needs of their students, would allow them to focus on getting to know their students, seeing what their strengths are, seeing where they have room for growth, and using the materials they’re given to help those students progress. And I think that is definitely a way where we could have a big impact at a large scale.

Eric Cross (37:39):

Courtney, same question: Magic wand, all power. You can change systems from the elementary perspective. What would you do? I’m assuming part of it’s gonna be changing that 18 to 20 minute time. But even for that to happen, what would you do? What would you change?

Courtney Plumley (37:57):

Well, I don’t know. Like, for it to change, I don’t know the answer to that. But yes, increasing the time would be great. And like Eric was saying, giving teachers— ’cause again, I’m coming in, not enough probably background in science—and then, you know, when I was, when I was teaching, we had one set of textbooks for the entire grade. Six classes, right? Like, share them. But third graders aren’t gonna read textbooks anyway, right? So instead I’m going to the teacher store. I’m pulling things off the shelf. And like, “OK, yeah, sure, I’ll use this.” And nowadays, teachers are going to Teachers Pay Teachers or whatever. Because I didn’t have anything good to use. So like Eric is saying, if I had instructional materials that were good instructional materials that were gonna teach my kids, that they were gonna be engaged, that they weren’t sitting and listening to science, but they were doing science, you know, and I had professional development to actually help me do it? That’s what I think we need to have. And I mean, I know there are some people out there that are working on that, but it’s not a lot. I mean, if you look at Ed Reports, they rate how well-aligned science curriculum are to standards. And there are two right now that have Ed Reports green lights. There’s Amplify and there’s OpenSciEd. You know, so there’s not much out there for teachers to use. And, so it’s hard. It’s hard. Where am I gonna go and get this stuff if it doesn’t exist? And so I’m making it up by myself. Which we already said is not the best use of teachers’ time, when they’ve got so many other demands on their time.

Eric Cross (39:27):

Eric and Courtney, listening to both of your responses, it created a visual in my mind. And Eric, I loved your analogy of…I started thinking of a chef, a welder, and a farmer. And I thought about the chef saying like, “You’re a great chef! Now, can you go farm, and make your own food, so that you can cook it?” Or the welder who has to make his own welding tools and go smelting. You know, making the different rods. I’m not a welder. But you know, all those different parts. Or the farmer who has to build his own tractor and innovate all that stuff. You’re absolutely right, the way you articulated that. And then Courtney, you essentially said, “Give them the tools and then teach them how to use it so they can go and actually be effective with it, because you’re in front of kids doing so many different things.” There’s only so much time in the day, and teachers want to do these things; they want to, but you end up having to triage when you’re asked to. Going back to Eric’s analogy, if you’re in the ER, but you’re also creating the vaccines and you’re also doing the research on which types of vaccines are gonna be the most effective, that’s, that’s a lot to ask. And so, I appreciate both your responses on that. Now, last question, what are you both working on now? This report came out in 2018. What’s, what’s next on the horizon? Actually literally, that’s no pun intended. <laugh> What’s next? <laugh> What’s next for, for you both? What are you working on?

Eric R. Banilower (40:42):

Well, you know, we would love to do another national survey, in a few years. We have to get funding to do it. And you know, that’s always something that takes effort and isn’t a guarantee. We’ve written grants to do these studies in the past, and there’s also the dealing with the reality of the situation. I think a lot of schools, still coming off the tail end of dealing with Covid, are overwhelmed. And we’ve had a hard time, I mentioned before, recruiting schools, and it gets harder every time, just ’cause they have so much on their plate. And I couldn’t see going to a school now and saying, “Hey, one more thing. Do you mind?” So I think we have to kind of wait a little bit for things to settle down before we can do another one of these studies. It just doesn’t seem feasible right now. But we’d love to in the not-too-distant future. Other than that, Courtney and I actually work on some projects together and some projects not together. One of the things that we’re working on together is a study of a fifth grade science curriculum that was developed by Okhee Lee at NYU and her colleagues, that is both aligned with the NGSS and purposely designed to support multilingual learners in developing both their science knowledge and skills as well as their language skills. And we’ve been working with the crew at NYU to study this curriculum and try to figure out, how well it’s working and under what circumstances. So that’s been a really interesting project that’s going on right now.

Courtney Plumley (42:26):

I recently worked on a report with the Carnegie Corporation in New York that actually I think, compliments what we’ve been talking about a lot. It’s about the status of K–12 education in the US—or science education in the US! <Laugh>—and so as part of that report we interviewed like 50 science education experts across the country. We surveyed teachers, people in the university settings, researchers, and everything to kind of get a little bit more update of the state of science education right now. And so a lot of the things we’ve been talking about, we still are talking about with the people in this report four years later. So, work in progress. <Laugh>

Eric Cross (43:09):

And again, going back to 1977, based on what Eric was saying earlier, we’re looking at these large systems, these systemic changes don’t happen overnight.

Eric R. Banilower (43:20):

That’s right.

Eric Cross (43:21):

It’s very slow-moving.

Eric R. Banilower (43:22):

That’s right. I would say there is progress. I think we’ve learned a lot. We are getting better. Are we there yet? No, we’re not happy with where we are. But I think, you know, I think it’s important to be hopeful about the direction things are going in.

Eric Cross (43:37):

Well-said. I agree. Courtney. Eric, thank you so much for unpacking that report that speaks to, that validates what so many teachers across the country are experiencing. And thank you for your advocacy for high-quality science education and your passion for supporting teachers and being that voice from a data-driven perspective of what teachers experience and then advocating for solutions for them. It’s super-encouraging for me, and I know it’s gonna be really encouraging for a lot of our listeners. So thank you.

Eric R. Banilower (44:10):

Thank you for having us.

Courtney Plumley (44:12):

Yeah. Thank you, Eric.

Eric Cross (44:15):

Thanks so much for listening to my conversation with Eric Banilower, Vice President of Horizon Research, and Courtney Plumley, Senior Researcher at Horizon Research. For much more, check out the show notes for a link to the 2018 National Survey of Science and Mathematics Education. And please remember to subscribe to Science Connections wherever you get podcasts, so that you’re not missing any of the upcoming episodes in Season three. Next time on the show, we’re gonna start laying out the road map for using science more effectively. And we’ll start by looking at the how and the why of integrating literacy instruction.

Susan Gomez Zwiep (44:49):

When we look at Science First and build language development around it, the experience tends to be more authentic and organic.

Eric Cross (44:58):

That’s next time on Science Connections: The Podcast. Thanks so much for listening.

Stay connected!

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What Eric R. Banilower says about science

“Our data is showing us places where the system needs to provide teachers and their students the opportunities to do great things.”

– Eric R. Banilower

Vice President of Horizon Research, Inc.

Meet the guests

Eric R. Banilower is a Vice President at Horizon Research, Inc. (HRI), and has worked in education for over 30 years. Eric was previously a high school physics and physical science teacher before he joined HRI in 1997, where he has worked on a number of research and evaluation projects. Most recently, he has been the Principal Investigator of the 2012 and 2018 iterations of the National Survey of Science and Mathematics Education, a nationally representative survey focusing on the status of the K–12 STEM education system.

A middle-aged man with light hair, glasses, and a short beard is smiling, wearing a plaid shirt. The photo has a circular frame with a star and decorative lines.

Courtney Plumley is a Senior Researcher at Horizon Research, Inc. She began her career in education as an elementary school teacher before starting at HRI in 2009. In her time at HRI she has worked on many K-12 STEM research and evaluation projects. Most recently, Ms. Plumley has worked with Carnegie Corporation of New York on mapping the landscape of K-12 science education in the US and is managing the field test for the OpenSciEd elementary materials.

A woman with wavy brown hair and a red top smiles at the camera, framed by a circular graphic with a star and accent lines.
A laptop screen displays the “Science Connections: The Community” private group page, with science-themed icons decorating the background and edges.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

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Welcome to Amplify Desmos Math California!

California educators, welcome to math that motivates. Introducing Amplify Desmos Math California, a new, curiosity-driven TK–12 program that builds lifelong math proficiency. Each lesson poses problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals. Students encounter math problems they are eager to solve; teachers spend more time where it’s most impactful: creating a collaborative classroom of learners.

Scroll to learn more about the program and explore sample materials.

About the program

Amplify Desmos Math California is a TK–12 core math program designed to meet the CA Math Framework and the Common Core State Standards for Mathematics. Offered in English and Spanish, Amplify Desmos Math California thoughtfully combines conceptual understanding, procedural fluency, and application through a structured approach to problem-based learning. Through engaging activities, Amplify Desmos Math California invites curiosity and math discourse into the classroom to create lifelong math proficiency.

Please scroll to learn more about the K–8 program and explore sample materials. (TK and high school materials are in development and will be available soon.)

A powerful math suite

Amplify Desmos Math California combines the best of assessment, problem-based core lessons, personalized practice, and intervention into a coherent and engaging experience for both students and teachers.

Laptop displaying a math problem interface with student assessment reports in the background.

Assessment

mCLASS benchmark assessments, along with daily formative checks, measure not only what students know, but also how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core instruction and intervention resources. Unit- and lesson-level core assessments give teachers data at their fingertips to guide and differentiate instruction. In grades 3–8, core assessments and performance tasks are designed to prepare students for success on the Smarter Balanced Assessment Consortium (SBAC) testing.

Core instruction

Amplify Desmos Math California core lessons pair problems students are eager to solve with clear instructional moves for teachers. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals. With built-in differentiation and Multilingual / English Learner support, Amplify Desmos Math California will allow every student to find success in the math classroom.

An educational game screen with a worm on a log and numbered blocks. Adjacent is a worksheet titled "Finding the Missing Pair" with instructions and incomplete equations.
A digital educational screen showing a math problem about converting meters to centimeters. It involves a diving toy sinking 5 meters into a pool. Text prompts users to input the conversion.

Personalized learning

Boost Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback adjusts to students’ work, providing item-level adaptivity to further support their learning.

Intervention

Integrated resources like Mini-Lessons, Fluency Practice, and Math Adventures provide targeted intervention on a specific concept or skill connected to the daily lesson. Extensions are also available to stretch students’ understanding.

Two pages of a math workbook displaying exercises on determining coordinates after rotation. The pages include diagrams, tables, and practice problems.
Network diagram with interconnected nodes labeled: Measure and Compare Objects, Represent Data, Dollars and Cents, Problem Solving with Measure, Skip Counting to 100, Number Strategies, Squares in an Array, Seeing Fraction in Shapes.

Big Ideas

The CA Mathematics Framework encourages a shift from power standards to thinking about math as a series of connected Big Ideas. Each Amplify Desmos Math California lesson supports one or more Big Ideas and the connections between Big Ideas. The grade-level diagram changes through the course based on the math concepts being addressed.

Focus, coherence, and rigor

Each lesson highlights why the content being covered is important, how students will engage with the mathematics, and what students will do with the learning. Our lesson opener helps teachers understand the most important concepts of the lesson, and includes the Drivers of Investigation (DI), Content Connections (CC), and Standards for Mathematical Practice (SMP) that drive learning in each lesson.

An educational slide on addition story problems, detailing goals for solving problems, language goals, and strategies using equal expressions, tens and ones, and number sense.
A screen titled "Match the Score" with a 2D target graph showing various scores. Instructions request four ordered pairs to total 400. Four pairs are listed: (4, 2), (7, 4), (7, 6), (10, 6). A "Try again" button is shown.

Built-in authentic tasks

Mathematics is not learning in isolation. Students are connected to each other’s thinking and can use math to understand the world. With accessible invitations to authentic tasks, all students can experience mathematical success. Amplify Desmos Math California provides these authentic invitations in a variety of ways:

Each unit begins with an “Explore” lesson, which allows students to engage with authentic exploration in low-floor, high-ceiling tasks. These tasks are designed in such a way that all students can access the basic mathematical concepts, but they also offer possibilities for advanced exploration and problem-solving for those ready for more complex work, promoting an inclusive and differentiated learning environment.

Our innovative course-level investigations are designed to facilitate multipart exploration. Students grapple with Big Ideas, diving deep into key concepts that encourage comprehensive understanding. Data science is infused into the approach, equipping students with a strong foundation in interpreting and applying data-driven solutions. The Environmental Principles and Concepts (EP&Cs) are also a focus of our investigations, enabling students to understand and appreciate the coherence and interrelationship of Earth’s environmental systems.

A focus on multilingual and English learners

Children sitting at desks in a classroom with a large illustrated caterpillar on the wall. Beside them are printed educational materials labeled “Amplify Desmos Math” and “Ying’s Aquarium Story.”.

In building Amplify Desmos Math California, we partnered with the English Learner Success Forum (ELSF) to provide guidance on our multilingual/English learner support for teachers. ELSF is a national nonprofit organization that advocates for high-quality instructional materials that are inclusive of multilingual learners. ELSF’s guiding documents reflect research-based instructional strategies that are critical to curriculum design and were created by researchers, linguists, and practitioners from across the country. ELSF reviewed our materials and provided directional guidance and feedback to ensure that the program fully supports multilingual/English learners.

A component of our K–5 curriculum is the engaging unit stories that interweave mathematics with real-life situations and relatable narratives. These unit stories are specifically crafted to inspire curiosity and foster a deep connection between the learner and the math concepts being explored. This unique approach not only makes learning fun and interesting, but also allows our young learners to see themselves in the math.

To help students grow their domain-specific and academic vocabulary, Amplify Desmos Math California provides embedded vocabulary routines, such as prompting teachers to use a Frayer Model. These routines allow students to make connections to new language and offer repeated opportunities to develop and refine language.

Amplify Desmos Math California recognizes the diverse language needs of our students and is designed to be inclusive. Each lesson in the program features a parallel language activity, designed to be available to all students, in the form of teacher guidance and student activities. The activities in the Math Language Development Resource has leveled ELD (Emerging, Expanding, Bridging) differentiation to support all levels of Multilingual and English Learners. This approach ensures that all students, regardless of their language skills, can participate fully, grasp the material, and excel in their mathematical journey.

Uploaded digital glossary for languages other than Spanish. Up to nine languages of translations will be provided for.

Amplify Desmos Math California will include support resources for Spanish-speaking students across TK–Algebra 1/Integrated I beginning in the 20262027 school year.

A computer displays an educational activity about measuring platform heights. A notebook page is layered behind it, with a colorful hamster-themed illustration.

K–5 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade. 

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

Screenshot of a kindergarten curriculum outline featuring units like Math in Our World, Numbers 1-10, Positions and Shapes, Understanding Addition, Making 10, and Shapes All Around Us. This comprehensive program utilizes New York Math standards to build foundational skills.
Program structure

Get to know the content and structure of Kindergarten Amplify Desmos Math California.

Cover of Amplify Desmos Math Grade K Teacher Edition featuring three children playing with math-related objects and a group of rabbits sitting nearby, aligning with the engaging curriculum seen in New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Counting and Comparing Objects.

Digital educational activity showing a blue backpack illustration with dots, a task to match dots on cards, and printed sheet featuring a similar dot-matching exercise.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition Kindergarten," featuring an illustration of three children playing with math-related toys. A group of small white animals, possibly hamsters, play nearby. The scene brilliantly captures the joy of New York math exploration for young learners.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Grade K Centers Resources" featuring a large, stylized red and pink "C" on a light pink background with simple geometric designs. This distinctive cover complements New York math curriculums with its engaging visual elements.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math: Grade K." The title is displayed with a geometric "I" illustration in the center. Subtitle reads "Intervention and Extension Resources" on a pink and white background, ideal for New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Illustration of a bear choosing a path with more mushrooms. Activity book page titled "A Furry Feast" with groups of objects to compare quantities.

In this lesson, students apply their understanding of how to compare groups of images as they determine which group has more or fewer and then compare their strategies by guiding a bear through a path that has more mushrooms than the other.

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

Grade 1 math curriculum overview displaying six units with instructional and assessment days: counting, addition, subtraction, numbers to 10, comparing numbers, measuring length, and geometry—aligned with the New York Math standards.
Program structure

Get to know the content and structure of Grade 1 Amplify Desmos Math California.

Children interact with math activities on a large tablet while observing fish illustrations. The text reads "Amplify Desmos Math Grade 1 Teacher Edition, aligned with New York Math standards.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Story Problems in Maui.

A digital educational activity showing a math problem about leaves on a kalo plant with a related worksheet on plant growth.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Illustration of three children engaged in math activities from the "Amplify Desmos Math: Student Edition 1" textbook. One child holds a number card, while the others manipulate counters and images, experiencing an exciting approach inspired by New York math techniques.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Interactive math activity for kids featuring a frog and number line for subtraction problems, asking to find differences to locate bugs.

In this lesson, students find differences when subtracting 1 and 2 from the same number by helping a frog reach a lily pad where it can eat a bug.

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

A curriculum overview for Grade 2 in New York Math displaying 8 units, including topics like comparisons, addition, subtraction, and geometric shapes, with details on the number of instructional and assessment days. This plan integrates resources from Amplify Desmos Math to enrich learning experiences.
Program structure

Get to know the content and structure of Grade 2 Amplify Desmos Math California.

Cover of the "Amplify Desmos Math" Grade 2 Teacher Edition, showcasing children measuring with rulers and a poster displaying a mathematical equation, set against whimsical scenery with a colorful dragon. Perfect for New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Adding and Subtracting.

Two digital worksheets about Theo's aquarium with tasks to estimate animal quantities using draggable graphs and illustrations of fish, frogs, and shrimps.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 2" showing three children performing a New York math activity with blocks and measurements.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of an educational book titled "Amplify Desmos Math Grade 2 Centers Resources" featuring a green "C" on a light green background, perfect for enhancing New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 2: Intervention and Extension Resources" featuring a green numeral 1 on a light green background, aligning with the New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Educational activity on a screen showing a worm and blocks with numbers. Another page shows an activity titled "Finding the Missing Pair," with numbered options and a video prompt.

Students continue to develop fluency by finding the number that makes 10 by helping a millipede reach its favorite food – a clump of leaves!

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

An educational curriculum outline for Grade 3 with seven units covering various mathematics topics, including multiplication, shapes, fractions, and measurement. Suggested instructional days are provided. The New York Math approach ensures a thorough understanding of each concept.
Program structure

Get to know the content and structure of Grade 3 Amplify Desmos Math California.

Cover of a "Grade 3 Amplify Desmos Math Teacher Edition" book, featuring a cutaway building with diverse students and a teacher working on New York math problems and organizing materials.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Concepts of Area Measurement.

Math activity screenshot showing a problem to calculate the area of an unpainted wall space with given side lengths in a room diagram.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 3" showcasing illustrated children engaged in various mathematical activities inside a glass house structure, reflecting the dynamic energy of New York math.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the Amplify Desmos Math Grade 3 Centers Resources book, featuring a 3D letter "C" in blue and white on a minimalistic background, perfect for aligning with New York math standards.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of an "Amplify Cover of the "Amplify Desmos Math" Grade 3 book featuring intervention and extension resources, with a blue geometric "I" on a light blue background, aligning with New York Math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Activity sheets showing a bar graph and a table for counting animal stickers: 7 rabbits, 5 raccoons, and 2 foxes. Includes instructions for arranging data points on a graph.

Students compare data represented on bar graphs with different scales by using animal stickers to create scaled bar graphs.

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

A course outline for Algebra 1 with 8 units, each detailing the number of instructional and optional days. The total suggested instructional days are 144 and 28 optional days, aligning with New York Math standards.
Program structure

Get to know the content and structure of Grade 4 Amplify Desmos Math California.

Cover of "Amplify Desmos Math: Teacher Edition Grade 4" showing children learning New York Math outdoors, using large mathematical tools and numbers, with one child in a wheelchair.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Size and Location of Fractions.

Screenshot of a digital math activity showing a fraction number line task with a log-cutting visual and an instruction page titled "Locating Fractions.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math, Student Edition, Grade 4," showcasing students collaborating on math problems involving shapes and numbers against a vibrant backdrop that blends cityscapes and natural scenery, capturing the essence of New York math learning.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the "Amplify Desmos Math" Grade 4 Centers Resources book, featuring a large, stylized blue letter "C" on a light blue background. This essential resource for New York math educators ensures engaging and effective instruction.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math, Grade 4: Intervention and Extension Resources," featuring a geometric illustration and a blue and orange color scheme inspired by New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational activity displays a drag-and-drop task to determine platform heights using tube lengths, showing a room scene and instructions on a digital interface.

Students choose tube lengths to connect to platform heights for hamster homes, identifying possible heights using what they know about multiples.

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

A Grade 5 curriculum scope and sequence chart with units covering volume, fractions, multiplication, shapes, place value, and measurement. Each unit lists instructional and assessment days to amplify Desmos Math activities.
Program structure

Get to know the content and structure of Grade 5 Amplify Desmos Math California.

Illustration of three students engaging with various math activities outdoors and around large blocks. Text at the top reads "Amplify Desmos Math, Grade 5, Teacher Edition" - a perfect resource for New York math educators.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Fractions as Quotients.

Activity worksheet and digital screen showing a panda on a cliff, with instructions about placing a missing bamboo shoot to help it reach the leaf.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition, Grade 5" featuring students engaged in various mathematical activities outside, such as block building, measuring, and gardening—a perfect resource aligning with New York math standards.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover image of "Amplify Desmos Math Grade 5 Centers Resources" featuring a large purple letter C on a light purple background, showcasing the innovative approach of Amplify Desmos Math that's making waves in New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 5: Intervention and Extension Resources," featuring a large, stylized number five in purple against a light purple background with minimal geometric patterns, ideal for New York math curriculum support.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Screen showing a student activity about decomposing a figure into prisms, with a drag-and-drop exercise and an adjacent worksheet labeled "Seeing Prisms.

Students decompose a figure into rectangular prisms and determine the volume of the figure by adding the volumes of the individual prisms.

A clear plastic box contains various math manipulatives, including counting cubes, geometric shapes, rulers, and dice, displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

6–A1 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade. 

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

Laptop showing a math activity with geometric shapes. Two textbooks titled "Amplify Desmos Math" are displayed above.
An educational document titled "Scope and Sequence" for Grade 6 math, designed in collaboration with Amplify Desmos Math, outlining six units with instructional and optional days for topics such as fractions, integers, and expressions.
Program structure

Get to know the content and structure of Grade 6 Amplify Desmos Math California.

Cover of the Grade 6 Amplify Desmos Math Teacher Edition, showcasing students engaging in various mathematical activities around a balance scale with variables, inspired by New York math educational standards.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from three sub-units on this site: Unit 1, Sub-Unit 1: Area; Unit 3, Sub-Unit 1: Units and Measurement; and Unit 6, Sub-Unit 1: Solving Equations.

A digital activity showing two model trains on a track with a question about speed. A printed page on the right is titled "Model Trains" with warm-up instructions.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of “Amplify Desmos Math, Student Edition, Grade 6” featuring an illustration of children engaging in various New York math-related activities outdoors.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover image of "Amplify Desmos Math" for Grade 6, featuring a 3D pink letter "I" and the text "Intervention and Extension Resources." This New York math edition supports students with comprehensive resources.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

A digital illustration of math balancing scales featuring boxes and a fox, alongside a worksheet displaying similar content and activities for learning math concepts.

Students use equations and tape diagrams to represent seesaw situations and to determine unknown animal weights, helping them make connections between diagrams that represent equations of the form `x+p=q` or `px=q`.

A clear plastic storage box filled with educational math manipulatives, including colorful blocks, shapes, measuring tools, and counting cubes displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

A Grade 7 math curriculum outline, featuring units on scale drawings, proportional relationships, measuring circles, rational numbers, operations, equations, angles, area, and probability with sequencing and days allocated. Perfectly aligned with Amplify Desmos Math for New York Math standards.
Program structure

Get to know the content and structure of Grade 7 Amplify Desmos Math California.

Cover image of "Amplify Desmos Math Teacher Edition Grade 7" featuring an illustration of students engaging in math-related activities with geometric shapes and construction elements against a New York cityscape background.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from three sub-units on this site: Unit 1, Sub-Unit 1: Scaled Copies; Unit 4, Sub-Unit 1: Percentages as Proportional Relationships; and Unit 6, Sub-Unit 1: Equations and Tape Diagrams.

Activity page showing a grid for shape creation with an area of 8 square centimeters. Includes shape options and instructions on rotation. A booklet page displays area challenges and warm-up tasks.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math, Student Edition, Grade 7" showing students engaged in math activities against a cityscape reminiscent of New York, with purple geometric structures and a crane in the background.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math: Grade 7 – Intervention and Extension Resources" featuring a stylized 3D "I" on a light purple background, ideal for both New York math and national curricula.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Screenshot of an educational website showing a math activity featuring a sheep named Shira. There is a graph and a worksheet on inequalities displayed.

Students solve inequalities with positive and negative coefficients to solve a variety of challenges featuring a fictional sheep who eats grass according to an inequality.

A clear plastic storage box filled with educational math manipulatives, including colorful blocks, shapes, measuring tools, and counting cubes displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

Grade 8 math curriculum chart featuring 9 units, such as Rigid Transformations and Congruence, with Suggested Instructional days. Each unit outlines instructional days, assessment days, and optional days—complemented by insights from Amplify Desmos Math to enhance your New York math learning experience.
Program structure

Get to know the content and structure of Grade 7 Amplify Desmos Math California.

Illustration of children engaging in learning activities outdoors near a large slide. The title "Amplify Desmos Math Grade 8 Teacher Edition" is shown at the top, highlighting its relevance to New York math curriculum standards.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from three sub-units on this site: Unit 1, Sub-Unit 1: Rigid Transformations; Unit 3, Sub-Unit 2: Linear Relationships; and Unit 6, Sub-Unit 2: Analyzing Numerical Data.

Image of a digital math activity titled "Line Capture #2" featuring a grid, equations, and instructions. A paper worksheet with graphs and a "Line Zapper" title is displayed alongside.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of the "Amplify Desmos Math" Student Edition for Grade 8, featuring students engaging in various mathematical activities in a stylized outdoor New York setting.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Grade 8: Intervention and Extension Resources" featuring a stylized "I" on a gray background, tailored for New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational worksheet on robots, featuring a graph with red, purple, and blue robot icons, and instructions for a warm-up activity.

Students connect points on a scatter plot with individuals in a population and rows of data in a table. The analysis of scatter plots continues with data about the eye distances and heights of robots.

A clear plastic storage box filled with educational math manipulatives, including colorful blocks, shapes, measuring tools, and counting cubes displayed outside the box.
Hands-on manipulative kit

An optional add-on to your Amplify Desmos Math California program, the manipulative kit provides hands-on learning tools designed to simplify and illustrate complex mathematical concepts.

A course outline for Algebra 1 with 8 units, each detailing the number of instructional and optional days. The total suggested instructional days are 144 and 28 optional days, aligning with New York Math standards.
Program structure

Get to know the content and structure of Algebra 1 Amplify Desmos Math California.

Cover of "Amplify Desmos Math: Algebra 1, Teacher Edition" featuring diverse characters engaged in mathematical activities, with a graph and a bridge in the background, illustrating the vibrant energy of New York math.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from two complete sub-units on this site: Unit 2, Sub-Units 1–2: One-Variable Equations and Multi-Variable Equations.

A digital educational interface shows a graph with data points and textual instructions comparing year and breeding pairs. Adjacent is a page discussing penguin populations with charts and illustrations.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math California has student print materials and digital recommendations.

Cover of "Amplify Desmos Math" Student Edition A1, featuring an illustration of diverse characters engaging in New York math activities against a backdrop of graphs and mathematical concepts.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

A digital math activity screen showing block arrangements and a worksheet page titled "Shelley the Snail" with related graphics.

Students represent the solutions of a situation using a table, a graph, and multiple forms of an equation to identify multiple combinations of blocks that can help Shelley the Snail cross a gap.

Contact us

For questions, samples, or more information, please contact your local Amplify Account Executive:

Erin King
Sales Director, CA
(512) 736-3162
eking@amplify.com

Northern CA
Wendy Garcia
Senior Account Executive
(510) 368-7666
wgarcia@amplify.com

Bay Area
Lance Burbank
Account Executive
(415) 830-5348
lburbank@amplify.com

Central Valley and Central Coast
Demitri Gonos
Senior Account Executive
(559) 355-3244
dgonos@amplify.com

Ventura and L.A. County
Jeff Sorenson
Associate Account Executive
(310) 902-1407
jsorenson@amplify.com

Orange and L.A. County
Lauren Sherman
Senior Account Executive
(949) 397-5766
lsherman@amplify.com

San Bernardino and L.A. County
Michael Gruber
Senior Account Executive
(951) 520-6542
migruber@amplify.com

Riverside and L.A. County
Brian Roy
Account Executive
(818) 967-1674
broy@amplify.com

San Diego County
Kirk Van Wagoner
Senior Account Executive
(760) 696-0709
kvanwagoner@amplify.com

Under 2300 students in Bay Area, Sacramento Valley, and Northern Counties
Kevin Mauser
Lead Account Executive
(815) 534-0148
kmauser@amplify.com

Under 2300 students in Southern CA, Central Coast, and Southern Central Valley Counties
Charissa Snyder
Account Executive
(720) 936-6802
chsnyder@amplify.com

Request additional samples.

Ready to learn more? Connect with an Amplify Desmos Math California expert to request additional program samples.

Families and caregivers, welcome to Amplify Desmos Math California
6–12!

Welcome to the Amplify Desmos Math California Grade 6–12 Caregiver Hub. We’ve designed this space to help you support your student at every stage of their math journey.

In class, your student engages with digital lessons using devices as well as write-in Student Edition books. They also may be assigned digital or print practice outside of class. Below, you’ll find some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math California.

Para la versión en español, haga clic aquí.

Ilustración de una persona en silla de ruedas con un casco que dirige la colocación de una pieza triangular, rodeada de símbolos matemáticos.

Caregiver Unit Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of each lesson, plus a problem to try with your student (and an answer key). These resources will be available in both English and Spanish, as well as a glossary of key terms in both languages.

  • Coming soon!
  • Coming soon!

Unit refresh videos

Unit 1

  • Sub-Unit 1a – Calculating the Area of Parallelograms
  • Sub-Unit 1b – Calculating the Area of Triangles
  • Sub-Unit 2 – Determining the Surface Area of Rectangular Prisms

Unit 2

Unit 3

Unit 4

  • Sub-Unit 1 – Dividing Fractions Using Tape Diagrams
  • Sub-Unit 2 – Dividing Fractions Using Common Denominators
  • Sub-Unit 3 – Determining the Volume of Prisms With Fractional Dimensions

Unit 5

  • Sub-Unit 1 – Adding and Subtracting Decimals
  • Sub-Unit 2 – Multiplying Decimals Using Area Models
  • Sub-Unit 3 – Dividing Decimals Using Fractions
  • Sub-Unit 4 – Converting Between Fractions, Percents, and Decimals

Unit 6

  • Sub-Unit 1 – Writing and Solving Equations
  • Sub-Unit 2 – Writing Equivalent Expressions Using the Area Model
  • Sub-Unit 3 – Evaluating Expressions With Exponents
  • Sub-Unit 4 – Interpreting Graphs

Unit 7

  • Sub-Unit 1 – Ordering and Comparing Positive and Negative Numbers
  • Sub-Unit 2 – Identifying Solutions to Inequalities
  • Sub-Unit 3 – Plotting Points on the Coordinate Plane

Unit 8

  • Sub-Unit 1 – Creating Dot Plots
  • Sub-Unit 2 – Calculating Mean Absolute Deviation
  • Sub-Unit 3 – Interpreting Box Plots
  • Sub-Unit 4 – Predicting Population Using Sample Data (For use with Amplify Desmos Math New York)
  • Sub-Unit 5 – Predicting Sample Spaces Using Proportional Relationship (For use with Amplify Desmos Math New York)

Unit 1

  • Sub-Unit 1 – Using Ratios to Determine the Scale Factor Between Scaled Copies
  • Sub-Unit 2 – Using Ratios to Determine Unknown Scales in Scale Drawings

Unit 2

  • Sub-Unit 1 – Determining the Constant of Proportionality
  • Sub-Unit 2 – Writing Equations for Proportional Relationships
  • Sub-Unit 3 – Comparing Proportional Relationships
  • Sub-Unit 4 – Representing Proportional Relationships with Multiple Representations

Unit 3

  • Sub-Unit 1 – Determining the Circumference of a Circle
  • Sub-Unit 2 – Calculating Areas of Complex Shapes

Unit 4

Unit 5

  • Sub-Unit 1 – Adding and Subtracting Positive and Negative Number
  • Sub-Unit 2 – Dividing Integers
  • Sub-Unit 3 – Solving Real-World Problems Involving Positive and Negative Numbers

Unit 6

  • Sub-Unit 1 – Writing Equations from Descriptions and Tape Diagrams
  • Sub-Unit 2 – Solving Equations With Positive and Negative Numbers
  • Sub-Unit 3 – Solving Inequalities

Unit 7

  • Sub-Unit 1 – Determining Unknown Angle Measures
  • Sub-Unit 2 – Determining If Three Segments Form a Triangle
  • Sub-Unit 3 – Calculating the Surface Area of Prisms

Unit 8

  • Sub-Unit 1 – Predicting Sample Spaces Using Proportional Relationships
  • Sub-Unit 2 – Predicting Population Using Sample Data

Unit 1

  • Sub-Unit 1 – Determining Coordinates After a Rotation
  • Sub-Unit 2 – Using Rigid Transformations to Determine if Two Figures on the Grid are Congruent
  • Sub-Unit 3 – Determining Unknown Interior and Exterior Angles

Unit 2

  • Sub-Unit 1 – Performing Dilations on a Square Grid
  • Sub-Unit 2 – Determining Missing Side Lengths in Similar Triangles
  • Sub-Unit 3 – Calculating Slope By Drawing Similar Triangles on a Coordinate Plane

Unit 3

  • Sub-Unit 1 – Writing Equations to Represent Proportional Relationships
  • Sub-Unit 2 – Interpreting Slope and Intercepts of Linear Relationships
  • Sub-Unit 3 – Calculating Slope Given Two Points

Unit 4

  • Sub-Unit 1 – Solve Single-Variable Equations with Parentheses
  • Sub-Unit 2 – Solving Systems of Linear Equations by Graphing

Unit 5

  • Sub-Unit 1 – Justifying Whether a Graph Represents a Function
  • Sub-Unit 2 – Comparing Properties of Linear Functions
  • Sub-Unit 3 – Calculating Volumes of Cylinders

Unit 6

  • Sub-Unit 1 – Interpreting Points on a Scatter Plot
  • Sub-Unit 2 – Using Lines of Fit to Make Predictions
  • Sub-Unit 3 – Calculating Missing Values in Two-Way Tables

Unit 7

Unit 8

  • Sub-Unit 1 – Approximating Square Roots
  • Sub-Unit 2 – Calculating Unknown Side Lengths
  • Sub-Unit 3 – Identifying Rational and Irrational Numbers

Unit 1

  • Sub-Unit 1 – Determining If a Sequence is Arithmetic, Geometric or Neither
  • Sub-Unit 2 – Using Visual Patterns or Terms in the Sequence to Write Explicit Expressions for Arithmetic and Geometric Sequences

Unit 2

  • Sub-Unit 1 – Solving Linear Equations
  • Sub-Unit 2 – Solving Multi-Variable Linear Equations
  • Sub-Unit 3 – Graphing Solutions of Two-Variable Linear Inequalities

Unit 3

  • Sub-Unit 1 – Calculating Values in Two-Way and Relative Frequency Tables
  • Sub-Unit 2 – Comparing Data Using Mean and Standard Deviation
  • Sub-Unit 3 – Interpreting Slope and y-intercept in Context

Unit 4

  • Sub-Unit 1 – Evaluating Function Notation
  • Sub-Unit 2 – Writing Domain and Range with Inequalities
  • Sub-Unit 3 – Graphing Piecewise-Defined Functions
  • Sub-Unit 4 – Writing Recursive Definitions in Function Notation

Unit 5

  • Sub-Unit 1 – Solving Systems of Linear Equations by Substitution
  • Sub-Unit 2 – Graphing Solutions to Systems of Inequalities

Unit 6

  • Sub-Unit 1 – Writing Exponential Functions from Graphs
  • Sub-Unit 2 – Calculating Percent Change in Exponential Functions
  • Sub-Unit 3 – Writing Equivalent Expressions Using Radicals and Rational Exponents
  • Sub-Unit 4 – Writing Exponential Functions Involving Compound Interest

Unit 7

  • Sub-Unit 1 – Describing Key Features of Parabolas
  • Sub-Unit 2 – Graphing Quadratic Functions in Factored Form
  • Sub-Unit 3 – Writing Quadratic Functions in Vertex Form

Unit 8

  • Sub-Unit 1 – Rewriting Factored-Form Expressions in Standard Form
  • Sub-Unit 2 – Solving Quadratic Equations by Graphing
  • Sub-Unit 3 – Solving Quadratic Equations by Completing the Square
  • Sub-Unit 4 – Solving Quadratic Equations Using the Quadratic Formula

Unit 1

  • Sub-Unit 1 – Determining If a Sequence is Arithmetic, Geometric or Neither
  • Sub-Unit 2 – Using Visual Patterns or Terms in the Sequence to Write Explicit Expressions for Arithmetic and Geometric Sequences

Unit 2

  • Sub-Unit 1 – Solving Linear Equations
  • Sub-Unit 2 – Solving Multi-Variable Linear Equations
  • Sub-Unit 3 – Graphing Solutions of Two-Variable Linear Inequalities

Unit 3

  • Sub-Unit 1 – Solving Systems of Linear Equations by Substitution
  • Sub-Unit 2 – Graphing Solutions to Systems of Inequalities
  • Sub-Unit 3 – Writing Equations for Parallel and Perpendicular Lines

Unit 4

  • Sub-Unit 1 – Evaluating Function Notation
  • Sub-Unit 2 – Writing Domain and Range with Inequalities
  • Sub-Unit 3 – Writing Recursive Definitions in Function Notation

Unit 5

  • Sub-Unit 1 – Writing Exponential Functions from Graphs
  • Sub-Unit 2 – Calculating Percent Change in Exponential Functions
  • Sub-Unit 3 – Writing Exponential Functions Involving Compound Interest

Unit 6

  • Sub-Unit 1 – Drawing Perpendicular Bisectors
  • Sub-Unit 2 – Determining Coordinates After a Rotation
  • Sub-Unit 3 – Using Rigid Transformations to Determine if Two Figures on the Grid are Congruent

Unit 7

  • Sub-Unit 1 – Calculating Values in Two-Way and Relative Frequency Tables
  • Sub-Unit 2 – Comparing Data Using Mean and Standard Deviation
  • Sub-Unit 3 – Interpreting Slope and y-intercept in Context

Access Amplify Desmos Math California at home.

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. Students can access the digital curriculum in school and at home by following these simple instructions.

  • Click the Amplify Desmos Math California button.
  • Select Log in with Amplify.
  • Enter the username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, you and your student can view work by opening previous assignments.

Learn how to navigate the student home page.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Relate math to daily activities at home, whether you’re baking, grocery shopping, or planning a trip. Your student can help you calculate the prices when you use a coupon, figure out how to cut a recipe in half, or determine the amount of gas you’ll need to make it to your destination.

Invite your student to walk you through how they solved each problem or talk about any parts that were challenging for them. To encourage the use of math language, consider asking, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students get stuck, consider asking questions like, “What information do you know here?” or “How could you represent this problem?”

Emphasize that getting stuck is part of the process and a necessary part of learning. Many students (and adults!) fear making mistakes, but research shows that making mistakes helps your brain grow. When your student gets stuck on a problem, encourage them to try different strategies, even if they think they can’t do it or will get it wrong.

We hope your student enjoys exploring math, working with friends to solve problems, and learning new and interesting concepts. And we hope you enjoy this exciting math journey with them!

Get more information.

Have a question about Amplify Desmos Math California? Visit our Help Library to search for articles with answers to your program questions. For additional support, please contact your student’s teacher.

Illustrative Mathematics-NEW

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Grade 6

Unit 1: Area and Surface Area

Illustrative MathematicsAmplify Classroom
Topic A: Reasoning to Find Area 
Lesson 1: Tiling the PlaneUnit 1
Lesson 1: Shapes on a Plane
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Unit 1
Lesson 3: Exploring Parallelograms
Topic 3: Triangles
Lesson 7: From Parallelograms to TrianglesUnit 1
Lesson 3: Exploring Parallelograms
Topic 5: Surface Area
Lesson 12: What is Surface Area?Unit 1
Lesson 10: Renata’s Stickers

Unit 2: Introducing Ratios

Topic 1: Introducing Ratios
Lesson 1: Introducing Ratios and Ratio LanguageUnit 2
Lesson 1: Pizza Maker
Lesson 2: Representing Ratios with DiagramsUnit 2
Lesson 1: Pizza Maker
Topic 2: Equivalent Ratios
Lesson 3: RecipesUnit 2
Lesson 4: Fruit Lab
Lesson 5: Defining Equivalent RatiosUnit 2
Lesson 1: Pizza Maker
Topic 4: Solving Ratio and Rate Problems
Lesson 11: Representing Ratios with TablesUnit 2
Lesson 10: Disaster Preparation

Unit 3: Rates and Percentages

Topic 2: Unit Conversion
Lesson 2: Anchoring Units of MeasurementUnit 3
Lesson 1: Many Measurements
Topic 3: Rates
Lesson 5: Comparing Speeds and PricesUnit 3
Lesson 6: Soft Serve
Lesson 6: Interpreting Rates
Lesson 7: Equivalent Ratios Have the Same Unit Rates
Unit 3
Lesson 6: Soft Serve
Topic 4: Percentages
Lesson 10: What Are percentagesUnit 3
Lesson 9: Lucky Duckies
Lesson 13: Benchmark percentagesUnit 3
Lesson 9: Lucky Duckies
Topic 5: Let’s Put It to Work 
Lesson 7: Equivalent Ratios Have the Same Unit RatesUnit 3
Lesson 6: Soft Serve

Unit 4: Dividing Fractions

Topic 2: Meanings of Fraction Division
Lesson 4: How Many Groups (Part 1)Unit 4
Lesson 3: Flour Planner 
Lesson 6: Using Diagrams to Find the Number of GroupsUnit 4
Lesson 6: Fill the Gap

Unit 5: Arithmetic in Base Ten

Topic 1: Warming Up to Decimals 
Lesson 1: Using Decimals in a Shopping ContextUnit 5
Lesson 1: Dishing Out Decimals
Topic 5: Let’s Put It to Work
Lesson 14: Using Operations on Decimals to Solve ProblemsUnit 5
Lesson 13: Movie Time

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and Equations
Lesson 2: Truth and Equations
Unit 6
Lesson 1: Weight for It
Lesson 3: Staying in BalanceUnit 6
Lesson 1: Weight for It
Topic 2: Equal and Equivalent
Lesson 8: Equal and EquivalentUnit 6
Lesson 1: Weight for It
Topic 9: The Distributive Property, Part 1Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10: The Distributive Property, Part 2
Lesson 11: The Distributive Property, Part 3
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic 5: Let’s Put It to Work
Lesson 19: Tables, Equations, and Graphs, Oh My!Unit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Unit 7: Rational Numbers

Lesson 1: Positive and Negative NumbersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Comparing Positive and Negative Numbers
Lesson 4: Ordering Rational Numbers
Unit 7
Lesson 4: Order in the Class
Topic 2: Inequalities
Lesson 9: Solutions of Inequalities
Lesson 10: Interpreting Inequalities
Unit 7
Lesson 7: Tunnel Travels
Topic 3: The Coordinate Plane
Lesson 15: Shapes on the Coordinate PlaneUnit 1
Lesson 1: Shapes on a Plane

Unit 8: Data Sets and Distributions

Topic 2: Dot Plots and Distributions
Lesson 3: Representing Data Graphically
Lesson 4: Dot Plots
Lesson 5: Using Dot Plots to Answer Statistical Questions
Unit 8
Lesson 3: Minimum Wage
Lesson 6: Interpreting Histograms
Lesson 7: Using Histograms to Answer Statistical Questions
Lesson 8: Describing Distributions on Histograms
Unit 8
Lesson 5: The Plot Thickens
Topic 4: Median and IQR
Lesson 13: MedianUnit 8
Lesson 11: Toy Cars

Grade 7

Unit 1: Scale Drawings

Illustrative MathematicsAmplify Classroom
Topic 1: Scaled Copies 
Lesson 1: What are Scaled Copies?Unit 1
Lesson 1: Scaling Machines
Topic 2: Scale Drawings 
Lesson 7: Scale DrawingsUnit 1
Lesson 7: Will It Fit?

Unit 2: Introducing Proportional Relationships

Topic 1: Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the OthersUnit 2
Lesson 1: Paint 
Topic 2: Representing Proportional Relationships with Equations 
Lesson 4: Proportional Relationships with EquationsUnit 2
Lesson 6: Two and Two
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Unit 2
Lesson 6: Two and Two
Topic 3: Comparing Proportional and Nonproportional Relationships 
Lesson 8: Comparing Relationships with EquationsUnit 2
Lesson 6: Two and Two
Topic 4: Representing Proportional Relationships with Graphs
Lesson 10: Introducing Graphs of Proportional Relationships
Lesson 11: Interpreting Graphs of Proportional Relationships
Lesson 12: Using Graphs to Compare Relationships
Lesson 13: Two Graphs for Each Relationship
Unit 2
Lesson 8: Dino Pops

Unit 3: Measuring Circles

Topic 1: Circumference of a Circle 
Lesson 1: How Well Can You Measure?Unit 3
Lesson 8: Toothpicks (coming soon!)
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Unit 3
Lesson 3: Measuring Around
Take Away (coming soon!)
Topic 2: Area of a Circle
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Unit 3
Lesson 9: Area Challenges
Take Away (coming soon!)

Unit 4: Proportional Relationships and Percentages

Topic 1: Proportional Relationships with Fractions 
Lesson 1: Lots of Flags
Lesson 2: Ratios and Rates with Fractions
Lesson 3: Revisiting Proportional Relationships
Lesson 4: Half as Much Again
Unit 4
Lesson 1: Mosaics
Topic 2: Percent Increase and Decrease 
Lesson 6: Increasing and DecreasingUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Topic 3: Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Unit 4
Lesson 12: Posing Percent Problems (coming soon!)
Topic 4: Let’s Put It to Work 
Lesson 16: Posing Percent ProblemsUnit 4
Lesson 12: Posing Percent Problems (coming soon!)

Unit 5: Rational Number Arithmetic

Topic 1: Interpreting Negative Numbers 
Lesson 1: Interpreting Negative NumbersUnit 5
Lesson 1: Floats and Anchors
Topic 2: Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Unit 5
Lesson 4: Draw Your Own
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Unit 6: Expressions, Equations, and Inequalities

Topic 1: Representing Situations of the Form px + q and p(+ q) = r 
Lesson 1: Relationships Between QuantitiesUnit 2
Lesson 1: Paint
Unit 4
Lesson 1: Mosaics
Topic 9 Dealing with Negative Numbers 
Lesson 10: Different Options for Solving One EquationUnit 6
Lesson 10: Collect the Squares
Topic 3: Inequalities 
Lesson 13: Reintroducing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiency Solving Inequalities
Unit 6
Lesson 16: Shira the Sheep
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Unit 6
Lesson 16: Shira the Sheep
Topic 4: Writing Equivalent Expressions 
Lesson 18: Subtraction in Equivalent ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Unit 6
Lesson 10: Collect the Squares

Unit 7: Angles, Triangles, and Prisms

Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Unit 7
Lesson 2: Friendly Angles
Lesson 4: Solving for Unknown AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 5: Using Equations to Solve for Unknown AnglesUnit 7
Lesson 4: Missing Measures
Topic 2: Drawing Polygons with Given Conditions 
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Unit 7
Lesson 5: Can You Build It?

Unit 8: Probability and Sampling

Topic 1: Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities
Topic 3: Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Unit 8
Lesson 10: Crab Island
Topic 4: Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Unit 8 
Lesson 10: Crab Island
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations with Friends
Unit 8
Lesson 10: Crab Island

Grade 8

Unit 1: Rigid Transformations and Congruence

Illustrative MathematicsAmplify Classroom
Topic 1: Rigid Transformations 
Lesson 1: Moving in the PlaneUnit 1
Lesson 1: Transformers
Lesson 2: Naming the MovesUnit 1
Lesson 2: Spinning, Flipping, Sliding
Lesson 3: Grid MovesUnit 1
Lesson 4: Moving Day
Lesson 4: Making the MovesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 5: Coordinate MovesUnit 1
Lesson 4: Moving Day
Lesson 6: Describing TransformationsUnit 1
Lesson 6: Connecting the Dots (coming soon!)
Topic 2: Properties of Rigid Transformations 
Lesson 8: Rotation PatternsUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Topic 5: Let’s Put It to Work
Lesson 17: Rotate and TessellateLesson 13: Tessellate

Unit 2: Dilations, Similarity, and Introducing Slope

Topic 1: Dilations
Lesson 1: Projecting and ScalingUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 2: Circular Grid
Lesson 3: Dilations with No Grid
Lesson 4: Dilations on a Square Grid
Lesson 5: More Dilations
Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Topic 2: Similarity 
Lesson 6: SimilarityUnit 2
Lesson 6: Social Scavenger Hunt
Topic 3: Slope
Lesson 10: Meet SlopeUnit 3
Lesson 4: Flags

Unit 3: Linear Relationships

Topic 1: Proportional Relationships 
Lesson 1: Understanding Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Graphs of Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 3: Representing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials 
Topic 2: Representing Linear Relationships
Lesson 5: Introduction to Linear RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 7: Representations of Linear RelationshipsUnit 3
Lesson 4: Flags
Topic 3: Finding Slopes 
Lesson 9: Slopes Don’t Have to be PositiveUnit 3
Lesson 4: Flags
Lesson 11: Equations of All Kinds of LinesUnit 3
Lesson 4: Flags
Topic 4: Linear Equations 
Lesson 13: More Solutions to Linear EquationsUnit 3 
Lesson 4: Flags

Unit 4: Linear Equations and Linear Systems

Topic 2: Linear Equation in One Variable 
Lesson 5: Solving Any Linear EquationUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Strategic SolvingUnit 4
Lesson 5: Equation Roundtable
Topic 3: Systems of Linear Equations
Lesson 11: On Both of the Lines
Lesson 12: Systems of Equations
Lesson 13: Solving Systems of Equations
Unit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Unit 5: Functions and Volume

Topic 1: Inputs and Outputs 
Lesson 1: Inputs and OutputsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Introduction to FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Topic 2: Representing and Interpreting Functions 
Lesson 3: Equations of FunctionsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Tables, Equations, and Graphs of Functions
Lesson 5: More Graphs of Functions
Unit 5
Lesson 5: The Tortoise and the Hare
Topic 3: Linear Functions and Rates of Change
Lesson 8: Linear FunctionsUnit 3
Lesson 4: Flags
Lesson 9: Linear ModelsUnit 5
Lesson 5: The Tortoise and the Hare
Topic 4: Cylinder and Cones 
Lesson 13: The Volume of a CylinderUnit 5
Lesson 11: Cylinders
Lesson 14: Finding Cylinder DimensionsUnit 5
Lesson 11: Cylinders
Lesson 15: The Volume of a ConeUnit 5
Lesson 13: Cones
Lesson 16: Finding Cone DimensionsUnit 5
Lesson 13: Cones

Unit 6: Associations in Data

Topic 2: Associations in Numerical Data 
Lesson 3: What a Point in a Scatter Plot MeansUnit 6 
Lesson 3: Robots
Lesson 4: Fitting a LineUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 5: Describing Trends in Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 7: Observing More patterns in Scatter PlotsUnit 6 
Lesson 3: Robots
Topic 3: Associations in Categorical data 
Lesson 9: Looking for AssociationsUnit 6
Lesson 11: Finding Associations
Lesson 10: Using Data Displays to Find associationsUnit 6
Lesson 11: Finding Associations

Unit 7: Exponents and Scientific Notation

Topic 1: Exponent Review 
Lesson 1: Exponent ReviewUnit 7 
Lesson 1: Circles
Lesson 2: Multiplying Powers of 10
Lesson 3: Powers of Powers of 10
Lesson 4: Dividing Powers of 10
Unit 7 
Lesson 3: Power Pairs
Topic 3: Scientific Notation 
Lesson 13: Defining Scientific Notation
Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
Unit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 15: Adding and Subtracting with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Unit 8: Pythagorean Theorem and Irrational Numbers

Topic 1: Side Lengths and Areas of Squares
Lesson 5: Reasoning about Square RootsUnit 8
Lesson 4: Root Down
Topic 2: The Pythagorean Theorem
Lesson 6: Finding Side Lengths of TrianglesUnit 8
Lesson 8: Triangle-Tracing Turtle
Lesson 10: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck
Topic 5: Let’s Put It to Work
Lesson 16: When Is the Same Size Not the Same Size?Unit 8
Lesson 10: Taco Truck

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

Families and caregivers, welcome to Amplify Desmos Math 6–12!

Welcome to the Amplify Desmos Math Grade 6–Algebra 2 Caregiver Hub. We’ve designed this space to help you support your student at every stage of their math journey. 

In class, your student engages with digital lessons using devices as well as write-in Student Edition books. They also may be assigned digital or print practice outside of class. Below, you’ll find some suggestions and resources for how you can support their learning at home.

Learn more about Amplify Desmos Math.

Para la versión en español, haga clic aquí.

Person wearing a construction hat and safety vest in a wheelchair, discussing with a phone and controlling the placement of a large triangular piece in a construction setting, with math symbols around.

Caregiver Unit Resources

For every unit of the program, we’ve created a Caregiver Resource that provides a summary of each lesson, plus a problem to try with your student (and an answer key). These resources are available in both English and Spanish, as well as a glossary of key terms in both languages.

Unit 1: Area and Surface Area

Unit 2: Introducing Ratios

Unit 3: Rates and Percentages

Unit 4: Dividing Fractions

Unit 5: Decimal Arithmetic

Unit 6: Expressions and Equations

Unit 7: Positive and Negative Numbers

Unit 8: Describing Data

Unit 1: Scale Drawings

Unit 2: Introducing Proportional Relationships

Unit 3: Measuring Circles

Unit 4: Proportional Relationships and Percentages

Unit 5: Operations With Positive and Negative Numbers

Unit 6: Expressions, Equations, and Inequalities

Unit 7: Angles, Triangles, and Prisms

Unit 8: Probability and Sampling

Unit 1: Rigid Transformations and Congruence

Unit 2: Dilations, Similarity, and Slope

Unit 3: Proportional and Linear Relationships

Unit 4: Linear Equations and Linear Systems

Unit 5: Functions and Volume

Unit 6: Associations in Data

Unit 7: Exponents and Scientific Notation

Unit 8: The Pythagorean Theorem and Irrational Numbers

Unit 1: Area and Surface Area

Unit 2: Introducing Ratios and Rates

Unit 3: Fractions and Decimals

Unit 4: Expressions and Equations

Unit 5: Proportional Relationships

Unit 6: Percentages

Unit 7: Positive and Negative Numbers

Unit 8: Data Sets and Distributions

Course Glossary

Unit 1: Rigid Transformations and Congruence

Unit 2: Scale Drawings, Dilations, and Similarity

Unit 3: Equations and Inequalities

Unit 4: Linear Relationships and Systems of Linear Equations

Unit 5: Functions

Unit 6: Associations in Data

Unit 7: Volume and Surface Area

Unit 8: Exponents and Scientific Notation

Unit 9: Pythagorean Theorem and Irrational Numbers

Course Glossary

Unit 1: Patterns and Sequences

Unit 2: Linear Equations and Inequalities

Unit 3: Describing Data

Unit 4: Describing Functions

Unit 5: Systems of Linear Equations and Inequalities

Unit 6: Exponential Functions

Unit 7: Quadratic Functions

Unit 8: Quadratic Equations

Unit refresh videos

Unit 1

  • Sub-Unit 1a – Calculating the Area of Parallelograms
  • Sub-Unit 1b – Calculating the Area of Triangles
  • Sub-Unit 2 – Determining the Surface Area of Rectangular Prisms

Unit 2

Unit 3

Unit 4

  • Sub-Unit 1 – Dividing Fractions Using Tape Diagrams
  • Sub-Unit 2 – Dividing Fractions Using Common Denominators
  • Sub-Unit 3 – Determining the Volume of Prisms With Fractional Dimensions

Unit 5

  • Sub-Unit 1 – Adding and Subtracting Decimals
  • Sub-Unit 2 – Multiplying Decimals Using Area Models
  • Sub-Unit 3 – Dividing Decimals Using Fractions
  • Sub-Unit 4 – Converting Between Fractions, Percents, and Decimals

Unit 6

  • Sub-Unit 1 – Writing and Solving Equations
  • Sub-Unit 2 – Writing Equivalent Expressions Using the Area Model
  • Sub-Unit 3 – Evaluating Expressions With Exponents
  • Sub-Unit 4 – Interpreting Graphs

Unit 7

  • Sub-Unit 1 – Ordering and Comparing Positive and Negative Numbers
  • Sub-Unit 2 – Identifying Solutions to Inequalities
  • Sub-Unit 3 – Plotting Points on the Coordinate Plane

Unit 8

  • Sub-Unit 1 – Creating Dot Plots
  • Sub-Unit 2 – Calculating Mean Absolute Deviation
  • Sub-Unit 3 – Interpreting Box Plots
  • Sub-Unit 4 – Predicting Population Using Sample Data (For use with Amplify Desmos Math New York)
  • Sub-Unit 5 – Predicting Sample Spaces Using Proportional Relationship (For use with Amplify Desmos Math New York)

Unit 1

  • Sub-Unit 1 – Using Ratios to Determine the Scale Factor Between Scaled Copies
  • Sub-Unit 2 – Using Ratios to Determine Unknown Scales in Scale Drawings

Unit 2

  • Sub-Unit 1 – Determining the Constant of Proportionality
  • Sub-Unit 2 – Writing Equations for Proportional Relationships
  • Sub-Unit 3 – Comparing Proportional Relationships
  • Sub-Unit 4 – Representing Proportional Relationships with Multiple Representations

Unit 3

  • Sub-Unit 1 – Determining the Circumference of a Circle
  • Sub-Unit 2 – Calculating Areas of Complex Shapes

Unit 4

Unit 5

  • Sub-Unit 1 – Adding and Subtracting Positive and Negative Number
  • Sub-Unit 2 – Dividing Integers
  • Sub-Unit 3 – Solving Real-World Problems Involving Positive and Negative Numbers

Unit 6

  • Sub-Unit 1 – Writing Equations from Descriptions and Tape Diagrams
  • Sub-Unit 2 – Solving Equations With Positive and Negative Numbers
  • Sub-Unit 3 – Solving Inequalities

Unit 7

  • Sub-Unit 1 – Determining Unknown Angle Measures
  • Sub-Unit 2 – Determining If Three Segments Form a Triangle
  • Sub-Unit 3 – Calculating the Surface Area of Prisms

Unit 8

  • Sub-Unit 1 – Predicting Sample Spaces Using Proportional Relationships
  • Sub-Unit 2 – Predicting Population Using Sample Data

Unit 1

  • Sub-Unit 1 – Determining Coordinates After a Rotation
  • Sub-Unit 2 – Using Rigid Transformations to Determine if Two Figures on the Grid are Congruent
  • Sub-Unit 3 – Determining Unknown Interior and Exterior Angles

Unit 2

  • Sub-Unit 1 – Performing Dilations on a Square Grid
  • Sub-Unit 2 – Determining Missing Side Lengths in Similar Triangles
  • Sub-Unit 3 – Calculating Slope By Drawing Similar Triangles on a Coordinate Plane

Unit 3

  • Sub-Unit 1 – Writing Equations to Represent Proportional Relationships
  • Sub-Unit 2 – Interpreting Slope and Intercepts of Linear Relationships
  • Sub-Unit 3 – Calculating Slope Given Two Points

Unit 4

  • Sub-Unit 1 – Solve Single-Variable Equations with Parentheses
  • Sub-Unit 2 – Solving Systems of Linear Equations by Graphing

Unit 5

  • Sub-Unit 1 – Justifying Whether a Graph Represents a Function
  • Sub-Unit 2 – Comparing Properties of Linear Functions
  • Sub-Unit 3 – Calculating Volumes of Cylinders

Unit 6

  • Sub-Unit 1 – Interpreting Points on a Scatter Plot
  • Sub-Unit 2 – Using Lines of Fit to Make Predictions
  • Sub-Unit 3 – Calculating Missing Values in Two-Way Tables

Unit 7

Unit 8

  • Sub-Unit 1 – Approximating Square Roots
  • Sub-Unit 2 – Calculating Unknown Side Lengths
  • Sub-Unit 3 – Identifying Rational and Irrational Numbers

Unit 1

  • Sub-Unit 1 – Determining If a Sequence is Arithmetic, Geometric or Neither
  • Sub-Unit 2 – Using Visual Patterns or Terms in the Sequence to Write Explicit Expressions for Arithmetic and Geometric Sequences

Unit 2

  • Sub-Unit 1 – Solving Linear Equations
  • Sub-Unit 2 – Solving Multi-Variable Linear Equations
  • Sub-Unit 3 – Graphing Solutions of Two-Variable Linear Inequalities

Unit 3

  • Sub-Unit 1 – Calculating Values in Two-Way and Relative Frequency Tables
  • Sub-Unit 2 – Comparing Data Using Mean and Standard Deviation
  • Sub-Unit 3 – Interpreting Slope and y-intercept in Context

Unit 4

  • Sub-Unit 1 – Evaluating Function Notation
  • Sub-Unit 2 – Writing Domain and Range with Inequalities
  • Sub-Unit 3 – Graphing Piecewise-Defined Functions
  • Sub-Unit 4 – Writing Recursive Definitions in Function Notation

Unit 5

  • Sub-Unit 1 – Solving Systems of Linear Equations by Substitution
  • Sub-Unit 2 – Graphing Solutions to Systems of Inequalities

Unit 6

  • Sub-Unit 1 – Writing Exponential Functions from Graphs
  • Sub-Unit 2 – Calculating Percent Change in Exponential Functions
  • Sub-Unit 3 – Writing Equivalent Expressions Using Radicals and Rational Exponents
  • Sub-Unit 4 – Writing Exponential Functions Involving Compound Interest

Unit 7

  • Sub-Unit 1 – Describing Key Features of Parabolas
  • Sub-Unit 2 – Graphing Quadratic Functions in Factored Form
  • Sub-Unit 3 – Writing Quadratic Functions in Vertex Form

Unit 8

  • Sub-Unit 1 – Rewriting Factored-Form Expressions in Standard Form
  • Sub-Unit 2 – Solving Quadratic Equations by Graphing
  • Sub-Unit 3 – Solving Quadratic Equations by Completing the Square
  • Sub-Unit 4 – Solving Quadratic Equations Using the Quadratic Formula

Access Amplify Desmos Math at home.

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. Students can access the digital curriculum in school and at home by following these simple instructions.

  • Click the Amplify Desmos Math button.
  • Select Log in with Amplify.
  • Enter the username and password provided by your student’s teacher.
  • Select the desired grade level.

Once logged in, you and your student can view work by opening previous assignments.

Learn how to navigate the student home page.

Support math learning at home.

You can support your student’s math learning outside of school in many ways:

Relate math to daily activities at home, whether you’re baking, grocery shopping, or planning a trip. Your student can help you calculate the prices when you use a coupon, figure out how to cut a recipe in half, or determine the amount of gas you’ll need to make it to your destination.

Invite your student to walk you through how they solved each problem or talk about any parts that were challenging for them. To encourage the use of math language, consider asking, “How do you know?,” “How can you show your thinking?,” or “How would you describe that?” If students get stuck, consider asking questions like, “What information do you know here?” or “How could you represent this problem?”

Remind your student that getting stuck is part of the process and a necessary—beneficial, even!—part of learning. Many students (and adults) fear making mistakes. But research shows that making mistakes helps our brains grow. When your student gets stuck on a problem, encourage them to keep trying different strategies, even if they’re not sure they’re right.

We hope your student enjoys exploring math, working with friends to solve problems, and learning new and interesting concepts. And we hope you enjoy this exciting math journey with them!

Get more information.

Have a question about Amplify Desmos Math? Visit our help library to search for articles with answers to your program questions. For additional support, please contact your student’s teacher.

S5-03. Cultivating a joy of learning with Sesame Workshop

A blue graphic with text reading "Math Teacher Lounge" in multicolored letters and "Amplify." at the bottom, with abstract geometric shapes and lines as decoration.

Listen as we chat with Dr. Rosemarie Truglio, senior vice president of curriculum and content for Sesame Workshop! Continuing our theme of math anxiety this season, we sat down with Dr. Truglio to chat about Sesame Street and her thoughts on how to spread a growth mindset to young children and put them on course to academic achievement and long-term success.
 
Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!

Download Transcript

Dr. Rosemarie Truglio (00:00):
Children don’t come with this math anxiety. Math anxiety is learned.

Bethany Lockhart Johnson (00:07):
Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:11):
And I’m Dan Meyer.

Bethany Lockhart Johnson (00:12):
Hello, Dan Meyer.

Dan Meyer (00:14):
Great to see you, Bethany. We are on episode three. Can you believe it?

Bethany Lockhart Johnson (00:18):
So, I feel like we’ve just started scratching the surface about math anxiety. We’ve talked to two amazing researchers. We’ve talked about what math anxiety is, how it’s often screened for some of the causes, some of the consequences … I mean, we’ve had some good conversations. Dan, what do you think?

Dan Meyer (00:38):
Definitely, I think that the consequences have only grown more dire in my head. I’m not sure how you feel about the consequences. But, you know, it is enough for me that we ask students to take mathematics for much of their childhoods, to worry about their anxiety, taking that. But to hear about from these researchers about all the different things that correlate with math achievement and math anxiety—talking about future careers, certainly, but even some other, more serious lifelong concerns? That gives me a lot of motivation to continue this study of math anxiety here with you on the show.

Bethany Lockhart Johnson (01:14):
It is really widespread. It has a big impact, not only on students, but on parents, on educators. You know, it’s—

Dan Meyer (01:23):
Multi-generational.

Bethany Lockhart Johnson (01:25):
Yes. And you know, so often when folks think of math anxiety, what I hear them say is, “Oh, yeah, in high school is when math really ramps up. That’s when anxiety starts.” But we know that it starts in our youngest learners. And our research has already backed that up. We know it. I’ve seen it in my classroom. You may have seen it with some students you work with. And let me tell you, it starts young.

Dan Meyer (01:52):
It does start early. Right now, I have a son that’s just started kindergarten, and he seems relatively math-positive, but we’ve known from our interviews on this show and other kinds of experiences that oftentimes, that feeling —that math is for me, and I am for math, and we are all friends — can turn on a single moment. It seems like one teacher says a thing that changes a student’s perception of themselves as a mathematician or of math itself. So I keep waiting with bated breath, hoping not to find that one moment that changes our current open posture towards mathematics. So now it’s time to really dive into some strategies for combating math anxiety.

Bethany Lockhart Johnson (02:34):
To help us out, we’ve called on a pretty exciting guest. I am so excited, Dan Meyer! We are being joined by Dr. Rosemarie Truglio. She is Senior Vice President of Curriculum and Content at Sesame Workshop. Sesame Workshop! As in, “Tell me how to get to Sesame Street.” Dan, I have to tell you, I spent many, many hours of my childhood watching Sesame Street. I have to ask, do you have happy Sesame Street memories? Is this part of your formation, Dan Meyer?

Dan Meyer (03:08):
At this point? In my advancing years, and the brain cells that I have left, Sesame Street is really kind of just a vibe in my head. But that vibe is such a pleasant one. One in which like nothing bad could happen. One in which learning is common and normalized and fun. And you just kind of feel at home, constantly.

Bethany Lockhart Johnson (03:33):
I don’t know about the “just the vibe” part, because for me, it is visceral. I’m there. I am actually … I mean, I might still be there.

Dan Meyer (03:42):
You could reenact some of the skits?

Bethany Lockhart Johnson (03:44):
. You didn’t watch Sesame Street with your kiddos when they were younger?

Dan Meyer (03:49):
We watched a lot of Elmo. A lot of Elmo. Yeah.

Bethany Lockhart Johnson (03:52):
Next-generation Sesame Street. Well, I think it’s so perfect that we’re gonna be talking about what Sesame Workshop does to help combat math anxiety and create a positive connection and relationship with mathematics. So I’m really excited to hear what Dr. Truglio and her team have been working on. And here’s our conversation with Dr. Truglio.

Dan Meyer (04:15):
Welcome to the show, Dr. Truglio. It is an honor.

Dr. Rosemarie Truglio (04:18):
Great to be here. Thank you for inviting me.

Dan Meyer (04:20):
You are Senior Vice President of Curriculum and Content at Sesame Workshop, which definitely sounds like the coolest job in the world to both four-year-old me and also Now me. Would you just help us help us with some backstory of how you ended up here, and what you do at Sesame Workshop?

Dr. Rosemarie Truglio (04:38):
Sure. It is a pretty cool job. And I am very fortunate that I’ve been in this position for the past 26 years. So, I am a developmental psychologist, and my job is to help Sesame Workshop identify curriculum needs, so that we could address them in the content that we create on the show and across our various platforms. So, Sesame Street is currently in its 53rd season. And we just, wrapped production for the 54th season, which we’ll debut next fall. And Sesame Street began with an experiment: Can television actually teach children school readiness skills, to have them better prepared for school? Especially those children who did not have access to formal education during the preschool years? And it is what we call a whole-child curriculum, because we’re dealing with all of the school readiness needs. So that that includes the academic needs, their social-emotional needs, and their health needs, as well as what we call these cognitive processing skills—how children learn content. Right? So it’s not just content skills, but how you approach learning and how you actually learn content. So as a grad student, I was fortunate to work at the Center for Research on the Influences of Television on Children. Very special center. It was at the University of Kansas. And my advisors, developmental psychologists, they studied the effects of television on children, both the positive effects and the negative effects. And so part of their research was to actually look at the longterm educational effects of Sesame Street. So I was working with Sesame Street content as a grad student, and then came to New York City. My first job was Assistant Professor at Teachers College, Columbia University. And when this position became available, Director of Research at the time, it was called, I took that job. And so my job was to oversee both the curriculum and the implementation of the curriculum, as well as the research. Because what we know, our co-founder, Joan Ganz Cooney has always said, for Sesame Street to be a successful educational program, production has to work closely with early childhood educators. They are the ones who know the curriculum and, and develop the curriculum goals, as well as the developmental psychologists who actually study how children are paying attention to the content. But more importantly, what are they comprehending from the content? And we all have to work together. Because even though we are the experts, the real experts are the children themselves. So nothing is deemed final until we actually show the children and see what they are learning from the content that we are producing.

Dan Meyer (07:54):
Are you referring to like, test audiences of kids then?

Dr. Rosemarie Truglio (07:57):
Yeah, I guess you could call it test audiences. I mean, I don’t. I don’t like to call it that because I see them as co-collaborators. I don’t see them as a test audience. Because, as I said, they’re the experts. It’s a collaboration. I mean, they’re the experts. And so I wanna know—

Dan Meyer (08:12):
As collaborators. I got it now. Yeah.

Dr. Rosemarie Truglio (08:14):
They help us. So that’s exactly what we tell the children too. So it’s called formative research. You know, we, we do what we call, um, storybook testing, an animated version of a storybook to have some little movement and see are they finding the story engaging, but more importantly, are they picking up on the intended educational lesson that we’re trying to teach in the story. So they are co-collaborators. they’re the ones who are helping us get the story just right for them.

Dan Meyer (08:46):
That’s really exciting, and makes me think about what classes might be like if students were regarded in that kind of lens as well. I just wanna say that my four-year-old self is on this interview as well, and is re-contextualizing all the stuff I saw as a kid. And it just felt like, at the time, you folks turned the camera on and went down to the street and we just had this real natural time. And it’s great to hear about all the intense preparation and co-construction at work and work that went into that time. Yeah,

Dr. Rosemarie Truglio (09:12):
It’s about a year preparation from start to finish. From the start of identifying, “What is the educational need? Is it an academic need? Is it a social-emotional need? Is it a health need? Is it a cognitive-processing need?” And then once we have the need identified, we have what we call a curriculum seminar. We bring in the experts who are studying this topic with preschoolers, because we wanna get it, we wanna get it right.

Bethany Lockhart Johnson (09:41):
Which, by the way, little behind the scenes: How often do you get to go to set?

Dr. Rosemarie Truglio (09:46):
So we’re in a production probably about six weeks out of the year. Covid really messed things up. ‘Cause we have to be really—we have very strict Covid protocols, but there is someone on my team—and sometimes we have to, you know, rotate for availability—but there’s always an educator on set.

Bethany Lockhart Johnson (10:06):
Awesome.

Dr. Rosemarie Truglio (10:07):
Because even though you stick to the script, questions arise; they wanna make changes; sometimes they have to cut; things are running too long and they have to cut and we gotta figure out where to cut. So there’s always an educator on set.

Bethany Lockhart Johnson (10:19):
But sometimes you go and have lunch, like—.

Dr. Rosemarie Truglio (10:21):
Oh, I go, yes. Sometimes I go—

Bethany Lockhart Johnson (10:23):
And just hang out with Big Bird, right?

Dr. Rosemarie Truglio (10:24):
Sometimes I go hang out with Big Bird. No, those are my friends!

Bethany Lockhart Johnson (10:27):
They are!

Dr. Rosemarie Truglio (10:28):
No, no, I go hang out with them. They’re my friends. Yes.

Bethany Lockhart Johnson (10:32):
When I think about Sesame Street and I think about … like, I can’t help but smile. Because I think I have such fond memories of the characters. I mean, we invited them, my mom invited them, into our home, right? And, you know, now I have a two-year-old and there’s no doubt that I’m gonna introduce him to Sesame Street. And I see how it really does feel like the folks who are doing this work, you and your team, you have a deep respect for children. So it makes sense that you call your test collaborators “collaborators,” right? They’re a part of it. And you know, I love that. And Sesame Street makes me smile. However, I’m like, we’re talking about math anxiety. And it’s so interesting, because as Dan and I were talking about our memories of Sesame Street … you know, it’s like Sesame Street feels like there’s not much anxiety. I mean, there are problems, and there’s problem solving, and it’s not like everything is perfect. But we figure it out. And it’s OK to make mistakes and it’s OK to try again. And a lot of times, we don’t see that in the math classroom—or at least, how folks talk about math. So, how do you all think about anxiety, about how to prevent it? Like, when you’re doing your work, you know that math anxiety is a real thing. But then that’s not translated in these experiences and the relationships with math that you’re building with your viewers.

Dr. Rosemarie Truglio (12:07):
Yeah, that’s a really good question, because it’s really easy, because our core audience are two- to four-year-olds and they love math. And what’s not to love, right? Because they are figuring the world out as they’re exploring the world. So you said something really interesting, that when you turn on the TV—when you turned on the TV when you were a child, and now you’re a mom of a two-year-old, we wanna make sure that the show represents content that is relevant and meaningful to our target audience. And that comes through with the characters. So all of our characters have very specific personalities, as all children do. And our characters represent all children, in terms of not only personality, but interest and learning styles, ’cause we wanna see—we wanna make sure that children see themselves in these characters. And we have a character who actually loves math. And he’s The Count.

Bethany Lockhart Johnson (13:12):
I’m like, “I know! I know who it is!” I will save you my impression. Although I have done it for my child. But I’ll save our listeners .

Dr. Rosemarie Truglio (13:20):
And you know, he’s an adult character. Some of our characters are preschoolers, like Elmo and Abby—they’re preschoolers—and Zoe. But The Count is an adult. He lives in the castle and he just loves numbers. But what’s really important is while we have The Count to explain—not explain to, but to portray to children, cause we don’t explain anything; we show children that math is more than number, right? Math is a pretty wide concept. Which is what I love about math. And the other thing about math is math language. The language of math. ‘Cause when we’re teaching children vocabulary words, we’re also teaching children the concept. Be it a math concept or a science concept or a social-emotional concept. So children don’t come with this math anxiety. Math anxiety is learned and it’s unfortunate. It’s picked up by their observations of the adults in their lives, who sometimes say out loud, “I don’t like math,” or “Math is hard,” or even worse, “I’m not good at math.” Or may even label it as math anxiety. That word won’t mean anything to a young child. But it then provides a, whaddya call it, like a negative valence for something that they never felt negative about. Because as they’re growing and interacting with the world, math is all around them. And there’s that sense of awe and wonder and joy, especially as they’re learning and they’re figuring it out. So I think we have to reframe math. Instead of saying “math anxiety,” we have to talk about the joy of math and all the wonderful joys that come with the exploration of these math concepts. Number is great. We know kids love numbers. We know that they love to count and use a big word here: enumerate . Because so many parents don’t make this distinction. They’ll say, “Oh, my child is counting!” Well, there’s rote counting, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, which is important. But then it’s like there’s an item for each number. So it’s one Cheerio, two Cheerios. And then as you point to each number, you are then figuring out what the set is, of the number of objects that you have. And then you get at what I love to call the meaningfulness of math. Right? Number has meaning. And as I said, it’s all part of your everyday activities. It’s part of—it’s in your kitchen; you’re following recipes; you’re measuring; you’re weighing. It’s at bath time, right? You could have the sorting of nested cups and you could, you know, and once again, the math language: big, bigger, biggest. These are relational concepts. You could then count what sinks and what floats, if you’re doing science. And then you could put them in two different buckets, and count. These are the items that sunk and these are the items that float. So math and bath time could be a lot of fun. And then there’s math and music. Music is so rich with math, as you talk about rhythm and tempo and dynamics and pitch and duration. That’s all math.

Bethany Lockhart Johnson (16:57):
The way that you talk about it, it is so rich, right? It is so multi-layered. And you know, I’ve shared on the podcast before: I’ve actually had parents in parent-teacher conferences say that, “Well, I wasn’t good at math either,” or “Math’s really not my thing.” And it’s really—it is, it’s rooted in that fear. And so I do see the way that you’re talking about it; I see that come through in Sesame Street. That, in a lot of ways, it’s reeducating parents, right? Because we hope that our caregivers are sitting next to their kiddo and enjoying it together and having conversations about it later. And there’s a way that parents then are also getting their own sense of what math can be, expanded. And I think there’s such a beauty in that. And I love the way that you talk about that, that you really are looking at, “Well, we wanna celebrate counting and the joyfulness of that. And let’s use math talk, you know, and let’s use these words and try out these ideas.” And it’s not because you’re trying to check some list. But you’re really exploring it and having fun together.

Dr. Rosemarie Truglio (18:03):
And you’re embracing it. And you mentioned the word “mistake.” So often when it comes to math, if you make a mistake—you make a mistake in counting or, you know, we’re not doing a lot of math equations on Sesame Street, but that’s when people feel like they can’t do math. ‘Cause they made a mistake. And that’s something that we are trying to address on Sesame Street, that it’s OK to make mistakes and you learn through mistakes. But you have to have—and I’m gonna come up with this other phrase now—you have to have what we call a growth mindset. What that means is that I may not be able to do this yet. Like, it’s called “the power of yet.” So we know that learning any concept, it takes time and practice. And how do we have children embrace the process, right? So often we focus on right and wrong. Now, there is right and wrong with math, of course. You know, there’s a right answer and there’s a wrong answer. But how do we focus, not on the end product, but the process through which you are engaging in? So let’s talk about measurement. Let’s talk about measuring the length and the width or the height of something. You might make some mistakes along the way, but you’re processing it. My son used to make all of these little structures for all his little play animals. Well, you know, he would measure and think he got it right. And then when he put the animals in, of course, you know, either the animal was too wide or it was too tall. And he would have to redo it. But you’re not redoing it from scratch, you’re redoing it now from experience. “I realize that if I’m gonna put the giraffe in with the elephant, I’m gonna need something wide as well as high.” Right? For the length, tall. And that’s process. And then, for children, when they figure it out, that “oops” and “aha”—the “aha” was like, “I did it!” And it’s so empowering, you know, giving them agency—not swooping in and saying, “All right, I’ll fix it for you. You know, we got the wide elephant and the tall giraffe and I’ll you know…”. NO! Having them do it. And another fun activity is in what we call informal measurement. And that’s like getting something of an equal size. It could be paper clips or it could be same-size blocks, and then measuring how long something is. So if it’s measured by blocks versus paperclips, you’re gonna have a lot more paperclips than you are blocks. And that kind of comparison is so fascinating for children. And so that’s measurement. And now we have counting. Like, how many paperclips long is something versus how many blocks long is something.

Dan Meyer (21:02):
So checking my understanding here, you’ve talked about how caregivers and other adults can transmit math anxiety by naming it and claiming it for themselves. And you’ve talked about, some really exciting ways that adults can involve students and kids in different kinds of math. I’d love to go upstream with you a little bit and wonder out loud, where does this anxiety come from initially? It’s gotta be more than adult one to kid two talking about anxiety, and transmitting it from human to human. What is the original spring from which all this anxiety flows?

Dr. Rosemarie Truglio (21:36):
Yeah. I do think it does—a lot of it does come from the adults in their lives. It’s unfortunate, because there is a lot of math talk about it, right? I can’t do math; I’m not good at math. Even when you’re at a restaurant and you get the bill and someone’s figuring out the tip, I can’t tell you how often it’s like, “Pass the bill, because I can’t do math.” Or if you actually then bring gender into it, you know, “Oh, girls aren’t good at math,” and that’s not true. There’s no evidence of that whatsoever, right? So in the younger grades, there’s no gender difference in terms of math ability. What’s also interesting about even socioeconomic status differences, you don’t see a lot of differences between low-income and middle-income children when it comes to math skills. Where you see differences is children’s ability to talk about their mathematical thinking. So if a child doing a math problem is asked, “How did you solve the problem?”, low-income children don’t often have the language to explain their thinking. So that’s something that we did on Sesame Street, where we focused a lot on what we call math talk. So, not just show number and show doing math, but actually narrate and giving the language. Because math literacy is one of the predictors of overall school achievement. So there’s that. They’re getting it from the adults in their lives. They’re getting it, unfortunately, sometimes from their teachers. But I think the anxiety comes from the fear of making mistakes. Because math, there is right and wrong, and always wanting to get the right answer. So that’s why this whole idea of reframing, and saying, “But really, it’s in the process.” So, you know, my son, math is not his strong suit. And I’ve been doing a lot of growth mindset with him as well. And there was a teacher that he had—I think in like 10th or 11th grade—who said, “In a test, I don’t wanna—I’m not even gonna look at the answer. I wanna see the process through which you GOT to this answer. And I’m going to grade the process. So the process could yield a right answer; it could yield a wrong answer. But you’re gonna get graded on the process. Because I wanna see how you are approaching the problem and how you’re thinking it through.” And I think that is a great example of, maybe, to try to reduce math anxiety. Because if you can get people excited about the process through which you’re learning—and that applies to all subjects, it’s not just math!

Bethany Lockhart Johnson (24:36):
I’m like, that applies to life! Right?

Dr. Rosemarie Truglio (24:38):
That applies to life!

Bethany Lockhart Johnson (24:39):
That’s so spot on. Wow. Yeah.

Dr. Rosemarie Truglio (24:41):
But I think that there’s so much focus on right and wrong, and not really understanding the value of the process. So on Sesame, we’ve been doing a lot of “oops” and “ahas.” You know, we’re gonna make mistakes, but what’s important is what do you DO when you make a mistake? So there’s a great episode with The Count. A couple of years ago. The Count was counting. Something he does every day. A lot of time, every day, ’cause he’s obsessed with counting and numbers. And he was counting an array of items.

Gladys the Cow (25:17):
I need 10 sandwiches all together.

The Count (25:22):
Well, of course.

Dr. Rosemarie Truglio (25:23):
And he made a mistake.

Elmo (25:25):
The Count?

The Count (25:25):
Hmm?

The Count (25:25):
Elmo thinks The Count made a little mistake.

The Count (25:31):
No mistake.

The Count (25:32):
Mm-hmm. Yeah.

Dr. Rosemarie Truglio (25:33):
And first time ever, did he make a mistake. And he fell apart.

The Count (25:38):
I must make sure that that never happens again. So I shall never count again.

Dr. Rosemarie Truglio (25:46):
And that’s an example of showing that, you know, you could get upset when you make a mistake, but what’s important is you gotta come back and you gotta come back to doing what you love. In his case, is counting and letting him know that it was an “oops.” But you learn that mistakes are OK. It’s OK to make a mistake and continue to do what you love.

The Count (26:13):
I must keep trying and you should, too.

Elmo (26:17):
Yeah!

The Count (26:17):
So come, let’s count the carrots together!

Elmo (26:18):
Oh, cool!

Bethany Lockhart Johnson (26:19):
And what a beautiful gift to show kiddos. Show that to kiddos, right? And to the adults. I wanna, you know, really acknowledge it, and say, “Hey look this, it’s OK.” And again, you’re giving them that language. That’s such a gift.

Dr. Rosemarie Truglio (26:34):
Thank you.

Dan Meyer (26:34):
We spend a lot of time wondering why other subjects don’t seem to suffer from this negative perception. And I think you’ve unlocked a lot of that. You’ve mentioned that there are issues that cut across different subject areas, but I think from my own experience and research and interviews, it seems that in ELA and the social sciences, there’s this aspect where you need to come up with a claim and “how are you seeing this?” And there are multiple defensible claims. And I love how you imported that generous pedagogy over into math with this example of a teacher who says, “You know what? It’s about the process here.” Disassociating answer and process.

Dr. Rosemarie Truglio (27:09):
And I think the other thing is like, when children are engaged in a project, for parents to point out: “You’re doing math!” Because they don’t realize that they’re doing math. Once again, math is so often equated solely with numbers and mathematical computations. So it was really interesting—the same is true for science. You know, when we’re talking to parents about the use of everyday—like, going to the supermarket or making dinner or bath time, there’s so much math and science in the everyday. And then when you point it out to them—”you’re doing math”—it’s like, “I’m doing math!” Like, you’re setting the table for a family of six: you’re doing math. That’s called one one-to-one correspondence. “I’m doing math: I’m setting the table.” Yeah, but you’re doing math. You can’t set the table because you have to know how many people are gonna be sitting at the table for dinner. You can’t follow a recipe without doing math. You can’t go shopping without doing math. There’s quantity; you gotta figure out how many peppers you gotta buy, or pounds. “I gotta get a bunch of potatoes and I gotta put ’em in the scale. And I have to get two pounds of potatoes.”

Bethany Lockhart Johnson (28:29):
So your book Ready for School: A Parent’s Guide to Playful Learning for Children Ages Two to Five. First, as a parent of a young toddler, I gotta say it’s such a tool; it’s such a resource. It’s very conversational. And I think about these ideas a lot, both in my work and, you know, just for fun. And yet, even if this wasn’t my chosen field, I still feel like it’s just so accessible. And I wanna flag something.

Dr. Rosemarie Truglio (29:01):
Thank you.

Bethany Lockhart Johnson (29:01):
Yeah, no. Thank YOU. . I wanna flag something that you said in the math chapter You were talking about the joy of math, and you said when it comes to our children, caregivers: “take pleasure in reading stories together, especially at bedtime, which in many households is a regular part of a child’s routine. But somehow the notion of introducing math concepts to our children seems daunting. In fact, some studies have shown that parents harbor a strong belief that while it’s important and pleasurable to support their child’s reading skills, it’s the responsibility of the schools to take care of teaching math.” And that quote, I highlighted it, I starred it! And I would love for you to say a little more about that, because you have given us already, like, a bounty of ideas that as caregivers we can do with our kiddos or the kiddos in our lives. And we’ve seen that even what they’re learning in school, it may not be the freeing, joyful math language that we hope our kiddos have access to.

Dr. Rosemarie Truglio (30:05):
Yeah, I’m glad you brought that up. Because a lot of our focus is on how children learn through playful experiences, and how they learn through play in particular. And there are so many playing, either a game or even playing ideas—like we talked about building, you know, a house for animals or building a fort. It’s just so filled with math. And I wish I could narrate for every young parent how I would hope that they would talk as they are co-engaged in this activity. And I think … we asked about, with the anxiety, the adults have to find the joy in math first. They have to see the math. That’s the problem. That’s why I hope that my book provides that. I want you to know that you are doing math and I want you to know that your child is what we call a mathematician—or in the science chapter, is a STEMist. Your child is already doing science, technology, engineering, and math. STEM is so integrated. So to acknowledge them—because babies are doing math! Babies know, they can distinguish between a small quantity and something that is a of a larger quantity and want the larger. Right? So, it’s natural for them. And they are taking it all in. I mean, the joy of watching a child just early counting: you know, one, two. And trying to then figure out the meaningfulness of two. It’s not three objects. There are actually two. And for a parent to see the joy in that I think is step one. And then to see the richness and how expansive math is, and that power of, oops, “I made a mistake, don’t freak out,” and then [not] say, “See, I’m not good at math,” but say, “Let me try again. I know I could figure this out.” Right? It’s all of that supportive language and supportive experiences that builds this mindset, a positive mindset. So that you hope that when you get into the higher grades, they’re not walking in and saying, “I can’t, I can’t do math.”

Dan Meyer (32:26):
Yeah. Super helpful. I think you point at one of the grownups—great powers in the world of kids, which is to label. To name things. And you know, you’ve talked about how grownups should ideally downplay some of their negative experiences with mathematics for the sake of the kid, but also to play up the positive stuff that they’re doing as mathematics. Like that right there, that’s math. I would love to know … you have an extremely loud megaphone to communicate messages about math and the world and everything through Sesame Street. One of the biggest that there is—and I just wonder if you could step out and imagine you had a magic wand to wave over the world in which students grow up, play and learn—what would you do like to help students have better associations or less math anxiety? And, you know, learn more about math itself?

Dr. Rosemarie Truglio (33:19):
If I had a magic wand, I would give everyone what we call a growth mindset that nothing is fixed and everything can be changed if you put the time and effort into the process, and enjoy the process. The joy of learning. I think, you know, it’s really sad. I don’t wanna be sad on your show. But when we were getting ready for the 50th anniversary, I was wondering, “What is gonna be the curriculum focus?” You know, we just came off of literacy and math literacy and social-emotional development. And we talked about the power of play. Playful learning. And building careers. Give children sophisticated play scenarios so that they could explore what they may wanna be when they grow up. Because there’s a concept: If I can see it, I can play it, I can be it. Right? So where are those portrayals? And it’s like, “What are we gonna do for the 50th?” And I had a convening of experts across all disciplines, and brought them into a room. And I said, you know, “What keeps you up at night? Like, what are you worried about?” Sort of like the State of the Union of Child Development. And this is where the sad part is. They talked about how that sense of joy, that sense of wonder, that sense of curiosity, that sense of flexible thinking and creative thinking, was disappearing in early childhood. Wow. If it’s disappearing in early childhood, we are in big, big trouble . ‘Cause I could see it disappearing later on, you know, as you advance in grade. But what do you mean, it’s disappearing in childhood? And then they talked about the fear of making mistakes. And that goes against—it’s the opposite of a growth mindset. And so we have to bring back that sense of joy, wonder, asking those why questions and embracing them. So it’s another problem parents have. They’re fine with the “why” questions until the “whys” become so difficult they don’t have the answers. And then they don’t want the “why” questions, because now they feel like they’re not smart enough to answer their child’s “why” questions. How do I flip that around to be much more positive and say, “You know, I don’t know! But let’s find out together. Let’s explore together; let’s experiment together.” That’s what I mean about the shift in the mindset, that growth mindset. We should not know all of the answers, but where’s the joy of, “Wow, I don’t know, let’s go find out together”? And that applies to math too. But you have to have that open mindset. You have to—you, as yourself, have to have that growth mindset.

Bethany Lockhart Johnson (36:20):
I love that magic wand. I want that magic wand! And I think what—like Dan said about this megaphone, this opportunity to reach so many young people, so many caregivers—what a gift! And I’m so grateful that you took time to be in the lounge with us, and that you have shared these ideas. Because truly, I think, like you said, it’s really our youngest learners, right? How can we create and cultivate these opportunities for our youngest learners to find the joy in mathematics and just in learning, right?

Dr. Rosemarie Truglio (36:54):
Yeah.

Bethany Lockhart Johnson (36:55):
So thank you. Thank you so much, Dr. Truglio. We are deeply grateful for your insight and for all the work you do. And we continue to invite the world of Sesame Street into our homes.

Dr. Rosemarie Truglio (37:08):
Thank you. Thank you for allowing us to come into your home, and for you to re-learn with your child as you’re watching Sesame Street. Because it’s very much a parenting show, as it is for a child-directed show, because we are blessed to have these wonderful human cast members who are the stand-ins for parents. And so we are often giving you the language for how to talk about and how to problem-solve together. So thank you.

Dan Meyer (37:43):
Thanks so much for listening to our conversation with Dr. Rosemarie Truglio, Senior Vice President of Curriculum and Content at Sesame Workshop.

Bethany Lockhart Johnson (37:51):
Dr. Truglio is also the author of Sesame Street Ready for School, A Parents Guide to Playful Learning for Children Ages Two to Five, and we’re gonna make sure we put a link to that in the show notes because it is really, really a rich resource. I’m diving in. I have so many ideas bookmarked that I wanna try out with my kiddo.

Dan Meyer (38:09):
Yeah, it’s really exciting to see—like, for a classroom educator, I just kinda assumed that a lot of math learning happens in the classroom context. That’s my lens. So yeah, I loved reading the book and seeing all the different opportunities for parents for just out there in the world, in front of your house, at the supermarket. All the different opportunities there are for mathematical thinking, and then to think about how to bring that into some of those routines and ideas into the classroom, into formal schooling.

Bethany Lockhart Johnson (38:35):
Exactly. Exactly. Like Dr. Truglio said, the caregivers’s disposition about mathematics matters so deeply. Your teachers’ dispositions about mathematics, their beliefs, the way that you hear people talking about math, that impacts our learners. That impacts—like, as a student, that impacts what you think is possible for yourself. So I love this, re-educating ourselves about what math can look like out in the world, in everyday conversations. I don’t know. I really, really appreciated this conversation with Dr. Truglio.

Dan Meyer (39:12):
Same. Yeah. We’d love to hear what you folks think about the work. the book, her ideas. Definitely get in touch with us. Subscribe to Math Teacher Lounge, wherever you get podcasts. And keep in touch with us on Facebook at Math Teacher Lounge Community, and on Twitter at MTL show.

Bethany Lockhart Johnson (39:27):
Also, if you haven’t already, please subscribe to Math Teacher Lounge wherever you get your podcast. And if you like what you’re hearing, please leave us a rating and a review. It’ll help more listeners find the show. And while you’re at it, let a friend know about this episode, because you enjoyed it; they might enjoy it. On our next episode, we’re gonna be chatting with Dr. Heidi Sabnani and taking a closer look at best practices for coaching teachers to reduce their own math anxiety.

Dr. Heidi Sabnani (39:56):
One of the teachers that I worked with had done her student teaching with a teacher who had math anxiety and who never taught math. And so she entered her teaching career never having taught math before or seeing it taught.

Dan Meyer (40:10):
Thanks again for listening, folks.

Bethany Lockhart Johnson (40:12):
Bye.

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What Dr. Rosemarie Truglio says about math

“We all have to work together, because even though we are the experts [on curriculum and education], the real experts are the children themselves.”

– Dr. Rosemarie Truglio

Senior Vice President of Curriculum and Content, Sesame Workshop

Meet the guest

Rosemarie T. Truglio, Ph.D. is the Senior Vice President of Curriculum and Content at Sesame Workshop. Dr. Truglio is responsible for the development of the interdisciplinary curriculum on which Sesame Street is based and oversees content development across platforms (e.g., television, publishing, toys, home video, and theme park activities).  She also oversees the curriculum development for all new show production, including  Bea’s Block, Mecha BuildersEsme & RoyHelpsters, and Ghostwriter. Dr. Truglio has written numerous articles in child and developmental psychology journals and presented her work at national and international conferences. Her current book is Ready for School! A Parent’s Guide to Playful Learning for Children Ages 2 to 5, published by Running Press (2019).

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

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Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

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Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Welcome, Central Kitsap, to Amplify Desmos Math!

Amplify Desmos Math K-5 thoughtfully combines conceptual understanding, procedural fluency, and application. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

Scroll to learn more about the program and explore sample materials.

About the program

We believe in math that motivates. Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students. 

The program motivates students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

A powerful suite of math resources

Amplify Desmos Math combines the best of problem-based lessons, intervention, personalized practice, and assessments into a coherent and engaging experience for both students and teachers.  Feel free to explore our grade-level ancillary samplers to learn more about assessment and reporting, intervention, and differentiation:

Grade K Ancillary Sampler

Grade 1 Ancillary Sampler

Grade 2 Ancillary Sampler

Grade 3 Ancillary Sampler

Grade 4 Ancillary Sampler

Grade 5 Ancillary Sampler

A digital interface displays a math screener report on the left and a math problem involving division, alongside a visual representation of students lined up on the right, integrating rich math resources from Amplify Desmos Math.

Assessment

mCLASS® Assessments, along with daily formative checks, measure not only what students know, but how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core and intervention resources. Visit our mClass Math site to learn more.

Two side-by-side math activities for children: on the left, a caterpillar-themed block challenge, and on the right, a worksheet for finding pairs that sum to 10. These exercises are fantastic ways to amplify children's engagement with math concepts.

Core instruction

Amplify Desmos Math lessons pair problems students are eager to solve with clear instructional moves for teachers. With low-floor, high-ceiling tasks every student can actively participate and be a part of the math community. Unit- and lesson-level core assessments give teachers data at their fingertips to guide and differentiate instruction.

A math lesson screen shows a toy sinking 5 meters into a pool. A textbox asks how many centimeters that is, with space for an answer and a "Try again" button. An avatar explains the question, using Desmos math tools to amplify understanding.

Differentiation

Boost Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback adjusts to students’ work, providing item-level adaptivity to further support their learning and offer personalized differentiation. Visit our Boost Math site to learn more. 

Two pages from a New York math textbook on determining coordinates after a rotation. Includes sections on modeled review, guided practice, and teacher's notes, with diagrams and examples that amplify the learning experience.

Embedded intervention

Integrated resources like Mini-Lessons, Fluency Practice, and Math Adventures provide targeted intervention on a specific concept or skill connected to the daily lesson. Extensions are also available to stretch students’ understanding.

Multilingual Learners

To support multilingual/English learners, Amplify Desmos Math incorporates research-based Math Language Routines (MLRs) by providing language modality strategies like sentence frames where appropriate, both in the teacher language provided for each task and in the differentiation support section found throughout the program. For further information on math language development, please see pg. 82 of the Amplify Desmos Math Program Guide.

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Review Resources

To support your review of Amplify Desmos Math here are links to important K-5 review resources:

Two women in an office setting are smiling while looking at a tablet. Various educational icons surround the image.

K-5 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade.  To see sample student responses, please click on the Teacher Edition pages and scroll to “Sample Student Work” (first one is about 30 pages in) or click on Intervention and Extension resources.   

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

Digital educational material showing an activity named "Hamster Homes" involving tube length and platform heights for a hamster cage. Includes a diagram with platforms measuring 9 inches.
Screenshot of a kindergarten curriculum outline featuring units like Math in Our World, Numbers 1-10, Positions and Shapes, Understanding Addition, Making 10, and Shapes All Around Us. This comprehensive program utilizes New York Math standards to build foundational skills.
Program structure

Get to know the content and structure of Kindergarten Amplify Desmos Math.

Cover of Amplify Desmos Math Grade K Teacher Edition featuring three children playing with math-related objects and a group of rabbits sitting nearby, aligning with the engaging curriculum seen in New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Counting and Comparing Objects.

Educational activity screen displaying a blue backpack with icons, dot groups on the left, and a grid background. Prompt reads, "Look inside the backpack. Then choose the group with the same number of dots." A great tool to amplify Desmos math learning in line with New York math standards.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition Kindergarten," featuring an illustration of three children playing with math-related toys. A group of small white animals, possibly hamsters, play nearby. The scene brilliantly captures the joy of New York math exploration for young learners.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Grade K Centers Resources" featuring a large, stylized red and pink "C" on a light pink background with simple geometric designs. This distinctive cover complements New York math curriculums with its engaging visual elements.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math: Grade K." The title is displayed with a geometric "I" illustration in the center. Subtitle reads "Intervention and Extension Resources" on a pink and white background, ideal for New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

A digital activity screen, crafted in the style of Amplify Desmos Math, shows two paths with different quantities of mushrooms. The user is prompted to choose the path with more mushrooms. A bear is on the left side of the screen.

In this lesson, students apply their understanding of how to compare groups of images as they determine which group has more or fewer and then compare their strategies by guiding a bear through a path that has more mushrooms than the other.

Grade 1 math curriculum overview displaying six units with instructional and assessment days: counting, addition, subtraction, numbers to 10, comparing numbers, measuring length, and geometry—aligned with the New York Math standards.
Program structure

Get to know the content and structure of Grade 1 Amplify Desmos Math.

Children interact with math activities on a large tablet while observing fish illustrations. The text reads "Amplify Desmos Math Grade 1 Teacher Edition, aligned with New York Math standards.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Story Problems in Maui.

A digital math exercise, amplified by Desmos Math, showcases a story problem about adding kalo plants with three illustrations and a filled-out number sentence 3 + 4 = 7. A "Check" button is present. This tool aligns perfectly with New York math standards.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Illustration of three children engaged in math activities from the "Amplify Desmos Math: Student Edition 1" textbook. One child holds a number card, while the others manipulate counters and images, experiencing an exciting approach inspired by New York math techniques.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Centers Resources" for Grade 1, featuring a yellow and white 3D letter "C" on a light background.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math, Grade 1: Intervention and Extension Resources" depicting a large, blocky number one and a yellow-themed design. Ideal for enhancing New York math curriculum.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational game screen, inspired by New York math standards, shows a subtraction problem, "4 - 1," with a frog moving along numbered lily pads to reveal the answer "3.

In this lesson, students find differences when subtracting 1 and 2 from the same number by helping a frog reach a lily pad where it can eat a bug.

A curriculum overview for Grade 2 in New York Math displaying 8 units, including topics like comparisons, addition, subtraction, and geometric shapes, with details on the number of instructional and assessment days. This plan integrates resources from Amplify Desmos Math to enrich learning experiences.
Program structure

Get to know the content and structure of Grade 2 Amplify Desmos Math.

Cover of the "Amplify Desmos Math" Grade 2 Teacher Edition, showcasing children measuring with rulers and a poster displaying a mathematical equation, set against whimsical scenery with a colorful dragon. Perfect for New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Adding and Subtracting.

Activity screen displaying a task to estimate the number of animals in an aquarium, featuring a bar chart for goldfish, frogs, and shrimp. Utilizing Desmos math tools, an illustration of an aquarium with various animals is also included to amplify learning.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 2" showing three children performing a New York math activity with blocks and measurements.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of an educational book titled "Amplify Desmos Math Grade 2 Centers Resources" featuring a green "C" on a light green background, perfect for enhancing New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 2: Intervention and Extension Resources" featuring a green numeral 1 on a light green background, aligning with the New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational activity where users must select the block with the correct number to make a total of 10 using the given block numbers. The UI, inspired by New York math standards, features a caterpillar and two tree stumps to amplify engagement with Desmos Math tools.

Students continue to develop fluency by finding the number that makes 10 by helping a millipede reach its favorite food – a clump of leaves!

An educational curriculum outline for Grade 3 with seven units covering various mathematics topics, including multiplication, shapes, fractions, and measurement. Suggested instructional days are provided. The New York Math approach ensures a thorough understanding of each concept.
Program structure

Get to know the content and structure of Grade 3 Amplify Desmos Math.

Cover of a "Grade 3 Amplify Desmos Math Teacher Edition" book, featuring a cutaway building with diverse students and a teacher working on New York math problems and organizing materials.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Concepts of Area Measurement.

Educational software displays a challenge to determine the area of an unpainted wall. The wall features a door and window with given dimensions, and a mouse pointer hovers near the question, amplifying the student's engagement.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 3" showcasing illustrated children engaged in various mathematical activities inside a glass house structure, reflecting the dynamic energy of New York math.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the Amplify Desmos Math Grade 3 Centers Resources book, featuring a 3D letter "C" in blue and white on a minimalistic background, perfect for aligning with New York math standards.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of an "Amplify Cover of the "Amplify Desmos Math" Grade 3 book featuring intervention and extension resources, with a blue geometric "I" on a light blue background, aligning with New York Math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

A page titled "Activity 2" features a table showing counts of rabbits, raccoons, and foxes, an image of animal stickers, and a bar graph representing the number of each animal, designed to amplify your New York math lesson with engaging visual data.

Students compare data represented on bar graphs with different scales by using animal stickers to create scaled bar graphs.

A course outline for Algebra 1 with 8 units, each detailing the number of instructional and optional days. The total suggested instructional days are 144 and 28 optional days, aligning with New York Math standards.
Program structure

Get to know the content and structure of Grade 4 Amplify Desmos Math.

Cover of "Amplify Desmos Math: Teacher Edition Grade 4" showing children learning New York Math outdoors, using large mathematical tools and numbers, with one child in a wheelchair.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Size and Location of Fractions.

Educational screen showing an interactive activity from Amplify Desmos Math where a user drags a point to cut a log into quarters. The progress is 2 out of 10.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math, Student Edition, Grade 4," showcasing students collaborating on math problems involving shapes and numbers against a vibrant backdrop that blends cityscapes and natural scenery, capturing the essence of New York math learning.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the "Amplify Desmos Math" Grade 4 Centers Resources book, featuring a large, stylized blue letter "C" on a light blue background. This essential resource for New York math educators ensures engaging and effective instruction.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math, Grade 4: Intervention and Extension Resources," featuring a geometric illustration and a blue and orange color scheme inspired by New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Interactive educational activity asking users to determine platform heights using a 3-inch tube. The interface, inspired by Desmos math tools, features a dragging function and feedback system with a checkbox and "Try another" option, amplifying the learning experience.

Students choose tube lengths to connect to platform heights for hamster homes, identifying possible heights using what they know about multiples.

A Grade 5 curriculum scope and sequence chart with units covering volume, fractions, multiplication, shapes, place value, and measurement. Each unit lists instructional and assessment days to amplify Desmos Math activities.
Program structure

Get to know the content and structure of Grade 5 Amplify Desmos Math.

Illustration of three students engaging with various math activities outdoors and around large blocks. Text at the top reads "Amplify Desmos Math, Grade 5, Teacher Edition" - a perfect resource for New York math educators.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Fractions as Quotients.

A digital activity prompt showing a scenic landscape with bamboo shoots and a panda. Using Desmos math tools, the task is to estimate the length where the third bamboo shoot should be placed for the panda to reach a leaf. This exercise is designed to amplify your understanding of spatial reasoning.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition, Grade 5" featuring students engaged in various mathematical activities outside, such as block building, measuring, and gardening—a perfect resource aligning with New York math standards.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover image of "Amplify Desmos Math Grade 5 Centers Resources" featuring a large purple letter C on a light purple background, showcasing the innovative approach of Amplify Desmos Math that's making waves in New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 5: Intervention and Extension Resources," featuring a large, stylized number five in purple against a light purple background with minimal geometric patterns, ideal for New York math curriculum support.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An interactive screen showing an activity about decomposing a figure into prisms, with a touch of Desmos Math integration. The user is asked to drag points to demonstrate the decomposition. Two prism illustrations are displayed, offering a glimpse of New York Math's approach.

Students decompose a figure into rectangular prisms and determine the volume of the figure by adding the volumes of the individual prisms.

Contact Us

If you have any questions throughout your review process or need additional samples, please don’t hesitate to contact:

Alicia O’Neil

Account Executive

425-890-6103

aoneil@amplify.com

Request additional samples

Ready to learn more? Connect with an Amplify Desmos Math expert to request additional program samples.

Desmos Math 6–A1 correlations with Carnegie Math Texas

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S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Promotional image for "Math Teacher Lounge" Season 3, Episode 4 titled "Ideas to Build Math Fluency," featuring Valerie Henry, Tracy J. Zager, and Graham Fletcher.

Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

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What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guests

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.

Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Welcome, Ellensburg, to Amplify Desmos Math!

Amplify Desmos Math K-5 thoughtfully combines conceptual understanding, procedural fluency, and application. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

Scroll to learn more about the program and explore sample materials.

About the program

We believe in math that motivates. Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students. 

The program motivates students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

A powerful suite of math resources

Amplify Desmos Math combines the best of problem-based lessons, intervention, personalized practice, and assessments into a coherent and engaging experience for both students and teachers.  Feel free to explore our grade-level ancillary samplers to learn more about assessment and reporting, intervention, and differentiation:

Grade K Ancillary Sampler

Grade 1 Ancillary Sampler

Grade 2 Ancillary Sampler

Grade 3 Ancillary Sampler

Grade 4 Ancillary Sampler

Grade 5 Ancillary Sampler

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Assessment

mCLASS® Assessments, along with daily formative checks, measure not only what students know, but how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core and intervention resources. Visit our mClass Math site to learn more.

Two side-by-side math activities for children: on the left, a caterpillar-themed block challenge, and on the right, a worksheet for finding pairs that sum to 10. These exercises are fantastic ways to amplify children's engagement with math concepts.

Core instruction

Amplify Desmos Math lessons pair problems students are eager to solve with clear instructional moves for teachers. With low-floor, high-ceiling tasks every student can actively participate and be a part of the math community. Unit- and lesson-level core assessments give teachers data at their fingertips to guide and differentiate instruction.

A math lesson screen shows a toy sinking 5 meters into a pool. A textbox asks how many centimeters that is, with space for an answer and a "Try again" button. An avatar explains the question, using Desmos math tools to amplify understanding.

Differentiation

Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback adjusts to students’ work, providing item-level adaptivity to further support their learning and offer personalized differentiation. Visit our Boost Math site to learn more. 

Two pages from a New York math textbook on determining coordinates after a rotation. Includes sections on modeled review, guided practice, and teacher's notes, with diagrams and examples that amplify the learning experience.

Embedded intervention

Integrated resources like Mini-Lessons, Fluency Practice, and Math Adventures provide targeted intervention on a specific concept or skill connected to the daily lesson. Extensions are also available to stretch students’ understanding.

Multilingual Learners

To support multilingual/English learners, Amplify Desmos Math incorporates research-based Math Language Routines (MLRs) by providing language modality strategies like sentence frames where appropriate, both in the teacher language provided for each task and in the differentiation support section found throughout the program. For further information on math language development, please see pg. 82 of the Amplify Desmos Math Program Guide.

Una profesora con un polo rojo ayuda a una estudiante con cabello largo y rizado que está leyendo un libro en su escritorio en un salón de clases. En la pared detrás de ellos se exhiben carteles con temas educativos.

Review Resources

To support your review of Amplify Desmos Math here are links to important K-5 review resources:

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K-5 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade.  To see sample student responses, please click on the Teacher Edition pages and scroll to “Sample Student Work” (first one is about 30 pages in) or click on Intervention and Extension resources.   

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

Digital educational material showing an activity named "Hamster Homes" involving tube length and platform heights for a hamster cage. Includes a diagram with platforms measuring 9 inches.
Screenshot of a kindergarten curriculum outline featuring units like Math in Our World, Numbers 1-10, Positions and Shapes, Understanding Addition, Making 10, and Shapes All Around Us. This comprehensive program utilizes New York Math standards to build foundational skills.
Program structure

Get to know the content and structure of Kindergarten Amplify Desmos Math.

Cover of Amplify Desmos Math Grade K Teacher Edition featuring three children playing with math-related objects and a group of rabbits sitting nearby, aligning with the engaging curriculum seen in New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Counting and Comparing Objects.

Educational activity screen displaying a blue backpack with icons, dot groups on the left, and a grid background. Prompt reads, "Look inside the backpack. Then choose the group with the same number of dots." A great tool to amplify Desmos math learning in line with New York math standards.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition Kindergarten," featuring an illustration of three children playing with math-related toys. A group of small white animals, possibly hamsters, play nearby. The scene brilliantly captures the joy of New York math exploration for young learners.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Grade K Centers Resources" featuring a large, stylized red and pink "C" on a light pink background with simple geometric designs. This distinctive cover complements New York math curriculums with its engaging visual elements.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math: Grade K." The title is displayed with a geometric "I" illustration in the center. Subtitle reads "Intervention and Extension Resources" on a pink and white background, ideal for New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

A digital activity screen, crafted in the style of Amplify Desmos Math, shows two paths with different quantities of mushrooms. The user is prompted to choose the path with more mushrooms. A bear is on the left side of the screen.

In this lesson, students apply their understanding of how to compare groups of images as they determine which group has more or fewer and then compare their strategies by guiding a bear through a path that has more mushrooms than the other.

Grade 1 math curriculum overview displaying six units with instructional and assessment days: counting, addition, subtraction, numbers to 10, comparing numbers, measuring length, and geometry—aligned with the New York Math standards.
Program structure

Get to know the content and structure of Grade 1 Amplify Desmos Math.

Children interact with math activities on a large tablet while observing fish illustrations. The text reads "Amplify Desmos Math Grade 1 Teacher Edition, aligned with New York Math standards.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Story Problems in Maui.

A digital math exercise, amplified by Desmos Math, showcases a story problem about adding kalo plants with three illustrations and a filled-out number sentence 3 + 4 = 7. A "Check" button is present. This tool aligns perfectly with New York math standards.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Illustration of three children engaged in math activities from the "Amplify Desmos Math: Student Edition 1" textbook. One child holds a number card, while the others manipulate counters and images, experiencing an exciting approach inspired by New York math techniques.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of "Amplify Desmos Math Centers Resources" for Grade 1, featuring a yellow and white 3D letter "C" on a light background.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math, Grade 1: Intervention and Extension Resources" depicting a large, blocky number one and a yellow-themed design. Ideal for enhancing New York math curriculum.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational game screen, inspired by New York math standards, shows a subtraction problem, "4 - 1," with a frog moving along numbered lily pads to reveal the answer "3.

In this lesson, students find differences when subtracting 1 and 2 from the same number by helping a frog reach a lily pad where it can eat a bug.

A curriculum overview for Grade 2 in New York Math displaying 8 units, including topics like comparisons, addition, subtraction, and geometric shapes, with details on the number of instructional and assessment days. This plan integrates resources from Amplify Desmos Math to enrich learning experiences.
Program structure

Get to know the content and structure of Grade 2 Amplify Desmos Math.

Cover of the "Amplify Desmos Math" Grade 2 Teacher Edition, showcasing children measuring with rulers and a poster displaying a mathematical equation, set against whimsical scenery with a colorful dragon. Perfect for New York math classrooms.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Adding and Subtracting.

Activity screen displaying a task to estimate the number of animals in an aquarium, featuring a bar chart for goldfish, frogs, and shrimp. Utilizing Desmos math tools, an illustration of an aquarium with various animals is also included to amplify learning.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 2" showing three children performing a New York math activity with blocks and measurements.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of an educational book titled "Amplify Desmos Math Grade 2 Centers Resources" featuring a green "C" on a light green background, perfect for enhancing New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 2: Intervention and Extension Resources" featuring a green numeral 1 on a light green background, aligning with the New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An educational activity where users must select the block with the correct number to make a total of 10 using the given block numbers. The UI, inspired by New York math standards, features a caterpillar and two tree stumps to amplify engagement with Desmos Math tools.

In this lesson, students find differences when subtracting 1 and 2 from the same number by helping a frog reach a lily pad where it can eat a bug.

An educational curriculum outline for Grade 3 with seven units covering various mathematics topics, including multiplication, shapes, fractions, and measurement. Suggested instructional days are provided. The New York Math approach ensures a thorough understanding of each concept.
Program structure

Get to know the content and structure of Grade 3 Amplify Desmos Math.

Cover of a "Grade 3 Amplify Desmos Math Teacher Edition" book, featuring a cutaway building with diverse students and a teacher working on New York math problems and organizing materials.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Concepts of Area Measurement.

Educational software displays a challenge to determine the area of an unpainted wall. The wall features a door and window with given dimensions, and a mouse pointer hovers near the question, amplifying the student's engagement.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math Student Edition 3" showcasing illustrated children engaged in various mathematical activities inside a glass house structure, reflecting the dynamic energy of New York math.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the Amplify Desmos Math Grade 3 Centers Resources book, featuring a 3D letter "C" in blue and white on a minimalistic background, perfect for aligning with New York math standards.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of an "Amplify Cover of the "Amplify Desmos Math" Grade 3 book featuring intervention and extension resources, with a blue geometric "I" on a light blue background, aligning with New York Math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

A page titled "Activity 2" features a table showing counts of rabbits, raccoons, and foxes, an image of animal stickers, and a bar graph representing the number of each animal, designed to amplify your New York math lesson with engaging visual data.

Students compare data represented on bar graphs with different scales by using animal stickers to create scaled bar graphs.

A course outline for Algebra 1 with 8 units, each detailing the number of instructional and optional days. The total suggested instructional days are 144 and 28 optional days, aligning with New York Math standards.
Program structure

Get to know the content and structure of Grade 4 Amplify Desmos Math.

Cover of "Amplify Desmos Math: Teacher Edition Grade 4" showing children learning New York Math outdoors, using large mathematical tools and numbers, with one child in a wheelchair.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Size and Location of Fractions.

Educational screen showing an interactive activity from Amplify Desmos Math where a user drags a point to cut a log into quarters. The progress is 2 out of 10.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math, Student Edition, Grade 4," showcasing students collaborating on math problems involving shapes and numbers against a vibrant backdrop that blends cityscapes and natural scenery, capturing the essence of New York math learning.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover of the "Amplify Desmos Math" Grade 4 Centers Resources book, featuring a large, stylized blue letter "C" on a light blue background. This essential resource for New York math educators ensures engaging and effective instruction.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math, Grade 4: Intervention and Extension Resources," featuring a geometric illustration and a blue and orange color scheme inspired by New York math standards.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

Interactive educational activity asking users to determine platform heights using a 3-inch tube. The interface, inspired by Desmos math tools, features a dragging function and feedback system with a checkbox and "Try another" option, amplifying the learning experience.

Students choose tube lengths to connect to platform heights for hamster homes, identifying possible heights using what they know about multiples.

A Grade 5 curriculum scope and sequence chart with units covering volume, fractions, multiplication, shapes, place value, and measurement. Each unit lists instructional and assessment days to amplify Desmos Math activities.
Program structure

Get to know the content and structure of Grade 5 Amplify Desmos Math.

Illustration of three students engaging with various math activities outdoors and around large blocks. Text at the top reads "Amplify Desmos Math, Grade 5, Teacher Edition" - a perfect resource for New York math educators.
Teacher Edition pages

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 1: Fractions as Quotients.

A digital activity prompt showing a scenic landscape with bamboo shoots and a panda. Using Desmos math tools, the task is to estimate the length where the third bamboo shoot should be placed for the panda to reach a leaf. This exercise is designed to amplify your understanding of spatial reasoning.
Digital experience

Explore our digital experience! Every lesson in Amplify Desmos Math has student print materials and digital recommendations.

Cover of "Amplify Desmos Math: Student Edition, Grade 5" featuring students engaged in various mathematical activities outside, such as block building, measuring, and gardening—a perfect resource aligning with New York math standards.
Student Edition pages

Motivate students with mathematics that is both rigorous and delightful.

Cover image of "Amplify Desmos Math Grade 5 Centers Resources" featuring a large purple letter C on a light purple background, showcasing the innovative approach of Amplify Desmos Math that's making waves in New York math education.
Centers Resources

Engaging, hands-on games for students to play collaboratively to strengthen their understanding of key skills and concepts.

Cover of "Amplify Desmos Math Grade 5: Intervention and Extension Resources," featuring a large, stylized number five in purple against a light purple background with minimal geometric patterns, ideal for New York math curriculum support.
Intervention and Extension Resources

Additional resources to reinforce and extend key concepts, including Mini-Lessons and Extensions.

An interactive screen showing an activity about decomposing a figure into prisms, with a touch of Desmos Math integration. The user is asked to drag points to demonstrate the decomposition. Two prism illustrations are displayed, offering a glimpse of New York Math's approach.

Students decompose a figure into rectangular prisms and determine the volume of the figure by adding the volumes of the individual prisms.

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S5-02. Uncovering the causes of math anxiety

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We’re continuing our season theme of math anxiety, going beyond the basics, diving deeper into what causes it, and how we can help students move forward. In this episode, we talk to Dr. Erin Maloney from the University of Ottawa to better understand what’s actually happening in the brain when a person experiences math anxiety, and how we can take steps to shift student mindsets in a positive direction.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page. 

Download Transcript

Dr. Erin Maloney (00:00):

It’s the anxiety itself in many ways that can cause people to underperform.

Bethany Lockhart Johnson (00:06):

Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:10):

And I’m Dan Meyer.

Bethany Lockhart Johnson (00:11):

This is episode two of our new season, all about math anxiety. Who has it? What is it? What do we do about it?

Dan Meyer (00:20):

I’m learning so much, learning a ton.

Bethany Lockhart Johnson (00:22):

I loved our first conversation with Dr. Gerardo Ramirez, episode one, our first episode of the season. Really, our goal with that conversation was just to—we need to talk about the basics of it, for reals. Like, what is math anxiety?

Dan Meyer (00:36):

What is it? How do you measure it? How’s it defined? Super-helpful stuff.

Bethany Lockhart Johnson (00:40):

There’s not only one way that it’s measured. But it’s like, in active research right now, how are folks making sense of it? And I think Dr. Ramirez did such a fantastic job of sharing that with our listeners. And I learned a lot. You learned a lot, Dan?

Dan Meyer (00:56):

I did. And I’m also super-excited to take that knowledge that we have developed together and go and build on top of it and keep on climbing up up the mountain here, and learn more about math anxiety. Which is why we’re super-excited to have a guest on, Dr. Maloney, who is going to help us learn more—especially about what happens to the brain when it’s experiencing math anxiety. There’s some really complex stuff that happens there, including the role of parents and educators in creating and resolving math anxiety. And I think we’ll also learn that the whole situation is a bit of a hot mess. And we’ll try to make it a little bit less messy together.

Bethany Lockhart Johnson (01:34):

Little bit less messy. Dan, if we do nothing else, can we make it a little less messy?

Dan Meyer (01:41):

I sometimes prefer more mess, but in this case I prefer less. So.

Bethany Lockhart Johnson (01:45):

I have a two-year-old, so everything is a mess.

Dan Meyer (01:47):

Your life is mess. Yes. <laugh> Right. Well, I’m excited for you folks to hear this. It was a delightful conversation, so yeah, tune in. We are joined by Dr. Erin Maloney.

Bethany Lockhart Johnson (01:56):

Let’s go. We are joined by Dr. Erin Maloney, associate professor in the School of Psychology at the University of Ottawa, where she directs the Cognition and Emotion Laboratory, as well as serving as the Canada Research Chair in Academic Achievement and Well-being. Welcome to the show, Dr. Maloney. We’re so excited to have you in the Lounge.

Dr. Erin Maloney (02:20):

Yeah, thank you so much for having me. This is fantastic.

Bethany Lockhart Johnson (02:24):

So our last season was all about math and joy. And even when I read your title, I felt more joyful. Like, somebody is thinking about academic achievement, but with well-being in mind. I love it.

Dr. Erin Maloney (02:39):

Aw, thank you.

Dan Meyer (02:40):

Cognition and emotion!

Bethany Lockhart Johnson (02:42):

E-mo-tion!

Dr. Erin Maloney (02:43):

I don’t think they can be separate. I think that you have to think about them together, ’cause they’re so intricately connected.

Dan Meyer (02:49):

Love that. People try, but we love that. Yeah. That’s our vibe here, too.

Bethany Lockhart Johnson (02:52):

People try. That was a big problem with my math anxiety. They just wanted…there was no room for my emotion. They’re like, stop weeping at your desk—

Dan Meyer (03:00):

It’s rearranging neurons….

Bethany Lockhart Johnson (03:01):

—you’re distracting the other children. So would you mind telling us the story of how you even got interested in this topic? You know, when you tell people that you study math anxiety—or, actually, I don’t know how you describe it to them; I’m hopeful you bring in that well-being part—but how did you get here? What do you, what do you, what do you…yeah, tell us! We love it!

Dr. Erin Maloney (03:23):

<laugh> I feel like what you’re actually asking is, “How did you make life choices that got you to here?” <Laugh>

Bethany Lockhart Johnson (03:29):

Justify your life choices! Ready? Go!

Dr. Erin Maloney (03:32):

<laugh> Whoo. OK. So, all right. So we often, in psychology, we joke that instead of doing research, we do “me-search.” And that’s, that’s admittedly true in my case. I was a student who absolutely loved math up until about eighth grade, and then something changed, and all of a sudden I was terrified of math and I had absolutely no sense of self-efficacy in it. Despite trying really hard, I was extremely anxious about it. And so I initially, I set out…my parents were completely convinced that I was absolutely capable of doing mathematics and that I was getting in my own way. And when I went to university, I decided to prove them wrong. So I set out to prove that some people just can’t do math, and that’s the end of it. And, you know, 20 plus years later, my parents were right. And it turns out that many people—well, I would argue virtually everyone—can do math. And that if you are really anxious about it, it can get in the way. And interestingly, you know, in, in the years that we’ve been doing this research, there’s really good strategies that can be used—that hopefully we get a chance to chat about—that can really help reduce the amount of anxiety that students are experiencing. But I really did set out, like the bold teenager that I was, to prove my parents wrong. And that backfired <laugh>. So I know it’s kind of a strange answer, but it’s the truth. So I was really interested in understanding why it was some people just could not do math.

Dan Meyer (05:10):

That makes two for two so far, on guests for this season who did a version of me-search. And I feel like this is pretty common for a lot of researchers. Like, I wanna figure out…my experience as a teacher, the part where you, I think, diverge from a lot of people I knew in grad school, myself included, is that you actually let counter evidence change your perspective on things. Whereas I feel like a lot of us go in: “I know this is true and I’m gonna gather data!” and lo and behold, I’m true! But only now, with the research TM, you know, trademarked research, attached to it. So that’s, really exciting. Thanks for sharing that.

Dr. Erin Maloney (05:43):

No, you’re welcome.

Bethany Lockhart Johnson (05:44):

But don’t people say that the more personal you get, the more universal it is? Right? So if you go and get your doctorate about something that you think is just your experience or in your brain, then people are gonna be gonna be like, “Wait a second; you think that too?” “Wait, that math anxiety isn’t just you?” I don’t know, it sounds like a pretty great path to me. When you tell folks that you study math anxiety or when you’re speaking to folks about your research, do you find that there is a lot of folks who relate to what you’re studying? Or how does that conversation typically go?

Dr. Erin Maloney (06:20):

Yeah, so it is I think an extremely relatable topic. Not in the sense that everyone experiences anxiety about math, but everyone seems to know somebody who’s really anxious about math. Or everyone’s at least aware of the stereotype that like some people are math people and some people aren’t, and that’s just the way it is. So it feels like everyone has feelings about math and everyone seems very happy to share those feelings. So one thing I’ve always found really interesting, and actually, so I, I know you mentioned that you had Gerardo on recently. Gerardo and I have had really interesting conversations about how people are really quick to tell you that they hate math and they can’t do math, and they’re anxious about math. And I’ve yet to have anyone ever tell me they hate reading, they can’t read, they’re really anxious about reading as an adult. So for some reason math seems really different. And in that sense people always seem to be pretty excited to talk about their feelings towards math.

Dan Meyer (07:23):

Yeah, definitely. Been on an airplane or two myself and had those conversations. You know, people asking to be reseated because they found out that I do math for a living or whatever. Or just unburdening themselves, for sure. I’m super-curious: I think that the fact that you are doing the me-search is reason enough to want to dedicate your life to this study. But I am curious: If you were gonna justify to someone else, why is math anxiety important to study? What are its consequences, even outside of math education? What would you say to that?

Dr. Erin Maloney (07:57):

So I think it’s probably not hard to convince people that success in math is important, right? So we know that children who start elementary school behind in mathematics tend to stay behind in mathematics, unless they have any kind of very targeted intervention. We know that children who do worse in mathematics throughout K to 12 education in general get lower-paying jobs when they’re older. We also know that when they do worse than mathematics relative to their peers, there’s fewer jobs that are open to them, relative to if they excelled in math. Right? And so I think in many ways there are really clear consequences for students who are not comfortable with math and who avoid it. But I think one of the really, really interesting things about math anxiety, and maybe part of why I’ve fallen in love with it as a research topic is that it’s the anxiety itself in many ways that can cause people to underperform. So it’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you career-wise. And I think that is really empowering.

Dan Meyer (09:18):

Hmm. Yeah, definitely. And I’d love for you to explore — your laboratory is the cognition and emotion laboratory, which I love, how you’re creating those linkages between how you feel about a thing and what your opportunities or your aptitude for learning it. I’m really curious, can you say more about the, the relationship there? How does feeling anxiety impair your ability to do mathematics?

Dr. Erin Maloney (09:41):

Yeah, so feeling anxiety, typically what you tend to experience is these negative thoughts and ruminations. So you can imagine, you’re somebody who doesn’t really love math, you’re pretty anxious about it; you know, Bethany, maybe you’ve had this kind of experience before. I’m gonna call you out on it. I’ve had it many times, where you sit down to do a math test and all of a sudden you’re not focusing on the actual math test in front of you. You’re focusing on things like the consequences of not doing well on this. Right? Or “my parents are gonna be really disappointed if I don’t pass this test,” or “my teacher is gonna think negatively negative of me,” or sometimes we see things like, “I’m a girl, girls don’t do math.” These types of stereotypes. And what happens is that those thoughts actually tie up really important cognitive resources, like, really important memory resources, that you need to do the math test. And so if you are trying to essentially do two things at once, right? You’re trying to deal with all these negative thoughts that are distracting you and you’re trying to do the math test, then you’re not going to do as well as someone who’s sitting down and doesn’t have all of these distracting thoughts to deal with. And we actually know that from research that we have in our lab right now, where we just ask people like, “Hey, when you did this math test, what kind of stuff are you thinking about?” what we find is that the people who are really anxious about math report a whole bunch of thoughts that are unrelated really to the math test, per se. It’s more about the consequences of doing poorly. And as a result of those thoughts, they actually end up doing worse.

Dan Meyer (11:14):

This has been really helpful to figure out, how the emotional state of doing math affects the ability to do math. And it’s really interesting how you’re saying that the direction of the causality can go from the emotions to the cognition. And I’m just curious then, what is the source of the bad emotions about math? Where does that come from? Is it nature? Is it nurture? Some combination? How do you see it?

Dr. Erin Maloney (11:39):

Yeah, so one, that’s a fantastic question. And there’s been a whole bunch of people all around the world that have been spending a lot of time really trying to pinpoint that down. And I think the answer is that it’s, you know, it’s complex. So most of what it’s looking like right now is that it is a combination of both. So essentially what we find is that kids who start elementary school who are a little bit behind in math—and for the question of why they’re behind, that’s also complex; it could be genetics, it could be just environmental input, before the child ever entered formal schooling kind of thing—but in essence, what we find is that kids that start school behind in mathematics, those are the children who are most likely to develop anxiety about math by the time they’re finished first grade. OK? But we also know that once they’ve developed the anxiety about math, then that’s when they get these thoughts and ruminations that kind of tie up those memory resources, that then is gonna make it harder for them to succeed in math tests. So you get into this sort of vicious cycle, right? Where maybe you start behind a little bit and then you develop the anxiety, the anxiety causes you to underperform relative to what you should be able to, so now you’re even further behind, you get more anxious because you’re not doing as well as you’d like to…but again, kind of coming back to the “Why are the children starting behind in the first place?” Some of that seems to be the role that parents are playing in the household. So some kids come from a household where parents are playing a lot more math games with them, talking about mathematical concepts on a regular basis. Maybe they have older siblings who are, you know, practicing arithmetic and, and mathematical processing in front of them. And so those kids are exposed to more math before they ever even start formal schooling. Those kids seem to do better. And then we also know that the parents’ attitudes matter a lot too. So what we find is that when parents are high in math anxiety themselves, especially when they help their children a lot with their math homework in really early ages, we find that those kids end up being more anxious about math by the end of the school year, and they also end up doing worse in mathematics. So it really does seem to be, you know, kind of a complex set of factors that have something to do with both maybe genetic predisposition to success in math and genetic predisposition to anxiety, but then also the social attitudes and stereotypes about math to which you’re exposed at home that really seem to be coming together to create this anxiety in young children.

Bethany Lockhart Johnson (14:24):

I feel like everything you’re saying is <laugh>…it makes so much sense and yet it’s so often not talked about, right? Because it’s just more like, it gets boiled down to, “Oh, they’re just not a math person,” instead of all these other factors that are at play. And I completely remember the anxiety I felt, whether it was a test or not, walking into my math classroom when I was in ninth grade. And there’s no way I was set up and ready to learn. Right? <Laugh>. And something with—we mentioned Dr. Ramirez, he was talking about validating that anxiety. If teachers validate that like, “Oh, you know what, sometimes you might feel stumped, or this might feel overwhelming.” Even the power in creating space for that in the classroom, right? And acknowledging that it doesn’t—math doesn’t have to “come easy” to you in order for you to have access or make sense, is such a powerful concept. And I love the way that you are looking at all these different factors and saying, “Hey, it’s both simple and also a lot more complicated than we’re we’re making it.” Right?

Dr. Erin Maloney (15:36):

No, and I agree with that sentiment so much. Like, I think, though—one thing I will sort of caution is that I think when teachers are validating the anxiety, or when parents are validating the anxiety, I think there’s a very fine line that needs to be walked where we need to be able to say, you know, “It’s OK to struggle with something. That’s, that is completely OK.” And as we’re, you know, as we’re working towards something that’s really valuable, right? We can, we can work hard at something and by working hard at it, we’re going to get better. And I think that type of validating is really, really important and valuable. I think what we wanna be careful of is not to say things like, “Oh, it’s OK. I also never loved math.” And, you know, “Oh, I was never a math person either.” And so even though we might be bringing comfort to the the child, I think that that’s sending the wrong message. And so sometimes it’s really well intentioned and really not great—

Bethany Lockhart Johnson (16:37):

A hundred percent.

Dr. Erin Maloney (16:38):

—in terms of the messaging. So that’s the only…so just for people listening, the only sort of caution that I would give there is that I think there’s nuances to the validating of the feelings that are important.

Bethany Lockhart Johnson (16:50):

I am so glad you said that because as a kindergarten teacher, I vividly remember—and this is as early as, you know, the kids are five years old, right?—and I remember in a parent-teacher conference, a parent saying, “Oh, I wasn’t a math person either,” or, “Oh, no, ugh.” And they were so quick, like you said, they wouldn’t say that about reading, but they were so quick to talk about their lack of natural math aptitude, right? And, and it was really interesting because you know that even if they’re not saying that specific thing at home, those attitudes are absolutely carrying over at home. And they’re absolutely carrying over to, to how they interact with their kiddo around math and around what’s happening in the conversations about math. And I felt like a lot of times my work as a teacher was also to help support parents through their own math anxiety, and help give them some new language for how they can talk about math. And that math is more than just getting to an answer quickly. Like, let’s talk about, let’s go on math walks, let’s go on number walks, what numbers are around the home? Or oh, is that bigger than this? Do you have more of this? And even those little things, I, my hope was that it was starting to shift the conversation around what math was possible in the home, particularly when you saw that it was the parents who had palpable math anxiety. Right? And how much you know that that’s gonna impact what’s happening when you sit down to do homework together.

Dr. Erin Maloney (18:22):

Yeah. And I love that you have worked to encourage parents to do that. So we do similarly. Like even from a research perspective, where I will often give talks to parents and teachers and we talk about the idea of trying to mathematize everything, right? So just the idea that math is absolutely everywhere, and you know, whether it’s a matter of playing games in the car with your kids where you’re thinking of a number and it’s “My number is higher than 42, but lower than 80, and what number do you think I might be thinking of?” And, and gradually trying to get the child to that number. Or, you know, asking questions like, “What’s your favorite even number and why?” And just little things like that that, that I think can make math fun for kids, that help—I don’t even know how to explain it, but just that idea of bringing joy into it, so it’s not always this heavy subject that kids have to come to. So we definitely try to talk to parents about the idea of, like I said, mathematizing everything. And usually it’s well-received, ’cause often parents find it empowering, right? They’re like, “Oh, well, I could do that! But like, that’s not math!” And you’re like, “No, but it is.”

Dan Meyer (19:33):

Yep.

Dr. Erin Maloney (19:34):

Like, it is! And sometimes parents will say like, “Well, I don’t know how to do fractions.” And you’re like, “OK, but how do you bake?” “Well, I don’t know! I just, like, I know how to do those fractions!” And you’re like, “OK, but that’s the starting point. Let’s work with that.” Like, let’s, you know. And I think a lot of times, it’s reminding the parents that they’re actually far more capable than what they think they are, despite the fact that maybe they struggled with math when they were younger.

Dan Meyer (19:58):

Yeah. This is so interesting. And I feel like part of the challenge around conversations about anxiety and math and how to, how to resolve it and where it comes from, is that it, like, it presupposes a single definition of math. And so, you know, we’re talking about like how to be more mindful about math. But you know, like if kids were walking every day through a treacherous street, you know, the solution might not be become more mindful about that street. It’s just like, we gotta fix the treacherous nature of the street, really. You know, I love that we’re talking also about redefining what math is, making it more playful. That feels like a super-important component here. I’d love to know more about what you know about the role of gender in all of this. Are there differences in the way boys and girls experience math anxiety and how it relates to achievement in math?

Dr. Erin Maloney (20:48):

Yeah, so, there’s really, really interesting research on gender in math anxiety. So in general, we find that girls tend to experience more anxiety about math than boys do. So one hypothesis is that it has to do with just social stereotypes that, you know, girls are, are good at reading; boys are good at math, kind of thing. So there’s some evidence to suggest that that might be playing a role. There’s other evidence to suggest as well that maybe boys actually do experience as much anxiety, they just don’t really own up to it.

Dan Meyer (21:20):

Ooh, yikes.

Dr. Erin Maloney (21:21):

So thoughts are, you know, there’s a bit of an apprehension for males to admit experiencing the anxiety. But I think one of the things that is extremely interesting about it—at least to me—is that we don’t tend to see gender differences in young children. So in early elementary school, even though we’ll see that kids as young as six years old will experience anxiety about math, and that that anxiety is related to how well they do in math and how much they enjoy math, it doesn’t seem to vary as a function of gender at that young age. It doesn’t seem to be related to gender until kids are at about sixth, seventh grade that we really start to see this gender difference coming online. And so that, to me, suggests that it’s probably something more social than biological at play. It probably has something more to do with these stereotypes and stuff. But another really interesting—or at least, I’m biased, but to me—another really interesting line of research that comes into play—and some of this is stuff out of my own lab—so we know that boys in general tend to do better at spatial processing than girls. And we know that spatial processing is really important for math, right? So math and space are pretty connected. And by spatial processing, I mean things like being able to picture something rotating in your mind or, you know, envisioning how these puzzle pieces might fit together. And so we know that boys tend to do better at that type of processing. And the gender difference there seems to be related to gender differences in math anxiety. So there’s some speculation, too, that it might be that as the math starts to become more reliant on spatial processing, that that’s when we see this separation between boys and girls with respect to how much anxiety they feel about math. So a lot of this is to say, I think the answer to the gender question right now is what I think what we would officially call a bit of a hot mess, <laugh> where I think there’s probably more questions than answers. But I think that there’s definitely something going on. And it really seems to be coming on later in elementary school.

Dan Meyer (23:32):

That’s a refreshingly honest admission from a social scientist, that it’s a hot mess and not perfectly clear, <laugh> so I appreciate that. It’s interesting what you said about the spatial reasoning. In our work creating curriculum at Amplify, I find we lean a lot on trying to tie abstract math towards spatial topics. Like, can you estimate a quantity before you calculate it? Can you identify a pattern and where it breaks before you prove it abstractly? And, I dunno, it’s just interesting to me. I’m just thinking out loud about how I feel like math becomes more abstract rather than more spatial. The farther you venture into secondary math…I’m wondering if I misunderstand what you’re meaning by spatial, and the progression of math from K–12.

Dr. Erin Maloney (24:20):

Yeah, so I think you can still have—you can have math be abstract, but still really relying on spatial processing. Right? And I think part of that is maybe a bit of us having different definitions of when we say “spatial.” So in cognitive science, when we talk about spatial representations or spatial reasoning, it’s really like anything you’re picturing in your mind, any time you’re really picturing these things in your mind and manipulating those images at all. So if you imagine, even like at a simple level, but it’s gonna hold when you’re going more complex as well. So doing like equivalence problems, for example, where you have to balance the equations.

Dan Meyer (24:58):

Yeah.

Dr. Erin Maloney (24:59):

Even just being able to envision things kind of moving around that equal sign and bringing one piece of the equation from this side to the other is actually an extremely spatial kind of reasoning. Right? Or when you’re expanding, that’s actually extremely extremely spatial, despite the fact that it might not feel like it initially. Obviously anything in geometry is going to be very spatial. So I think, in that sense, we would argue that the spatial processing is still playing a pretty important role. But it’s maybe a different type of spatial processing than what we’re seeing at a very early level in elementary school. That said, you can completely disagree with me too. ‘Cause I could also just be wrong, and that’s fair. My kids tell me I’m wrong all the time. So I’m used to <laugh> being told that I’m wrong.

Dan Meyer (25:47):

Well, we’re a bit more deferential on this here show, with our guests. So I would not do that. But it makes sense, what you’re saying about how these are things that you manipulate in your mind, whether they are Xs and Ys or numbers and fractions. These are all things that we manipulate. That ties into differences in this spacial reasoning category, it sounds like, which then contributes to math anxiety. And it does start to feel like there’s a lot going on here, is what it feels like.

Bethany Lockhart Johnson (26:14):

You mean hot mess?

Dan Meyer (26:16):

I meant hot mess.

Dr. Erin Maloney (26:17):

Yeah. <laugh>, I think that’s the technical term, right? I’m pretty sure that’s the technical term for it.

Dan Meyer (26:21):

I didn’t know the citation for it. So I didn’t say it. But I knew who in literature named that. But yeah.

Dr. Erin Maloney (26:28):

I’ll write something at some point.

Dan Meyer (26:30):

We’ll cite Maloney, 2022. Yeah. Yes.

Bethany Lockhart Johnson (26:34):

So I will say that one of my dreams in thinking about this season and last season, but particularly this season, since we’re really getting to talk to some researchers who get to think about this, and have really interesting conversations about it all the time…one of my dreams is that we’re bringing—’cause we do have some folks who are researchers that are listening, right? But then we also have teachers and folks who are in the classroom every day, and parents and caregivers listening. And so I think one of the beautiful things about the way that I hear you talking about it is you’re thinking about the research, but it’s so applicable. Right? And I wonder if there’s anything else you can say around it. I wanna reduce that divide, that gap, between the research that’s happening and then what’s happening with the kiddos and in the classroom and at home. And I don’t know if it’s like a magic wand thing where like <laugh> if there were changes you’d wanna see at a societal level, to try to combat math anxiety, but you see where I’m going. You know, it’s like <laugh>….

Dr. Erin Maloney (27:39):

  1. So I’m gonna answer maybe in two ways. So I think the first thing that I’m hearing from you is that idea of diminishing this divide, right? And so one thing I try to keep in mind, as someone who’s a researcher and working in the lab, I will often be called in to talk to teachers and give professional development sessions. And they often want the sage-on-the-stage academic, that stands up there and tells you the answers to things. And one of the first things that I’m gonna admit when I get up there is, “I am not on the front lines.” So what I do in the lab, for me to tell you that that’s gonna work in a classroom of 30 kids who may or may not have eaten dinner that day, and may or may not have snow pants, and may or not…like it’s–

Bethany Lockhart Johnson (28:23):

Mmm, yes.

Dr. Erin Maloney (28:24):

You know, I think we also need to be a little bit reasonable. So I try really hard in my own program of research to make sure that I’m always talking to teachers and to principals and to curriculum designers to make sure that the ideas that I have make sense. In fact, one of the most recent book chapters that I wrote, I wrote in collaboration with a really good friend of mine who’s a principal, an elementary school principal, and a former math consultant. And we wrote it together, to really say like, “Hey, here’s how we can help each other inform how research can inform practice and how practice can also inform research.” ‘Cause he can come to me and say, “I’m doing this. I can’t find anything in the literature to support this, but I’m sure it works!” And we can design something in the lab to test whether or not it seems like it’s gonna work.

Bethany Lockhart Johnson (29:11):

That’s huge. Yeah.

Dr. Erin Maloney (29:12):

Empirically. And so I think that open communication is massive. One thing that we’re doing in my own lab to try to keep that open communication available. So to anyone listening who’s ever tried to get access to a journal article, they’re held behind paywalls, right? So one, the way it works, my understanding of this anyway, is that the journal owns the formatted version of the paper. So what we do is we put up audio recordings of all of the research papers that we ever publish. So I’m pretty sure I own the words as the author, and the journal owns the prettified version that you can buy. So we audio-record all of our papers, so that if teachers or parents ever want to hear the actual science that’s going into some of these decisions, they have access to at least the stuff that we do in our lab. And we also put up an infographic for every paper, just highlighting kind of the main questions and main findings. And we do that because I think that the only way for the information to actually be useful is if it gets into the hands of the stakeholders that actually need that information.

Bethany Lockhart Johnson (30:21):

And is accessible. That’s huge. That’s huge!

Dr. Erin Maloney (30:24):

Yeah. Yeah. So that’s one way that we try to do it. And like I said, the other thing, we try to always be working with principals and with teachers. I joke that the way that I remedied this in my own life…so my husband’s a teacher; it’s like, I just married one! It’s fine! <laugh> I can grill him on a regular basis, and be like, “I wanna try this experiment. Do you think it’s gonna work?” And he can say, like, “It’s not going to. Here’s why.”

Dan Meyer (30:47):

That’s awesome. Marrying a participant—you know, a research participant—is unethical, of course. Would not clear IRB. But turning your partner into a participant? Like, what are you gonna do? That’s great.

Dr. Erin Maloney (30:57):

Yeah, no, that’s fair game.

Dan Meyer (30:58):

Yep.

Dr. Erin Maloney (30:59):

Yeah. So that’s—I think we we compensate each other <laugh>. So, no…so I do joke a little bit about that. He was a teacher simply ’cause he wanted to be one. Not ’cause I needed him to be one. But, I think that communication part is, is really key. That’s one thing. Then the other part of the question or the other sort of piece of the question that I was hearing is that idea of, how do we fix math anxiety. Right? Like, what’s the great, “I’m glad that there’s a whole bunch of time and effort and energy going into trying to understand this, but what, where are we at?” And I think with that, it’s really, really promising. So there’s been a lot of research coming out looking at how best to help children or even adults manage their own anxiety about math. And there’s a few really interesting strategies that seem to be quite effective. So one, and I don’t know if—um, it feels weird calling him Dr. Ramirez, just ’cause I know him well!—but I don’t know if Dr. Ramirez would’ve talked about this when he chatted with you, but he has some really interesting work on expressive writing. Did he chat about that at all?

Bethany Lockhart Johnson (32:07):

He didn’t, but I’ve read some of his work about it and I think it’s so fascinating.

Dr. Erin Maloney (32:11):

Yeah! So, OK, well, I’ll tell you about his work on it.

Bethany Lockhart Johnson (32:13):

Yes, please. Please.

Dr. Erin Maloney (32:14):

Because it’s super-useful. So when we talked about that idea of how anxiety causes these thoughts and ruminations, and they tie up the memory resources that you need, what Gerardo has found is that when you get students to write about their anxiety for about 10 minutes before they do a test, what ends up happening is they end up doing better on the test, relative to if they would not have written about their anxiety at all. And this is particularly true for students who are really high in anxiety. OK? And the idea is that all of those thoughts that they were going to have about the test or the consequences of the test, et cetera, you just kind of get ’em…it’s like a mind dump where you get ’em all onto the page at first before you even go to do the test. And now when you go to do the test, you’re not having to do two things at once. You’re no longer dealing with these thoughts ’cause you got ’em all out on the paper beforehand. And so Gerardo has some really interesting work showing that that works for math anxiety. And then it also works for just testing anxiety in general. And so that’s a strategy that I love. I also—part of what I really love about it is it’s so low-cost, right? You need a paper and a pencil and it’s great. So those are always my favorite strategies, the ones that don’t really cost us anything. So that’s one way of dealing with like the cognitive part of the anxiety. The other thing you can do is try to deal with the anxiety part of the anxiety. So for that, what we find is that the typical strategies that you’re gonna see for anxiety tend to work for math anxiety. So things like focused breathing. Right? Making sure you’re doing deep inhales and exhales. That really diaphragmatic breathing seems to be quite helpful. We know that what we call progressive desensitization is really key. That’s the idea of doing things, you know, starting with the questions that you know how to handle. And then gradually working up to the more difficult questions. So you’re sort of gradually exposing yourself to the more complex stuff. And how that can play out on an actual test at school is, you sit down, and instead of just starting with question number one, you actually read the whole test, see which questions you feel like you know the best, start with those questions, and that helps build your confidence so that you’re better able to tackle the questions that are maybe a little bit outside of where you’re currently at. So that seems to be really helpful. The other part that I will say, too, that’s extremely helpful: So we know that anxiety really ties up those memory resources. And so the more you can make the math automatic, the more immune it’s going to be to anxiety in the moment. And so I know that this part can be a little bit controversial, because we don’t wanna necessarily demotivate children, and kill the enthusiasm for math that we’re trying to cultivate…but really, you know, really committing your arithmetic facts to memory can be extremely helpful. So really learning those times tables, really learning your addition and subtraction facts. ‘Cause what happens is, then when you’re in a situation where you need that information, even if you’re anxious and you’re working with fewer cognitive resources than what you would normally have, you actually don’t need that many cognitive resources to be able to pull something from memory that you’ve memorized. So it really helps to kind of protect you against some of the negative impacts of the anxiety while you’re doing that test.

Bethany Lockhart Johnson (35:37):

And you’re not using all your cognitive resources to figure out seven times eight, because you can really focus on what you’re trying to do with that. Oh, that’s fascinating. Yeah. Yeah.

Dr. Erin Maloney (35:47):

Yes. No, a hundred percent right. And so I know that’s one that, like I said, I know it can be somewhat controversial because it’s…you know, we’ve talked about—or we haven’t talked about in this conversation, but we often talk about—the idea of drilling and killing. Right? So you drill the facts, you kill the, the enthusiasm. But I think that there are ways that we can drill arithmetic facts, or help make them automatic, but still fun, right? It doesn’t have to always be in a high-pressure kind of way.

Bethany Lockhart Johnson (36:16):

Totally. And we’ve talked about fluency, and I’m sure we’ll talk about it more in the Lounge. And that is interesting, that link between anxiety when the fluency isn’t there, that—or, of course we hear about anxiety with timed tests, but the idea of that IS something you can do to reduce it, because you have those facts just at your ready. Right?

Dr. Erin Maloney (36:37):

Yeah. So I actually, again, I’m gonna be a little bit controversial. So I don’t hate timed tests in the way that a lot of people do. But I love time to practice. So I think once we’ve got to a point where children have a fairly decent understanding of skills, of a skill, once they’ve got a fairly decent grasp on it, then I love the idea of the timed practice. So it can be still in a low-pressure situation, where in many ways it doesn’t matter if you get the answer to the question correct. But we’re practicing doing it in a situation in which you might be feeling a little bit of pressure, but it’s not real pressure, if that makes sense. And I think that can be really, really useful for students. And again, it can be done in a fun way, right? It doesn’t have to be these super-intense ways. It can be fun. But I think that in life there are situations in which the time that it takes you to complete a problem matter. And I think that we have to make sure that we don’t get too far away from that.

Dan Meyer (37:40):

Yeah. It feels like we should do an entire other episode thinking about ways to develop that fluency and automaticity that don’t contribute to anxiety, or create further disparities between people who are high math anxiety and low math anxiety. Not a small question, I’m sure. And I appreciate you alluding to all of that. You know, this whole thing, as you said, is quite the hot mess. And I feel like you, Dr. Maloney, have helped us make this a little less messy, in our heads, and hopefully the listeners’ heads. I really appreciate that. I just love…you’ve mentioned lots of resources that you have. You’ve alluded to them: audiobook-style readings of your research, which I need ’cause I just finished, you know, Harry Potter, the seventh book, so I need a new thing to listen to like that. Also infographics. Can you tell our listeners where they can find this work of yours, and if there are any other kinds of resources that you wanna plug for our listeners here?

Dr. Erin Maloney (38:32):

Yeah, for sure. So all of our resources can be found on my lab website. So the address for that is www.ErinMaloney.ca. So there we have, like you said, the infographics and the audio articles and all that stuff. And then we also have a link to a new kids’ book out, actually, that a colleague of mine and I have published recently, that really walks through some of these strategies on combating math anxiety. The book is written as a children’s book, so it’s Peyton & Charlie Challenge Math. But it secretly is a book that would also work for adults. So if you are a parent that’s a little bit anxious about math, or a teacher that maybe is a little bit anxious, and you wanna see how some of these strategies can play out, in that book—we linked to it on the website, but it is available for purchase on Amazon. And the one thing I will say about the book, ’cause this is something that we were pretty proud of, so Sheri-Lynn Skwarchuk, who is a school psychologist, and I wrote the book. And it’s available for purchase at our cost price, so we don’t actually make any money on the book. It was literally just a way of getting some of the science out to people who might be able to benefit from it.

Bethany Lockhart Johnson (39:45):

Reducing that divide!

Dr. Erin Maloney (39:46):

Yeah, well that’s what we’re trying to do! Right? So I think in the U.S., I think it’s like $6 on Amazon. And then in terms of other resources, we’re in the process right now of creating some informational videos and and stuff like that that hopefully will be useful for parents and for teachers, just in terms of understanding a little bit more about the anxiety and understanding how to deal with the anxiety in the classroom more, at home or wherever it might be coming up.

Dan Meyer (40:15):

Well, thanks so much. I really appreciate—we appreciate!—you coming on, and hearing about how you’re trying to bridge so many different barriers from research to practice, and school to home. It’s just really inspiring. And we’d love to have you back on sometime. So thank you so much for joining us.

Bethany Lockhart Johnson (40:29):

I feel like we’ve just hung out! Don’t you, Dan?

Dan Meyer (40:31):

Are we rolling here? Oh my gosh, we’re rolling. I just thought we’re just hanging. Yeah,

Bethany Lockhart Johnson (40:34):

I thought we were just hanging!

Dr. Erin Maloney (40:36):

I know, I do, I really appreciate that it has a very kind of chill vibe to it.

Dan Meyer (40:41):

Chill vibe. Like a lounge.

Bethany Lockhart Johnson (40:42):

It’s the lounge!

Dan Meyer (40:43):

Thank you. You get us; you get us. <laugh>

Bethany Lockhart Johnson (40:45):

Dan Meyer. I was shopping for children’s books, and there was this book, and it was talking about being at home with Mom. And it’s going through all the things that the child did that day with Mom. It’s like, “We played outside, we ran through the sprinklers, we even did some homework.” And it shows them sitting at the table with the homework, that’s clearly math homework, in front of them. And the mom is like, “Harrumph!” Like a very perplexed, anxious face. And there’s all these question marks above her. And it’s just like,

Dan Meyer (41:24):

“There should not be numbers on that paper!”

Bethany Lockhart Johnson (41:25):

Exactly. And the child is like, “Ohhhh,” you know. And I mean, I have to give credit to the illustrator, because they really did capture the clear message of this interaction, which was sitting down to do math homework or think about math together is a source of angst. Right? According to this author and according to too many people. And so I think what’s really important is that we recognize those images when we see them out there and speak back to them, and say, “Hey, wait a second.” Yeah, it can feel like that, and it doesn’t have to. And what’s going on that that’s just the assumed way that it’s gonna feel, to sit down and math together. You know?

Dan Meyer (42:11):

Yeah. It feels like we all have a lot of work to do on the whole math-anxiety front. Dr. Maloney helped us see how parents play a part, educators play a part, society and how they create people plays its own part in how we all define math as a thing where we evaluate student thought or where students play it with their thoughts, has its own huge part as well. So yeah, it was a really fantastic conversation with Dr. Maloney. I hope you folks will check out the show notes, where you will find links to Dr. Maloney’s website. A lot of her work, which as you heard, is very geared towards practitioners and parents and even directly at kids, especially the new children’s book she co-authored, Peyton & Charlie Challenge Math.

Bethany Lockhart Johnson (42:55):

Next time we’re gonna dive even more into the nitty gritty of combating math anxiety. To do that, we’re actually gonna be joined—I am so excited about this—by Dr. Rosemarie Truglio from Sesame Workshop.

Rosemarie Truglio (43:09):

Our core audience are two- to four-year-olds, and they love math. And what’s not to love? Children don’t come with this math anxiety. Math anxiety is learned.

Dan Meyer (43:23):

So excited.

Dr. Erin Maloney (43:24):

Sesame Street was a huge part of my childhood and my toddler doesn’t know it yet, but Sesame Street is coming. It’s coming. Like, we’re we’re gonna introduce Sesame Street to him. We just haven’t yet.

Dan Meyer (43:37):

Sesame Street straight raised me.

Bethany Lockhart Johnson (43:38):

Right?

Dan Meyer (43:39):

Yeah. Don’t tell my parents. But that’s, yeah, that’s true. I’m excited, too. It’s gonna be a blast.

Bethany Lockhart Johnson (43:45):

I’m really excited. I think that the more we dive into this topic—which, again, we’re gonna look at math anxiety from a lot of different angles—and I’m excited to talk to Dr. Truglio about how we can take this research and these conversations that are happening about math and how it can actually impact what’s happening in homes. ‘Cause we wanna help create positive relationships with mathematics, with kids in math. I’m so excited. And I hope you folks keep listening. We love having you here in the Lounge. And if you haven’t already, please subscribe to Math Teacher Lounge, wherever you get podcasts. And if you like what you’re hearing, please leave us a rating and a review. It helps more listeners to find the show, and let other folks know about this show. Recommendations are great. Thanks so much for listening.

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What Dr. Erin Maloney says about math

“If we can change their mindset, then we can set students on a path to more opportunities and success.”

–Dr. Erin Maloney

Associate Professor in the School of Psychology, Director of the Cognition and Emotion Laboratory, and the Canada Research Chair (Tier II) in Academic Achievement and Well-Being, all at the University of Ottawa

Meet the guest

Erin Maloney is an Associate Professor and Canada Research Chair at the University of Ottawa. Her research sits at the intersection of Cognitive Psychology, Developmental Psychology, and Education and focuses on cognitive and emotional factors that relate to academic achievement. She is a world-renowned expert on the study of math anxiety, conducting research in the lab, in homes, and in classrooms with children, parents, and their teachers. She is passionate about both knowledge mobilization and equity, diversity, and inclusion within education and science.

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

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Grade 6

Unit 1: Area and Surface Area

Lesson 2: Finding Area by Decomposing and RearrangingShapes on a Plane
Lesson 3: Reasoning to Find AreaLetters
Lesson 4: ParallelogramsExploring Parallelograms, Part 2
Lesson 5: Bases and Heights of ParallelogramsExploring Parallelograms, Part 1
Lesson 6: Areas of ParallelogramsOff the Grid, Part 1
Lesson 7: From Parallelograms to TrianglesTriangles and Parallelograms
Lesson 8: Areas of TrianlgeExploring Triangles
Lesson 10: Bases and Heights of TrianglesOff the Grid, Part 2
Lesson 11: PolygonsPile of Polygons
Lesson 15: More Nets, More Surface AreaRenata’s Stickers

Unit 2: Introducing Rations

Lesson 3: RecipesPizza Maker
Lesson 5: Defining Equivalent RatiosFruit Lab
Lesson 12: Navagating a Table of Equivalent RationsDisaster Preparation

Unit 3: Unit Rates and Percentages

Lesson 1: Anchoring Units of MeasureMany Measurements
Lesson 4: Comparing Speeds and PriceWorld Records
Lesson 5: Interpreting RatesSoft Serve
Lesson 6: Equivalent Ratios Have the Same Unit RatesWelcome to the Robot Factory
Lesson 8: Solving Rate ProblemsMore Soft Serve
Lesson 9: More about Constant SpeedModel Trains
Lesson 11: Representing Percentages with Double Number Line DiagramsLucky Duckies

Unit 4: Dividing Fractions

Lesson 4: How Many Groups? (Part 1)Flour Planner
Lesson 6: Using Diagrams to Find the Number of GroupsFill the Gap
Lesson 13: Rectangles with Fractional Side LengthsPuzzling Areas

Unit 5: Arithmetic in Base 10

Lesson 1: Using Decimals in Shopping ContextDishing Out Decimals

Unit 5: Arithmetic in Base 11

Lesson 2: Using Diagrams to Represent Addition and SubtractionDecimal Diagrams and Algorithms

Unit 5: Arithmetic in Base 12

Lesson 15: Making and Measuring BoxesMovie Time

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and EquationsFive Equations
Weight for It
Lesson 3: Staying in BalanceHanging Around
Lesson 4: Practice Solving EquationsHanging It Up
Lesson 5: Represent Situations with EquationsSwap and Solve
Lesson 9: The Distributive Property: Part 1Products and Sums
Lesson 17: Two Related Quantaties, Part 2Subway Fares

Unit 7: Rational Numbers

Lesson 3: Comparing Positive and Negative NumbersOrder in the Class
Lesson 5: Using Negative Numbers to Make Sense in ContextMinimum Wage
Lesson 8: Writing and Graphing InequalitiesTunnel Travels

Unit 8: Data Sets and Distributions

Lesson 5: Using Dot Plots to Answer Statistical QuestionsMinimum Wage
Lesson 6: Interpreting HistogramsThe Plot Thickens
Lesson 11: Variability and MADHoops
Lesson 13: MedianToy Cars

Grade 7

Unit 1: Scale Drawing

Lesson 1: What are scaled copies?Scaling Machines
Lesson 2: Correspond Parts and Scale FactorsMake it Scale
Lesson 3: Making Scaled CopiesScaling Robots
Lesson 5: The Size of the Scale FactorScale Factor Challenges
Lesson 6: Scaling AreaTiles
Lesson 6: Scaling AreaWill It Fit

Unit 2: Introducing Proportional Relationships

Lesson 1: One of These Things is Not Like the OtherPaint
Lesson 5: Two Equations for Each RelationshipTwo and Two
Lesson 10: Introducing Graphs of Proportional RelationshipsDinoPops

Unit 3: Measuring Circles

Lesson 2: Exploring CirclesMeasuring Around
Lesson 7: Exploring the Area of a CircleWhy Pi?
Lesson 9: Applying Area of a CircleArea Challenges

Unit 4: Proportional Relationships and Percentages

Lesson 6: Increasing and DecreasingMosaics
100%
Lesson 7: One Hundred PercentMore and Less
Back in My Day
Lesson 8: Percent Increase and Decrease with EquationsAll the Equations
Lesson 11: Percentage ContextsPercent Machines

Unit 5: Rational Number Arithmetic

Lesson 3: Changing ElevationFloats and Anchors
Lesson 5: Representing SubtractionMore Floats and Anchors
Lesson 6: Finding DifferencesDraw Your Own
Lesson 13: Expressions with Rational NumbersInteger Puzzles

Unit 6: Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative NumbersKeeping it True
Lesson 13: Reintroducing InequalitiesI Saw the Signs
Lesson 14: Finding Solutions to Inequalities in ContextUnbalanced Hangers
Lesson 15: Efficiently Solving InequalitiesShira the Sheep
Lesson 16: Interpreting InequalitiesBudgeting
Lesson 17: Modeling with InequalitiesWrite Them and Solve Them
Lesson 20: Combining Like Terms (Part 1)Collect the Squares

Unit 7: Angles, Triangles, and Prisms

Lesson 2: Adjacent AnglesFriendly Angles
Lesson 5: Using Equations to Solve For Unknown AnglesMissing Measures
Lesson 7: Building Polygons (Part 2)Can You Build It

Unit 8: Probability and Sampling

Lesson 1: Mystery BagsHow Likely
Lesson 3: What are Probabilities?Prob-bear-bilities
Lesson 4: Estimating Probabilities through Repeated ExperimentsIs It Fair?
Lesson 13: What Make a Good Sample?Crab Island

Grade 8

Unit 1: Rigid Transformations and Congruence

Lesson 1: Moving the PlaneTransformers
Lesson 2: Naming the MovesSpinning, Flipping, Sliding
Lesson 3: Grid MovesMoving Day
Lesson 4: Making MovesTransformation Golf
Lesson 5: Coordinate MovesGetting Coordinated, Part 1
Lesson 6: Describing TransformationsGetting Coordinated, Part 2
Lesson 16: Parallel Lines and Angles in a TrianglePuzzling It Out
Lesson 17: Rotate and TesselateTessellate

Unit 2: Dilations, Similarity, and Introducing Slope

Lesson 1: Projecting and ScalingSketchy Dilations
Lesson 3: Dilations with No GridDilation Mini Golf
Lesson 7: Similar PolygonsSocial Scavenger Hunt

Unit 3: Linear Relationships

Lesson 1: Understanding Proportional RelationshipsTurtle Time Trials
Lesson 5: Introductions to Linear RelationshipsFlags
Lesson 6: More Linear RelationshipsStacking Cups (Optional)
Lesson 8: Translating y=mx+bTranslations
Lesson 9: Slopes Don’t Have to Be PositiveWater Cooler
Lesson 10: Calculating SlopeUps and Downs

Unit 4: Linear Equations and Systems

Lesson 5: Solve Any Linear EquationEquation Roundtable
Lesson 12: Systems of EquationsMake Them Balance
Lesson 13: Solving Systems of EquationsLine Zapper

Unit 5: Functions and Volume

Lesson 1: Inputs and OutputsGuess My Rule
Lesson 5: More graphs of FunctionsTurtle Crossing
Lesson 6: Even More Graphs of FunctionsThe Tortoise and the Hare
Lesson 13: The Volume of a CylinderCylinders
Lesson 15: The Volume of a ConeCones

Unit 6: Associations and Data

Lesson 3: What a Point on a Scatter Plot MeansRobots
Lesson 4: Fitting a Line to DataDapper Cats
Lesson 5: Describing Trends in Scatter PlotsInterpreting Scatter Plots
Lesson 6: Slope of a Fitted LineFind the FIt (called Fit Fights in Desmos Math)
Lesson 7: Observing More Patterns in Scatter PlotsScatter Plot City
Lesson 8: Analyzing Bivariate DataInterpreting Slopes
Lesson 9: Looking for AssociationAnimal Brains
Lesson 10: Using Data Displays to Find AssociationFinding Associations

Unit 7: Exponents and Scientific Notation

Lesson 1: Exponent ReviewCircles
Lesson 6: What about Other Bases?Power Pairs
Lesson 12: Applicatios of Arithmetic with Powers of 10Balance the Scale
Lesson 13: Definition of Scientific NotationSpecific and Scientific (formerly Solar System)

Unit 8: Pythagorean Theorem and Irrational Numbers

Lesson 5: Square Roots on the Number LineRoot Down
Lesson 7: Finding Side Lengths of TrianglesTriangle Tracing Turtle
Lesson 11: Applications of the Pythagorean TheoremTaco Truck

Algebra 1

Intro/Launch

Unit 1: One Variable Statistics

Lesson 12: Standard DeviationFinding Desmo

Unit 2: Linear Equations and Systems

Lesson 4: Equations and Their SolutionsWorking Backwards
Solving Strategies
Same Position
Lesson 5: Equations and Their GraphsShelley the Snail
Five Representations
Lesson 6: Equivalent EquationsSubway Seats
Lesson 7: Explaining Steps for Rewriting EquationsVarious Variables
Lesson 12: Writing and Graphing Systems of Linear EquationsLizard Lines
Lesson 13: Solving Systems by SubstitutionShape It Up

Unit 3: Two Variable Statistics

Lesson 5: Fitting LinesCity Slopes
Penguin Populations
Lesson 6: ResidualsResidual Fruit
Lesson 7: Correlation CoefficientCorrelation Coefficient
City Data
Lesson 8: Using the Correlation CoefficientHow Hot Is It?
Lesson 9: Causal RelationshipsBehind the Headlines

Unit 4: Linear Inequalities and Systems

Lessons 4-6: Graphing Linear Inequalities in Two VariablesPizza Delivery
Lesson 7: Solutions to Systems of Linear Inequalities in Two VariablesQuilts
Seeking Solutions
Lesson 8: Solving Problems with Systems of Linear Inequalities in Two VariablesCarlos’s Fish

Unit 5: Functions

Lesson 1: Describing and Graphing SituationsCraft-a-Graph
Lesson 7: Using Graphs to Find Average Rate of ChangePlane, Train, and Automobile
Lesson 12: Piecewise FunctionsPumpkin Prices
Lesson 15: Inverse FunctionsChip the Robot

Unit 6: Introduction to Exponential Functions

Unit 7: Introduction to Quadratic Functions

Lesson 1: A Different Kind of ChangeRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
Lesson 10: Graphs of Quadratic Functions in Standard and Factored FormsOn the Fence
Stomp Rockets
Plenty of Parabolas
Two for One
Lesson 11: Graphing Quadratics from the Factored FormParabola Zapper
Shooting Stars
Lesson 14: Quadratic Graphs that Represent SituationsRobot Launch

Unit 8: Quadratic Equations

Lesson 2: When and Why Do We Write Quadratic Equations?Sorting Relationships
Lesson 12-14: Completing the SquareSquare Tactic
Lesson 24: Using Quadratic Equations to Model Situation and Solve ProblemsStomp Rockets in Space

Disclaimer

This document is for informational purposes only; references to third-party programs do not imply endorsement or affiliation, and all trademarks are the property of their respective owners.

S4 – 01. Joyful math teaching with Kanchan Kant

Podcast cover for "Math Teacher Lounge," Season 4, Episode 1, titled "Joyful math teaching," featuring Kanchan Kant, described as a math educator and transformative leader.

This season on the Math Teacher Lounge podcast, we follow the theme “joyful math” and uncover its meaning.

In this episode, Kanchan Kant joins Bethany Lockhart Johnson and Dan Meyer to discuss the key, early investment she makes at the start of the school year to ensure her math teaching will be joyful for herself and for her students for the rest of the year.

Explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:00):
Okay, we are recording. Hey folks. Welcome back to Math Teacher Lounge. (laugh)

Bethany Lockhart Johnson (00:06):
Hardly off to a rocking start.

Dan Meyer (00:06):
Yeah. Yeah. <laugh> Did you like my energy there? Hey folks. Welcome back to Math Teacher Lounge. It’s a new season with your host Dan Meyer. And…

Bethany Lockhart Johnson (00:15):
I’m Bethany, Lockhart Johnson. How’s your summer Dan?

Dan Meyer (00:22):
Summer for me feels really hectic as we prepare, here at Amplify, for the new school year, and everyone’s starting these new math programs. So I’ve been feeling quite amped up, like usual in the summer. But also, my kids started big kid school. So I’ve been seeing the educational system from the role of a parent and all the anxieties and I worry, will I be my kids’ teacher’s most annoying parent <laugh> … So what kind of math curriculum you using? Oh, have you heard of core counting? Can I lead a math center? What’s this worksheet about? I’m really worried my kids are just overall gonna hate my vibe when I come around their classes. Uh, <laugh> so lots going on with me.

Bethany Lockhart Johnson (01:06):
It’s already happening for me and I have a toddler.

Dan Meyer (01:10):
<laugh> There we go. Anyway, that’s what I’m up to. That’s how I’m feeling. I’m curious how you’re doing. We haven’t chatted in a while. We’re excited about the podcast, but it’s been a bit, you know? Bethany got a break from me and my antics over the summer. So, how are we finding you here, as we ramp up to the new season?

Bethany Lockhart Johnson (01:24):
Uhhhh. Well, let me just tell you, I have a toddler. That’s kind of all I need to say. Except that’s not all I will say. Of course, I’ll say more. I am exploring, I’m dipping my toe into the extracurricular toddler activities; the music classes of the toddler world, the creative movement of the toddler world. And yeah, I have lots of opinions and lots of things to say about the teachers. And I’m like, Ugh, I can’t wait to be room mom. And just like…<laugh>

Dan Meyer (01:55):
Just let it rip, you know?

Bethany Lockhart Johnson (01:57):
I have opinions on everything and just hope I don’t get kicked out of the class.

Bethany Lockhart Johnson (02:05):
It’s been an eventfully recharging summer and we are ready for this new season. And in fact, we’re so ready that we decided that we were gonna mix up this season. Just a, just a tiny bit. Shall I explain Dan?

Dan Meyer (02:21):
Yeah. Let’s do it.

Bethany Lockhart Johnson (02:22):
So we have loved all the different topics that we have explored in the Math Teacher Lounge world, but we kind of feel like we need to do some more deep dives. So for this season and the foreseeable seasons …

Dan Meyer (02:38):
We’ll see how it goes.

Bethany Lockhart Johnson (02:38):
Let’s stick with this season. For this season. We’re going to be exploring a singular theme.

Dan Meyer (02:46):
We’re not bouncing around. Yep. We’re not bouncing around from a guest to guest going on whatever shiny thing in the river bed catches our eye. We’re gonna take one theme and see where it goes. What we working with here this season?

Bethany Lockhart Johnson (02:57):
This season, we are going to be exploring the idea of joyful math, joyful math. And Dan, the question I have for you is, is the term joyful math one that you use on the regular?

Dan Meyer (03:10):
No, it definitely is not. I think that joy and math are very rarely, you know, connected in the popular mind. Number one, and number two, you know, I’m kind of an ornery fellow, so that’s not my natural kind of description of math. But we decided that it feels like an important one at the moment, because a lot of math teaching–a lot of teaching in general, math teaching in particular–math teaching is often not a joyful discipline for students, where, you know, I’ve done some research where you look at what people type into Google. And I looked at like, what they…why am I bad at X? And I looked at that for where X is math, where it’s science, where it’s reading, where it’s history. And it was just wild to see how many more hits there are out there on the Internet for “why am I bad at math?” People don’t really associate math with joy, but also we’re looking at joyful math in terms of joyful math teaching. Math teaching, teaching in general, is a tough field at the moment with a lot of teachers leaving teaching. And those who remain are having a lot of soul searching and thinking about, why am I here and how do I sustain this work? And in an environment that seems hostile to my interests or my talents, or work-life balance. And so that’ll be the theme that we’re gonna kind of uncover over the course of our season, talking to various interesting guests, including one today about, yeah, joyful math teaching and joyful math.

Dan Meyer (04:43):
And to help us think about what joyful math teaching looks like, we figured we’d first look at what UN-joyful math teaching looks like. It happens to be the case that we’ve been in a pandemic as you might be aware, and teaching has been challenging. And the NEA, our National Education Association, surveyed its member teachers and asked them the following question … Gave a list of issues that school employees have experienced and asked, for each one indicate how serious of a problem this is for you. This is a survey where more than half of members said they are more likely to leave or retire sooner than planned because of the pandemic. And this is almost double the numbers from July, 2020. It’s really hard to keep track of teacher departures and unfilled vacancies across states. So I don’t wanna like blow this up out of proportion, but it does indicate some real challenges in teaching. So Bethany, I was curious, what do you think like at the top of the list, like what kinds of factors, issues facing educators would you imagine there are?

Bethany Lockhart Johnson (05:48):
So if I’m to understand you correctly, these are reasons someone is not actively experiencing joy in the profession of teaching. Like why would they leave?

Dan Meyer (05:58):
Exactly.

Bethany Lockhart Johnson (05:59):
Well, the number one thing that came to mind for me, well, okay. Wait, wait, one other caveat I need to ask about, you said specifically pandemic-related or just in general, because if it’s pandemic-related, then I think, well, there’s health issues, right? That people are concerned about, but in general, the thing that came to mind was a lack of support from administration districts, lack of funding, and overcrowding in classrooms. Like, you know, I saw somebody had 40 students in their classroom. So those are the two things that I can imagine like top on someone’s list that would make them experience less than a joyful day.

Dan Meyer (06:44):
Yeah. There’s a bunch of you’re kind of identifying here. So number seven on the list is lack of respect from parents and the public, which is like 76% of teachers call that out as serious for them. Others that you kind of circled around in terms of resources go like, not enough planning or unstructured time in the job kind of ties into resources. Yeah. But there’s others that are on the list that I’m curious, you wanna take on the swing at it, given what I’ve said here,

Bethany Lockhart Johnson (07:15):
I feel like too much being asked of them, like being asked to wear too many hats, like they’re being asked to not only teach their class, but also cover all the vacancies and supervise recess and, you know, make a delicious, nutritious lunch. That’s what came to mind. Am am I close?

Dan Meyer (07:33):
Yeah. Number four on the list, unfilled job openings leading to more work for remaining staff. People covering, you know, not just the kind of external to teaching work like you’re describing, but also just taking on like losing your prep period, to take on a class that has been unfilled for all kinds of reasons. Yeah.

Bethany Lockhart Johnson (07:54):
Yeah. I’ve only gotten the fourth. Give me one clue, one clue about …

Dan Meyer (07:59):
So, I mean like, so number one is general stress from the coronavirus pandemic, you know, which I feel like …

Bethany Lockhart Johnson (08:06):
I mentioned that.

Dan Meyer (08:07):
I’ll give you that one. Yep, yep, sure. And then number two, close behind, is feeling burned out, which I think ties into what you’re describing as well. I’m giving Bethany credit on that one. The third one is very different from the ones you’ve been describing. I think I cannot in good faith give you even partial credit for this one. I’ll just say it. Student…

Bethany Lockhart Johnson (08:28):
Wait! Dan, this is not how you give clues.

Dan Meyer (08:31):
Here’s a clue. It’s student absences due to COVID19. It’s really hard to deal student absences. That’s your clue.

Bethany Lockhart Johnson (08:40):
That wasn’t a clue that you told me.

Dan Meyer (08:43):
Yeah, let’s see. I think that’s largely it. There’s also pay is too low, is on the list; student behavioral issues, on the list. And I think that about covers it. So all of that, that basket of items has led to more than half of teachers in this survey, saying that they’re more likely to leave or retire from education sooner than planned. And I don’t know. I think we all know teachers who have bailed.

Bethany Lockhart Johnson (09:08):
I’ve never played a board game with you, Dan, but if we ever play a board game, we’re gonna work on your clue giving, ’cause I want to keep guessing. And you just told me.

Dan Meyer (09:22):
Yeah. Yeah.

Bethany Lockhart Johnson (09:22):
In all seriousness, the <laugh>. In all seriousness, I think yes, the stress of the pandemic and students being absent, what some folks are calling unfinished learning, all of those pieces do play into it. But a lot of those things that you’re mentioning on the list are things that are not unique to the pandemic, right? Like those are things that I feel like there is some modicum of control that we could have over shifting the way the culture of the teaching profession is going so that we could create a more joyful experience for educators, administrators, and students.

Dan Meyer (10:03):
Yeah. Good call out. That’s exactly right. We could tax the people who are not in the classrooms more and increase the pay to classroom teachers. You know, there we go.

Bethany Lockhart Johnson (10:11):
Oh. Bingo. Why didn’t we ask you sooner Dan, for your wisdom.

Dan Meyer (10:15):
Yeah. I’m … solved by Dan. Yeah, good point though. So I read that and yeah, I think that there’s been some … people have critiqued the NEA for being very alarmist about teacher departures as the year has ramped up. It has not been quite the flood of departing teachers as was predicted and thank heavens for that, but we should still be very bummed if teachers are unhappy and wanting to leave and feel like they can’t leave. That is definitely not good. So we were really excited to bring to the table, someone who is just a very joyful teacher and one in a very intentional way. Someone who has a lot of discipline in how she approaches the job and the students in it and tries to create a joyful environment for herself, Kanchan Kant. Kanchan is a math and computer science teacher at Newton North High School in Newton, Massachusetts. She’s been sharing her love for math with her students for the past four years, while also being instrumental in setting the culture and ethos of the math department at her school in her role as the assistant department head. We welcome you on the show Kanchan to help us understand joy and math teaching. Thanks for being here.

Bethany Lockhart Johnson (11:29):
Welcome!

Kanchan Kant (11:30):
Thank you for having me. I really appreciate it.

Bethany Lockhart Johnson (11:33):
One of my friends, her son was asked as his first math homework assignment to write out his math bio. And I loved that idea because we got to hear a little bit about your bio from like a broader perspective. But if we were to ask about your math bio, I will speak for myself to say like, automatically certain images flash into my mind, right? To think about my relationship, my evolving relationship with math. But I’m so curious if I was to ask you, what’s your math bio? How did you become the person, mathematically speaking, that you are today? Would you mind sharing a bit about that?

Kanchan Kant (12:10):
Of course I would love to. So I was born and raised in India and I belong to a family which considers mathematics to be extremely important to succeed in life. My father used to have me add and subtract license plates since I was four years old, when we were out and about. I loved math in school, it just made like complete sense to me. It was logical and you know, it was my favorite subject. I loved it all through high school. I had a confidence speed breaker in undergrad. When in my second semester I almost failed the engineering math course that I took. That was the first time math felt like too much and not like my best friend, which it was supposed to be. So it was a while before I could summon the courage to take on another math course in college.

Kanchan Kant (12:56):
But once I did that, it was like old times. I realized I had to persevere through the challenging bits. And once I did that, it started to make sense again. And through my journey, as an educator speaking to people from various backgrounds and like coming to the United States, I realized that math is challenging for everyone at one time or another. For some people that is elementary school. And for some others, it is college or even later. Either way does not mean that you are not a math person. When I was in college, I felt I was not a math person. Whereas my sister, my very own sister said the same thing about math in middle school. Both of us use math every day. And we are definitely, definitely math people. So for me to be a math person is to persevere, to approach problem-solving in a logical manner, and to find the joy in the process ,as well as the answer.

Dan Meyer (13:47):
That’s wonderful. Yeah. A lot of people, have a moment where they feel like almost betrayed by what they thought was a close friend of theirs, with math, where it’s like, wait, I thought we were tight. You know, I thought we were cool. You and me. And there’s that moment. And I wonder if that’s been a useful moment for you to, you know, bring back now and then as a teacher with students who might feel that even, you know, in high school or in a secondary school as a kid.

Kanchan Kant (14:15):
Absolutely. Like when I talk to students and tell them, yes, I had difficulty in math too. It has not always been easy for men and there are still things I struggle with sometimes, then it’s like more modeling for them that you have to persevere, you should persevere. And once you do that, it makes sense and you can feel successful. So, almost every year I end up sharing the story with my students.

Bethany Lockhart Johnson (14:38):
There’s so much value in that, right? That you are sharing that vulnerability with students. And to say your relationship with mathematics has not been, you know, smooth sailing the whole way through. There were times when you had to work harder than others.

Dan Meyer (14:55):
Yeah. Really fun to hear about you and your father as well. I tried to ask my five-year-old to do some skip counting the other day, like, okay, cool, you’re hot stuff. You can count, you know, up by ones, but what about by twos? And the moment really fell flat. And I watched myself becoming the kind of parent who is whose enthusiasm for math is one day resented by his children. I feel a lot of, yeah, I felt your anxiety Kanchan, with math itself. And now I feel anxiety as like someone who loves math and loves to teach math and may one day alienate the people closest to him. <laugh>

Kanchan Kant (15:31):
I don’t like that future. I have a three-month-old. I do not like this future of mine. If I have to go through what you’re going through. Uh, oh, <laugh>

Dan Meyer (15:38):
You got this. So Kanchan, you’re going back to the classroom coming up here at the time of this recording. It’s a few weeks out. And we’re thinking about like the kind of ways that math teachers sustain a disposition that is joyful. How are you feeling right now, as far as going back to class after this summer? Are you feeling excited, anxious, some combo, tell us about it.

Kanchan Kant (16:01):
I would say combo, but more excited than anxious. I was on maternity leave, as I mentioned, before the school year ended, and I missed the students dearly. Like, my students are what gives me hope in the darkest times. They are thoughtful. They’re empathetic. They’re so eager to learn. And very soon into my teaching career, I realized that if I take the time to get to know my students and make them feel safe and seen in my class, teaching them math would be so much easier and so much more fun. So I’m a little worried about this being like fourth year into the pandemic, but let’s see. Last year I felt the students were finding it difficult to interact with and work with their classmates because they had not been doing it for so long. So I’m hoping this year would go a little better and I’m really looking forward to working with them and building community and see how it goes.

Dan Meyer (16:53):
So if I’m understanding you correctly, you are feeling very well recharged here. You had basically an extended summer with this maternity leave, basically just like a lot of rest and relaxation over the last, like several months. Um, if I get you here. So anyway, I’m glad for that for you. And, yeah. I also hear you on the difficulties of teaching post pandemic or mid pandemic. Anyway, thanks for sharing that.

Bethany Lockhart Johnson (17:19):
What I love is I hear you being so intentional, like thinking about those relationships and thinking about that community that you want to build, you know? How do you hope that you’re gonna cultivate joy in your teaching this year? I mean like, are there certain routines or disciplines that you specifically call forth or that you think other teachers should think about?

Kanchan Kant (17:41):
So at the start of every school year, I dedicate like about three to four weeks to set up the classroom culture, both social and academic. I call my classroom a learning community. We start with community circles, we do icebreaker activities, group building and all those kinds of things. But most importantly, we do a lot of collective problem solving. So I try to present students with problems, which can be solved using multiple strategies and have multiple entry points, basically they are low floor, high ceiling problems. These could be stretch problems that they have seen before, like concepts that they already know or logical puzzles, or just wrapping their heads around different problems. Then I have students share their strategies. The more strategies they have on the board, the more successful I think the problem was. Every year, inevitably, students come up with strategies that I’ve never ever seen before for the same problems that I do.

Kanchan Kant (18:35):
And so I have students come up to the board, they would share their strategies. If they’re not ready for that, they would walk me through their strategies. And I would write their name on the board with different colored markers and everything. Basically to give them choice and agency. It also shows them that the process of doing the problem is so much more important than just getting the right answer and that it is okay to make mistakes in our learning community. I use a lot of vertical whiteboards, some concepts and problems align so well with the vertical surfaces, especially when students can explore together, learn from each other. So I do a lot of that. As for routines, I would say consistency is the key. I consistently reinforce that I want to hear multiple strategies, that it is okay to make mistakes. I am willing to learn from you as much as you’re willing to learn from me. So all like that consistency in culture more than the routines, is I feel important to bring that joy.

Dan Meyer (19:29):
That’s super interesting. Thanks for that. So I’ve heard, I hear two common objections or two common concerns to using rich tasks or doing problem solving. And I think I heard like answers to those two common reservations within what you described there, but I wonder if we can kind of bring it to the surface. And so one of the reservations is around the time that those problems take and another is that teachers often feel like, well, I might be surprised, you know, I might not know what to do with what a student does. And I thought I was hearing like some very interesting answers to both of those kinds of reservations from you, but would you just surface those up if you have some.

Kanchan Kant (20:09):
So in terms of time, I feel if I spend the time at the beginning of the year, setting up that community and doing those problems, it makes learning the math and learning the concepts much more faster throughout the rest of the year. And even when I am trying, like, even throughout the year, if we are doing a warm up problem, as I call it, which has multiple strategies, that’s gonna clarify so many more concepts when we talk about those five, 10 strategies of doing the same problem, then going through multiple problems to clarify those concepts. So for me, it actually saves time instead of taking more time.

Dan Meyer (20:43):
Hmm. That’s super interesting. It’s an investment I’m hearing from you that, yeah, you might not be hitting the curriculum quite as hard early on, but that all of a sudden you’re in the spring and it’s like, oh wow, we’ve been moving so much faster through territory that has been more challenging. What would you say to you know, comfort concerned educators or to address the concern that I don’t know what I’ll do with these five, 10 different strategies. You say, I always see strategies that I’ve never anticipated. Like, it’s a good thing, you know, like you’re happy about that. I think that’s a very intimidating thing for lots of educators. What would you say to that?

Kanchan Kant (21:19):
I think like, for me, it’s a good kind of discomfort. That means like a student is teaching me something, which is actually doing two things. One modeling for them that I’m willing to learn and that I don’t know everything. And two, also telling them that they’re mathematicians. They know what they’re doing. They’re not just receivers of math, they’re actually creating it. So for me, that is very, very important.

Bethany Lockhart Johnson (21:43):
I love that so much. When you think about your students and you’re about to start this new school year, how do you hope your students will experience math in your classroom?

Kanchan Kant (21:53):
So I hope my students can see the beauty and joy of math. They can see that math is a way to see the world and not as something we have to do to get through school. So my hope for my classroom is that we can learn to problem-solve and persevere through problems and learn from each other and not just get through the curriculum. Because like, I think math is a wonderful way to learn these skills, which are so important when you get out of high school. Most importantly, I just wanna make sure that my students see themselves as mathematicians. And like one of the things that like I have to share with you that, because one of my highlights for the year has to be the Desmos art project. I do it every year for the past three years, I think since I’ve started teaching sophomores. And I do it as a unit assessment for functions and my students design something that is meaningful to them, using all the different kinds of functions and colors and shading and everything that you can think of in Desmos.

Kanchan Kant (22:49):
Thank you so much for that though. It is such a cool way for me to see them do that. Like I have seen such amazing creations. One of my students once made a scaled working model of a solar system wherein the planets were rotating at relative speed. The Saturn had rings and they were like asteroids and everything. And then it was beautifully done. Then there was another one who did a very, very detailed whale scenery, her reasoning. I wanna be a Marine biologist and I wanna study whales. So this is what is meaningful to me. So like that one project is just a culmination of everything that I want students to see in math and in my classroom. And like I do more of those kinds of things, but that is one thing that it’s one of the highlights of my year.

Dan Meyer (23:32):
That’s awesome. I love hearing that. Yeah. Shout out to the team at Desmos Studio for building and continuing to develop a tool list that so good for art and animation, even, in addition to some mathematics with a more computational kind. Yeah, that’s really exciting. What’s interesting to me is that you teach high school, and I think that like students at that age have a very well-defined sense of what math is and who they are as mathematicians. And then along you come, you know, and like offer this really interesting disruption, you know, in their sophomore year of high school that like, oh, this can be totally different, this relationship who I am. And that’s just really exciting. I imagine it’s a very surprising year. I would imagine that first month, I would imagine is a very surprising month for a lot of your sophomores.

Kanchan Kant (24:20):
Yeah, it is. I mean, that’s why I take that time to build that community because then that sets the tone and the relationship that we’re gonna have for the rest of the year. Students get to know how to work with each other. They get to know each other, that whole piece is like super important because of that.

Dan Meyer (24:35):
Yeah. That’s awesome. So here’s the thing, like we’re exploring these ideas about joyful math teaching and what it will take to cultivate restore, reclaim joy in math, teaching this next year. And you’ve offered us these really interesting ideas some, some very, you know, philosophical and some technical about how you spend time in ways that lead to joy in the spring for you and your students. Love that. We don’t want to as hosts, as researchers, investigators of this joyful math teaching idea, we don’t wanna say it’s all up to teachers to change their mindset, to do different technical practices, and that will lead to joy. We also wanna be really attentive to the environment that surrounds you, the people who are around to support you, the policy makers, the social structures that influence your joy in very significant ways. So what we would love to know from you is, how are you supported by the greater educational community in keeping your joy in your work? I’m thinking, especially about administrators, you know, front office, staff, parents, even, can you name a few ways for those sorts of people who listen to this podcast, how they can cultivate a math teacher’s joy this coming year?

Kanchan Kant (25:54):
I would say trust. I think more than anything, educators want administrators, parents, the greater educational community, to trust them to be professionals and experts in what they do. That does not mean that we don’t want to learn, that we don’t want feedback, that we don’t wanna get better. It just means that we keep the wellbeing of our students as our top priority. And we would like to be trusted to do just that. Also just keeping in mind that whether we like it or not, we are still adjusting to the new normal while recovering from the worst of the pandemic times. A lot of us are recovering from trauma, a lot of our students are recovering from trauma, and we need time and space for our social and emotional wellbeing.

Dan Meyer (26:35):
Yeah. I’m really curious, Kanchan, you’ve done a lot of work in your area with your grading team and in thinking about equitable and biased resistant instruction. I’m curious how you see those efforts lining up with creating joyful math learning conditions for all students, not just students from a dominant culture of math doing, let’s say.

Kanchan Kant (26:55):
For me, creating an equitable environment in a classroom is most important because once you have that, that’s when you have the relationships, that’s when you have the culture, that’s when all students actually thrive. So to that end, our school and our department has been doing a lot of work around grading practices. We actually assess how we grade students, where the bias is, what we can do to make them more bias resistant. Should we move to mastery based grading? Like that’s something I’ve been experimenting with for the past two years. Through the pandemic, I started doing mastery based grading so that my students can get more opportunities to show that they have learned the content. And so like just little things which help bridge the opportunity gap. I would say another project that our school undertakes is called the calculus project wherein we have students in Black, Latinx, and low income families sign up for that and are recommended for that. And then we do summer classes and yearlong support to preview the material for next year, not as a remedial class, but to actually set students up for success in AP classes for the coming year. So we have the community buildup. We have the courses we have like math support. It’s a very beautiful thing actually. And I’ve been working with that program for four years now. So yeah, so those are my ways of creating more equity in our school.

Bethany Lockhart Johnson (28:19):
That’s so beautiful and I deeply, deeply wish you had been my high school math teacher. And I have to say that the theme that I kind of keep hearing is this intentionality. How you are so intentional about your work, not just with what your students are learning, but how they’re learning it, how they are engaging with this subject and how they are building their own relationship. You talked a little bit about your relationship over the years with mathematics, but how are your students building that relationship? And so I’m just very appreciative of you sharing that with us and with our listeners. And we are so excited to have learned a little bit about, like, I feel like I got a little mini peek into your classroom.

Kanchan Kant (29:03):
Thank you.

Bethany Lockhart Johnson (29:04):
And can I say that if you are listening to this prior to October at NCTM Los Angeles, you will get to hear Kanchan Kant speak at Shadow Con. Can I give that away, Dan? Is that, is that …

Dan Meyer (29:23):
You can drop that. Yeah, It’s pretty top secret.

Bethany Lockhart Johnson (29:26):
Can I drop it?

Dan Meyer (29:27):
Yeah. Do it. Yeah.

Bethany Lockhart Johnson (29:28):
Dan and I will be in the audience cheering you on. It’s been a joy to learn with and from you, and we are so excited to just, you know, kind of keep marinating on some of these ideas about how we can continue to be intentional about creating joyful math spaces for our students. Thank you so much for joining us today.
Kanchan Kant (29:49):
Thank you so much. It was a real pleasure.

Dan Meyer (29:57):
So Bethany, I loved hearing Kanchan talk about both her, just her joyful personality, but how she cultivates joy through craft and technique through, you know, through the various ways she interacts with students in intentional ways, that those make the job more joyful for her. And I thought it was really interesting to hear her talk about how autonomy is the thing that she needs most in her job environment to feel like she can be joyful in her work. In that context, I saw … something on Twitter popped up for me in my, you know, my many Twitter wanderings. This is a segment we might call, Dan finds something on Twitter and shares it with Bethany. Which we’ll tighten that up a little bit, but I’m sending this over to you right now, and I’d love to know as you check this out, what you’re seeing and what you’re thinking and we’ll chat about how it relates to our interview here in a moment.

Bethany Lockhart Johnson (30:47):
All right. I’m ready, send it over. It’s opening. So this appears to be a document by the way, outlining, maybe it’s a district, maybe it’s administration, they’re outlining expectation type and expectation guidelines. Hmm. Okay. And these are lesson plan expectations. Expectation type. Timeliness. Plans are due no later than 6 p.m.. Friday prior to the week of instruction. Comprehensive, all activities for the week for all subjects taught should be included and complete by due date and time. Plans should have at minimum, the following, see template for detail. Okay. So then it goes through the things that the plans need to have, the topic title, target, the objective, the activities, the sequence, the display agendas to be displayed backward design. Okay. So basically <laugh>, we were just talking about, overwhelm. And when I see this document, listeners, have you ever received something from your administrator or anyone, let’s take it more broadly, that is requesting something of you that would take so much time to complete and be so out of touch with your lived reality that it really genuinely sucks the joy out of the experience.

Bethany Lockhart Johnson (32:25):
So the first thing that I see that this document, and again, the goal of whichever district’s plan this is, is that these expectations will lead–now, mind you, I am a fan of like, you know, looking ahead, I’m not a like, oh, hey, what am I gonna teach in five minutes? No, but the idea that then it lays out all of the things in such detail that you’re gonna be teaching feels like one of those pacing guides where, oh, move on to the next page, whether or not your students have any sort of sense making whatsoever. So my first thought is, oh, sad. I have to stay here. I’ll be there past 6 p.m. But I’m gonna be there trying to make the plans for the next week based on what I think my students have learned. Hmm it’s sounds like a little bit of a bummer. Dan, what did you think when you saw this and did I do a fair description of what it is?

Dan Meyer (33:25):
No, it’s, it’s a tough one to describe, ’cause it’s basically a wall of text and commands from an administrator who like, I just have to imagine has just like acres and acres of teachers trying to beat down their door to teach at this school, if this is how you’re gonna treat your teachers. I mean just, yeah. The idea of having a week… I’m with you, you don’t wanna just like, just jump in by the seat of your pants, but the idea of having a full week of lessons for every section you teach, every prep you teach, planned and submitted with every minute, basically morseled out to different goals. It says down here, you gotta like, for all of these, download a CSV of grades and whatnot and attach those. It’s the sort of thing, like you said, there are some edicts that you get from administration where you just have to laugh or just like, you have definitely missed like what I am willing to do here. It’s so far beyond. Yeah. I can’t imagine it. And it just felt like, yeah, it was a great way to get teachers like Kanchan to feel like a real lack of autonomy. Like it’s this would not work. I don’t think.

Bethany Lockhart Johnson (34:33):
And it’s not even like willing to do. Like, let’s say you’re even willing to produce it. Let’s say that me, the rule follower is like, okay. I’m gonna attempt to meet these demands. One, most teachers were just, you know, they probably would put baloney down there anyway. Not saying that I would, but I’m saying like, it’s clearly just a hoop that they’re having to jump through and two…

Dan Meyer (35:04):
Yeah. Compliance, right?

Bethany Lockhart Johnson (35:05):
Yeah. Compliance, compliance. There you go. And two, yeah, it feels like it’s about control and not trusting the teacher. And I love that. Kanchan said that trust is what she needs. Right? You’re hiring me. Yes. I still have lots to learn, but you’re trusting me and you’re creating an environment where I can continue to learn from and with my students. And if I was being asked to submit this tome every Friday before six, that is predicting, what does it say, anticipating the steps necessary for student mastery? You know, I kind of feel like maybe it’s like that one or two teachers where maybe they feel like, oh, I don’t trust that teacher or that teacher isn’t doing a good job, whatever. We better do this for all of the teachers, but then it’s not gonna change the practices of that one teacher and all the other teachers are gonna be resentful.

Dan Meyer (36:00):
Like if there was like feedback that came back to you on, you know, on lesson plans or there was some like something that was very constructive or productive, like maybe that would be different, but it really just feels like these are gonna go into a digital drawer somewhere and not be looked at, at all.

Bethany Lockhart Johnson (36:15):
Yes. The digital drawer. Like I’m gonna send you this report and then nothing is going to happen with it. Except that four hours of my time. Well, you wouldn’t do it, but <laugh>…

Dan Meyer (36:29):
You’ve worn me down. You’ve worn me down. I’m now putty in your hands and more compliant for the next thing. And I also just wanna shout out the administrator today, who I emailed asking about like a teacher participating in a project and this administrator said, I have a standing policy not to email teachers over summer break, which you know, as administrators out there doing just the good work, you know, trusting teachers, watching out for them, trying to be a force multiplier for teachers, making the road wider, the way easier for teachers. So shout out to y’all doing the out there. Really appreciate that.

Bethany Lockhart Johnson (37:04):
Okay. Wait, wait. About that email thing, quick question. Did you ever check your email over the summer?

Dan Meyer (37:11):
Uh, yeah. That’s one way in which I was the, you know, I just love email, you know? Oh. Someone wanted to reach out. Oh, oh, Banana Republic wants to tell me about new clothes that are on offer. <laugh> I mean like, it’s just, I love those personal emails. So yeah, I did check my email over the summer.

Bethany Lockhart Johnson (37:26):
Somebody emailed me recently and they emailed me at like two in the morning. And because I currently have a toddler, I received the email at four in the morning because you know, the best thing to help myself fall back asleep is to hop on my phone, right? Like I’m already up trying to get my toddler back to sleep. I might as well start scrolling. Anyway, so the person had this little thing at the bottom of their email and it said, I have, something to the effect of, I have really like wonky work hours. I may be sending this outside of the like more standard nine to five. But please don’t feel pressure in any way to respond outside of your time. Would you appreciate that, seeing that or does it make you feel like you should respond? ‘Cause I almost responded at four in the morning, and maybe that says something about …

Dan Meyer (38:15):
They’re telling you not to respond.

Bethany Lockhart Johnson (38:16):
I know it was helpful.

Dan Meyer (38:18):
It says don’t, but you’re like, what if they’re saying that because they really expect me to respond and this is one of many ways that you and I are different. I’m always happy to see that.

Bethany Lockhart Johnson (38:29):
Do you respond? I’ve texted you in the evening because you know I have some wonky hours. Do you respond to things, like where’s your boundary there? Or when you were in the classroom, where was your boundary there? Did parents have your phone number?

Dan Meyer (38:43):
No. I gave kids my cell phone number for a couple years and it was a wobbly experiment. But parents will email, you know, back and forth with you. And I think the best thing to like … I love just like adding some friction, some latency into the kind of the chain, you know, like I hate going like back and forth, like da, da, da, da, and then like respond and then da, da da respond. And it just like goes back and forth. So just like just sitting back for an hour or two hours, you know, not responding, just let someone cool down, calm down. Email just gets you more email. That’s like if you send an email, you are just making it more likely to get more email. It’s a, you know, it’s a problem.

Bethany Lockhart Johnson (39:20):
Are you one of the zero people?

Dan Meyer (39:23):
My inbox is at zero. Most days before work.

Bethany Lockhart Johnson (39:26):
You’re joking!

Dan Meyer (39:28):
I end work every day with inbox, at zero.

Bethany Lockhart Johnson (39:31):
You’re joking!

Dan Meyer (39:32):
That’s just, you know.

Bethany Lockhart Johnson (39:33):
Who are you?

Dan Meyer (39:34):
You know, you should take my life coaching, Bethany. I’ll give you a discount since we’re math teacher, lunch pals. But, um yeah. I can help.

Bethany Lockhart Johnson (39:44):
Thank you for qualifying where our pal-dom lives. I wouldn’t even tell you how many are in my inbox. Point is, if you are actively starting the school year, we celebrate you and we are here and over the next few months, we’re gonna be diving into joyful math and that definition’s gonna keep evolving. But I wanna say something that is making me feel a little joyful, Dan. You ready?

Dan Meyer (40:15):
Tell me.

Bethany Lockhart Johnson (40:16):
You and I, in person, at NCTM, the National Council for Teachers and Mathematics. It’s coming up and we are going to be recording Math Teacher Lounge, live. Live, in person! And I hear there’s gonna be like a t-shirt cannon and there’s gonna be, you know, like musicians marching through the aisles or something.

Dan Meyer (40:46):
A marching band?

Bethany Lockhart Johnson (40:46):
A marching band!

Dan Meyer (40:46):
Trained animals. Yeah.

Bethany Lockhart Johnson (40:48):
But the point is, I’m so excited, Dan. And you know, when I see you, I might just, it’s been so long since I’ve seen you, Dan. I’d love to give you a big old embrace.

Dan Meyer (41:04):
You might just, you might just cry. Yeah. Yeah. It’ll be great. Yeah. It’s gonna be awesome for you folks to see me and Bethany have a real awkward first hug since the pandemic. And, uh, but it’s gonna be a blast to hang with us in person. We’ll have some special guests, probably, some interesting segments. You folks should stop on by at NCTM, if you’re gonna be there. Highly recommended.

Bethany Lockhart Johnson (41:29):
Now, we will be broadcasting that episode. You’re gonna get to hear … we’re gonna record it live. It’s gonna happen. In the meantime, you can find us at MTLshow on Twitter, or you can find us in our Facebook group, Math Teacher Lounge. We can’t wait to hear from you. And we’d love to hear what makes math joyful for you? Where can we add a little bit more joy to you this, this season? So thrilled to be back. Thanks for listening.

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What Kanchan Kant says about math

“Creating an equitable environment in the classroom is most important because once you have that, that’s when you have the relationships, and that’s when all students actually thrive.”

– Kanchan Kant

Meet the guest

As a math and computer science teacher at Newton North High School, Newton, MA, Kanchan has been sharing her love for math with her students for the past four years. Kanchan is instrumental in setting the culture and ethos of the mathematics department at her school in her role as the Assistant Department Head. Kanchan also leads the Math Department Grading Team and has been instrumental in making grading policies which are more equitable and bias resistant. In her new role as a Transformative Leaders of Massachusetts Fellow in collaboration with Springpoint and Barr Foundation, Kanchan looks forward to making equity and joy of learning the foundation of many more classrooms.

Businesswoman with long dark hair, wearing a dark blazer and blue blouse, poses in a professional portrait against a light background, representing math programs.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Big Ideas

Grade 6

Chapter 2: Fractions and Decimals

Big IdeasDesmos Classroom
Lesson 2: Dividing FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 2: Decimal Diagrams and Algorithms
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 7: Dividing DecimalsUnit 5
Lesson 13: Movie Time

Chapter 3: Ratios and Rates

Lesson 1: RatiosUnit 2
Lesson 1: Pizza Maker
Lesson 4: Fruit Lab
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 3: Using Ratio TablesUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Graphing Ratio RelationshipsUnit 2
Lesson 10: Disaster Preparation
Lesson 5: Rates and Unit RatesUnit 3
Lesson 6: Soft Serve
Lesson 6: Converting MeasuresUnit 3
Lesson 1: Many Measurements

Chapter 4: Percents

Lesson 1: Percent and FractionsUnit 3
Lesson 9: Lucky Duckies
Lesson 2: Percent and DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Chapter 5: Algebraic Expressions and Properties

Lesson 2: Writing ExpressionsUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 3: Properties of Addition and MultiplicationUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 4: The Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)

Chapter 6: Equations

Lesson 1: Writing Equations in One VariableUnit 6
Lesson 1: Weight for It

Chapter 7: Area, Surface Area, and Volume

Lesson 1: Areas of ParallelogramsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Lesson 5: Surface Area of prismsUnit 1
Lesson 10: Renata’s Stickers

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Lesson 1: IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 2: Comparing and Ordering IntegersUnit 7
Lesson 4: Order in the Class
Lesson 3: Rational NumbersUnit 7
Lesson 4: Order in the Class
Lesson 7: Writing and Graphing InequalitiesUnit 7
Lesson 7: Tunnel Travels

Chapter 9: Statistical Measures

Lesson 1: Introduction to StatisticsUnit 8
Lesson 3: Minimum Wage
Lesson 2: MeanUnit 8
Lesson 11: Toy Cars
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 4: Measures of VariationUnit 8
Lesson 11: Toy Cars

Chapter 10: Data Displays

Lesson 2: HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 4: Choosing Appropriate MeasuresUnit 8
Lesson 3: Minimum Wage
Lesson 11: Toy Cars

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Big IdeasDesmos Classroom
Lesson 1: Rational NumbersUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Adding Integers
Lesson 4: Subtracting Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Adding Rational Numbers
Lesson 5: Subtracting Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 10: Integer Puzzles

Chapter 3: Expressions

Lesson 1: Algebraic ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 2: Adding and Subtracting Linear ExpressionsUnit 6
Lesson 10: Collect the Squares
Lesson 3: The Distributive PropertyUnit 6
Lesson 10: Collect the Squares

Chapter 4: Equations and Inequalities

Lesson 1: Solving Equations Using Addition or Subtraction
Lesson 2: Solving Equations Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 4: Writing and Graphing InequalitiesUnit 6
Lesson 16: Shira the Sheep
Lesson 5: Solving Inequalities Using Addition or Subtraction
Lesson 6: Solving Inequalities Using Multiplication or Division
Unit 6
Lesson 16: Shira the Sheep
Lesson 7: Solving Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Chapter 5: Ratios and Proportions

Lesson 1: Ratio and Ratio TablesUnit 2
Lesson 1: Paint
Lesson 3: Identifying Proportional RelationshipsUnit 2
Lesson 6: Two and Two
Lesson 3: Measuring Around
Lesson 5: Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops

Chapter 6: Percents

Lesson 1: Fraction, Decimals, and PercentsUnit 4
Lesson 1: Mosaics
 
Lesson 4: Percents of Increase and DecreaseUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 5: Discounts and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)

Chapter 7: Probability

Chapter 8: Statistics

Lesson 1: Samples and PopulationsUnit 8
Lesson 10: Crab Island
Lesson 2: Using Random Samples to Describe populationsUnit 8 
Lesson 10: Crab Island
Lesson 3: Comparing Populations
Lesson 4: Using Random Samples to Compare Populations
Unit 8
Lesson 10: Crab Island

Chapter 9: Geometric Shapes and Angles

Lesson 1: Circle and CircumferenceUnit 3
Lesson 3: Measuring Around
Lesson 2: Areas of CirclesUnit 3
Lesson 9: Area Challenges
Lesson 5: Finding Unknown Angle MeasuresUnit 7
Lesson 4: Missing Measures

Grade 8

Chapter 1: Equations

Big ideasDesmos Classroom
Lesson 2: Solving Multi-Step EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 3: Solving Equations with Variables on Both SidesUnit 4
Lesson 5: Equation Roundtable

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Lesson 2: Angles and TrianglesUnit 1
Lesson 12: Puzzling It Out
Lesson 4: Using Similar TrianglesUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Chapter 4: Graphing and Writing Linear Equations

Lesson 1: Graphing Linear EquationsUnit 3 Lesson 4: Flags
Lesson 2: Slope of a LineUnit 3 Lesson 4: Flags
Lesson 3: Graphing Proportional RelationshipsUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Graphing Linear Equations in Slope-Intercept FormUnit 3
Lesson 4: Flags

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Chapter 6: Data Analysis and Displays

Lesson 1: Scatter PlotsUnit 6
Lesson 3: Robots
Lesson 2: Lines of FitUnit 6
Lesson 4: Dapper Cats
Lesson 3: Two-Way TablesUnit 6
Lesson 11: Finding Associations

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Representations of FunctionsUnit 5
Lesson 5: The Tortoise and the Hare

Chapter 8: Exponents and Scientific Notation

Lesson 1: ExponentsUnit 7
Lesson 3: Power Pairs
Lesson 2: Products of Powers PropertyUnit 7
Lesson 3: Power Pairs
Lesson 6: Scientific Notation
Lesson 7: Operations in Scientific Notation
Unit 7
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 4: Root Down
Lesson 3: Finding Cube RootsUnit 8
Lesson 4: Root Down

Chapter 10: Volume and Similar Solids

Lesson 1: Volumes of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volumes of ConesUnit 5
Lesson 13: Cones

Centering students in math curriculum adaptations

Starting with a high-quality math program

In her research article, “Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula”, Janine Remillard described curriculum use as a dynamic and ongoing relationship between teachers and resources—a relationship shaped by both the teacher and characteristics of the resource.

I have found that while certain characteristics can make a math curriculum high-quality, it is only through its relationship with teachers that it creates truly meaningful math experiences for students.

In my own teaching experiences and now back in classrooms with teachers, I am convinced that no matter how well-constructed a lesson, it only gets better as teachers plan collaboratively and center their students.

Shaping lessons for the students in your classroom can be challenging because there is not one right way or time to adapt a lesson, and the reasons we adapt vary.

Sometimes we make relatively small tweaks to the wording of a prompt, a question the teacher should pose, or the timing of an activity.

Other times we make more substantial changes to the task or task structure in order to more clearly move toward the learning goal based on what we are seeing and hearing from students.

And then there are the times we realize in the midst of an activity we should have made an adaption in our planning.

I recently taught a 5th grade fractions lesson that provided a perfect example of the dynamic nature of the work.

Engaging in a math curriculum activity

This particular lesson falls at the end of the fraction addition and subtraction unit.

The Warm-Up of this lesson is a Number Talk, which made sense to the 5th grade teachers and I, given the unit focus.

We reviewed the mathematical concepts and problems in our planning session, anticipated that students might find common denominators, and agreed that the synthesis discussion around denominator choice aligned with the problems. 

Four addition problems with fractions—1/8 + 5/8, 1/8 + 6/16, 1/8 + 1/3, and 1/8 + 5/12—are arranged vertically to support math students and center student ideas in the math curriculum.

While we anticipated that students would successfully add, the number choices in the string led students to solve each one the same exact way, with the only difference being whether they stated their sum in simplest form or not.

Halfway through, we could see the majority of the students were getting bored and it was hard to infuse curiosity and excitement around denominator choice because students had already generalized a way of finding a common denominator—which at this point in the unit was great!

In the midst of the Number Talk, we paused and debated pivoting our focus to the problems in relation to one another rather than denominator choice. But we knew that doing that would add extra time to the lesson, when we needed the majority of the time for the activities that followed.

So we wrapped it up and moved on, knowing we had time to discuss our choice in an upcoming planning session.

Adapting in ways that center student ideas

After class, I couldn’t stop thinking about revisions I would make if we had the opportunity to plan it all over again. Because although the problems in the string supported mental calculation and aligned with the lesson activities, the students needed something different at this point in their learning.

After reflecting with colleagues, we decided the timing of that particular Number Talk for these students was too late in the unit and wondered if a different routine would have made it more engaging.

Using that Number Talk as a rough draft (shout out to Mandy Jansen), I played around with different number choices and routines we might use in a second take on that lesson. 

If we wanted to stick with the same task structure, we could adjust the numbers to create a new Number Talk or True or False? routine that more explicitly encouraged relational reasoning and use of the properties.

For example, the following problem strings still attend to denominators when adding fractions but also open up the space for more interesting and engaging student discourse. 

Number Talk

Four horizontal equations invite math students to add fractions with different denominators—1/8 + 5/8; 1/8 + 1/2; 1/8 + 1/2 + 9/24; and 1/8 + 1/2 + 9/24 + 6/4—centering student ideas as part of a dynamic math curriculum.

True or False?

Four lines of math equations with fractions involve addition, comparison, and equality symbols—featuring denominators like 8, 16, 3, 7, and 24—centered on student ideas to enhance the math curriculum for eager math students.

If we wanted to use a different structure altogether, we could try the Which One Doesn’t Belong? routine to provide opportunities for students to notice other interesting aspects.

In this activity, students share reasons why one of four items—in this case, equations—doesn’t belong. There is no single right answer because each object could both belong and not belong, depending on the student’s criteria. (If you’ve never tried this routine, it’s a must!)

A set of four boxes labeled A to D, each showing a math equation involving the addition of two fractions and their simplified sum—perfect for centering student ideas and matching student needs in any math curriculum.

Because I couldn’t wait until this lesson next year to see what students would do with one of these ideas, I asked them to write about the Which One Doesn’t Belong? The variation among their ideas was exciting.

While I could still see attention to the denominators as in the original Warm-Up, students were now describing their ideas in much more unique ways. If this had been the original Warm-Up, it’s not hard to imagine how much more engaged students would have been—and how much more teachers would have learned about their thinking. 

A worksheet from the math curriculum asks which fraction equation doesn't belong; all options are shown worked out, and a handwritten note concludes that none are wrong if you do the math, centering student ideas and matching student needs.
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A
Student response 2 to the "Which One Doesn't Belong Question" This students picks option B
Student response 2 to the "Which One Doesn't Belong Question" This students picks option B
Student response 2 to the "Which One Doesn't Belong Question" This students picks option C
Student response 2 to the "Which One Doesn't Belong Question" This students picks option D
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A and D

Learning from within the work of teaching

Curriculum materials have shaped my teaching and learning since the beginning of my time in the classroom. They then became the focus of my work at Illustrative Mathematics and now in my current work at Amplify.

I am a strong advocate for high-quality curriculum materials, and at the same time, I also believe that every curriculum can always be improved to better meet the needs of students and teachers.

I continually recognize and appreciate the time I get to spend planning, teaching, and reflecting with teachers about their dynamic and ongoing relationship with curriculum materials.

These opportunities to learn from within the work of teaching are invaluable inputs to our current work at Amplify, where we have the exciting opportunity to improve the characteristics of math resources currently in schools. 

Want to learn more from Kristin Gray? Watch her webinar!

S3 – 06. Bethany and Dan take on Twitter!

Promotional graphic for Math Teacher Lounge Season 3, Episode 6, featuring Bethany Lockhart Johnson, Educator, and Dan Meyer, Director of Research at Desmos.

In this episode, Bethany and Dan take a look at several tweets that caught the most fire on Twitter during the 2021-2022 school year. The pair answer questions about viral teaching methods, the best teaching advice you can give in three words, and if students should use pencils or pens in class. Join them as they take on those questions and several others in a fast-paced episode.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:02):

Hey folks. Welcome back to the Math Teacher Lounge. I’m your co-host, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I am Bethany Lockhart Johnson. And I’m your co-host, Dan! Hi!

Dan Meyer (00:12):

We’re co-hosts! Hey! Great to see you.

Bethany Lockhart Johnson (00:13):

Dan, this is the last episode of Season 3. Three seasons!

Dan Meyer (00:19):

It’s gotta have a cliffhanger. What will the cliffhanger be? You know?

Bethany Lockhart Johnson (00:22):

The cliffhanger is that we love having guests! It’s one of our most favorite things, because selfishly, we love to talk to all of these amazing folks who are doing this interesting research and thinking about amazing things. But for this last episode, it’s just you and I, Dan. Cliffhanger!

Dan Meyer (00:40):

Yeah. I like this. I like this. So the cliffhanger was last episode, and people are all like, “So who’s the last guest gonna be of the season before we roll out into summer?” And yes, as Bethany said, we love all the fascinating guests we’ve had on throughout these last few seasons. And we realized…who is more fascinating to each other than both of us? You know, let’s talk to each other about things, right? <Laughs> You get that! You get that! Or am I alone here in this? We had this idea about what we should talk about here, and that’s this: I am on Twitter a lot. I’m @DDMeyer on Twitter; throw me a follow; might follow back; who knows? I don’t tweet much. Bethany, what’s your handle on Twitter? Let ’em know.

Bethany Lockhart Johnson (01:22):

I’m @LockhartEdu, and I was much more active pre-mamahood. But I’m still up in there. Go ahead.

Dan Meyer (01:30):

Yep. In there. Yeah, great. So I’ve been keeping track of the hottest conversations in math education Twitter, the conversations that the most people who kind of describe themselves as math teachers in their bios and whatnot have been replying to. We’ve got some little things working in the background, keeping track of this sort of thing. And so we are gonna bring you folks some of those extremely hot conversations, and even better than the questions—which we hope you’ll reply to and tag us in your replies—even more than those questions, we’ll bring you our answers—our answers!—to those questions. Can you believe that? We’ll fully settle these questions! Won’t we, Bethany? My gosh, won’t we?

Bethany Lockhart Johnson (02:15):

Jeez Louise! No! Dan Meyer, the point is not our final word on it! The point is this episode, we’re furthering the conversation. We wanna hear from listeners about what do you think?

Dan Meyer (02:25):

Right. You’re right. You all need someone in your life like Bethany who will help you become the best version of yourself. So here’s the deal. We have several questions in a few different categories. We’re gonna bust through some quick ones, pretty quick. And, uh, there’s some meaty ones as well. Let’s get into it! The first questions come to you all, and us, courtesy of MTL guest Howie Hua, who has a renowned knack for just creating math memes, but also conversation starters that really capture the curiosity and answers of of a grateful nation. So Howie’s first question, which I’ll pose to Bethany, is, “What’s your favorite number?” Bethany? And why is it your favorite number?

Bethany Lockhart Johnson (03:14):

Oh, I love it. OK. Well, the first thing that came to my mind is 12. ‘Cause It’s a highly divisible number. I mean, 2, 6, 3, 4—I love it. And it coincides with the day and month of my birth. Which, like, the double-digit…come on, 12, 12, 12, 12. I dunno, am I giving away, like, my bank security code <laugh> or anything by saying that?

Dan Meyer (03:41):

Yeah. What’s your favorite PIN?

Bethany Lockhart Johnson (03:43):

Let me change my PIN. Yeah, it’s just such a happy, happy number. Well, 12 is, you know, 10 and 2. Two more. Anyway. Love it. What about you, Dan? What’s your favorite number and why?

Dan Meyer (03:55):

I’m into it. I’m into it. I think I would choose 16. Because it’s the first number for me when it was like, “Oh, you can keep on making numbers forever!” Where I’m like, OK, 2times 2 is 4. Great. That’s kind of an elemental expression in mathematics. Four times 2 is 8. OK. But then, 8 times 2 is 16, and it’s like, “Oh, you can just keep doubling that thing over and over and over again!” And I can recall feeling pretty excited that numbers are just like, out there for the finding. For the taking. Cool stuff.

Bethany Lockhart Johnson (04:33):

I’m sorry. Wait, I have to interrupt. You went 2 times 4 is 8 and you didn’t go 4 times 4 is 16? You went 8 times 2 is 16? You wanted to keep the 2 the same?

Dan Meyer (04:49):

Yup. Yup. You can keep on doubling. You can keep on doubling numbers and it just keeps on going.

Bethany Lockhart Johnson (04:53):

More evidence that our brain works very differently.

Dan Meyer (04:56):

We learn more about each other…let me keep this rolling with Howie questions. OK? Howie says, “If you could co-teach with one teacher from Twitter, who would you choose?”

Bethany Lockhart Johnson (05:06):

Oh, oh, it has to be a teacher?

Dan Meyer (05:11):

Or anybody, I guess. I mean, like, I know you love Oprah.

Bethany Lockhart Johnson (05:15):

Can I co-teach with Oprah?

Dan Meyer (05:16):

Yup, yeah, so there we are. <Laugh> Yup. OK. Fair enough. We have to work Oprah into every single episode.

Bethany Lockhart Johnson (05:23):

I’d just love to sit and like, we’d read together, we’d read to the students, and then we’d talk…I mean, obviously it’d be Oprah. But if we’re thinking more of like MTBoS, like math Twitter blogosphere-land, I suppose the person I would wanna co-teach with honestly would probably be Allison Hintz. One of our former guests as well. Her book, Mathematizing Children’s Literature, with Antony Smith, that book—I just love the idea of sitting and doing a read-aloud and then diving into some juicy math that’s inspired by what comes out of that read-aloud. So yes, that’s who I pick. Allison! Let’s co-teach!

Dan Meyer (06:00):

<Laugh> Shout-out to Allison.

Bethany Lockhart Johnson (06:01):

What about you?

Dan Meyer (06:03):

I would choose MTL guest Idil Abdulkadir—because, and this relates to Allison and also Elham Kazemi—they talked about, in our episode about teacher time-outs. And I’m choosing someone who I think is—like I’ve never seen Idil teach, but I work with Idil at Desmos and think she’s fantastic. But what I really want in a co-teacher is someone that I can say, “Whoa, time out, do you see what’s going on here? This is really interesting. What should we do next about this?” And have a little strategy sesh in front of the kids and no one gets freaked out by that. And I think that that’d be a pile of fun. Idil seems like she’d be receptive to that kind of interaction, teacher to teacher. So that’s my vote right there.

Bethany Lockhart Johnson (06:48):

Opportunity for you to grow your own practice, Dan.

Dan Meyer (06:52):

Yeah, yeah, exactly. 100%.

Bethany Lockhart Johnson (06:56):

So Dan, I actually have a question for you from Howie. If we’re on the Howie tweet train, I have one from Howie too.

Dan Meyer (07:04):

Howie had some fire tweets, some fire tweets this current year. Yep.

Bethany Lockhart Johnson (07:08):

Dan, I wanna know: Do you prefer doing math in pen or pencil?

Dan Meyer (07:16):

Ooh, yeah. Oh, I see that Howie says, “I don’t mean to start any drama, BUT,” and then asks the question–

Bethany Lockhart Johnson (07:23):

But!

Dan Meyer (07:24):

I think that Howie lives for drama. I think he knows he’s messy. He lives for drama. He knows what he’s doing this with this question here. He knows.

Bethany Lockhart Johnson (07:32):

DRAAAAMAAAA!

Dan Meyer (07:32):

He knows what he’s doing. Yup. So I would just say it depends. Is that cheating? Like if I’m doing math to learn, or if we are learning in that process, then I want to use pen, actually. I wanna see the tracks of the thinking. And if we’re doing it for presentation, like if I’m presenting something, I wanna…I guess that’s an area where I’d be fine to not erase things. I don’t wanna prep it so it’s, you know…I guess you could use pen for presentation also. Just pen. Period. But I wanna see the tracks of the thinking if we’re doing some learning versus presentation. What about you?

Bethany Lockhart Johnson (08:09):

Well, I heard the voice in my head telling one of my kindergartners, “No, you cannot do that in sparkly pen. You need to do it in pencil.” And I was like, “Wait, whose voice is that?” It was one of my math teachers telling me I couldn’t do it in pen! Why couldn’t this kid do it in pen? Sure! Do it in a sparkly pen! So I wanna say do it in pen. And since usually pen is what I have around…I mean, I do crosswords in pen, Dan.

Dan Meyer (08:36):

Wow, wow. With a piece of paper and math, you have lots of room to re-revise and cross off…but those little, little boxes on the crossword, that says a lot about your commitment to pen.

Bethany Lockhart Johnson (08:46):

I got really good at making an A into an H or a P or whatever we need. So I would say, “Hey, if you’re in the room with your kiddos and you’re doing math, if somebody wants to do pen, let them do pen.” But I do know that I’ve seen teachers say you need to do pen so that I can see all of your thinking. So I think I hear what you’re saying. But do you think it should be like a classroom rule or something?

Dan Meyer (09:13):

Oh, no, no, no. I mean, I’m gonna ask you like, “How’d you get to this destination?” And I wanna know process somehow, and I think you’ll get tired of having to explain it verbally rather than just, like, showing. Just don’t erase stuff. Don’t scratch stuff off. Let’s let’s see how you’re getting there. That is what I’m into.

Bethany Lockhart Johnson (09:30):

Thanks, Howie, for that trio of thought-provoking tweets, because I genuinely wanted to know what Dan thought and what our listeners think. I mean, Dan, I gotta say: Howie, you say you don’t wanna cause drama, but I gotta say I’m with Dan on that—

Dan Meyer (09:50):

Got the gift. Got the gift for drama. We’re still friends though. So I’m happy about that. Our next section, I got a few more questions queued up here and these ones relate to advice for educators, advice for yourself. Good advice, bad advice, that kind of thing. So let’s jump in. I would love to know—this one’s from Pernille Ripp—I’m very curious, Bethany, what is the worst teaching advice you have gotten in your life, ever?

Bethany Lockhart Johnson (10:19):

<Laugh> Ooh. OK. Um, worst teaching advice was: “That’s OK, just move on anyway.” And that was in terms of pacing. It was like, students needed to do a deeper dive and the teacher who I was chatting with said, “No, no, it’s fine; it’s fine; just move on. Just move on to the next chapter.” That was probably the worst advice, because no, I don’t think that’s what I should have done at all! <Laugh>

Dan Meyer (10:48):

Right.

Bethany Lockhart Johnson (10:48):

But I was a first-year teacher and I was trying to figure it out. And I learned that that was not good advice. And I understand the pressure of pacing. But it was totally antithetical to the type of listening to my students that I want to do in my craft. And this teacher meant well, but that was not good advice, teacher! <Laugh> What about you, Dan? What is the worst teaching advice?

Dan Meyer (11:13):

I dig that. That feels similar to one of the replies to Pernille here. Frances Klein says, “Never let them know you’ve made a mistake” being particularly bad advice. You know, just this like idea of like moving along, covering your tracks, not backtracking or admitting mistakes, those all feel kind of a piece. The worst advice I think I’ve ever received, and I wasn’t given this often, but it’s echoed by a lot of the commenters here on this tweet, which is “Don’t smile until X, Y, or Z,” where X, Y, and Z are like Christmas, October, December, January. Just the idea that you’ve gotta develop—

Bethany Lockhart Johnson (11:54):

Wait, what?

Dan Meyer (11:55):

<Laugh> Did you never hear this from anybody? Don’t smile until Christmas? Perhaps this is more—

Bethany Lockhart Johnson (11:59):

I’m a kindergarten teacher! Can you imagine? If I don’t smile the second they walk in? The tears?! The parents’ tears?! The kids’ tears?! If I’m just like, stoic?

Dan Meyer (12:07):

Yeah. Well.

Bethany Lockhart Johnson (12:08):

So explain it to me.

Dan Meyer (12:10):

Well, the idea is, is that, you know, for older kids, they’re scoping you, they’re clocking you for weakness, they’re looking at you, they’re looking to take advantage. And so “don’t smile until Christmas” is like, hey, you can always relax. You can always relax your discipline, but you can’t UN-relax it if you start out, you know, Mr. Happy Pants Meyer. Which—

Bethany Lockhart Johnson (12:33):

Smile perceived as weakness.

Dan Meyer (12:36):

Yeah. Very obviously poor advice. Eventually you come to realize that like having a rapport and a relationship that is trusting and warm and demanding, that has high expectations, that’s the best kind of classroom management. Not some kind of persona built around intimidation or stoicism, that kinda thing. So, terrible, terrible advice!

Bethany Lockhart Johnson (13:01):

I feel like I did have a few of those math classes. Yeah.

Dan Meyer (13:04):

Yeah, exactly. <Laugh> You loved them, right? They were like your favorite math classes. It was a blast, right?

Bethany Lockhart Johnson (13:11):

<Laugh> So we have to ask the opposite. Thank you, Daniel Willingham, who said, “What’s the best advice you got?” But hold on, Dan, he didn’t just want the best advice. He wanted the best advice in three words.

Dan Meyer (13:26):

Oh yeah. He doesn’t, he doesn’t want a book or dissertation or even a blog post or even a tweet. He wants just three words.

Bethany Lockhart Johnson (13:32):

I think maybe that might have been to me. <Laugh>

Dan Meyer (13:34):

This is someone who’s doesn’t have much time for this advice, wants it distilled down. I’m just obviously stalling here as I try to think about this. I don’t know, there’s just like so much nuance lost here. I would say, listen to students, listen to students. I can’t say more that, I guess. I guess I’m done. I can’t say more than that there. But you’re in a bad place if you’re not listening carefully to students. How about you?

Bethany Lockhart Johnson (14:04):

  1. Mine is “Ask…lots…questions.”

Dan Meyer (14:11):

Nice. ‘Cause I filled in the word! I filled in the word! I was able to kinda infer that. I did that. I got that.

Bethany Lockhart Johnson (14:17):

Wait, wait, wait, wait! I could have said many! Wait, I could have said “Ask many questions.”

Dan Meyer (14:22):

Strong, strong.

Bethany Lockhart Johnson (14:25):

So yeah. You know, no isolation, like don’t put yourself in a bubble. Ask, not just, not just your students, but the teachers! Ask a lot of questions. You don’t have to have it all figured out.

Dan Meyer (14:34):

Into it. Very much into it.

Bethany Lockhart Johnson (14:37):

Thanks. Daniel. Thanks, Pernille.

Dan Meyer (14:40):

Yeah. Daniel and Pernille, Both great questions there about advice, best and worst. Another fire tweet popped up earlier this year from Dr. Khristopher Childs, which was “Name one thing every educator should stop doing.”

Bethany Lockhart Johnson (14:57):

Oh, I don’t know. This kind of ties into my best advice about asking questions.

Dan Meyer (15:03):

Stop not asking questions?

Bethany Lockhart Johnson (15:06):

<Laugh> Avoid the isolation. I really love this idea of when we can, popping into each others’ classrooms, co-teaching, building this collaborative nature. Elham Kazemi, in our interview, talked about this idea of, like you said, the teacher time-outs, learning from each other. So I feel like if we could stop isolating ourself…and I don’t mean at lunch—sometimes you need to not be in the teacher lounge at lunch. Like if you need a minute, take the minute! But in general, as a practice, how can we not be isolated and instead be learning with, and from, each other? How can we stop the isolation? That’s what I would hope every educator would stop doing. What about you, Dan?

Dan Meyer (15:54):

I think that educators should…this is gonna require a little bit of elaboration. I think educators should stop taking responsibility for things that are not in their zone of influence. I think that as a society we are asking teachers to do more and more, to become more and more of a central fixture holding together with chewing gum and twine all the various parts of a student’s life. From their health, their fitness, emotional health, that we feed students at school. It becomes very tempting, I think, there’s a lot of pressures to blame outcomes, disparate and unjust outcomes later on in life, on teachers. And teachers should just flatly refuse. And to yeah, understand what the job has been set up to do. What it’s good for. And do that with excellence and intent and a lot of effort. And then not take responsibility for the rest of it.

Bethany Lockhart Johnson (16:53):

If I asked five different people about the definition of what a teacher should be doing, I would get five different answers. So I think it’s really interesting that you say that because yeah, many, many hats, which I think, yes, can lead to burnout. Can lead to all sorts of things. We’re asking schools to be all things to all, all people. Interesting. I’m gonna think about that more. I need to hear folks’ response on that, Dan.

Dan Meyer (17:18):

Mm-Hmm. I’m curious too. I mean, yeah, there are definitely things that are in teachers’ responsibility and some that are not. That’s a tough one.

Bethany Lockhart Johnson (17:26):

OK, for help, name an example of each. And what’s something that you think every teacher should not and should be doing. ‘Cause I feel like my brain goes to some things like, you know, I had teachers who were saying, “Well, I don’t wanna have my kids have to have breakfast in my classroom in the morning. That shouldn’t be my responsibility to serve breakfast in the morning.” But I’m like, “But then your kids are eating and they’re gonna be able to learn and be more focused.” Should that be the teacher’s responsibility? I’m not saying it necessarily should, but I’m saying…I don’t know. It gets murky for me.

Dan Meyer (18:06):

Yeah, for sure. I mean, I think that we should, as a country, have a really generous social welfare net so that everyone has food at home. Where a school is not the place where some students have to go to in order to receive nutrition and nourishment. That seems sad to me. And uncommon in developed nations. I think that teachers should watch out for, should be responsible for, the mathematical development of the students they teach, up to a point, they should be responsible for learning math and creating relationships in their classes. I don’t think that teachers should accept responsibility for larger kinds of outcomes, like the health of a democracy or international competition, who goes to the moon first. That kind of thing has historically been placed at the feet of teachers. And it’s tempting when you’re a teacher, I think, to take on that responsibility because it kind of develops your social importance. And I just say, we should say no to that. And get compensation, not in terms of social importance, but rather like in spendable dollars and monies.

Bethany Lockhart Johnson (19:10):

I’m learning more about you, Dan. And you know, this is what I’ve gotten from that answer: If you’re gonna dream, dream big. Right?

Dan Meyer (19:17):

Is that what you got from that? I don’t know. I think I’m trying to dream realistically.

Bethany Lockhart Johnson (19:23):

No, like if we’re gonna say, “Maybe teachers shouldn’t be responsible for serving breakfast in the morning,” well, because we want every child to have access to nutritious and filling food at home and time to eat it in the morning, right? It’s bigger than just, “I don’t want the teacher to have to do this.” So we’re dreaming big. We’re saying this should be the LEAST that students have access to, right?

Dan Meyer (19:53):

Yeah. Yeah. I’m here now. I’m with you. I like that dream. Where we take care of folks in their lives outside of schools. So schools don’t have to be the one linchpin for every kind of social outcome. Like currently a lot of them run through a school ’cause we don’t do a good job of setting up other ways to meet those needs. And we should.

Bethany Lockhart Johnson (20:16):

And we’re also recording this in, what, two weeks, a week, after a tragedy where students and teachers were killed in the classroom. And I think both of us are taking some deep breaths and recognizing that there’s a lot of debate that is happening about what teacher’s role should be in preventing this in the future. And I don’t know if you’ve done drills in your classroom that are supposed to help mitigate disaster, but you know—collective deep breaths— <laugh> is where we’re at right now.

Dan Meyer (20:52):

Yep. The idea of “we should arm teachers” is another example of no, we should not do that. We should solve the tendency towards violence outside of the classroom so that teachers and students can teach and learn. That sounds awesome to me.

Bethany Lockhart Johnson (21:06):

Collective deep breath. Whew. OK. So what else you got for me, Dan?

Bethany Lockhart Johnson (21:33):

Ooh. So I feel like I’ve heard that in many teaching PDs. “I Do, you do, we do.” Actually I feel like I’ve seen like more “I do, we do, you do.” Like graduated release. I do it, then we’ll do it a little bit together, and then now you have permission to do it. And I feel like in directed draw, that’s a hundred percent true. Like I’m gonna show you this and then you draw it. And then you cut here and then you do it. If we’re trying to create this, like I’m teaching this new art technique. But in mathematics, I feel like that’s really not what I want my classroom to look like. I want to support my students and set them up for sense-making, and then I want them to try it out and I don’t want them to solve it the way it first comes to mind for me. I wanna see how they make sense of it and how they solve it. And then I want us to share it with each other so we can grow together. So I think time and place for “I do, you do, we do,” or “I do, we do, you do.” Or shoo-be-doo-be-doo-be. Yeah. You?

Dan Meyer (22:44):

I’ve got nothing. I have nothing to add. I thought that was just an excellent summary of a classroom I would love to be a part in, love to teach. I think it’s a certain tool in the toolbox that I think is overused. But it’s also a tool that can be useful in the case of certain kinds of operations. There are some operations that do benefit from “let me just show you how, like one way you might do this.” I don’t know. I’m like helping my kid whack a nail into a board and there’s a moment where it’s like, “Hey, actually, lemme just show you one way you can do this,” and do it, and then that’s helpful in some moments. But for so much of math, a lot of math does not relate to the operational kinds of fluency. And in those instances, it’s a little bit…it’s not a useful tool, I don’t think, for those kinds of skills and ideas.

Bethany Lockhart Johnson (23:34):

I’m thinking of tool talks in my classroom. So in kindergarten, many of the tools that we use in math and just in class in general, are new to the students. And if I tell them, this is exactly how you should use this tool, then I feel like I’m taking a lot of the sense-making away from them. But if I introduce the tool, show them how to use the tool safely, show them this is not a safe way to use the tool, chewing on this is not safe. That’s not how we use this tool. This is how we take care of it, et cetera. But then support different modes of using the tool that are gonna help them use it to solve problems and make sense, I think…but I guess—Dan, have you heard “I do, you do, we do,” or is it “I do, we do, you do”?

Dan Meyer (24:22):

I’m with you. And I think that it got clarified post-tweet. But yeah, it typically is “I do, we do, you do,” the gradual release of responsibility it’s often called. And I, I have heard people do what you described, which is…what is it? It’s “You do, we do, I do”? Like an inversion of that? Like have people do a thing that I can do that’s not too, too abstract for them, and then like “We all do something together, and then I’ll offer a summary of what we learned,” is one way that goes. I like that tool as well.

Bethany Lockhart Johnson (24:53):

I think particularly, at least I’ve seen in elementary classrooms, there’s sometimes this fear of letting students just try it out before I’ve really showed them, “but this is how it has to be.” And what I am most excited about is supporting students and creating a classroom environment where students don’t need my permission or need my direct “this is the only way to do it.” Instead, it’s like, yes, there’s lots of things we model. But there’s also like, “Hey, what do you think? How do you think this should be used?” And the joy of that exploration.

Dan Meyer (25:30):

Yeah. There’s a feeling of efficiency that comes from “I do, we do, you do,” for some kinds of math, but it’s undercut in my experience by what it cultivates in the students, which is “I’ve gotta wait until the teacher does before I can do anything.” So it pays off real diminishing returns over time. And it’s, just for me, an exhausting way to teach. Always being the bottleneck for new learning is a total drag.

Bethany Lockhart Johnson (25:55):

Ooh, what a great way to describe it. You do not wanna be the bottleneck. You want to be…what’s the other thing? The facilitator? What’s the opposite of a bottleneck? The flowing river? The…The…Help me!

Dan Meyer (26:10):

Hit us up in the replies. I dunno. The opposite of a bottleneck. That’s what you wanna…you wanna not be the opposite? No, you want, yeah. We got this here. We’ll figure it out. We’ll get back to you. <Laugh> OK. Well, folks, those were a few of this year’s fire tweets. It’s been fantastic chatting with you—

Bethany Lockhart Johnson (26:29):

Dan.

Dan Meyer (26:29):

—Bethany, About all those—

Bethany Lockhart Johnson (26:32):

Dan. You know, my favorite thing to do is interrupting you, Dan. I have to interrupt you because we can’t end fire tweets, Dan, without including a tweet from you.

Dan Meyer (26:43):

Oh, that’s true. I do have my moments. Yeah, we should. We really should. <Laugh> Do you have one in mind?

Bethany Lockhart Johnson (26:50):

No. Dan. Yes. I loved…you tweeted recently, “How many years have you been teaching?” Which, OK. “What Has been like the most influential? Like, what, OK, blah, blah, blah.” <blathering noises> You tweeted, “How many years have you been teaching? And at this point, what has most influenced how you teach?” And you gave some ideas: A methods course, PD sessions, curriculum, TV and movies, et cetera, et cetera. And I love that you put that out there because this episode is coming out as we’re wrapping up another school year. And it also got me thinking about summer and what teachers sometimes do during the summer, but what we might need to do this summer for self-care. But I’m really curious. I love that tweet. And I’m curious, Dan, what did folks say was the thing that had most influenced their teaching and what’s most influenced your teaching?

Dan Meyer (27:49):

Ooh, yeah. People’s responses to this one were really fantastic. I came into this, I was flying to the Association of Mathematics Teacher Educators conference. And I just found myself wondering, so, the pre-service year, the one year of, like, you’re learning how to teach, is how we did it in California. Like how much of that has still infused my practice? And in what ways? I don’t think I think about that stuff consciously, but I think that did like set me up with a lot of images that I would be unpacking for going on two decades now working in education. I think conversations with people, I think observing classes, I don’t think that like the one-day PDs, the one-day development days throughout the year, four times per year, I don’t think those stuck to me much. I think that this summer, I have learned so much, just an embarrassment of riches, from non-educational sources. From other disciplines. From storytelling, for instance. From how people have constructed movies I like. I am proud of the way…one of the aspects of my character that I’m proud of—it takes a lot to admit this, as I’m sure you understand, Bethany—but to integrate lots of wacky stuff and pick from it and use that to affect my practice and teaching has been really positive. So for this summer, I hope that people read a good beach book and just kinda let your teaching mind rest a little bit. And in doing so, create some openings for new ideas about education from other parts of the world. Kids! Having kids has been helpful. I don’t know! Just everything! It’s such a big job, education. Everything has so helpful. What about you? What’s an influence on your practice that might surprise me or other folks out there in MTL land?

Bethany Lockhart Johnson (29:52):

Well, I don’t know about surprise. I mean, I definitely feel similarly, like methods courses absolutely impacted my teaching. But I feel like opportunities where I was able to observe other teachers and where I was able to have conversations with folks about their practice, that has deeply impacted me. And books I’ve read. I mean, honestly, I’ve learned so much from sharing with other teachers. Like, for example, maybe I’ll bring student work and we’ll talk about it. And we kind of create this conversation together about how we wanna come back to the students based on the work we see. Those type of moments where we’re collaborating and we’re bringing multiple perspectives to the table, that I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day. So that continues to surprise and delight me. And thinking about this summer, I think there’s a lot of creativity and joy that can come out of the marination process, when you’re just kind of sitting back and healing yourself, whether through sleep or sunshine or time with friends and family or whatever that looks like for you. I think there’s a lot of creativity that can come from that place of fertile, you know, wellness. I never think of that as wasted time. I think of that as getting the soil ready for all that’s gonna come in the fall. And that being said, I also think it could be a fun time to dip your toes into something that you are excited to read, that you might not have a chance to read during the school year that could be teaching-related. So it’s like very low pressure, like, “Oh, I’ve really wanted to read more by this author. I’ve wanted to read this article. I’ve wanted to dip into this topic.” And not with a pressure, but just with a curiosity. And, yeah, I think so often we as teachers love learning, and to give yourself space to learn in whatever that looks like can be a real gift.

Dan Meyer (32:09):

Yes. And if you need book recommendations, hit the MTL back catalog of episodes. Loads of folks that we interviewed have real good books out.

Bethany Lockhart Johnson (32:16):

Yes!

Dan Meyer (32:16):

Think about it. Think about it.

Bethany Lockhart Johnson (32:22):

One quick recommendation: Again, gotta plug Antony Smith and Allison Hintz’s book. I read Mathematizing Children’s Literature before we did the interview, but this summer I wanna read all the children’s books that they mention. I just wanna go to the library and read all those children’s books. I wanna read them to my son. I wanna read ’em to myself. So, you know, diving into some good YA, children’s books, just, like, TLC. Dan, thank you for such a rich season and a chance to have so many interesting conversations. It is genuinely a joy to learn with and from you.

Dan Meyer (33:00):

Likewise. And always hope to see you folks on Twitter now and then. Let us know what you’re up to this summer at MTLShow on Twitter or in our Facebook group, Math Teacher Lounge. We’ll be there tuning in now and then. It’s been a treat interacting with you folks over this last season. Take care and until the new season, so long.

Stay connected!

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What Bethany Lockhart Johnson says about math

“I’ve learned so much from sharing with other teachers… Those type of moments where we’re collaborating and bringing multiple perspectives to the table, I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day.”

– Bethany Lockhart Johnson

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

A woman with curly hair and glasses smiles outdoors; a man with short dark hair smiles indoors in front of a blurred math teacher lounge, highlighting valuable math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Welcome to Amplify Desmos Math California!

California educators, welcome to math that motivates. Introducing Amplify Desmos Math California, a curiosity-driven TK–12 program that builds lifelong math proficiency. Each lesson poses problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals. Students encounter math problems they’re eager to solve, while teachers spend more time where it’s most impactful—creating a collaborative classroom of learners.

Keep reading to learn more about the program and explore sample materials.

About the program

Amplify Desmos Math California is a TK–12 core math program designed to meet the CA Math Framework and the Common Core State Standards for Mathematics. Amplify Desmos Math California thoughtfully combines conceptual understanding, procedural fluency, and application through a structured approach to problem-based learning. Through engaging activities, Amplify Desmos Math California invites curiosity and math discourse into the classroom to create lifelong math proficiency.

Continue reading to learn more about the K–8, Algebra 1, and Math 1 programs and to explore sample materials. (Spanish, TK and high school materials are in development and will be available in the 2026–27 school year. Geometry and Algebra 2 beta pilots will be available in the 2025–26 school year.)

A powerful math suite

Amplify Desmos Math California combines the best of assessment, problem-based core lessons, personalized practice, and intervention into a coherent and engaging experience for both students and teachers.

Laptop displaying a math problem interface with student assessment reports in the background.

Screening and progress monitoring

mCLASS Math benchmark assessments, along with the embedded program assessments, measure not just what students know, but how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core instruction and intervention resources. Unit- and lesson-level core assessments give teachers data at their fingertips to guide and differentiate instruction. In grades 3–8, core assessments and performance tasks are designed to prepare students for success on the Smarter Balanced Assessment Consortium (SBAC) testing.

Core instruction

Amplify Desmos Math California core lessons pair problems students are eager to solve with clear instructional moves for teachers. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals. With built-in differentiation and multilingual/English learner support, Amplify Desmos Math California enables every student to find success in the math classroom.

A digital math activity asks users to choose a block that makes 10 with a given number; a worksheet shows a similar "make 10" math exercise with blank spaces to fill in.
A digital educational screen showing a math problem about converting meters to centimeters. It involves a diving toy sinking 5 meters into a pool. Text prompts users to input the conversion.

Personalized Learning

Boost Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback adjusts to students’ work, providing item-level adaptivity to further support their learning.

Differentiation and intervention

Amplify Desmos Math views differentiation as an ongoing process where teachers are both reactive and proactive to student needs, ensuring that all students have clear pathways to proficiency. Through rich data and teacher support, Amplify Desmos Math uses flexible categories of intervention and enrichment that adjust daily according to student thinking.

In-the-moment differentiation supports are available for every lesson, both digitally and in the print Teacher Edition.

Two pages of a math worksheet and teacher’s guide about determining coordinates after a rotation, featuring diagrams, tables, and step-by-step problem-solving instructions.

An approach that supports teachers

Clear, step-by-step instructional moves help teachers plan and teach student-centered lessons that use
student thinking to differentiate instruction and guide to grade-level understanding. They include:

  • Guidance on what to listen for and how
    to respond.
  • Clear learning objectives to keep learning on
    track for each activity and lesson.
  • Daily reinforcement activities to provide direct
    instruction when needed.
A woman writes on a whiteboard using math teaching resources while a man sits at a desk, smiling. There are books and papers on the desk.
Network diagram with interconnected nodes labeled: Measure and Compare Objects, Represent Data, Dollars and Cents, Problem Solving with Measure, Skip Counting to 100, Number Strategies, Squares in an Array, Seeing Fraction in Shapes.

Big Ideas

The CA Mathematics Framework encourages a shift from power standards to thinking about math as a series of connected Big Ideas. Each Amplify Desmos Math California lesson supports one or more Big Ideas and the connections between them. The grade-level diagram changes through the course based on the math concepts addressed within.

Please refer to the following Keeping the Big Ideas at the Center documents to review specific lesson designs and alignments with the Big Ideas for each grade level.

Click here to see how the Big Ideas are represented within the K–8 core lessons.

Focus, coherence, and rigor

Amplify Desmos Math California incorporates the Drivers of Investigation (DIs) and Content Connection (CCs) throughout the program. Throughout the year, students engage with open and authentic tasks of varying durations—from lesson activities to unit-level Explore lessons and longer course-level Investigations. Every lesson and investigation opportunity is grounded in the why, how, and what of the learning experience, and helps teachers bring mathematical concepts to life.

An educational slide on addition story problems, detailing goals for solving problems, language goals, and strategies using equal expressions, tens and ones, and number sense.

Please refer to the following Amplify Desmos Math California alignments to the Standards for Mathematical Practice, provided by grade level.

A screen titled "Match the Score" with a 2D target graph showing various scores. Instructions request four ordered pairs to total 400. Four pairs are listed: (4, 2), (7, 4), (7, 6), (10, 6). A "Try again" button is shown.

Built-in authentic tasks

Mathematics is not learning in isolation. Students are connected to each other’s thinking and can use math to understand the world. With accessible invitations to authentic tasks, all students can experience mathematical success. Amplify Desmos Math California provides these authentic invitations in a variety of ways:

Each unit begins with an “Explore” lesson, which allows students to engage with authentic exploration in low-floor, high-ceiling tasks. These tasks are designed to promote an inclusive and differentiated learning environment—allowing all students to access basic mathematical concepts, while offering advanced exploration and problem-solving for those ready for more complex work.

Our innovative course-level investigations are designed to facilitate multi-part exploration. Students grapple with Big Ideas, diving deep into key concepts that encourage comprehensive understanding. Data science is infused into the approach, giving students a solid foundation from which to interpret and apply data-driven solutions. They’re also encouraged to understand and appreciate the interrelatedness of Earth’s environmental systems via our lesson’s focus on the Environmental Principles and Concepts (EP&Cs).

Explicit support for multilingual/English learners

Three overlapping educational worksheets for first grade math, including a cover page, a list of learning goals, and a lesson plan with bilingual English and Spanish text.

Amplify partnered with the English Learner Success Forum (ELSF), a national nonprofit organization that advocates for high-quality instructional materials that are inclusive of multilingual/English learners (ML/ELs). ELSF reviewed Amplify Desmos Math California, and provided directional guidance and feedback to ensure that the program reflects their research-based instructional strategies for multilingual/English learners.

Amplify Desmos Math California recognizes the diverse language needs of our students and is designed to be inclusive. Each lesson in the program features a parallel language activity, designed to be available to all students, in the form of teacher guidance and student activities. The activities in the Math Language Development Resources have level ELD differentiation to support all levels of ML/ELs. This approach ensures that all students, regardless of their language skills, can participate fully, grasp the material, and excel in their mathematical journey.

Our Multilingual Glossary includes, in addition to Spanish, nine languages: Simplified Mandarin, Tagalog, Vietnamese, Arabic, European French, Russian, Brazilian-Portuguese, Haitian-Creole, and Urdu.

Amplify Desmos Math California will include Spanish student-facing materials beginning in the 2026–27 school year.

Assessments

By starting with what students already know, Amplify Desmos Math helps build a strong foundation for success to guide and support future learning. Teachers are empowered to transform every classroom into an engaged math community that invites, values, and develops student thinking. With explicit guidance on what to look for and how to respond, teachers can effectively support students as they develop their understanding.

Open math workbook showing an End-of-Unit Assessment with multiple-choice and written response questions on fractions and equivalent values.

Program assessments

A variety of performance data in Amplify Desmos Math provides evidence of student learning while helping students bolster their skills and understanding.

Unit-Level Assessments

Our embedded unit assessments offer key insights into students’ conceptual understanding of math. These assessments provide regular, actionable information about how students are thinking about and processing math, with both auto-scoring and in-depth rubrics that help teachers anticipate and respond to students’ learning needs.

Lesson-Level Assessments

Amplify Desmos Math lessons are centered around sense-making and in-the-moment feedback. Daily moments of assessment provide valuable evidence of learning for both the teacher and student.

Data and reporting

Amplify Desmos Math provides teachers and administrators with unified reporting and insights so that educators have visibility into what students know about grade-level math—and can plan instruction accordingly for the whole class, small groups, and individual students.

A table displays students' performance levels across various items, with a detailed score distribution for a specific assessment shown in a separate overlay. Geometric design elements accented the background, providing an engaging visual touch ideal for any math classroom using Amplify Desmos Math.

Assessment reports

Reporting functionality integrates unit assessments, lesson assessments, personalized learning, Benchmark assessments, and Progress Monitoring for a comprehensive look at student learning.

Our reports show proficiency and growth by domain, cluster, standard, and priority concept using performance data from unit assessments. Then our reports highlight areas of potential student need to allow teachers to modify their instruction and target differentiated support.

At-a-glance views of unit-level assessment results inform your instructional planning, and you can also drill down to item-level analysis.

Standards reports

Our standards report allows you to monitor proficiency at the class and individual student levels. Proficiency and growth are shown by domain, cluster, standard, and priority concepts. Areas of potential student need are highlighted to allow teachers to modify their instruction and target differentiated support.

Administrator reports

Amplify Desmos Math provides a complete picture of student, class, and district performance, allowing administrators to implement instructional and intervention plans.

  • Track student, class, and district performance with usage, completion, and assessment data.
  • Accurately group students and classes with the Benchmark and Progress Monitoring data of mCLASS Assessments and allow teachers to reliably implement and track the progress of Tier 2 and Tier 3 intervention.
  • Provide one data-driven solution that educators can rely on for high-quality math instruction.

Elementary review resources

To learn about the elementary program, please start by watching the Amplify Desmos Math California Elementary Program Overview video.

For additional program information and helpful navigation tips, download the Amplify Desmos Math California Elementary Program Guide.

View the Elementary Program Components Guide here. 

View the Hands-on manipulatives brochure here.

Middle School review resources

To learn about the middle school program, please start by watching the Amplify Desmos Math California Middle School Program Overview video.

For additional program information and helpful navigation tips, download the Amplify Desmos Math California Middle School Program Guide.

View the Middle School Program Components Guide here.

View the middle school manipulative kit components here.

The digital experience

In Amplify Desmos Math, embedded interactions and animations allow students to test predictions, get feedback, share ideas, and connect representations.

The digital interactions included in lesson activities are designed to elicit student thinking in a way that feels fun and inviting. As students play and explore math concepts, teachers can highlight the ideas that students share, connect those ideas to other students’ ideas, and build on their thinking through productive class discussion.

Watch the video to preview the digital experience and for helpful platform navigation tips.

A laptop displays a math activity about platform heights and tube length, while a worksheet titled "Hamster Homes" is visible in the background.

Explore grade level samples

All lessons in Amplify Desmos Math California include print materials and rich digital experiences. Every lesson is supported with Student Edition pages, teacher presentation screens, and interactive digital resources for practice and differentiation. Some lessons also enable students to use devices to interact with lesson content.

You’ll find sample materials by grade level in the following drop-downs. Please refer to your physical samples and the digital platform (accessed through the demo account provided by your account executive) for a comprehensive program review.

Scope and Sequence

Math 2–3 is currently being developed and will be available in the 2026–27 school year.

Cover of "Amplify Desmos Math California Teacher Edition GEO Volume 1" featuring abstract geometric illustrations and people engaged in mathematical activities.
Scope and Sequence (National Edition)

The Amplify Desmos Math Geometry Beta National Edition is available for piloting in the 2025–26 school year. Amplify Desmos Math California Geometry will be available in the 2026–27 school year.

Cover of "Amplify Desmos Math California Geo Volume 1 Student Edition" featuring geometric shapes and small illustrated people interacting with mathematical elements.
Geometry sampler

This sampler includes Teacher Edition front matter for program overview information, plus Teacher Edition and Student Edition pages for Units 1–2.

Cover of "Amplify Desmos Math California A2 Teacher Edition," featuring a Ferris wheel, math graphs, and students interacting with mathematical concepts.
Scope and sequence (National Edition)

The Amplify Desmos Math Algebra 2 Beta National Edition is available for piloting in the 2025–26 school year. Amplify Desmos Math California Algebra 2 will be available in the 2026–27 school year.

Cover of "Amplify Desmos Math California Student Edition A2 Volume 1" featuring mathematical graphs, a Ferris wheel, and students interacting with math concepts.
Algebra 2 sampler

This sampler includes Teacher Edition front matter for program overview information, plus Teacher Edition and Student Edition pages for Units 1–2.

Contact us

For questions, samples, or more information, please contact your local Amplify account executive:

Erin King
Sales Director, CA
(512) 736-3162
eking@amplify.com

Northern CA
Wendy Garcia
Senior Account Executive
(510) 368-7666
wgarcia@amplify.com

Bay Area
Lance Burbank
Account Executive
(415) 830-5348
lburbank@amplify.com

Central Valley and Central Coast
Demitri Gonos
Senior Account Executive
(559) 355-3244
dgonos@amplify.com

Ventura and L.A. County
Jeff Sorenson
Associate Account Executive
(310) 902-1407
jsorenson@amplify.com

Orange and L.A. County
Lauren Sherman
Senior Account Executive
(949) 397-5766
lsherman@amplify.com

San Bernardino and L.A. County
Michael Gruber
Senior Account Executive
(951) 520-6542
migruber@amplify.com

Riverside and L.A. County
Brian Roy
Senior Account Executive
(818) 967-1674
broy@amplify.com

San Diego County
Kirk Van Wagoner
Senior Account Executive
(760) 696-0709
kvanwagoner@amplify.com

Under 2300 students in Bay Area, Sacramento Valley, and Northern Counties
Kevin Mauser
Lead Account Executive
(815) 534-0148
kmauser@amplify.com

Under 2300 students in Southern CA, Central Coast, and Southern Central Valley Counties
Charissa Snyder
Account Executive
(720) 936-6802
chsnyder@amplify.com

Reveal Math

Grade 6

Module 1: Ratios and Rates

Reveal MathDesmos Classroom
Lesson 1: Understand ratiosUnit 2
Lesson 1: Pizza Maker
Lesson 2: Tables of Equivalent RatiosUnit 2
Lesson 10: Disaster Preparation
Lesson 4: Compare Ratio RelationshipsUnit 2
Lesson 4: Fruit Lab
Lesson 6: Convert Customary Measurement UnitsUnit 3
Lesson 1: Many Measurements
Lesson 7: Understand Rates and Unit RatesUnit 3
Lesson 6: Soft Serve

Module 2: Fractions, Decimals, and Percents

Lesson 1: Understand PercentsUnit 3
Lesson 9: Lucky Duckies
Lesson 3: Relate Fractions, Decimals, and PercentsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Compute with Multi-Digit Numbers and Fractions

Lesson 1: Divide Multi-Digit Whole NumbersUnit 5
Lesson 13: Movie Time
Lesson 3: Divide Whole Numbers by FractionsUnit 4
Lesson 3: Flour Planner
Lesson 4: Divide Fractions by FractionsUnit 4
Lesson 6: Fill the Gap
Lesson 5: Divide with Whole and Mixed NumbersUnit 4
Lesson 6: Fill the Gap

Module 4: Integers, Rational Numbers, and the Coordinate Plane

Lesson 1: Represent IntegersUnit 7
Lesson 1: Can You Dig It?
Lesson 3: Compare and Order IntegersUnit 7
Lesson 4: Order in the Class

Module 5: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions
Lesson 4: Evaluate Algebraic Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 6: Use the Distributive PropertyUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 7: Equivalent Algebraic ExpressionsUnit 6
Lesson 1: Weight for It

Module 6: Relationships in Geometry

Lesson 2: One-Step Addition Equations
Lesson 3: One-Step Subtraction Equations
Unit 6
Lesson 1: Weight for It
Lesson 6: InequalitiesUnit 7
Lesson 7: Tunnel Travels

Module 7: Relationships Between Two Variables

Lesson 4: Multiple RepresentationsUnit 6
Lesson 16: Subway Fares
Take Away (coming soon!)

Module 8: Area

Module 9: Volume and Surface Area

Lesson 2: Surface Area of Rectangular PrismsUnit 1
Lesson 10: Renata’s Stickers

Module 10: Statistical Measures and Displays

Lesson 1: Statistical QuestionsUnit 8
Lesson 3: Minimum Wage
Lesson 2: Dot Plots and HistogramsUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Measures of CenterUnit 8
Lesson 11: Toy Cars
Lesson 7: Interpret Graphical DisplaysUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Proportional Relationships

Reveal MathDesmos Classroom
Lesson 1: Unit Rates Involving Ratios of FractionsUnit 2
Lesson 1: Paint
Lesson 3: Tables of Proportional ReasoningUnit 2
Lesson 1: Paint
Lesson 4: Graphs of Proportional ReasoningUnit 2
Lesson 8: Dino Pops
Lesson 5: Equations of Proportional ReasoningUnit 2
Lesson 6: Two and Two

Module 2: Solve Percent Problems

Lesson 1: Percent of ChangeUnit 4
Lesson 5: Percent Machines
Lesson 12: Posing Percent Problems (coming soon!)
Lesson 3: Tips and MarkupsUnit 4
Lesson 5: Percent Machines
Lesson 4: DiscountsUnit 4
Lesson 5: Percent Machines

Module 3: Operations with Integers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 4: Operations with Rational Numbers

Lesson 1: Add Integers
Lesson 2: Subtract Integers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 3: Multiply IntegersUnit 5
Lesson 10: Integer Puzzles
Lesson 5: Apply Integers OperationsUnit 5
Lesson 10: Integer Puzzles

Module 5: Simplify Algebraic Expressions

Lesson 2: Add Linear Expressions
Lesson 3: Subtract Linear Expressions
Unit 6
Lesson 10: Collect the Squares
Lesson 4: Solve Inequalities Using Addition or SubtractionUnit 6
Lesson 16: Shira the Sheep

Module 6: Write and Solve Equations

Lesson 1: Write and Solve One-Step EquationsUnit 6
Lesson 16: Shira the Sheep

Module 7: Write and Solve Inequalities

Lesson 6: Wirte and Solve Two-Step InequalitiesUnit 6
Lesson 16: Shira the Sheep

Module 8: Geometric Figures

Lesson 1: Vertical and Adjacent AnglesUnit 7
Lesson 4: Missing Measures
Lesson 2: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 3: TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 4: Scale DrawingsUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?

Module 9: Measure Figures

Lesson 1: Circumference of CirclesUnit 3
Lesson 3: Measuring Around
Lesson 2: Area of CirclesUnit 3
Lesson 9: Area Challenges

Module 10: Probability

Lesson 1: Find Likelihoods
Lesson 2: Relative Frequency of Simple Events
Lesson 3: Theoretical Probability of Events
Unit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities

Module 11: Sampling and Statistics

Lesson 1: Biased and Unbiased SamplesUnit 8
Lesson 10: Crab Island
Lesson 2: Make Predictions
Lesson 3: Generate Multiple Samples
Unit 8 
Lesson 10: Crab Island
Lesson 4: Compare Two PopulationsUnit 8
Lesson 10: Crab Island

Grade 8

Module 1: Exponents and Scientific Notation

Reveal MathDesmos Classroom
Lesson 1: Powers and ExponentsUnit 7 
Lesson 1: Circles
Lesson 2: Multiply and Divide MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 3: Power of MonomialsUnit 7 
Lesson 3: Power Pairs
Lesson 5: Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale
Lesson 6: Compute with Scientific NotationUnit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: Real Numbers

Lesson 2: RootsUnit 8
Lesson 4: Root Down

Module 3: Solve Equations with Variables on Each Side

Lesson 1: Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 2: Write and Solve Equations with Variables on Each SideUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Determine the Number of Solutions

Module 4: Linear Relationships and Slope

Lesson 1: Proportional Relationships and SlopeUnit 3
Lesson 1: Turtle Time Trials
Lesson 2: Slope of a LineUnit 3
Lesson 4: Flags
Lesson 5: Slope-Intercept FormUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Graph Linear EquationsUnit 3
Lesson 4: Flags
Unit 5
Lesson 5: The Tortoise and the Hare

Module 5: Functions

Lesson 1: Identify FunctionsUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 6: Qualitative GraphsUnit 5
Lesson 5: The Tortoise and the Hare

Module 6: Systems of Linear Equations

Lesson 1: Solve Systems of Equations by GraphingUnit 4 
Lesson 11: Make Them Balance

Module 7: Triangles and the Pythagorean Theorem

Lesson 2: Angle Relationships and TrianglesUnit 1 
Lesson 12: Puzzling It Out

Module 8: Transformations

Lesson 1: Translations
Lesson 2: Reflections
Lesson 3: Rotations
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Lesson 4: DilationsUnit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf

Module 9: Congruence and Similarity

Lesson 3: Similarity and TransformationsUnit 2
Lesson 6: Social Scavenger Hunt

Module 10: Volume

Lesson 1: Volume of CylindersUnit 5
Lesson 11: Cylinders
Lesson 2: Volume of ConesUnit 5
Lesson 13: Cones

Module 11: Scatter Plots and Two-Way Tables

Lesson 1: Scatter PlotsUnit 6 
Lesson 3: Robots
Lesson 2: Draw Lines of FitUnit 6 
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 4: Two-Way TablesUnit 6
Lesson 11: Finding Associations
Lesson 5: Associations in Two-Way TablesUnit 6
Lesson 11: Finding Associations

Program questions

Amplify Science is a flexible, blended K-8 science curriculum that addresses the following disciplines: Life Science, Earth and Space Science, Physical Science, and Engineering Design. Together, the units address 100% of the Next Generation Science Standards for grades K-8 and a significant number of the Common Core State Standards for English Language Arts, Literacy in Science and Technical Subjects, and Math. School districts that implement our elementary and middle school science curriculum are outfitted with print and digital resources as well as hands-on materials kits and engage with highly-qualified professional learning specialists to start strong.

We support both. The Lawrence Hall of Science has spoken to thousands of districts across the country and one of the many things they learned was that no one solution works for everyone; therefore, they developed Amplify Science to provide the maximum amount of flexibility so each district wouldn’t be forced into a single model of instruction.

We have suggested sequences for both the integrated and discipline-specific models. If you have a specific sequence that you want to teach, we can work with you to design a sequence that meets your needs.

Yes. Rather than separating Performance Expectations into physical science units, earth and space science units, and life science units, Amplify Science units are organized around anchoring phenomena designed to give students opportunities to dive deeply into certain disciplinary core ideas while also drawing from or applying to others. In organizing the Amplify Science middle school units, we have carefully sequenced these ideas within each grade level to support the development of deep and coherent understanding.

Many real-world phenomena cross the domain boundaries of life, physical, or earth and space science (as well as engineering). Each Amplify Science unit begins with an intriguing real-world phenomenon that poses a problem that needs to be understood and/or solved. By the end of the unit, students will have analyzed the anchor phenomenon across multiple scientific domains, possibly designed and tested an engineering solution, and always applied what they have learned in a different context.

For example:
In the unit Light Waves, students investigate the anchoring phenomenon of why Australia has a much higher skin cancer rate than countries at similar latitudes like Brazil. The focus of this unit is on disciplinary core ideas related to wave properties (PS4.A) and electromagnetic radiation (PS4.B). Students explore these physical science ideas deeply within the unit, and also draw on ideas from earth science (e.g., latitudinal variation of the sun’s energy) and life science (e.g., the effect of energy on the DNA in the nucleus of a cell) in order to explain the central phenomenon.

Yes. We believe hands-on experiences are critical to the study of science. Every unit in our curriculum comes with a kit of hands-on materials to allow students to roll up their sleeves and conduct hands-on investigations.

Absolutely. Amplify Science integrates all four STEM disciplines—science, technology, engineering, and math—in addition to English language arts throughout the curriculum.

Every lesson in Amplify Science explicitly calls out which CCSS Math and CCSS ELA standards are addressed. Amplify Science is not a math program, nor an ELA program; therefore, it does not address all of the Common Core standards. But the program does address a significant number of the standards as they pertain to science.

Yes, the program includes multiple summative assessments opportunities.

  • Grades 6–8 Science Seminars and final written arguments (formative and summative components): Culminating performance task for each core unit where students are introduced to a new real-world problem, collect and analyze evidence, examine a number of claims, and then engage in a full-class discussion where they must state which claims are best supported by the evidence, all while making clear their reasoning that connects the evidence to the claims. After the seminar, students then individually write their final scientific argument, drawing on the DCIs, SEPs, and CCCs they have used over the course of the unit to develop a sophisticated and convincing argument that addresses the problem they’ve been investigating. Rubrics, scoring guides, and examples of student responses at each scoring level are provided to teachers to support the assessment of students’ understanding of concepts and specific practices.
  • End-of-Unit Assessments: Targeted conversations (K–1), written responses (grades 2–5) or a combination of auto-scored multiple-choice questions and rubric-scored written responses (grades 6–8). Summative assessments for each unit are designed to provide valid, reliable, and fair measures of students’ progress and attainment of three-dimensional learning.
  • Benchmark assessments: Delivered four times per year in grades 3–5 and three times per year in grades 6–8, benchmark assessments report on students’ facility with each of the grade-level appropriate DCIs, SEPs, CCCs, and performance expectations of the NGSS.

No. While we do provide suggested sequences for integrated and domain courses, there are other logical ways to sequence the units and we expect that teachers will present the units in a variety of different orders and in any combination. There are a few notable exceptions. For example, students completing the Metabolism Engineering Internship should have completed the Metabolism core unit beforehand, or a unit that provides students with the same information. Amplify Science specifies prerequisites for each unit in the event that teachers are interested in using an Amplify Science unit in combination with other materials.

Amplify Science provides enough instructional content to fill 180 days of instruction.

For grades K-2, we offer 66 lessons that will address 100% of the NGSS and a substantial number of the CCSS-ELA for each grade.

For grades 3-5, we offer 88 lessons that will address 100% of the NGSS for each grade and a substantial number of the CCSS-ELA.

For grades 6-8, we offer 146 lessons that will address 100% of the NGSS for Middle School and a substantial number of the CCSS-ELA. Each lesson is designed to last 45 minutes; therefore, it will take some teachers more than 146 classroom days to teach all the lessons.

Some classes might last longer than one session due to a number of reasons (e.g., enthusiastic student conversations, challenging topics requiring deeper dives, more time needed to accommodate diverse learners, etc.). Also, teachers might want to supplement Amplify Science curriculum with some of their own favorite lessons. Lastly, the 146 lessons account for the inevitable assembly days, class trips, testing schedules, etc. We also offer a number of additional lessons that are not core to each unit, in the event teachers want to go deeper or expand upon a unit topic.

Grades K-1 lessons are designed for 45 minutes of science instruction.

Grades 2-5 lessons are designed for 60 minutes of science instruction.

Grades 6-8 lessons are designed for 45 minutes of science instruction.

It is not a problem if you do not allocate 45 mins of science instruction at K-1, or 60 mins at 2-5. Since there are a total of 66 lessons to address 100% of NGSS at grades K-2, and 88 lessons to address 100% of NGSS at 3-5, you can easily teach the lessons in smaller blocks and cover all of the content over the course of the school year.

Technical questions

To ensure that your hardware and network meet the minimum technical requirements for optimal performance and support of your digital curriculum products please see Amplify’s customer requirements page.

Dyscalculia: What educators should know

Two children seated at a table engage with colorful number cubes and a pencil beside a worksheet—a delightful way to explore math. This playful setup subtly acts as an informal dyscalculia screener, helping spot characteristics of dyscalculia in young learners.

Some kids love math. Some kids like math. Some kids struggle with math, or struggle with math anxiety. And some kids have dyscalculia, a specific learning disorder that affects one’s ability to understand numbers and learn math facts.

As awareness has continued to grow, educators today are curious to know: What are the characteristics of dyscalculia? How can I help a child with dyscalculia? What should I know about dyscalculia screeners? We’re here to provide some answers.

Dyscalculia: What it is and is not

According to the Child Mind Institute, dyscalculia (sometimes called “developmental dyscalculia”) is a term used to describe specific learning disabilities that affect a child’s ability to understand, learn, and perform math and number-based operations.

Honora Wall, Ed.D., founder of the Dyscalculia Training and Research Institute, calls it “a type of neurodivergence: A difference in brain development or function.”

That’s an important distinction: Dyscalculia is a neurological condition that affects numerical cognition and processing. It has nothing to do with being “bad at math” or not “trying hard enough.”
Between 5 and 7% of elementary school-aged children may have dyscalculia, which is believed to affect girls and boys equally.

It is important to note that not all difficulties in math are caused by dyscalculia. Dyslexia, ADHD, and other conditions can also pose challenges for math students.

Nor is dyscalculia simply “math dyslexia.” Dyscalculia and dyslexia are entirely separate learning disorders that affect different areas of cognition and involve distinct difficulties.

How dyscalculia might present itself

Dyscalculia manifests in various ways in the math classroom. Here are some examples of how it can appear:

  • When engaging in activities like games involving dice, students may need to count the individual dots to recognize a number rolled, rather than intuitively recognizing it.
  • Students might have difficulty connecting the numerical symbol “5” (for example) to the word “five.” Making this connection is essential for associating numbers with their meanings.
  • Students may be delayed in learning to count, or lose track or rely on visual aids (like their fingers) when they count.

Such students may also have a hard time:

  • Solving math problems.
  • Recognizing or creating patterns.
  • Learning basic math functions.
  • Estimating how long a task will take.
  • Processing visual-spatial ideas such as charts and graphs, or even telling left from right.
  • Remembering phone numbers or zip codes.
  • Playing games that involve counting or keeping score.
  • Telling time.

The connection between mathematics anxiety and dyscalculia

Math anxiety is an emotional response to math that presents as apprehension or fear. Some call it mathematics phobia. It may include physical symptoms such as sweating, rapid heartbeat, shortness of breath, and other physical symptoms of anxiety. It’s similar to other types of anxiety, but it’s exclusive to math.

But, most important in this context, it’s not itself a neurological or cognitive condition.

So dyscalculia and math anxiety are not the same, but they may go hand in hand—perhaps with one exacerbating the other. Students with dyscalculia might develop math anxiety due to repeated challenges and frustrations in learning math.

Understanding this connection—and working to alleviate math anxiety—is crucial for educators aiming to create a supportive learning environment.

Tips for assisting students with dyscalculia

Here are some practical strategies educators can use to support students with dyscalculia:

  • Teach positive self-talk and persistence: Encourage students to develop a “growth mindset,” reinforcing that effort and persistence (as well as making mistakes) are essential to overcoming challenges.
  • Provide organizational aids: Use graph paper to help students line up numbers correctly, which aids in precision during calculations.
  • Use manipulatives: Tools like counters and blocks can make math feel more tangible, helping students grasp abstract concepts.
  • Focus on singular tasks: Present one math problem at a time to prevent students from feeling overwhelmed and allow for focused attention.
  • Allow more time: Give students the opportunity to work at their own pace, acknowledging that they may need more time to process numerical information.
  • Grant calculator access: Allowing calculators can reduce stress and help students solve problems more efficiently.
  • Make math fun and engaging: Incorporate interactive platforms such as Desmos Classroom to create an enjoyable and interactive learning experience.

More to explore

Why fluency matters in K–5 math education

An illustration showing a caterpillar, a hand matching shapes and colors on tiles, and another hand holding numbered cards—perfect for read-aloud math activities or exploring math in picture books with children.

If you’re fluent in Farsi, let’s say, you don’t search for every word or stop to translate every sentence in your head. You understand, process, and respond automatically, in real time.

Math fluency works the same way. This kind of fluency is something you can use naturally to understand what’s presented and respond to it meaningfully.

In K–5 math, fluency allows students to move beyond getting through the problem toward real mathematical thinking. Without it, even confident students can get stuck. With it, students gain access to deeper understanding, flexibility, and confidence.

What is math fluency?

Fluency in math is sometimes misunderstood as speed or memorization—but research and classroom experience tell a fuller story.

The National Council of Teachers of Mathematics defines procedural fluency as the ability to: “…apply procedures efficiently, flexibly, and accurately; to transfer procedures to different problems and contexts; to build or modify procedures from other procedures; and to recognize when one strategy or procedure is more appropriate to apply than another.”

In other words, the skills often referred to as computational fluency and math fact fluency tell only part of the story. Full mathematical fluency means knowing how and why strategies work, and being able to choose among them.

Memorization does have a role in math learning, but it alone does not lead to fluency. A student who has memorized facts but doesn’t understand relationships between numbers may still struggle when problems change slightly or require reasoning.

By contrast, a fluent student can adapt. They can explain their thinking, check whether an answer makes sense, and shift strategies when needed.

This is why fluency acts as a bridge between conceptual understanding and procedural application. It connects what students know to what they can do, and helps them do it with confidence.

Why procedural fluency matters in K–5 math

In the elementary grades, students are building the foundational math skills they’ll rely on for years to come. When procedural fluency is weak, students can feel overwhelmed by basic calculations, leaving little mental energy for problem-solving or new concepts.

Students without strong procedural fluency often feel stuck. For them, math can start to feel like an endless series of obstacles rather than a meaningful, engaging exploration—and that experience does not set anyone up to feel like a math person.

Fluency is what frees students up to focus on the heart of a problem. When they’re not bogged down by calculations, they’re able to reason, explore patterns, and tackle more complex tasks. Fluency opens doors—to higher-level math, to confidence, and to a more positive math identity.

In their paper, “Eight Unproductive Practices in Developing Fact Fluency,” Gina King and Jennifer Bay-Williams write: “Being fluent contributes to a productive disposition about mathematics, opens doors to a range of mathematics topics, and arms students with a skillset applicable to whatever they wish to pursue.”

What teaching math fluency looks like in the classroom

Effective K–5 math instruction treats fluency as something that develops over time, through meaningful practice, discussion, and reflection. Students need opportunities to explore number relationships, explain their thinking, and revisit strategies in different contexts.

In classrooms where math fluency is developing, instruction consistently supports flexible thinking, reflection, and revisiting ideas over time. You might see and hear the following:

  • Revisiting strategies across problems. Students are encouraged to solve the same problem in more than one way and to compare approaches. Classroom discussions focus on how strategies work and when one might be more efficient than another, helping students build strategic thinking and confidence.
  • Frequent, well-spaced opportunities for practice. Key facts and strategies reappear over time rather than being practiced once and set aside. This spacing helps students retain learning and apply it more accurately and efficiently when they encounter familiar ideas in new contexts.
  • Regular routines that emphasize reasoning. Short, consistent routines invite students to mentally compute, explain their thinking, and listen to others’ ideas. The focus is on understanding number relationships and reasoning through solutions rather than relying on memorized steps.
  • Thoughtful use of visual representations. Tools such as number lines, arrays, and other models help students see how numbers and operations relate. These representations support flexible thinking and make procedures more meaningful and accessible.

Across these experiences, fluency is something you can hear as well as see. Students explain their reasoning, reference strategies they’ve used before, and check whether their answers make sense, building accuracy, efficiency, and flexibility over time.

Math fluency helps students open their minds to the richness of math, and to their own power as math learners.

Math that motivates your K–5 students

As a K–5 teacher, your day is a constant balance of subjects, personalities, and priorities. With so many different dynamics and responsibilities, math class shouldn’t be another struggle to muscle through!

That’s why we’ve compiled a wealth of resources and activities to help you engage students; meet instructional goals; and encourage fluency, number sense, and discussion in your classroom. 

Three children paint the walls of a room; one holds a paper with the fraction 2/3, while math symbols and a tree appear in the background.
A booklet titled "The Power of Fluency: Cultivating Flexible, Confident Problem-Solvers" with an illustrated cover and an open page showing text and graphics about classroom fluency.

The power of fluency

Teachers work to achieve so many outcomes during their math block. While balancing multiple priorities, it’s important to remember that procedural fluency remains integral to student learning. Access this guide to unpack the power of fluency and find free math fluency practice to use in your next lesson.

10 low-prep, high-impact math activities that get to some serious math

Envision your classroom engaged in a difficult math task—all students are participating, leveraging different scaffolds that you intentionally prepared ahead of time. Engagement is high, and students are both challenged and motivated. Make this a reality in your school with our free activities designed to encourage productive struggle while reaching all learners.

A teacher holds a clipboard while a student points at a chalkboard labeled "Guinea Pig," "Millipede," and "Goldfish" in a classroom setting.
A presentation slide titled "Three Practices to Support Problem-Based Learning" features students and teachers engaged in classroom activities and math instruction.

Three practices to support problem-based learning

As educators, we want all students to develop a rich and deep understanding of the math they experience in our classrooms. A problem-based learning approach supports this by centering problem-solving in ways that build lifelong mathematical proficiency. Read this guide for practical tips on introducing problem-based learning and deeper conceptual understanding into your math classroom.

Best practices from real educators like you

Learn tried and true strategies for leveling up math instruction from Beyond My Years podcast guests like Amplify’s own Dan Meyer, teacher and My Kindergarten Math Workbook author Keri Brown, educator and speaker Mike Flynn, teacher and I Hate Math author Ian Brown, and more!

More free resources for K–5 educators

Two children paint a wall while holding a "2/3" sign; another child on the floor holds a "3 x 3" sign near a bookshelf.

K–5 Insider

Sign up for our monthly email to get new K–5 content and activities directly in your inbox.

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A printed guide titled "What are math routines, and how can you use them?" for grades K–5, with instructions and example math routine cards displayed.

K–5 instructional routine cards

Find easy-to-implement routines to keep students interacting and engaged with a lesson.

Download

A student and a teacher look at a laptop screen and smile in a classroom with colorful posters on the wall.

Math that motivates: Success stories

See how real teachers and students are unlocking new levels of engagement and comprehension, proving that everyone can be a math person.

LEARN MORE 

Ready to make every student a math person?

Connect with a product expert today.

FAQ for K–5 educators

Procedural fluency is the ability to use procedures flexibly, accurately, and efficiently to solve problems. Procedural fluency goes beyond memorization—students develop fluency when they understand number relationships and can choose from multiple strategies based on the numbers involved.

Students who understand why procedures work feel confident tackling challenging problems. When students can choose strategies that make sense to them, rather than relying on rote memorization, they develop agency and see themselves as capable mathematical thinkers.

Understanding how numbers connect helps students develop flexible thinking and multiple solution strategies. Timed tests often prioritize speed over understanding, which can create math anxiety and discourage the productive struggle that deepens learning.

Teachers can achieve this balance by using a predictable routine: warm-ups for fluency practice, a core problem-solving activity during which students explore multiple strategies, and structured discussion to connect different approaches. This structure ensures both skill-building and mathematical discourse happen daily.

Synthesizing learning means bringing the lesson together by highlighting the key mathematical idea that students have just explored. After students share strategies, the teacher helps them make connections between different approaches and names the big takeaway, often through a brief summary or exit ticket.

The Five Practices for Orchestrating Productive Mathematical Discussions are: 1) Anticipating student strategies before the lesson, 2) monitoring student work during the activity, 3) selecting specific students to share, 4) sequencing presentations in a purposeful order, and 5) connecting different strategies to the mathematical goal.

Productive struggle is when students grapple with challenging problems that require genuine thinking, but that remain accessible with appropriate support. It’s essential for deeper understanding, because it compels students to think critically, test strategies, and build perseverance, moving beyond surface-level memorization.

They can celebrate mistakes as learning opportunities and emphasize that understanding develops through effort and persistence. They can also create a safe classroom environment in which all students feel comfortable sharing their developing ideas and foster structured discussions during which multiple strategies are valued, helping students see that there’s more than one right way to think mathematically.

These are problems accessible to all students (that’s the low floor) but open enough to challenge advanced thinkers (that’s the high ceiling). Tasks like these allow multiple entry points and solution strategies, making them ideal for generating rich classroom discussion in which every student can participate meaningfully.

Such routines build number sense and fluency while making discussions predictable and low stakes. These brief, structured activities (5–10 minutes) activate prior knowledge, help students see number relationships, and give everyone practice explaining their thinking—all without requiring extensive preparation or materials.

They can do so by maintaining meaningful objectives while providing varied supports—ensuring that students understand what’s being asked, offering manipulatives and visual tools, allowing partner discussion before whole-class sharing, asking guiding questions without giving away the answer, and strategically grouping students. The goal is supporting access to challenging work, not making it easier.

Welcome to Amplify Desmos Math!

Your Amplify Desmos Math Experience Kit includes teacher and student materials for one sub-unit of instruction to try in your classroom. Click the orange button below to access the digital lessons for your grade.

A laptop displays a math problem on its screen with illustrations of fish and a clock, alongside two math activity books titled "Amplify Desmos Math" for grades 3 and 5.

About the program

Our structured approach to problem-based learning systematically builds on students’ curiosity to develop lasting grade-level understanding.

Amplify Desmos Math combines and connects conceptual understanding, procedural fluency, and application. Lessons are designed with the Proficiency Progression™, a model that provides teachers with clear instructional moves to build from students’ prior knowledge to grade-level learning.

Educational materials featuring various graphs and applications, including rocket motion and quadratic functions, displayed on Desmos and paper.
Interactive digital math lesson interface with colorful graphics showing parabola exploration and plotting tools on screen, enhanced by the New York math curriculum.

Structured approach to problem-based learning

  • Differentiation and personalized practice
  • Easy-to-follow instructional guidance
  • Robust assessments and reports
  • Spanish student materials
A classroom dashboard displays student names and their progress in activities, with checkmarks indicating completed tasks and circles showing ongoing or incomplete tasks.

Math that motivates

  • Powerful teacher-facilitation supports and tools
  • Students talking and building from each other’s ideas 
  • Every lesson has fully compatible print and digital materials for a collaborative classroom
Illustration of an Amplify Desmos math learning tool on a student screen showing abacus representations for the sums 8+7, 7+4+5, 3+8+4

Student thinking is made evident

  • Curiosity-driven lessons that motivate students with interesting problems they are eager to solve
  • Explicit guidance for teachers on what to look for and how to respond
  • Technology that provides Responsive Feedback and is designed to reveal mathematical thinking

Experience Kit digital lessons

Use the grade-specific links below to explore our interactive digital lessons. Learn more about assigning a lesson to your class using a single-session code.

In addition to the sample lessons below, you can view the Experience Kit brochure, which includes helpful print and digital navigation tips.

Grades K–5 brochure

Grades 6–A1 brochure

A digital math activity screen showing block arrangements and a worksheet page titled "Shelley the Snail" with related graphics.
A girl in a red and pink uniform kicks a soccer ball while two players in yellow attempt to block, showcasing teamwork akin to problem-solving strategies in Amplify Desmos Math. Another player runs in the background.
Kindergarten, Unit 6: Numbers 0–20

Sub-Unit 1: Counting Teen Numbers

A crowd gathers outdoors near a path lined with blueberry displays; musicians play on a stage, and people interact as a woman and child stand in the foreground holding drinks.
Grade 1, Unit 5: Adding Within 100

Sub-Unit 1: Adding Without Making a Ten

A family stands by a mailbox labeled "Three Hundred Two." In New York, a child holds a letter as an adult pats their head. Another adult, with a desmos math guide in hand, looks on proudly.
Grade 2, Unit 5: Numbers to 1,000

Sub-Unit 1: The Value of Three Digits

In an outdoor setting, a girl with glasses attentively washes a chicken in soapy water, surrounded by hills, trees, and buildings. Soap bubbles and leaves float in the air as she ponders New York math challenges amidst this tranquil scene.
Grade 3, Unit 6: Measuring Length, Time, Liquid Volume, and Weight

Sub-Unit 1: Measurement Data on Line Plots

In "Pat's Lei Shop," amidst the floral artistry, one can almost sense the precision akin to solving a New York math problem, with each lei meticulously assembled on a table with scissors, thread, and flowers.
Grade 4, Unit 6: Multiplying and Dividing Multi-Digit Numbers

Sub-Unit 1: Multi-Digit Multiplication

At a bustling puzzle stand, a person interviews a young individual holding a puzzle box. Various puzzles, including "Autumn Day," catch the eye. A sign proudly boasts, "Jonathan & Omar's Pleasing Puzzles!"—where New York math enthusiasts find joy in every challenge.
Grade 5, Unit 5: Place Value Patterns and Decimal Operations

Sub-Unit 1: Numbers to Thousandths

Three raccoons on a seesaw balance with a 21-pound weight in a city park setting under a clear sky.
Grade 6, Unit 6: Expressions and Equations

Sub-Unit 1: Solving Equations

A sheep stands on grass near a number line, with an orange point at zero; a festive sheep with a hat and party blower appears in a thought bubble.
Grade 7, Unit 6: Expressions, Equations, and Inequalities

Sub-Unit 3: Inequalities

Four colorful robots stand in front of a whiteboard with a graph in a classroom setting.
Grade 8, Unit 6: Associations in Data

Sub-Unit 2: Analyzing Numerical Data

A laptop screen displays a math activity with a question about a rocket's height. Icons of a rocket and mathematical functions are on the side.
Algebra 1, Unit 7: Quadratic Functions

Sub-Unit 1: Introduction to Quadratic Functions

Looking for help?

Support is always within reach. Our team is dedicated to supporting you throughout your review and can be reached at any time by emailing or calling us directly.

  • Live chat: Click the orange icon while logged in to get immediate help.
  • Phone: Call our toll-free number: (800) 823-1969.
  • Email: Send an email to help@amplify.com. In the message body, please include your name and question. Provide as much detail as possible, so we can more quickly help you find a solution.
A laptop screen displays a curriculum dashboard with a list of core units and colorful thumbnails for a sixth-grade ELA program.

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Discovering and exploring mathematics in every story

Smiling young boy sits at a classroom desk holding an open book, developing reading comprehension, while two other children are seen in the background engaged in activities.

Every picture book on your classroom shelf holds mathematical treasures waiting to be discovered! What if every read-aloud could go beyond a literacy moment to become a catalyst for mathematical sense-making? This question lies at the heart of Allison Hintz and Antony T. Smith’s delightful and informative book, Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion.

Many teachers have used traditional counting books and shape-focused stories to support students in connecting mathematics to literature. According to Hintz and Smith, you can challenge readers to extend and expand upon these experiences in ways that provide more space for them to make sense of stories; ask their own questions; see mathematics authentically in the world; and make connections between the stories, the math, and their lives. That’s the promise of mathematizing—approaching any story with a mathematical lens.

The concept of “mathematizing” goes beyond simply finding numbers in a story. Children are naturally curious and construct meaning by noticing, exploring, explaining, and modeling. The story context becomes a place to play and practice seeing math everywhere in our world. As we read a story aloud and pause to ask, “What do you notice? What do you wonder?,” students are able to surface structure, compare quantities, model situations, and justify their ideas, all while staying rooted in characters, plot, setting, and theme. The result is a classroom where math feels joyful, meaningful, connected, and accessible.

In this post, we’ll explore simple moves to mathematize your next read-aloud, sample prompts to elevate discussion, and follow-up activities to turn your library into a launchpad for mathematical thinking!

Mathematizing process and structure

While there’s no one way to facilitate a mathematical read-aloud, the following steps can help you get started:

  1. Explore books in your current library. There are no hard and fast rules for choosing the right book to mathematize, because a book can spark mathematical ideas in many ways. Look for books that a) are overtly ‘mathy’ where the math is central to the story’s plot, b) have illustrations that provide opportunities to explore the math in them, and/or c) have a story that inspires mathematical thinking, even if the math isn’t central to the story’s plot.
  2. Read the book aloud for the first time. The first read is a wonderful opportunity for students to hear and enjoy the story itself.
  3. Ask students what they noticed and wondered. As students share their responses, record them on a piece of chart paper to revisit later. If no responses pertain to the math in the story, you can follow up with the question, “Where did you see math in the story?”
  4. Reread the book a second time or revisit a specific page in the book. At this point, you want to start to focus on the math the students will explore in the book. You can either reread the entire story and pause on strategic pages that center on the mathematical ideas, or revisit specific pages in the story. (If the story is longer,it will probably be easiest to just flip back to specific pages.)
  5. Elicit student thinking. Ask students what math questions they could ask based on the pages they revisited.
  6. Give students a follow-up math activity. This could be based on a question the students mentioned earlier in this process, or one the teacher has planned.

Mathematizing examples

To save you time finding a book to use, we’ve outlined a plan based on some of our favorite books to mathematize (listed by grade band).

Grade levelK–1
Book title and authorBear Says Thanks by Karma Wilson
Mathematical focusCounting, addition, and mathematical representations
LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How many friends visited Bear? What different food items did Bear’s friends bring?”
Pages to revisitAs students describe the different foods, revisit those pages. Identify any foods the students didn’t mention. As you revisit each page, ask students, “How many of that food item did that friend bring? ”Record their responses on a piece of chart paper for each friend. 
ActivityArrange students in small groups of 3–4 and give them a piece of poster paper. Ask students to show each friend’s food items. They can represent them using pictures, counters, ten-frames, etc. After they’ve correctly represented each friend, ask them to show how many total food items Bear’s friends brought using numbers and equations. When they’ve finished, have them visit one another’s posters to see how others represented and added the food items. 
Grade level2–3
Book title and author100 Hungry Ants by Elinor J. Pinczes
Mathematical focusConnecting arrays to expressions
LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How did the ants rearrange themselves throughout the book?”
Pages to revisitAs students describe the different arrangements of ants, revisit those pages so students have a visual of the array. As you revisit each page, ask students, “How many ants are in each row? Each column? What is an equation we can write to represent the array?” Record their responses on a piece of chart paper. 
ActivityArrange students in small groups of 3–4 and give them a piece of poster paper. Give each group a different number of ants. Suggested numbers are: 12, 24, 36, 20, 18. Ask students to draw all of the different ways their number of ants could rearrange themselves and record an equation to match each. If it’s helpful, you can give each group a set of cubes, counters, or beans to represent the ants so they can manipulate them. Wrap up the activity by having students visit one another’s posters and discussing the similarities and differences between them. 
Grade level4–5
Book title and authorDozens of Doughnuts by Carrie Finison
Mathematical focusMultiplication and division
LaunchRead the story aloud. Ask students, “What do you notice? What do you wonder?” Record their responses on a piece of chart paper. And ask students, “How many ways did Luanne share her doughnuts as friends arrived at her door?”
Pages to revisitAs students describe the different ways Luanne shared her doughnuts, revisit those pages. As you revisit each page, ask students, “How many doughnuts were being shared? By how many animals? ”Record their responses on a piece of chart paper. 
ActivityArrange students in small groups of 3–4 and give them each a piece of poster paper. Ask them to show all of the ways Luanne shared her doughnuts. To enable variation, refrain from specifying the representation they should use. After they’ve finished, ask them to do a Gallery Walk to each other’s posters to get ideas to add to their poster. If none of the groups have a multiplication and division equation for each way, ask students to record those as well. Ask students how Luanne could have shared a dozen doughnuts with the following number of animals showing up at her door: 5, 8, 10, 14, 16, and 18. Encourage students to show their work and record multiplication and division equations. 

And with all the upcoming holidays and opportunities to gather with friends and family, we were also inspired to use Spaghetti and Meatballs for All! by Marilyn Burns in a mathematizing read-aloud. Follow this link to find K–2 and 3–5 lesson plans for this book that you can use right away!

Invest in high-quality professional development.

Amplify’s professional development (PD) provides a variety of learning experiences over multiple years to incrementally develop and apply the knowledge and skills needed for effective and self-sustaining implementation.

Gain insights into effective instructional techniques and develop a deeper understanding of your Amplify program(s) by investing in PD.

The foundation for long-lasting and sustainable change

Partner with us to plan long-lasting and sustainable change for your school or district. Change achieved deliberately is much more likely to stick and get results. We can support you through this journey to drive your professional improvement, enrich your instructional practice, and increase student impact.

Professional learning journey

Prepare

You’ll understand research-based practices to support new program implementation.

Prepare learning experiences will help shift literacy and math instruction in areas such as the Science of Reading and/or problem-based approaches to math.

Begin

You’ll build the foundational knowledge and skills necessary to begin teaching with your Amplify program(s).

Program-aligned packages will support those who are new to Amplify’s programs.

Practice

You’ll refine instrucional skills, expand knowledge of your Amplify program(s), and explore more advanced insturctional strategies.

Program-aligned packages will support those who have experience using Amplify’s programs.

Advance

You’ll deepen understanding of content and pedagogy and build-in house capacity to support a robust, sustainable implementation.

Program-aligned offerings will support advanced implementation, build capacity for instructional leaders, certify in-house trainers to deliver Launch sessions, and more.

Learn more about our curated catalog of packages and sessions to support each stage of your learning journey.

Multi-program, suite packages

Core program packages

Literacy

  • Amplify Texas ELAR/SLAR K–5
  • Amplify Texas ELAR 6–8

STEM

  • Amplify Math
  • Amplify Desmos Math (K–A2)
  • Amplify Science
 

Supplemental program sessions

  • Boost Reading Texas K–8
  • Boost Lectura K–2

Assessment program packages

  • mCLASS Texas Edition
  • mCLASS Lectura Texas

mCLASS Intervention K–6 program sessions

 

Empower teachers to continuously improve.

Professional development helps teachers stay motivated and inspired to grow professionally. Demonstrate your commitment to your staff by empowering them with professional development packages that include on-site or virtual Launch, Strengthen, or Coach sessions, all of which will orient you and your team to the full features of Amplify programs.

You can also personalize your learning experience by adding enhancement sessions to base packages.

Launch

Launch sessions introduce Amplify programs and support strong implementation.

After learning about the program’s foundational principles and key features, you’ll practice administering the program within a collaborative environment.

Strengthen

Strengthen sessions deepen understanding of the program. Session offerings are targeted and meant to take your practice—and your students’ learning—to the next level.

Offered as part of core packages, as well as enhancements, Strengthen sessions are intended to effectively address your students’ needs. Examples include:

  • A focus on data analysis.
  • Examining student writing.
  • Targeted intervention instruction.

Coach

Coach sessions elevate instructional practice and help meet teachers’ and schools’ specific needs.

Partner with an Amplify coach who will support you in planning a day tailored to meet the needs of teachers and/or leaders. Your customized session will leverage our menu of support, which can include:

  • Lesson modeling by an Amplify facilitator.
  • Classroom observations and debriefs.
  • Grade-level planning.

Coach sessions are customized to you with an Amplify facilitator.

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Learning may ebb and flow between phases depending on your teachers’ and leaders’ needs, experiences, and professional goals. Amplify PD aims to continually grow, develop, and refine instructional practices to support student learning and achievement.

Frequently asked questions

We value your partnership and aim to provide you with the highest quality learning experiences. Check out our frequently asked PD questions below, along with responses.

Additional learning

Once you become an Amplify customer, you’ll have access to many opportunities to continue learning how to get the most out of your Amplify program(s).

To get a sense of our support, check out some of our free resources:

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Biliteracy supports

Sessions are available to support educators teaching with both Amplify ELAR and Amplify SLAR core programs, or both mCLASS Texas Edition and mCLASS Lectura Texas assessment programs.

Facilitated in both English and Spanish, these specialized sessions should be scheduled for biliteracy teachers using both curriculums and/or assessments. Substitute a biliteracy session for the six-hour initial training in your package, or add these sessions on to your package for your biliteracy teachers.

Speak to our team to learn more!

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If you’re ready to submit your price quote, purchase order, or payment, please visit our Ordering Support site for more information.

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We are educators supporting educators. Every member of Amplify’s national team of highly experienced and qualified facilitators is a former educator with years of hands-on classroom and/or administrative experience. Our facilitators are passionate about supporting educators in the implementation of their Amplify programs and creating transformational change for all students.

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Elk Grove Science K5

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Getting started with Amplify Science California

Dear Elk Grove K–5 teachers,

Welcome to the Amplify Science California family! Below you’ll find everything you need to successfully kick off your science instruction this year.

– Your California team

Amplify Science - Student reading a book remote & hybrid

Program introduction

Onboarding videos

To start using Amplify Science California quickly in your classroom, check out the following onboarding videos. They cover what you need to know to get started fast, from unpacking materials to quickly start using Amplify Science in your classroom and navigating the digital Teacher’s Reference Guide.

Program pacing

Hands-on materials kit

The following videos give you a quick look into our Amplify Science California classroom kits. For each grade level, you’ll find a “How to unpack your kit” video for the first unit of the program.

Teacher digital resources

Watch this video to understand the basic organization of the digital teacher experience and how to navigate the platform.

Want some practice? Download this exploration guide to practice toggling between teacher view, presentation view, and student view.

Our new digital experience also makes it easy to assign work through our LMS integrations.

Our new digital experience also makes it easy to view student work in real time.

Student digital resources

Watch this video to take a peek at the various student digital resources available to your class.

Use this Student Login Click Path document to support students and families logging in from home.

Essential resources

Your Teacher’s Reference Guide is a tremendously rich resource. It’s also packed! That’s why teachers getting started with Amplify Science love our condensed Unit Guides, lesson planners, and device calendars.

Unit Guides

These short and sweet guides provide a big picture overview of each unit’s phenomenon and storyline, the key questions that guide learning, and how the storyline develops from chapter to chapter. We even spoil the big reveal at the end by pointing out ahead of time what students figure out throughout the unit.

A laptop displays an educational website titled "The Earth System" with lesson modules; a printed Teacher’s Guide with a similar cover design is shown beside it.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Lesson planners

Our lesson planners give you easy access to direct links to key resources within the program.

Kindergarten

Grade 1

Grade 2

Grade 3

Grade 4

Grade 5

Teacher-provided materials

Your Amplify Science classroom kit includes a wide variety of consumable and non-consumable items. In fact, each kit contains enough non-consumables to support a class of 36 students working in small groups, and enough consumables to support 72 student uses.

In addition to these provided items, there are some teacher-provided items required in each unit. For a consolidated list of teacher-provided items per unit, download the appropriate PDF below.

Device calendars

Our at-a-glance device calendars make device management and sharing between grade-level colleagues a breeze. With one calendar per unit (beginning in grade 2), you can easily see which lessons utilize devices.

Approach to assessment

The Amplify Science California assessment system is grounded in the principle that students benefit from regular and varied opportunities to demonstrate understanding through performance. In practice this means that conceptual understanding is revealed through engagement in the science and engineering practices.

Assessment types at a glance

In your classroom, you’ll be utilizing a variety of formative (F) and summative (S) assessments:

  • End-of-Unit Assessment (S): Assessments toward the end of each unit feature a combination of targeted discussions, student-generated models, and written explanations to gauge students’ knowledge and growth.
  • Pre-Unit Assessments (F): Discussion, modeling, and written explanations to gauge students’ knowledge.
  • On-the-Fly Assessments (OtFA) (F): Multi-dimensional tasks integrated regularly throughout the lessons. OtFA opportunities were designed to help teachers make sense of student activity during a learning experience (e.g., student-to-student talk, writing, and model construction) and to provide evidence of how a student is coming to understand core concepts and developing dexterity with SEPs and CCCs. Three-dimensional assessment opportunities make measuring progress toward NGSS learning goals possible.
  • Self-assessments (F): One per chapter; brief opportunities for students to reflect on their own learning, ask questions, and reveal ongoing wonderings about unit content.
  • Critical Juncture Assessments (F): Variety of multidimensional performance tasks intended to assess student progress, occurring at the end of each chapter. Examples include writing scientific explanations, engaging in argumentation, developing and using models, and designing engineering solutions. Based on student performance on the assessment, teachers have access to recommendations for targeted student interventions, suggested follow-ups, or differentiating classroom instruction.
  • End-of-Unit Assessment (S): Assessments toward the end of each unit feature a combination of targeted discussions, student-generated models, and written explanations to gauge students’ knowledge and growth.

Pre-Unit Assessments

Most Pre-Unit assessments are embedded within an activity of the first lesson of a unit. In kindergarten and grade 1, the Pre-Unit assessment (as well as the End-of-Unit assessment) is oral. In grades 2–5 they are typically written. Refer to the Digital Resources area of the Lesson Brief for materials needed for the assessment activity, such as the Clipboard Assessment Tool (K–1 only), copymasters (grades 2–5 only), and an Assessment Guide that will help you interpret and leverage students’ responses.

If you and your students have Interactive Classroom licenses, students can complete their assessment digitally instead of using the copymaster.

When students complete the assessment pages digitally, you’ll be able to review their work on the View Work page.

Critical Juncture Assessments

Critical Juncture assessments typically occur towards the end of each chapter. The Materials and Preparation section will indicate when there is a Critical Juncture to prepare for, but you can also tell when an activity is designed to be a Critical Juncture assessment by the hummingbird icon that will appear within it. Selecting the hummingbird icon will tell you how to assess students’ understanding with the activity, and how to tailor instruction based on what you find. If you need guidance on the “answers” to the assessment activity, refer to the “Possible Responses” tab.

If you are using Classroom Slides or Interactive Classroom, you’ll see a hummingbird or “Critical Juncture” label in the bottom right corner of one of the slides of the activity.

The notes about assessing understanding and tailoring instruction are located in the notes of that slide (on the right-hand side of the Teacher’s Guide tab in the Interactive Classroom experience; underneath the slide in Classroom Slides).

End-of-Unit Assessments

End-of-Unit assessments are typically the last lesson of a unit. In some units, these are two-part assessments that take place over two lessons. The easiest way to find the End-of-Unit assessment is to skim through the lesson titles. Lessons containing End-of-Unit assessments will always have that noted in the title.

Like the Pre-unit assessment, you can find materials for the End-of-unit assessments in the Digital Resources area of the Lesson Brief.

On-the-Fly Assessments

These embedded assessments leverage the formative opportunities in the learning experience students are already engaged in, such as creating models, analyzing data, actively reading, conducting investigations, and more. Refer to the Critical Juncture section above for guidance on finding information about using them.

Unit-level assessment information

You can find overall information about an individual unit’s assessments in the “Assessment System” resource, which is located within the Teacher References section on the Unit Overview page.

The Assessment System resource contains a comprehensive list of all of the assessment opportunities in the unit, including the assessment’s location, a brief indication of what students are doing in that particular activity, what type of assessment it is, which Disciplinary Core Ideas, science and engineering practices, and cross-cutting concepts it specifically addresses, and the kind of evaluation guidance you can expect for it. If you are in a kindergarten or first grade unit, you will also find information on the Clipboard Assessment Tool (used for supporting oral assessment) in this section.

If you’re interested in focusing on information related to the unit’s Critical Juncture and On-the-Fly assessments in particular, check out the “Embedded Formative Assessments” resource, also located within the Teacher References section on the Unit Overview page.

Three-dimensional assessment connections

All assessment opportunities within Amplify Science California include clear labeling around the Disciplinary Core Ideas (DCIs), Crosscutting Concepts (CCCs), and Science and Engineering Practices (SEPs) to help teachers connect formative and summative assessments to specific NGSS dimensions.

Coming soon

Unlike other publishers, we don’t make you wait until your next adoption to get the latest and greatest from Amplify. We’re always launching new and exciting features. In fact, on this page is a list of new features you can look forward to using during the 2023-2024 school year.

FAQs

Program questions

Amplify Science California is a flexible, blended K–8 science curriculum that addresses 100 percent of the Next Generation Science Standards for California and a significant number of the California English Language Development Standards and Common Core State Standards for English Language Arts, Literacy in Science and Technical Subjects, and Math. Together, the units deliver three-dimensional instruction across the following disciplines: Life Science, Earth and Space Science, Physical Science, and Engineering Design.

Amplify Science California does indeed feature some powerful and engaging digital components, which are gradually introduced beginning at grade 2. However, as a fully blended and flexible program, Amplify Science California can be (and has been) implemented in a wide variety of scenarios.

All lessons were designed with device sharing in mind, and never assume that every student has a separate device. While 1:1 scenarios are great, they aren’t required. When devices are necessary for students to fully experience a concept, teachers can opt to share devices across pairs or small groups, or simply display the Sim or Modeling Tool to the whole class and allow students to “drive” using your device.

Rather than introducing a concept on Monday, testing for mastery on Friday, and knowing students will forget everything by the next Tuesday, we set out to help students build meaningful and lasting knowledge that they can retain and transfer over the course of the entire unit. We accomplish this by giving students multiple opportunities (a.k.a. “at-bats”) to encounter, explore, and experience a concept. Said another way, Amplify Science California is actually made up of a series of multi-modal “mini-lessons.” This intentional, cyclical, and iterative design mirrors the 5Es, allows teachers the flexibility to speed up or skip ahead once students have demonstrated mastery, and empowers students to learn concepts more deeply than any other program.

Yes. Rather than separating performance expectations into physical science units, earth and space science units, and life science units, Amplify Science California units are organized around anchoring phenomena designed to give students opportunities to dive deeply into certain Disciplinary Core Ideas (DCIs) while also drawing from or applying to others. In organizing the Amplify Science California middle school units, we’ve carefully sequenced these ideas within each grade level to support the development of deep and coherent understanding.

Many real-world phenomena cross the domain boundaries of life, physical, or earth and space science (as well as engineering). Each Amplify Science California unit begins with an intriguing real-world phenomenon that poses a problem that needs to be understood and/or solved. By the end of the unit, students will have analyzed the anchor phenomenon across multiple scientific domains, possibly designed and tested an engineering solution, and applied what they’ve learned in a different context.

For example:
In the Light Waves unit, students investigate the anchoring phenomenon of why Australia has a much higher skin cancer rate than countries at similar latitudes like Brazil. The focus of this unit is on Disciplinary Core Ideas related to wave properties (PS4.A) and electromagnetic radiation (PS4.B). Students explore these physical science ideas deeply within the unit, and also draw on ideas from earth science (e.g., latitudinal variation of the sun’s energy) and life science (e.g., the effect of energy on the DNA in the nucleus of a cell) in order to explain the central phenomenon.

Absolutely. Hands-on learning is at the heart of Amplify Science California. Integrated into every unit are opportunities for students to take on the role of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend their claims.

In addition, our unique combination of focus and flex activities means teachers have more options, opportunities, and materials to make learning active. Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

What’s important to remember is that more hands-on doesn’t necessarily mean better, at least according to the California NGSS. That’s because only two of the eight Science and Engineering Practices (SEPs) are directly related to hands-on learning.

Just as scientists gather evidence from many types of sources, students in the Amplify Science California program gather evidence not just by making physical models, but also by making and interpreting digital models; reading texts; watching videos; and analyzing photographs, maps, and data sets. By doing do, students are provided with more opportunities than any other program to use all of the practices called out in the California NGSS Framework:

  • Asking questions
  • Developing and using models
  • Planning and carrying out investigations
  • Analyzing and interpreting data
  • Using mathematics and computational thinking
  • Constructing explanations
  • Engaging in arguments from evidence
  • Obtaining, evaluating, and communicating information

While all of our units engage students in gathering evidence from a rich collection of sources, the reliance on different types of evidence (and evidence sources) varies according to unit. For instance, some units lend themselves to meaningful hands-on experiences, while in other units the phenomena students are investigating are too slow, too dangerous, or too big to be observed directly. In those units, students rely more heavily on other evidence sources such a physical models or simulations.

Unit types in grades K–5

In each K–5 grade, there is one unit that emphasizes investigation, one that emphasizes modeling, and one that emphasizes design. In addition, in grades 3–5, there is also one unit that emphasizes argumentation.

Unit types in grades 6–8

Each 6–8 grade features three types of units: LaunchCore, and Engineering Internships. Each year has one Launch unit, six Core units, and two Engineering Internships.

For teachers who want to supplement the lessons with even more hands-on activities, optional “flextension” activities are included in many units.

Yes indeed. Amplify Science California integrates all four STEM disciplines—science, technology, engineering, and math, in addition to English Language Arts—throughout the curriculum. In addition, each grade level features specific units that emphasize engineering design.

Yes, the program includes multiple opportunities for summative assessments.

End-of-unit assessments: At grades K–1 these look like targeted conversations, at grades 2–5 we incorporate written responses, and at grades 6–8 we assess through a combination of auto-scored multiple-choice questions and rubric-scored written responses. These summative assessments for each unit are designed to provide valid, reliable, and fair measures of students’ progress and attainment of three-dimensional learning.

Benchmark assessments: Delivered four times per year in grades 3–5 and three times per year in grades 6–8, benchmark assessments report on students’ facilities with each of the grade appropriate DCIs, SEPs, CCCs, and performance expectations of the California NGSS.

Science Seminars and final written arguments (formative and summative components): In grades 6–8, culminating performance tasks for each core unit invite students to figure out a new real-world problem. They collect and analyze evidence, examine a number of claims, and then engage in a full-class discussion where they must state which claims are best supported by the evidence, all while making clear their reasoning that connects the evidence to the claims. After the seminar, students then individually write their final scientific argument, drawing on the DCIs, SEPs, and CCCs they have used over the course of the unit to develop a sophisticated and convincing argument that addresses the problem they’ve been investigating. Rubrics, scoring guides, and examples of student responses at each scoring level are provided to teachers to support the assessment of students’ understanding of concepts and specific practices.

Amplify Science California provides more than enough instructional content to fill 180 days of instruction. However, unlike other programs that expect you to complete 180 discrete lessons, Amplify Science California includes built-in wiggle room.

For example, the typical elementary classroom delivers science instruction only two times per week. Rather than asking teachers to wade through unnecessary content, we designed our program to address 100 percent of the California NGSS in just 66 days at grades K–2 and 88 days at grades 3–5. When it comes to middle school, we address 100 percent of the California NGSS in 146 lessons.

Some classes might last longer than one session due to a number of reasons (e.g., enthusiastic student conversations, challenging topics requiring deeper dives, more time needed to accommodate diverse learners, etc.). Also, teachers might want to supplement Amplify Science California with some of their own favorite lessons. Lastly, we’ve accounted for the inevitable assembly days, class trips, testing schedules, etc. For teachers that want to go deeper or expand upon a unit topic, we also offer a number of additional lessons that are not core to each unit.

Amplify Science California lessons are designed to be completed in the following time frames:
Lessons in grades K–1 are designed for 45 minutes of science instruction.
Lessons in grades 2–5 are designed for 60 minutes of science instruction.

That said, it’s not a problem if you can’t allocate 45 minutes of science instruction every day at K–1, or 60 minutes per day at 2–5. Since there are a total of 66 lessons to address 100 percent of California NGSS at grades K–2, and 88 lessons to address 100 percent of California NGSS at grades 3–5, you can easily teach the lessons in smaller blocks and cover all of the content over the course of the school year.

Each lesson of every Amplify Science California unit includes point-of-use differentiation strategies and embedded teacher and student supports for diverse learners, including English learners, students who need more support, and students who are ready for more challenge. These strategies and methods ensure that all students have access to the same content as their peers.

Two notable categories of suggested modifications are:

  • English-learner-specific strategies such as English/Spanish glossaries, native language supports, and provision of cognates and other content-specific language scaffolds are provided in each unit.
  • Relatively small alterations and additional scaffolds that provide students with greater access to the content.
    These types of scaffolds benefit all learners and include suggestions such as providing graphic organizers, practice with multiple-meaning words, etc.

With Amplify Science California, the use of technology is always purposeful.

For example:

  • The curriculum has a strong emphasis on literacy, with students reading and analyzing informational texts, and writing scientific explanations and arguments.
  • Digital elements are gradually introduced to students in grades 2–3, with the greatest use of digital elements taking place in grades 4–5, as the phenomena at these grades become more challenging to observe directly.
  • The curriculum’s readers and interactive notebook pages are available in both print and digital across all K–5 units.

This curriculum addresses a significant number of the standards as they pertain to science. Throughout each unit, students read science texts, engage in science talk and argumentation, and write evidence-based science explanations. The curriculum supports vocabulary, language, and reading comprehension development. Students also use measurement tools with precision, record and analyze data, make sense of scientific phenomena, and develop solutions to problems experienced in the real world.

Digital questions

Teacher Support notes including sample teacher talk, student responses, pedagogical support, and possible student responses are provided within your student-facing slides. Simply click “Teach” and reference your private Teacher Guide tab. Students will only see the lesson slides that you are presenting.

You, the teacher, must “Start class” to launch the presentation tab. (Remember, without the presentation tab, students would be able to see your teacher notes.)

Clicking “Starting class” also brings students to the correct slide, which is particularly important for young students who are learning to navigate.

Teachers can either press the “End class” button in the bottom right corner of the slide navigation, or they can simply close the presentation tab.

Clicking “End class” also enables students to navigate through the lesson on their own. That means they’ll be able to return to slides and books to review content, to the Sims and Modeling Tools to replay them, or to notebook pages to update their work.

You can click on the “Student preview” option in the bottom right corner (within the menu that opens when you click the three dots) to open a new browser tab where you can preview the student view using your teacher account.

Any work you complete in this student preview (or elsewhere in the teacher experience) will be automatically saved to your account.

Looking for help?

For login or technology issues, please submit an EGUSD Heat ticket. For curriculum and pedagogical questions, please refer to the support resources below.

Powerful (and free!) pedagogical support

Amplify provides a unique kind of support you won’t find from other publishers. We’ve developed an educational support team of former teachers and administrators who provide pedagogical support for every Amplify curriculum, assessment, and intervention program. This service is completely free for all educators who are using our programs and includes:

  • Guidance for developing lesson plans and intervention plans.
  • Information on where to locate standards and other planning materials.
  • Recommendations and tips for day-to-day teaching with Amplify programs.
  • Support with administering and interpreting assessment data and more.

To reach our pedagogical team, use our live chat within your program, call (800) 823-1969, or email edsupport@amplify.com

Timely technical and program support

Our technical and program support is included and available from 4 a.m. to 4 p.m. PT, Monday through Friday, through a variety of channels, including a live chat program that enables teachers to get immediate help in the middle of the school day.

For your most urgent questions:

  • Use our live chat within your program.
  • Call our toll-free number: (800) 823-1969.

For less urgent questions:

Connect with other teachers

Our Amplify Science Facebook group is a community of Amplify Science educators from across the country. It’s a space to share best practices, ideas, and support on everything from implementation to instruction. Join today.

Welcome Reviewers, to Amplify Desmos Math!

Amplify Desmos Math thoughtfully combines conceptual understanding, procedural fluency, and application. Each lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

Scroll to learn more about the program and explore sample materials.

About the program

We believe in math that motivates. Our structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students. 

The program thoughtfully combines conceptual understanding, fluency, and application, motivating students with interesting problems they are eager to solve. Teachers can spend more time where it’s most impactful: creating a collaborative classroom of learners.

A powerful suite of math resources

Amplify Desmos Math combines the best of problem-based lessons, intervention, personalized practice, and assessments into a coherent and engaging experience for both students and teachers.

A digital interface displays a math screener report on the left and a math problem involving division, alongside a visual representation of students lined up on the right, integrating rich math resources from Amplify Desmos Math.

Screening and progress monitoring

mCLASS® Assessments, along with daily formative checks, measure not only what students know, but also how they think. The asset-based assessment system provides teachers with targeted, actionable insights, linked to core instruction and intervention resources.

Two side-by-side math activities for children: on the left, a caterpillar-themed block challenge, and on the right, a worksheet for finding pairs that sum to 10. These exercises are fantastic ways to amplify children's engagement with math concepts.

Core instruction

Amplify Desmos Math lessons provide a structured approach to problem-based learning, helping teachers create a collaborative math community with students at its center. Each lesson systematically builds on students’ curiosity to develop lasting grade-level understandings for all students.

Two pages from a New York math textbook on determining coordinates after a rotation. Includes sections on modeled review, guided practice, and teacher's notes, with diagrams and examples that amplify the learning experience.

Differentiation and intervention

Integrated resources like Mini-Lessons, Fluency Practice, and Math Adventures provide targeted intervention on a specific concept or skill connected to daily instruction. Extensions are also available to stretch students’ understanding.
Boost™ Personalized Learning activities help students access grade-level math through engaging, independent digital practice. Responsive Feedback™ adjusts to students’ work, providing item-level adaptivity to further support their learning.

Two pages from a New York math textbook on determining coordinates after a rotation. Includes sections on modeled review, guided practice, and teacher's notes, with diagrams and examples that amplify the learning experience.

An approach that supports teachers

Clear, step-by-step instructional moves help teachers plan and teach student-centered lessons that use student thinking to differentiate instruction and guide to grade-level understanding. They include:

  • Guidance on what to listen for and how to respond.
  • Clear learning objectives to keep learning on track for each activity and lesson.
  • Daily reinforcement activities to provide direct instruction when needed.

A structured approach to problem-based learning

Problem-based learning asks students to make sense of and think strategically about mathematically interesting problems. This approach allows students’ ideas to take
center stage, so they are active and engaged in their learning process. Teachers are able to hear and respond to student thinking in real time, guiding and differentiating instruction right in the moment.

Moving from “I do, We do, You do” to “You do, We do, I do”
Lessons begin by activating student’s prior knowledge and curiosity, inviting them to explore the math, collaborate, and refine their thinking. By focusing on developing student thinking first, teachers can better connect ideas, guide learning, and synthesize learning objectives.

Lessons that are rigorous and delightful

Every lesson in Amplify Desmos Math is designed to put students at the center of their learning. Utilizing research-based best practices, students engage in meaningful work based on rich problems and real-world experiences.

Two young girls build with colorful blocks at a table while an adult woman observes and assists them in a classroom setting.

Warm-Up

Lessons begin by inviting every student to contribute to the mathematical discussion. Instructional routines are often used to build fluency, set the context, activate prior knowledge, or highlight a strategy that may be helpful in the lesson. 

Rich learning activities

Math knowledge is built through experiences and meaningful interactions. Students notice, wonder, explore, calculate, predict, measure, explain their thinking, use math to settle disputes, create challenges for their classmates, and more. Teachers serve as a guide, using a Launch, Monitor, Connect framework:

  • Launch: Teachers offer a short introduction to the problem or challenge
  • Monitor: As students work individually, in pairs, or in groups, teachers ask questions and provide support to move student thinking closer to the intended math goal.
  • Connect: Teachers connect student ideas to the Key Takeaway of the activity to help students synthesize and solidify the big ideas.

Synthesis

Teachers ensure that students end the lesson with accurate and enduring understandings of the math goal through synthesis of student ideas, explicit instruction, and reflection.

A short Show What You Know assessment allows students to show what they know about the learning goals of the lesson and reveal what they are still learning.

Differentiation and practice

Lasting understanding requires reinforcement. Every lesson offers Lesson Practice instructional recommendations to Support, Strengthen, and Stretch learning.

Two side-by-side math activities for children: on the left, a caterpillar-themed block challenge, and on the right, a worksheet for finding pairs that sum to 10. These exercises are fantastic ways to amplify children's engagement with math concepts.

Print for every lesson with engaging digital experiences

Whether in print or digital form, engaging interactions enable students and teachers to openly exchange ideas. Each lesson includes student print materials, interactive teacher Presentation Screens, and digital resources for practice and differentiation. Some lessons also use manipulatives or provide options for students to use devices individually or in pairs. Device recommendations for student use are age-appropriate, with more frequent usage in middle and high school.

Demo access

Please login to the digital platform to experience our full program as part of your review. In order to access the digital platform, you’ll need to log into using your unique login credentials below.

  • Click the orange button below to access the platform.
  • Click “Log in with Amplify.”
  • Enter the username and password:
    • Username:
    • Password:
  • View the video for helpful platform navigation tips.

Assessments

By starting with what students already know, Amplify Desmos Math helps build a strong foundation for success to guide and support future learning. Teachers are empowered to transform every classroom into an engaged math community that invites, values, and develops student thinking. With explicit guidance on what to look for and how to respond, teachers can effectively support students as they develop their understanding.

Open math workbook showing an End-of-Unit Assessment with multiple-choice and written response questions on fractions and equivalent values.

Program assessments

A variety of performance data in Amplify Desmos Math provides evidence of student learning while helping students bolster their skills and understanding.

Unit-Level Assessments

Our embedded unit assessments offer key insights into students’ conceptual understanding of math. These assessments provide regular, actionable information about how students are thinking about and processing math, with both auto-scoring and in-depth rubrics that help teachers anticipate and respond to students’ learning needs.

Lesson-Level Assessments

Amplify Desmos Math lessons are centered around sense-making and in-the-moment feedback. Daily moments of assessment provide valuable evidence of learning for both the teacher and student.

Data and reporting

Amplify Desmos Math provides teachers and administrators with unified reporting and insights so that educators have visibility into what students know about grade-level math—and can plan instruction accordingly for the whole class, small groups, and individual students.

A table displays students' performance levels across various items, with a detailed score distribution for a specific assessment shown in a separate overlay. Geometric design elements accented the background, providing an engaging visual touch ideal for any math classroom using Amplify Desmos Math.

Assessment reports

Reporting functionality integrates unit assessments, lesson assessments, personalized learning, Benchmark assessments, and Progress Monitoring for a comprehensive look at student learning.

Our reports show proficiency and growth by domain, cluster, standard, and priority concept using performance data from unit assessments. Then our reports highlight areas of potential student need to allow teachers to modify their instruction and target differentiated support.

At-a-glance views of unit-level assessment results inform your instructional planning, and you can also drill down to item-level analysis.

Standards reports

Our standards report allows you to monitor proficiency at the class and individual student levels. Proficiency and growth are shown by domain, cluster, standard, and priority concepts. Areas of potential student need are highlighted to allow teachers to modify their instruction and target differentiated support.

Administrator reports

Amplify Desmos Math provides a complete picture of student, class, and district performance, allowing administrators to implement instructional and intervention plans.

  • Track student, class, and district performance with usage, completion, and assessment data.
  • Accurately group students and classes with the Benchmark and Progress Monitoring data of mCLASS Assessments and allow teachers to reliably implement and track the progress of Tier 2 and Tier 3 intervention.
  • Provide one data-driven solution that educators can rely on for high-quality math instruction.

Differentiation and intervention

Amplify Desmos Math views differentiation as an ongoing process where teachers are both reactive and proactive to student needs, ensuring that all students have clear pathways to proficiency. Through rich data and teacher support, Amplify Desmos Math uses flexible categories of intervention and enrichment that adjust daily according to student thinking.

In-the-moment differentiation supports are available for every lesson, both digitally and in the print Teacher Edition.

A teacher sits at a table with two students, using small objects and a workbook to provide individualized instruction during a Boost Math lesson in a classroom with large windows.
A table showing differentiation teacher moves with examples of representing groups in different ways, support prompts, and a stretch question about patterns with more teams.

In-lesson differentiation

Within every lesson activity, teachers can use the suggestions in the Differentiation Teacher Moves table to provide in-the-moment instructional support while students are engaged in the work of the lesson. This table can help teachers anticipate the ways students may approach the activity, and provides prompts that they can use during the lesson to Support, Strengthen, and Stretch individual students in their thinking. Teachers are provided with clear student actions and understanding to look for, each matched with immediately usable suggestions for how to respond to the student thinking illustrated in each row of the table. In addition to using these suggestions in the moment as teachers monitor student work, teachers can review the Differentiation table in advance to help them anticipate how students are likely to approach the activity.

Differentiation: Beyond the Lesson

Teachers are provided with recommendations for resources to use with each group of students needing support, strengthening, and stretching after each lesson. Support, Strengthen, and Stretch resources include:

  • Mini-Lessons: 15-minute, small-group direct instruction lessons targeted to a specific concept or skill
  • Item Banks: Space for teachers to create practice and assessments by using filters and searching for standards, summative-style items, and more
  • Fluency Practice: Adaptive, personalized practice built out for basic operations and more
  • Centers (K–5): Lesson-embedded routines and practice for students that are vertically aligned across grade levels
  • Extensions: Lesson-embedded Teacher Moves including possible stretch questions and activities for students
  • Lesson Practice: Additional practice problems support every lesson
  • Math Adventures: Strategy-based math games where students engage with math concepts and practice skills in a fun digital environment
Two pages from a math workbook on determining coordinates after a rotation, with diagrams, problem sets, and instructional text, displayed on a yellow and gray background.
A classroom teaching guide displays strategies for discussing pre-image and image in math, goals for a parallelogram lesson, and tips for supporting multilingual learners.

Multilingual/English Learner supports

Supports for multilingual/English learners (ML/ELs) are called out at intentiSupports for multilingual/English learners (ML/ELs) are called out at intentional points within each lesson. These suggested supports are specific, targeted actions that are beneficial for ML/ELs. They often describe a modification to increase access to the task or provide support with contextual or mathematical language development that can often be helpful to all learners. ML/EL supports may also be attached to Math Language Routines.onal points within each lesson. These suggested supports are specific, targeted actions that are beneficial for ML/ELs. They often describe a modification to increase access to the task or provide support with contextual or mathematical language development that can often be helpful to all learners. ML/EL supports may also be attached to Math Language Routines.

Math Language Development

Every lesson in Amplify Desmos Math includes opportunities for all students to develop mathematical language as they experience the content. Amplify Desmos Math purposefully progresses language development from lesson to lesson and across units by supporting students in making their arguments and explanations stronger, clearer, and more precise. This systematic approach to the development of math language can be broken down into the following four categories of support:

  • Vocabulary: Units and lessons start by surfacing students’ language for new concepts, then building connections between their language and the new vocabulary for that unit.
  • Language goals: Language goals attend to the mathematics students are learning, and are written through the lens of one or more of four language modalities: reading, writing, speaking, and listening.
  • Math Language Routines: Math Language Routines are used within lessons to highlight student-developed language and ideas, cultivate conversation, support mathematical sense-making, and promote meta-cognition.
  • Multilingual/English learner supports: Supports for multilingual/English learners (ML/ELs) are called out at intentional points within each lesson.
Two girls sit at a table with open books, one making hand gestures while smiling, the other looking at her and giving a thumbs up. Behind them are shelves filled with books, capturing the lively atmosphere of a math classroom.
Digital educational material showing an activity named "Hamster Homes" involving tube length and platform heights for a hamster cage. Includes a diagram with platforms measuring 9 inches.

K-5 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade. For a full program review, please login to the digital platform or request physical samples.

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

Cover of Amplify Desmos Math Grade K Teacher Edition featuring three children playing with math-related objects and a group of rabbits sitting nearby, aligning with the engaging curriculum seen in New York math classrooms.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 2: Counting and Comparing Images.

Cover of "Amplify Desmos Math: Student Edition Kindergarten," featuring an illustration of three children playing with math-related toys. A group of small white animals, possibly hamsters, play nearby. The scene brilliantly captures the joy of New York math exploration for young learners.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 2, Sub-Unit 2: Counting and Comparing Images.

Cover of "Amplify Desmos Math Grade K Centers Resources" featuring a large, stylized red and pink "C" on a light pink background with simple geometric designs. This distinctive cover complements New York math curriculums with its engaging visual elements.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

A digital activity screen, crafted in the style of Amplify Desmos Math, shows two paths with different quantities of mushrooms. The user is prompted to choose the path with more mushrooms. A bear is on the left side of the screen.

In this lesson, students apply their understanding of how to compare groups of images as they determine which group has more or fewer and then compare their strategies by guiding a bear through a path that has more mushrooms than the other.

Children interact with math activities on a large tablet while observing fish illustrations. The text reads "Amplify Desmos Math Grade 1 Teacher Edition, aligned with New York Math standards.

Skills Unit 2 Teacher Guide

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 1: Adding and Subtracting Within 10.

Illustration of three children engaged in math activities from the "Amplify Desmos Math: Student Edition 1" textbook. One child holds a number card, while the others manipulate counters and images, experiencing an exciting approach inspired by New York math techniques.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 1: Adding and Subtracting Within 10.

Cover of "Amplify Desmos Math Centers Resources" for Grade 1, featuring a yellow and white 3D letter "C" on a light background.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

An educational game screen, inspired by New York math standards, shows a subtraction problem, "4 - 1," with a frog moving along numbered lily pads to reveal the answer "3.

In this lesson, students find differences when subtracting 1 and 2 from the same number by helping a frog reach a lily pad where it can eat a bug.

Cover of the "Amplify Desmos Math" Grade 2 Teacher Edition, showcasing children measuring with rulers and a poster displaying a mathematical equation, set against whimsical scenery with a colorful dragon. Perfect for New York math classrooms.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 1: Adding and Subtracting.

Cover of "Amplify Desmos Math Student Edition 2" showing three children performing a New York math activity with blocks and measurements.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 1: Adding and Subtracting.

Cover of an educational book titled "Amplify Desmos Math Grade 2 Centers Resources" featuring a green "C" on a light green background, perfect for enhancing New York math education.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

An educational activity where users must select the block with the correct number to make a total of 10 using the given block numbers. The UI, inspired by New York math standards, features a caterpillar and two tree stumps to amplify engagement with Desmos Math tools.

Students continue to develop fluency by finding the number that makes 10 by helping a millipede reach its favorite food – a clump of leaves!

Cover of a "Grade 3 Amplify Desmos Math Teacher Edition" book, featuring a cutaway building with diverse students and a teacher working on New York math problems and organizing materials.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 3: Data on Scaled Graphs.

Cover of "Amplify Desmos Math Student Edition 3" showcasing illustrated children engaged in various mathematical activities inside a glass house structure, reflecting the dynamic energy of New York math.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 3: Data on Scaled Graphs.

Cover of the Amplify Desmos Math Grade 3 Centers Resources book, featuring a 3D letter "C" in blue and white on a minimalistic background, perfect for aligning with New York math standards.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

A page titled "Activity 2" features a table showing counts of rabbits, raccoons, and foxes, an image of animal stickers, and a bar graph representing the number of each animal, designed to amplify your New York math lesson with engaging visual data.

Students compare data represented on bar graphs with different scales by using animal stickers to create scaled bar graphs.

Cover of "Amplify Desmos Math: Teacher Edition Grade 4" showing children learning New York Math outdoors, using large mathematical tools and numbers, with one child in a wheelchair.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 2: Using Factors and Multiples.

Cover of "Amplify Desmos Math: Teacher Edition Grade 4" showing children learning New York Math outdoors, using large mathematical tools and numbers, with one child in a wheelchair.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 2: Using Factors and Multiples.

Cover of the "Amplify Desmos Math" Grade 4 Centers Resources book, featuring a large, stylized blue letter "C" on a light blue background. This essential resource for New York math educators ensures engaging and effective instruction.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

Interactive educational activity asking users to determine platform heights using a 3-inch tube. The interface, inspired by Desmos math tools, features a dragging function and feedback system with a checkbox and "Try another" option, amplifying the learning experience.

Students choose tube lengths to connect to platform heights for hamster homes, identifying possible heights using what they know about multiples.

Illustration of three students engaging with various math activities outdoors and around large blocks. Text at the top reads "Amplify Desmos Math, Grade 5, Teacher Edition" - a perfect resource for New York math educators.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you review the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 3: Volume of Solid Figures.

Cover of "Amplify Desmos Math: Student Edition, Grade 5" featuring students engaged in various mathematical activities outside, such as block building, measuring, and gardening—a perfect resource aligning with New York math standards.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 1, Sub-Unit 3: Volume of Solid Figures.

Cover image of "Amplify Desmos Math Grade 5 Centers Resources" featuring a large purple letter C on a light purple background, showcasing the innovative approach of Amplify Desmos Math that's making waves in New York math education.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Centers Resources, Additional Practice, and Math Language Development Resources.

An interactive screen showing an activity about decomposing a figure into prisms, with a touch of Desmos Math integration. The user is asked to drag points to demonstrate the decomposition. Two prism illustrations are displayed, offering a glimpse of New York Math's approach.

Students decompose a figure into rectangular prisms and determine the volume of the figure by adding the volumes of the individual prisms.

6-A1 sample materials

Click the links in the drop-down sections below to explore sample materials from each grade. For a full program review, please login to the digital platform or request physical samples. 

For helpful navigation tips and more program information, download the Amplify Desmos Math Program Guide.

You can also watch a product expert walk through a lesson and the available program components.

A laptop displays a math warm-up activity with shapes and a scale, in front of two Amplify Desmos Math teacher edition books for grades 1 and 7.
Cover of the Grade 6 Amplify Desmos Math Teacher Edition, showcasing students engaging in various mathematical activities around a balance scale with variables, inspired by New York math educational standards.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 1: Solving Equations.

Cover of “Amplify Desmos Math, Student Edition, Grade 6” featuring an illustration of children engaging in various New York math-related activities outdoors.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 1: Solving Equations.

Cover image of "Amplify Desmos Math" for Grade 6, featuring a 3D pink letter "I" and the text "Intervention and Extension Resources." This New York math edition supports students with comprehensive resources.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Additional Practice, and Math Language Development Resources.

A digital math activity shows foxes on a seesaw balanced with 18-pound weights. A multiple-choice question and text box ask for the weight of a fox in pounds.

Students use equations and tape diagrams to represent seesaw situations and to determine unknown animal weights, helping them make connections between diagrams that represent equations of the form `x+p=q` or `px=q`.

Cover image of "Amplify Desmos Math Teacher Edition Grade 7" featuring an illustration of students engaging in math-related activities with geometric shapes and construction elements against a New York cityscape background.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 3: Inequalities.

Cover of "Amplify Desmos Math, Student Edition, Grade 7" showing students engaged in math activities against a cityscape reminiscent of New York, with purple geometric structures and a crane in the background.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 3: Inequalities.

Cover of "Amplify Desmos Math: Grade 7 – Intervention and Extension Resources" featuring a stylized 3D "I" on a light purple background, ideal for both New York math and national curricula.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Additional Practice, and Math Language Development Resources.

A digital math activity screen shows a character above a number line and a box with the inequality "x > -10" entered. A cursor points to the "Edit my response" button.

Students solve inequalities with positive and negative coefficients to solve a variety of challenges featuring a fictional sheep who eats grass according to an inequality.

Illustration of children engaging in learning activities outdoors near a large slide. The title "Amplify Desmos Math Grade 8 Teacher Edition" is shown at the top, highlighting its relevance to New York math curriculum standards.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 2: Analyzing Numerical Data.

Cover of the "Amplify Desmos Math" Student Edition for Grade 8, featuring students engaging in various mathematical activities in a stylized outdoor New York setting.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from a complete sub-unit on this site: Unit 6, Sub-Unit 2: Analyzing Numerical Data.

Cover of "Amplify Desmos Math Grade 8: Intervention and Extension Resources" featuring a stylized "I" on a gray background, tailored for New York math standards.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Additional Practice, and Math Language Development Resources.

A graph plots four robot colors by height and eye distance; on the right, matching colored robots stand side by side, labeled Red, Purple, Blue, and Green.

Students connect points on a scatter plot with individuals in a population and rows of data in a table. The analysis of scatter plots continues with data about the eye distances and heights of robots.

Cover of "Amplify Desmos Math: Algebra 1, Teacher Edition" featuring diverse characters engaged in mathematical activities, with a graph and a bridge in the background, illustrating the vibrant energy of New York math.

Teacher Edition

Planning and instructional guidance is visual, organized, and easy-to-follow. To help you preview the program, we have included samples from two complete sub-units on this site: Unit 2, Sub-Units 1–2: One-Variable Equations and Multi-Variable Equations.

Cover of "Amplify Desmos Math" Student Edition A1, featuring an illustration of diverse characters engaging in New York math activities against a backdrop of graphs and mathematical concepts.

Student Edition

Motivate students with mathematics that is both rigorous and delightful. To help you preview the program, we have included samples from two complete sub-units on this site: Unit 2, Sub-Units 1–2: One-Variable Equations and Multi-Variable Equations.

Cover of an Amplify Desmos Math Algebra 1 ancillary sampler, featuring students interacting with graphs and mathematical models, including a rocket and a parabola.

Ancillary sampler

Included in the ancillary sampler are examples from the program Assessment Resources, Intervention and Extension Resources, Additional Practice, and Math Language Development Resources.

A math activity screen shows a cartoon snail, purple blocks, and a table comparing blocks and a math equation; a cursor hovers over the "Edit my response" button.

Students represent the solutions of a situation using a table, a graph, and multiple forms of an equation to identify multiple combinations of blocks that can help Shelley the Snail cross a gap.

Plan your professional development

We’re excited to partner with you on your Amplify journey. Flexible professional development pathways have been designed to meet your needs.

Illustration of a rocket labeled "Launch" for beginning of the year, and a woman lifting a dumbbell labeled "Strengthen" for mid-year or end of year program implementation steps.

Recommended Professional Development Plan

Our team has curated a recommended professional learning path from initial launch to continuous support. Use the Professional Development Planning Guide below to discuss the plan that best meets your school or district needs with your Account Executive.

Sessions overview

Recommended sessions are highlighted below.
Title Duration Modality
Elementary school sessions
Initial training (online course) Self-paced (approximately 3 hours) Online course
Initial training 2 hours Onsite/Remote
Initial training, 2 sessions in 1 day 2 2-hour sessions Onsite/Remote
Initial training, 3 sessions in 1 day 3 2-hour sessions Onsite/Remote
Initial training (add-on session) 2 hours, scheduled consecutively with another Amplify training Onsite
Initial training: Train the Trainer 2½ hours Onsite/Remote
mCLASS® Initial training with Boost Reading Texas overview This Boost Reading Texas session occurs during the last hour of a 1-day mCLASS initial training. Onsite/Remote
Teacher dashboard reporting and analysis (online course) Self-paced (approximately 3 hours) Online course
Teacher dashboard reporting and analysis 2 hours Onsite/Remote
Comprehensive implementation PD package 2 2-hour sessions, scheduled separately Remote
Administrator reporting  2 hours Onsite/Remote
Middle school sessions
Initial training  2 hours Onsite/Remote
Initial training, 2 sessions in 1 day 2 2-hour sessions Onsite/Remote
Initial training, 3 sessions in 1 day 3 2-hour sessions Onsite/Remote
Initial training: Train the Trainer 2½ hours Onsite/Remote
Deeper dive 1 hour Remote
Elementary and middle school sessions
Initial training package 2 2-hour sessions Remote

Elementary school sessions

Initial training (online course)

Self-paced

Our self-paced, on-demand online course contains approximately three hours of training. Teachers in grades K-5 who are new to Boost Reading Texas will learn how to implement the program by learning about the structure of the program, the student experience, data reporting, and implementation setup.

As this is a self-paced, on-demand online course, participants will be able to access the course anytime, move as quickly or slowly as needed through different sections, and revisit the course up to one year as a refresher in the future.

Audience: Teachers (administrators welcome)
Modality: Online course

Initial training

2 hours

Teachers in grades K-5 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Initial training

2 sessions in one day

Teachers in grades K-5 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. Two training sessions will be scheduled consecutively in one day to accommodate a larger number of teachers (up to 60 teachers, with 30 participants per session.)

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Initial training

3 sessions in one day

Teachers in grades K-5 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. Three training sessions will be scheduled consecutively in one day to accommodate a larger number of teachers (up to 90 teachers, with 30 participants per session).

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Initial training (add-on session)

2 hours

Scheduled consecutively with another Amplify training.

Teachers in grades K-5 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite

Initial training: Train the Trainer

2½ hours

Educators in grades K-5 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. As this is a Train the Trainer session, participants will have increased time to deepen their knowledge and receive greater hands-on support from an Amplify facilitator. Participants will also receive annotated session materials in order to turnkey the session to colleagues.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

mCLASS initial training with Boost Reading overview

6 hours

This training includes both mCLASS® and Boost Reading training. The first five hours are mCLASS Texas initial training, where educators will learn how to administer the mCLASS assessment. The last hour is a Boost Reading Texas overview, where educators will receive an overview of Boost Reading Texas and how it connects with their mCLASS data in grades K-5. This Boost Reading Texas session occurs during a one-day mCLASS Texas initial training.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Teacher dashboard reporting and analysis (online course)

Self-paced

Our self-paced, on-demand online course contains approximately three hours of training. After teachers in grades K-5 have used Boost Reading Texas for at least six weeks, they will learn how to analyze data on the Teacher dashboard and use that data to identify small groups and target instruction.

As this is a self-paced, on-demand online course, participants will be able to access the course anytime, move as quickly or slowly as needed through different sections, and revisit the course up to one year as a refresher in the future.

Audience: Teachers (administrators welcome)
Modality: Online course

Teacher dashboard reporting and analysis training

2 hours

Delivered after teachers in grades K-5 have used Boost Reading Texas for at least six weeks, this training will help teachers analyze the data on their teacher dashboard and use that data to identify small groups and target instruction.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Comprehensive implementation PD package

2 2-hour sessions

This package is intended for schools and/or districts that want the highest level of support in launching Boost Reading Texas! The first session is an initial training session and prepares teachers in grades K-5 to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. The second session is the Boost Reading Teacher dashboard session and is delivered after at least six weeks of usage. This session will support K-5 teachers in analyzing the data on their teacher dashboard and using that data to identify small groups and target instruction.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Remote

Administrator reporting

2 hours

This training supports K-5 administrators in accessing and leveraging Boost Reading Texas reports.

Audience: Administrators, maximum 30 participants
Modality: Onsite/Remote

Middle school sessions

Initial training

2 hours

Teachers in grades 6-8 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Initial training

2 sessions in one day

Teachers in grades 6-8 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. Two training sessions will be scheduled consecutively in one day to accommodate a larger number of teachers (up to 60 teachers, with 30 participants per session.)

Audience: Teachers (administrators welcome), maximum 30 participants per session
Modality: Onsite/Remote

Initial training

3 sessions in one day

Teachers in grades 6-8 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. Three training sessions will be scheduled consecutively in one day to accommodate a larger number of teachers (up to 90 teachers, with 30 participants per session.)

Audience: Teachers (administrators welcome), maximum 30 participants per session
Modality: Onsite/Remote

Initial training: Train the Trainer

2½ hours

Educators in grades 6-8 who are new to Boost Reading will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup.

As this is a Train the Trainer session, participants will have increased time to deepen their knowledge and receive greater hands-on support from an Amplify facilitator. Participants will also receive annotated session materials in order to turnkey the session to colleagues.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Onsite/Remote

Initial training

3 sessions in one day

Teachers in grades 6-8 who are new to Boost Reading Texas will prepare to implement the program in their classrooms by learning about the student experience, data reporting, and implementation setup. Three training sessions will be scheduled consecutively in one day to accommodate a larger number of teachers (up to 90 teachers, with 30 participants per session.)

Audience: Teachers (administrators welcome), maximum 30 participants per session
Modality: Onsite/Remote

Deeper dive

1 hour

This training supports educators in grades 6-8 in understanding how Boost Reading Texas was designed to benefit students and how to leverage data to inform instructional next steps.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Remote

Elementary and middle school sessions

Initial training package

2 2-hour sessions

This package consists of two 2-hour remote sessions and is intended to support schools or districts launching Boost Reading Texas in grades K–8. One session will be geared toward K–5 teachers, and the other session will be geared toward 6–8 teachers. In each session, teachers who are new to Boost Reading Texas will prepare to implement their respective program (either elementary or middle school) in their classrooms by learning about the student experience, data reporting, and implementation setup.

Audience: Teachers (administrators welcome), maximum 30 participants
Modality: Remote

Pricing

We offer the following pricing for training sessions and packages:

Session typePricing
Online course$49 per individual seat
1-hour remote session$500
2-hour remote session$750
2 sessions in 1 day, remote$1,200
3 sessions in 1 day, remote$1,500
2-hour onsite session$2,200
2 sessions in 1 day, onsite$2,800
3 sessions in 1 day, onsite$3,200
2-hour add-on to onsite training$1,200
2 ½-hour Train the Trainer session, remote$950
2 ½-hour Train the Trainer session, onsite$2,400
1-day mCLASS initial training with Boost Reading Texas overview, remote$1,200
1-day mCLASS initial training with Boost Reading Texas overview, onsite$3,200
Comprehensive implementation PD package$1,500
Elementary and middle school initial training package$750

Please note that the prices are general ranges and may be subject to change.

Contact

Amplify welcomes the opportunity to partner with schools and districts to design professional development plans and answer your questions.

If you would like to order any of our professional development services, please contact your local Amplify sales representative or call (800) 823-1969.

Frequently asked questions

Still have questions? We have answers. Check out the following FAQ.

A teacher discusses educational content in front of a whiteboard while students in the classroom raise their hands eagerly.

Program questions

Amplify Science California is a flexible, blended K–8 science curriculum that addresses 100 percent of the Next Generation Science Standards for California, and a significant number of the Common Core State Standards for English Language Arts, Literacy in Science and Technical Subjects, and Math, as well as the California English Language Development Standards. Together, the units deliver three-dimensional instruction across the following disciplines: Life Science, Earth and Space Science, Physical Science, and Engineering Design.

Since Amplify Science California is a blended curriculum, districts who adopt it are outfitted with a variety of print and digital resources as well as hands-on materials kits. To explore the specific components of the program, visit the What’s Included portion of our site.

As our customers will tell you, when you adopt Amplify Science California, you aren’t just buying a science curriculum, you’re joining a family. As such, along with materials, your adoption of Amplify Science California also includes care and support through a variety of staff and resources, including customer support specialists, pedagogical support specialists, implementation specialists, professional learning specialists, educational partnership managers, and more.

Amplify Science California does indeed features some powerful and engaging digital components, which are gradually introduced beginning at grade 2. However, as a fully blended and flexible program, Amplify Science California can be (and has been) implemented in a wide variety of scenarios.

All lessons were designed with device sharing in mind, and never assume that every student has a separate device. While 1:1 scenarios are great, they aren’t required. When devices are necessary for students to fully experience a concept, teachers can opt to share devices across pairs or small groups, or simply display the Sim or Modeling Tool to the whole class and allow students to “drive” using your device.

Rather than introducing a concept on Monday, testing for mastery on Friday, and knowing students will forget everything by the next Tuesday, we set out to help students build meaningful and lasting knowledge that they can retain and transfer over the course of the entire unit. We accomplish this by giving students multiple opportunities (a.k.a. “at-bats”) to encounter, explore, and experience a concept. Said another way, Amplify Science California is actually made up of a series of multi-modal “mini-lessons.” This intentional cyclical and iterative design mirrors the 5Es, allows teachers the flexibility to speed up or skip ahead once students have demonstrated mastery, and empowers students to learn concepts more deeply than any other program.

We support both. No one solution works for everyone; therefore, in partnership with the Lawrence Hall of Science, we developed suggested sequences for both the integrated model of instruction and the discipline-specific model. Because it’s our goal to provide districts the maximum amount of flexibility, we’re also happy to support districts interested in implementing a different sequence of instruction.

Yes. Rather than separating Performance Expectations into physical science units, earth and space science units, and life science units, Amplify Science California units are organized around anchoring phenomena designed to give students opportunities to dive deeply into certain disciplinary core ideas (DCIs) while also drawing from or applying to others. In organizing the Amplify Science California middle school units, we’ve carefully sequenced these ideas within each grade level to support the development of deep and coherent understanding.

Many real-world phenomena cross the domain boundaries of life, physical, or earth and space science (as well as engineering). Each Amplify Science California unit begins with an intriguing real-world phenomenon that poses a problem that needs to be understood and/or solved. By the end of the unit, students will have analyzed the anchor phenomenon across multiple scientific domains, possibly designed and tested an engineering solution, and always applied what they’ve learned in a different context.

For example:
In the unit Light Waves, students investigate the anchoring phenomenon of why Australia has a much higher skin cancer rate than countries at similar latitudes like Brazil. The focus of this unit is on disciplinary core ideas related to wave properties (PS4.A) and electromagnetic radiation (PS4.B). Students explore these physical science ideas deeply within the unit, and also draw on ideas from earth science (e.g., latitudinal variation of the sun’s energy) and life science (e.g., the effect of energy on the DNA in the nucleus of a cell) in order to explain the central phenomenon.

Absolutely. Hands-on learning is at the heart of Amplify Science California. Integrated into every unit are opportunities for students to take on the role of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend their claims.

In addition, our unique combination of focus and flex activities means teachers have more options, opportunities, and materials to make learning active. Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

What’s important to remember is that more hands-on doesn’t necessarily mean better, at least according to the California NGSS. That’s because only two of the eight Science and Engineering Practices (SEPs) are directly related to hands-on learning.
Just as scientists gather evidence from many types of sources, so do students in the Amplify Science California program. Like scientists, students gather evidence from physical models, digital models, texts, videos, photographs, maps, and data sets. By doing do, we provide students more opportunities than any other program to practice using all of the practices called out in the California NGSS Framework.

NGSS 8 Science Practices

  1. Asking questions
  2. Developing and using models
  3. Planning and carrying out investigations
  4. Analyzing and interpreting data
  5. Using mathematics and computational thinking
  6. Constructing explanations
  7. Engaging in arguments from evidence
  8. Obtaining, evaluating, and communicating information

While all of our units engage students in gathering evidence from a rich collection of sources, the reliance on different types of evidence (and evidence sources) varies according to unit. For instance, some units lend themselves to meaningful hands-on experiences, while in other units the phenomena students are investigating are too slow, too dangerous, or too big to be observed directly. In those units, students rely more heavily on other evidence sources such a physical models or simulations.

Unit types in grades K-5

In each K–5 grade, there is one unit that emphasizes investigation, one that emphasizes modeling, and one that emphasizes design. In addition, in grades 3–5, there is also one unit that emphasizes argumentation.

Unit types in grades 6-8

Each 6–8 grade features three types of units: Launch, Core, and Engineering Internships. Each year has one Launch unit, six Core units, and two Engineering Internships.

For teachers who want to supplement the lessons with even more hands-on activities, optional “flextension” activities are included in many units.

Yes indeed. Amplify Science California integrates all four STEM disciplines—science, technology, engineering, and math—in addition to English Language Arts—throughout the curriculum. In addition, each grade level features specific units that emphasize engineering design.

Every lesson in Amplify Science California explicitly calls out which CCSS ELA and CCSS Math standards are addressed. That said, this is not a math program, nor an ELA program; therefore, it does not address all of the Common Core standards. But the program does address a significant number of the standards as they pertain to science.

Yes, the program includes multiple opportunities for summative assessments.

End-of-unit assessments: At grades K–1 these look like targeted conversations, at grades 2–5 we incorporate written responses, and at grades 6–8 we assess through a combination of auto-scored multiple-choice questions and rubric-scored written responses. These summative assessments for each unit are designed to provide valid, reliable, and fair measures of students’ progress and attainment of three-dimensional learning.

Benchmark assessments: Delivered four times per year in grades 3–5 and three times per year in grades 6–8, benchmark assessments report on students’ facility with each of the grade-level appropriate DCIs, SEPs, CCCs, and performance expectations of the California NGSS.

Science Seminars and final written arguments (formative and summative components): In grades 6–8, culminating performance tasks for each core unit invite students to figure out a new real-world problem. They collect and analyze evidence, examine a number of claims, and then engage in a full-class discussion where they must state which claims are best supported by the evidence, all while making clear their reasoning that connects the evidence to the claims. After the seminar, students then individually write their final scientific argument, drawing on the DCIs, SEPs, and CCCs they have used over the course of the unit to develop a sophisticated and convincing argument that addresses the problem they’ve been investigating. Rubrics, scoring guides, and examples of student responses at each scoring level are provided to teachers to support the assessment of students’ understanding of concepts and specific practices.

No. While we do provide suggested sequences for integrated and domain courses, there are other logical ways to sequence the units and we expect that teachers will present the units in a variety of different orders and in any combination. There are a few notable exceptions. For example, students completing the Metabolism Engineering Internship should have completed the Metabolism core unit beforehand, or a unit that provides students with the same information. Amplify Science California specifies prerequisites for each unit in the event that teachers are interested in using an Amplify Science California unit in combination with other materials.

The typical elementary classroom delivers science instruction only two times per week. Yet, most curricula provide 180 days of lessons. Rather than asking teachers to wade through unnecessary content, we designed a program that addresses 100 percent of the NGSS in just 66 days at grades K–2 and 88 days at grades 3–5. With plenty of wiggle room built right into the program, teachers can relax knowing that there’s ample time to get it all done.

Amplify Science California provides more than enough instructional content to fill 180 days of instruction. However, unlike other programs that expect you to complete 180 discrete lessons, Amplify Science California includes built in wiggle room.

For example, the typical elementary classroom delivers science instruction only two times per week. Rather than asking teachers to wade through unnecessary content, we designed our program to address 100 percent of the California NGSS in just 66 days at grades K–2 and 88 days at grades 3–5. When it comes to middle school, we address 100 percent of the California NGSS in 146 lessons.

Some classes might last longer than one session due to a number of reasons (e.g., enthusiastic student conversations, challenging topics requiring deeper dives, more time needed to accommodate diverse learners, etc.). Also, teachers might want to supplement Amplify Science California with some of their own favorite lessons. Lastly, we’ve accounted for the inevitable assembly days, class trips, testing schedules, et cetera. For teachers that want to go deeper or expand upon a unit topic, we also offer a number of additional lessons that are not core to each unit.

Amplify Science California lessons are designed to be completed in the following timeframes:
Grades K-1 lessons are designed for 45 minutes of science instruction.
Grades 2-5 lessons are designed for 60 minutes of science instruction.
Grades 6-8 lessons are designed for 45 minutes of science instruction.

That said, it’s not a problem if you can’t allocate 45 mins of science instruction every day at K-1, or 60 minutes per day at 2-5. Since there are a total of 66 lessons to address 100 percent of California NGSS at grades K-2, and 88 lessons to address 100 percent of California NGSS at grades 3-5, you can easily teach the lessons in smaller blocks and cover all of the content over the course of the school year.

Technical questions

To ensure that your hardware and network meet the minimum technical requirements for optimal performance and support of your digital curriculum products please see Amplify’s customer requirements page.

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Slow and steady progress at middle-of-year highlights the urgency of data-driven instruction.

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S4 – 02. Bethany and Dan share their math biographies

Promotional graphic for "math teacher lounge," season 4 episode 2, featuring photos and names of math teaching guests Bethany Lockhart and Dan Meyer.

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:00):

We’re recording. What’s up, everybody. This is Dan Meyer with Math Teacher Lounge.

Bethany Lockhart Johnson (00:08):

And I’m Bethany Lockhart Johnson. We are so excited to be back. Season Four, Episode Two. Hi, Dan.

Dan Meyer (00:16):

Hey, Bethany, how are you doing today?

Bethany Lockhart Johnson (00:18):

I’m so excited to be talking with you! You know, as we record this, our reunion at NCTM is getting closer and closer.

Dan Meyer (00:28):

The NCTM live show is gonna be bonkers. I don’t think people are ready for it. You think you know what we’re about on MTL from listening to us, but the live show is gonna be outta control. You cannot imagine how many clowns and elephants Bethany wants to have at the live show. We’re still—we’re trying to talk her down from like three to one, but we’ll see.

Bethany Lockhart Johnson (00:44):

All I want is the t-shirt cannon. Because I used to go to these baseball games and they would have a t-shirt cannon. And I thought, I wanna operate a t-shirt cannon! So like, if I could be standing on stage aiming t-shirts at people who are jumping up and down requesting a t-shirt? I don’t know. Doesn’t that sound fun?

Dan Meyer (01:01):

Sounds awesome. High point of my college education was catching a t-shirt. No, it was—it was a burrito. It was a burrito cannon. But I think it was just a t-shirt cannon, but it was a burrito cannon. And I caught a burrito at a game and it was probably the most memorable moment of all of college education for me.

Bethany Lockhart Johnson (01:16):

Was the burrito still warm?

Dan Meyer (01:18):

Oh yeah. I think it got—like, I think it might’ve been warm at one point and then it got warmed back up through the muzzle velocity of the cannon. So it was a pretty great system they had going on there. <Laugh> Yeah. <Laugh> Anyway, I’m off topic, but, we’re thrilled to—I’m thrilled to chat with you and we’re thrilled to be listened to by you folks out there in MTL land. In the lounge itself. We got a fun show today.

Bethany Lockhart Johnson (01:40):

So if you listen to Episode One—which if you haven’t, hope you go back and listen to it—if you listen to Season Four, Episode One, you’re gonna hear—we asked Huon, KT, who is this delight of a joyful teacher. We asked her to talk to us about what’s her math bio. And we want to ask all of our guests—like, I wanna go back and ask every single guest we’ve ever had to tell us their math bio.

Dan Meyer (02:06):

Yep.

Bethany Lockhart Johnson (02:06):

Because, while seemingly simple in nature, our students enter our math classroom already having had this relationship with math and these notions about their role in math or what they think about math. And it impacts our school year with them if we’re a teacher. And it impacts our relationship with math as we move through our education and beyond. Right? And I I’m so excited about this question, ’cause I think it also ties into this theme for Season Four, which is joyful math, and diving into “When has math felt joyful? When has it not? Does it feel like—how do we think about how our math bio, our relationship with math, has evolved into a joyful or less joyful place?”

Dan Meyer (02:54):

I get it. And what’s really key here, I think, is that teaching more than other professions is a generational profession. You know what I’m saying? Like, no one is like, “Well, you know, I sold insurance to you and now you’re selling insurance to, you know, my grandkids; that’s amazing!” But people are always posting photos when, like, you teach someone who then becomes a teacher later. Teaching is a generational sort of thing. So the kinds of joyful experiences that we offer or don’t offer students now affect the experiences that students who haven’t even been born yet will have, you know, some 20, 30 years later. That, to me, is a trip. And well-worth exploring, you know, how we got here, mathematically speaking.

Bethany Lockhart Johnson (03:39):

I remember a friend had sent me this image of an assignment that her son got that was asking for their Mathography. They wanted to know about their history of mathematics. And this was their first assignment. And this teacher, I would like to imagine, read them all and used it to inform conversations about students’ relationship with math. And, you know, some of the questions they asked were thinking about whether you consider yourself, quote, unquote, “good at math.” Like “what kind of experiences have you had? What do you like or dislike about math? What is, you know—what do you expect to learn in math this year?” Just asking students to actually pause and examine and reflect on their relationship and then also looking forward to, like, what kind of a classroom community do we wanna create? And I loved that assignment. And yeah, so today’s episode Dan, guess what?

Dan Meyer (04:32):

What’s going on? What’s happening?

Bethany Lockhart Johnson (04:33):

I figured we should ask each other about our math bio.

Dan Meyer (04:39):

I think the people out there would love to know this about us. ‘Cause you know, we’re both awesome. But also what’s really cool here is that like, I don’t know this about you. Like not, not a lot. You know, the folks at Amplify, they kind of assembled me and Bethany together in the same way that record labels assembled pop boy bands, girl bands, that kind of thing, back in the day. You know, grabbing some stars from screen or film and just like throwing ’em together and saying, “All right, now you’re here to perform together.” And so it’s just a really good moment for us to, like, settle back and just know who we’ve been working with for the last three seasons and change here. I love it.

Bethany Lockhart Johnson (05:15):

Well, I don’t know. I don’t actually agree with that, Dan. Because don’t you remember? We knew each other beforehand. And while I would like to think of us as…oh, I’ll say One Direction—well, no, One Direction is now defunct. Who’s another band that got formed by one of those shows and is still together and still—

Dan Meyer (05:33):

BTS! K-Pop, you know! Let’s go!

Bethany Lockhart Johnson (05:35):

K-pop. BTS.

Dan Meyer (05:38):

Let’s go, Bethany <laugh>.

Bethany Lockhart Johnson (05:39):

So can we incorporate some K-pop into the NCTM Math Teacher Lounge live episode? Don’t answer now. Don’t answer now. OK. So not only are we gonna share our math bios, but we want to encourage you listeners to share your math bio with somebody in your life. It could be a child in your life, maybe talking to your kiddo about what was it like. What was math like for you? It could be a student that you have. It could be a partner, a friend, a parent. I mean, the sky’s the limit. Share your math bio. And most of all, share with us. We wanna hear about your math bio and you can share it with us at Twitter, at MTLShow, or in our Facebook group, Math Teacher Lounge.

Dan Meyer (06:26):

Stop on by, please. All right. I’m gonna just share like, just a couple of quick, signposts. Not the full bio. Gotta leave them wondering about something here. But here’s a few quick highlights and lowlights of my math bio and how, maybe, it made me the teacher that I was and the educator I am. Is that cool?

Bethany Lockhart Johnson (06:44):

Wait, I didn’t even, I didn’t ask you yet.

Dan Meyer (06:46):

Ask me what?

Bethany Lockhart Johnson (06:47):

Hey, Dan!

Dan Meyer (06:49):

Is there like a magical word? Like, what’s your math bio? <Laugh> Oh, go for it. No, no, that’s right. They won’t know what I’m talking about. Why is he talking about his math bio? Bethany—

Bethany Lockhart Johnson (06:57):

That whole lead-in that we just gave? They might not know.

Dan Meyer (07:00):

Yeah. We just talked about math bios for the last 20 minutes. But yeah, they might not know what we’re—

Bethany Lockhart Johnson (07:04):

<laugh> So Dan, why don’t you go first? ‘Cause I know you were gonna ask me to go first, but why don’t you go first? Dan? What’s your math bio?

Dan Meyer (07:12):

Oh, wow. Well, thank you for the formal invitation to share my math bio, Bethany Lockhart Johnson. So, I’ll just share—I just wanna share a couple items here, not the full history. Gotta leave ’em—leave a little mystery in there, you know what I’m saying? But here’s a few highlights and lowlights, and I think what it means for me as an educator. So, I was homeschooled for eight years. That was big—did a lot of math learning on my own. Couple of lowlights from that, a lot of highlights, in terms of just like being able to, like, learn at my own rate and just jump on ahead and pursue different wacky things. But I tried to switch into public school in fourth grade and I lasted, um, four hours. I didn’t even go to class. I enrolled and then it was like, boom, I was out of there. Because we went to the school; we met the teacher, saw the room, very nice person and place. But I got the homework assignment and the homework assignment was gibberish. I had no idea what to do and such was this feeling of just, like, despair and hopelessness, I was like, I cannot be a part of this. I remember the assignment. It was about identifying scalene, isosceles, and equilateral triangles. I’ll tell you this: I am quite good at that now. But at the time, like, I didn’t know what those words meant. And you know, at that moment we had Encyclopedia Britannica, could not Google this or even Ask Jeeves or AltaVista this so well back then. It just—it was an entry moment of failure and realizing that so much of math is like a, kind of a social kind of construct. And if you’re not part of that social circle, what can you do? So that was a bummer. Another bummer was eighth-grade math, learned it all by way of videotape. You know, put in the tape and watch—not gonna say the person’s name and not this person’s fault—but it was just like watching someone work on a whiteboard. Kind of a precursor to Khan Academy, kind of a drag. Went to high school—

Bethany Lockhart Johnson (09:02):

Wait, wait, wait, wait. We were—I’m not ready to jump to high school. Wait. Can you pause for just a second?

Dan Meyer (09:06):

Yeah. Rock on.

Bethany Lockhart Johnson (09:07):

I just need you to go back to the triangle thing. So in that moment, what did that mean for you that you had had all these experiences with math and then you encounter math in a completely different sphere, a public school, and it did not have a connection or meaning to you because prior to that, it sounds like it was pretty positive. Right? Explore these things you’re curious about; there’s not, like, a level you need to stick with…

Dan Meyer (09:33):

Yep, yep. Yeah. I think that’s right. Maybe it was a little bit of a classic, like, “Oh, I didn’t have a growth mindset; my mindset was like, ‘Oh, I’m good at math because I am, you know, born that way,’” and all of a sudden, that identity was, you know, thrown into question. And, you know, my foundation was all of a sudden quite shaky. And yeah, that’s—you know, I think I taught a lesson recently where I was like, “Hey, this whole thing with a less-than or equal-to sign and a greater-than or equal-to sign, like what those signs are: it’s just, it’s language. And if it’s confusing to you, it’s not because you’re bad at math; it’s ’cause language is oftentimes confusing ’cause people have to agree on it.” So I dunno, that sort of thing is kind of filtered in, filtered back in periodically, some sympathy for like how a lot of math is like just socially agreed upon ways of working with, you know, numbers, shapes, patterns, that kind of thing.

Bethany Lockhart Johnson (10:20):

OK.

Dan Meyer (10:21):

Anyway.

Bethany Lockhart Johnson (10:21):

  1. And in this home school—I have a lot of questions about that, but I’ll stick to one—were you in a community of people that you talked about these math ideas with? Were you homeschooled solo? You have a sibling, so I think you were together, right?

Dan Meyer (10:39):

Yeah. Yeah. I’ve got a twin sister. So we were, you know, like, right on with each other the whole way through there. And yeah, so we had—but it wasn’t, it wasn’t like a—it was a lot of individual work, with my flavor of homeschooling.

Bethany Lockhart Johnson (10:54):

  1. Got it. And the tapes—wait, before you go to high school, the tapes, the VHS tapes, which I’m just loving this image—

Dan Meyer (11:02):

Yeah.

Bethany Lockhart Johnson (11:02):

Was that a positive experience? Was that because that was an area of math that whoever was homeschooling you wasn’t that comfortable with? Why was it that route for the tapes, and what was that? Was that joyful for you?

Dan Meyer (11:15):

Yeah, definitely not joyful. Yeah, it was like, if you had questions, you couldn’t really ask them of the VHS tape. It didn’t work out so well in that way. And it was a lot of operational-type math. It was, you know—there was no give and take; it was all kind of take. From the video teacher. And yeah, I was doing that because my homeschool teacher, my mom, who is very smart in lots of areas, did not have the math knowledge or confidence, especially to help with math at eighth grade. And that was a big reason why, flash-forward to the next year, went to high school.

Bethany Lockhart Johnson (11:48):

Nice segue. OK.

Dan Meyer (11:50):

<laugh> You caught up to high school…I encountered just like four years of just crazy-good, just bonkers-good math teachers who just really changed a lot for me. Especially, Mr. Bishop and Mr. Cavender, very cool folks who did a lot. And especially, I think Mr. Bishop and Cavender both modeled for me what curiosity from a knowledgeable adult looks like. Like someone who, you know, now I can say to myself, “Oh, they were kind of like putting on an act of being very curious about answers they were hearing for the 2000th time from a student,” let’s say, but what a powerful experience that was for me to feel like, “Oh, wow, my thoughts are interesting to someone besides myself.” I got like, maybe it’s two real highlights that I’ll just point to, from my math bio that made me the math teacher and person that I am. Let’s see here. Maybe three, if you you’ll indulge me. One is just like the idea that you could do math wherever you have your brain, a pencil and a paper. And so I remember like in high school, I was in church with my family and kind of a little bit bored of whatever’s going on. And I just had the Bolton and I like drew a pentagon, a regular one, then a hexagon, a regular one, and kept on drawing, like adding sides to the shape. And it was like, it was becoming a circle. And, you know, I was able to take the area of each of those shapes and say, you know, “What happens as you send the number of sides to infinity?” And watch as the formula for area of a circle, Pi R squared, popped out. And it was kind of a literal religious experience, in that moment, just like, “Wow, like my brain’s so cool and math is so cool and paper and pencil’s so cool.” And so there’s that. Just that kind of experience was pretty awesome. And then I would just say like, I’ve had some really fantastic experiences with math in the world itself. Stuff like—let’s see, this is gonna invite more questions from Bethany, probably, maybe I should avoid—I got, I have a Guinness—I have a Guinness world record that’s almost 20 years old. This Guinness world record is—it’s old enough to drive basically at this point. And almost old enough to drink. But like it was—it was a record for chaining the longest paper clip chain together in 24 hours. And the only way I was able to break that record was through mathematics. Where, like, I would be finishing a box of clips. And I would say to my buddy who was there, “I just finished a box of clips.” And that person would type in the number of clips that I had just done. And then a mathematical formula that I had created would tell me how many—how long the chain was at that point. It was being rolled around a spool. And like, it’s just like, wow. So math just made this possible. You know, math revealed that the record I was trying to beat was beatable, because I did the math on it. It was, like, thousands of feet long in 24 hours. And other folks might be like, “Oh, like, that’s that’s huge!” But me, I was like, “All right, let’s divide this out. You know, divide by 24 hours in a day, divide by 60 minutes an hour, 60 seconds in a minute. Oh, that’s like one clip every four seconds. That’s really slow.” You know, think about that <counts aloud>, “Clip, two, three, four. Clip two, three…” It was just slow. So math helped me, you know, wreck that record. Which to my knowledge still still stands. Don’t get any ideas, Math Teacher Lounge Folks! Is this news to you, Bethany? You haven’t blinked in the last, like, five minutes. I’m curious if this is new.

Bethany Lockhart Johnson (15:20):

It is news to me. And I have so many questions. Because OK, if four seconds was slow, so then what was your like—so then I’m assuming a hundred clips per box? Like, what was the rate, you know, per box? How long did it take you to complete a box? What did this friend like? Did this friend stick with you for the whole 24 hours? Did you really do it for 24 hours? Or once you beat the record, did you rest? How did you account for biological function? Like, needs? Like a restroom?

Dan Meyer (15:51):

<Interrupting> Like what?

Bethany Lockhart Johnson (15:51):

Eating.

Dan Meyer (15:51):

Like what, Bethany? OK.

Bethany Lockhart Johnson (15:52):

Um, Sleep.

Dan Meyer (15:55):

So yeah, maybe we dive into some of the specifics in a different time.

Bethany Lockhart Johnson (15:59):

Just tell me one of ’em. Tell me one.

Dan Meyer (15:59):

I’ll just say. So as to discourage other Math Teacher Lounge listeners from taking this on—back off of the record, folks!—this was back in college, so I was a little more limber back then. But I did one—I think it was 1.8 seconds per clip. For an entire 24 hours. Just like, so just like think about it, would you? If you’re gonna step to me on this one, just think about that, OK? And then, and then, you know, make an informed decision.

Bethany Lockhart Johnson (16:28):

Wait. Wait, wait, I just wanna tell you one thing. I’m picturing somebody with a straw, and like, giving you water as you keep clipping. I’m picturing, like, music, I…

Dan Meyer (16:37):

That’s not far. That’s not far. That’s not far from—yeah.

Bethany Lockhart Johnson (16:40):

So many questions! OK. Go on. Sorry, sorry, sorry. Go on. This is your bio.

Dan Meyer (16:44):

We gotta, I gotta wrap this up. I wanna hear your bio. But, like, I would just say like this move to this sense that math is actually a thing that’s useful for more than just a grade; it’s useful for more than just, you know, the societal, you know, adulation that comes from being a math nerd. That kind of thing. And so that, I think that affected a lot of math teaching for me. And, if I gotta, like, summarize math teaching itself in a journey, it went from like, “Hey kids, aren’t I awesome?” to, “Hey kids, isn’t math awesome?” to “Hey kids, aren’t you awesome?” And like that journey was facilitated by lots and lots of people, you know, a lot of personal growth, but at this point, at one point I was like, “Hey, math can help you get records and whatnot. It’s really useful.” And now I’m like, “Wow, your brain’s just doing just really interesting things. I can help you understand how interesting those things are, and maybe make them more interesting, or interesting in a different way, with some help here.” Let’s put a pin in that. That’s the math bio.

Bethany Lockhart Johnson (17:50):

  1. So I have no doubt that if you ask someone in your life, listeners, for their math bio, that you will discover things about them that you never knew. Literally the questions that I have…I have so many question. And Dan is very good at, you know, bringing me back. Bring me back, like, come on, come on. But I just wanna say, overall, your journey seems pretty joyful. It seems pretty joyful. It seems pretty full of confidence. I don’t wanna say “ego” in a negative way, but I wanna say you were buoyed by these experiences that allowed you to feel like math was a place for you to thrive.

Dan Meyer (18:36):

Right.

Bethany Lockhart Johnson (18:36):

Where you could try out things. You could try it out and just, “I could do that!” Right? Like…your relationship just felt very, like…you felt like you had autonomy, agency, perhaps much like you, you operate in this world. Dan, is that, is that right <laugh>?

Dan Meyer (18:54):

Yeah, I think it’s fair to say. And without telling too much of her story, my twin sister with whom I share most things, including genetics, you know—she had a very different experience in math early on. She’s brilliant. She’s a doctor. And not, you know, the book kind of doctor that I am, but like a real, you know, medical doctor. She’s brilliant. But we were—we encountered different messages about who math was made for, early on in, you know, in our entire math learning. And she—we both digested the messages that we were sent, and took, you know, different, different paths because of them, for sure.

Bethany Lockhart Johnson (19:31):

Funny how that works. I thank you, Dan. I do. For in all sincerity, I appreciate you sharing that. And I think that it’s exciting to hear how it influenced your teaching. It feels like you want to cultivate those experiences for your students. And I’ve been in the room when you’ve presented; I was in a room where you taught a class live. It felt like you were making space for the students to have these aha moments. And it feels like in your work at Desmos, and now Amplify, you’re trying to create these products that allow folks to recreate these amazing math moments. Right? And that it’s for everyone and that it’s accessible and it can be very positive. I feel like I have this new perspective on kind of the energy you bring to your teaching. So thank you for sharing that.

Dan Meyer (20:24):

Yeah. Been a pleasure. Thanks for your questions here, Bethany. And it’s been—it’s been fun to reflect on it. And I do—I do feel very lucky in lots of ways. Privileged. Lucky. I know, like—I think the world has been set up for my success in lots of ways, as who I am. But I do just…yeah, I feel—I want more people to experience what it’s like when you walk into a math classroom and it’s like, “Hey, this place is for you. You have interesting thoughts about this. Let’s get ’em out.” So that’s awesome. I would love to hear about you and how you…I mean, we have taught different kinds of kids. You know, I taught kids who I think were somewhat set in, they’re a little bit more solid at secondary in who they are as a math learner. Like “I know who math is and who I am with math.” And I’m really excited to hear what your math bio allowed you to do with students who were perhaps open to the idea that they are very mathematical or at least not yet closed off to those possibilities. So, yeah. What are some of the high, the, you know, the high and low water marks of the making of Bethany Lockhart Johnson, math teacher? <Laugh>

Bethany Lockhart Johnson (21:24):

Thanks for asking, Dan. <Laugh> I’ve shared aspects of my math bio because I think it really informs the way that I talk to people about math and think about math. And I like to share it because I want folks to consider their own journey with math, as we like engage with problem-solving and sense-making and thinking about the students in our classroom. My dad is a math and computer science major. So he had a computer very early on. I wish he had invested in Apple early on when he had like one of the first Apple computers ever. And, sorry, dad, but it’s true. I do wish you had done that.

Dan Meyer (22:10):

I’m sure he does too.

Bethany Lockhart Johnson (22:11):

Oh, he does. So math and computers and conversations about counting, you know, it felt like it was kind of just normal. Like it was around me. And I went to Montessori, which is a private school that—oh, they have some public Montessori—but it’s very self-directed. And so we would have these kind of charts, these goals for the day that you explored. And so we would explore math in very, I don’t know, very organic ways, with these natural materials. And I feel like I excelled at math, but it wasn’t something that I was conscious of. It was just like, “Oh, well, yeah. Math, it’s, you know, something we do.” And then when I went to—when I left Montessori in fourth grade, I remember that year being a lot of like repetition. I was like, well, we did this. We covered this. And except for the mission project that we hadn’t done, that was all new. And that’s it. For another time I’ll share about that. But <laugh> then, they actually, I was moved with a group of students to the fifth grade math class, ’cause we had already done the work that we were doing. And so, it wasn’t that it felt like it came easily, but it did make sense. What we were doing made sense. And then it all kind of changed. There was a lot of change in my family. There was, like, missed school time. And we moved and I went to a new middle school and I was in this environment with students who—it was like an accelerated program. And so I was in this environment with students who were pretty competitive with each other. And I remember going—and I was not from of a competitive environment; like Montessori is not competitive. It’s not about that.

Dan Meyer (24:02):

Right. Right.

Bethany Lockhart Johnson (24:02):

It’s—it was very strange to me that I would be competing against anyone, even competing against myself. And I, you know, knew how to set goals. But it was a different level of energy. And I felt like, because I wasn’t competitive in that nature, I felt like that kind—I felt on the outside of a lot of the energy. Besides the regular, like, middle-school feeling outside of things. And I remember the first friend that I made. Hi, Susan! She had said to me, this was like maybe our second week of school, she’s like, “Oh, at lunchtime, come with me to math club.” And I was like, “OK.” And I remember walking into that room and I had no idea what was going on. And so that was one of the first times where I was just like, “Whoa, I have absolutely no concept of what they’re talking about or what.” These are my peers. I felt very—it was very—it was strange. It was strange. I was like, “This doesn’t feel like a space for me at all.” When I think ordinarily I was kind of excited about the idea of going to math club at lunch, you know? And over middle school, I kind of just got progressively more and more behind. It started with missing some work and then missing more and then checking out. And, you know, the problem was that I really made it about myself. That, like, it wasn’t something that I was then good at or could do. When really it was that well, pre-algebra, I was having a really hard time in like the rest of my life. And so I wasn’t real present in that class. And so when I got to algebra, it didn’t make a whole lot of sense. And then if I missed Monday, Tuesday, and Wednesday, well, Thursday is gonna be hard, you know? And, it just got progressively harder and harder. So I had this great idea that between eighth grade and ninth grade, I was going to take this accelerated geometry class. ‘Cause that was the ninth grade class, it was geometry. And I would take it. It was like geometry in three weeks or something. So then when I entered high school, I would’ve gotten this like jumpstart. But I wish I had said, “Oh, I’ll take this, and then in ninth grade I’ll take geometry.” So like I’ve already kind of gotten a preview of the material. But instead I went to the 10th grade math, which was like intermediate algebra, trigonometry. I had absolutely no clue what was going on. And I had a very, very difficult time and I wasn’t ready for that class. But it was exacerbated by the fact that this teacher felt very free to let the freshmen in that class know that they shouldn’t be in that class. That this class was for 10th graders.

Dan Meyer (26:49):

Oh wow. Oh, wow.

Bethany Lockhart Johnson (26:51):

And we had a rather contentious relationship. And I will never forget that we were in the hallway, and he says to me, “You don’t belong here.” And I’ve talked to—I’ve talked to a girlfriend of mine about her experiences with this teacher and she has the fondest memories.

Dan Meyer (27:13):

Wow.

Bethany Lockhart Johnson (27:14):

She—in fact, almost everyone I’ve spoken with, you know, if we are talking about past teachers or, “Oh, what was that class like?” I mean, they just have these wonderful memories! And for me, my sense of like belonging was already so on a tight rope anyway, that to have this adult, this teacher, tell me, “You do not belong here,” just crushed me. And in hindsight, I think he was saying like, “This class is too hard for you.” I mean, maybe. <Laugh> But all I heard was “You don’t belong here.” And I extrapolated it to connect to math and to anything having to do with math in general. And it just got worse and worse through high school in the world of math. My next math class was even—I had to repeat that class, and still didn’t understand what was going on, and felt more out of place, and, you know, it’s one of those things that I just kind of had started to accept that, I guess, math isn’t for me. I guess I’m just not a math person. Or whatever these stories are that I started to create and build and find evidence for around me that was informing that this wasn’t for me. And I had always done well in school. I was in, you know, accelerated classes. I felt like I was capable of problem solving. And yet in math, I just felt like I had all of this evidence saying that I didn’t belong there. And so when I went to college, I took whatever two math classes were—you know, I was in performing arts and then I did ethnic studies as well. And I remember you had to take two math classes that were GEs. There were these classes that if you don’t wanna deal with math, you go take those classes. And I was like, “Oh yeah, I’ll take that. I’ll take that.” The gulf widened, you know? <Laugh> And I didn’t feel like anxiety when I had to do things like balance my checkbook or navigate math in everyday spaces. It was just, it would never occur to me that I would like seek out opportunities to engage with math or think about it or talk about it.

Dan Meyer (29:35):

That is—yeah, that’s just so wild, how, I don’t know, like it’s often, from the student’s perspective, it is them in a vacuum with math, and the two of them interact and decide if, you know, if they’re right for each other. But from the grown-up perspective, it’s just, you know, it’s a little bit clearer that your story with math was not just you in math, but you with, you know, various external things happening. With family, various teachers playing their different roles—sometimes, you know, really tragic and horrible roles—and then like the compounding mathematical debt that it feels like you were kind of building up, as challenges in one year didn’t get resolved and moved into the next year and so on. And all that makes me wonder—it makes me, like really, really scared, first of all, because I would bet that your teacher might not even remember that moment, that for you is part of just a pivotal moment in your math story, and how many kids have I played—have I been a part of their story in that way and wouldn’t even recall? You know what I’m saying? So that’s a scary part. And then also I’m just wondering, like, how can we, how can we help kids who are in those moments recognize that, “Oh, this kid is like absent a bunch,” and give them more resources to be successful rather than say, “Well, you just gotta try harder now.” Those are things I’m wondering, hearing your story. Thank you for sharing that. I’d love to know more about how you then became a teacher and what all that did for you as you helped students.

Bethany Lockhart Johnson (31:06):

Well, but to answer what you were saying, it wasn’t that I wasn’t—I was always absent physically, but at least like mentally at that point, because it had become so difficult. It didn’t make sense to me. So I was just really checked out in math class, you know? So in hindsight, you know, as a teacher, for sure I can look back, and especially hearing these stories and these experiences my friend had with this teacher and just like chalks up as one of like her most favorite teachers ever! And you know, he clearly did a great job for so many students. But for me, and I think for some people, they would’ve taken those challenges and, you know, it would have fortified them in a different way or something. But for me, I took it upon myself to mean certain things about myself and about my ability and what I was capable of. And so I think, I think in some ways, you know, yeah, it’s all, it’s all interconnected. You know, when your students walk in the door, they’re not this—the things that are impacting them in their life are coming into the room with them. And I don’t think we can take that for granted and think, “Well, if they just focus hard enough…”

Dan Meyer (32:21):

Yeah.

Bethany Lockhart Johnson (32:23):

So let’s go back to my love of Oprah. You know, Oprah talks about living your best life. And something I really appreciate about Oprah is that she encourages you to examine, like, sticking points, right? Like she doesn’t just say, “Well, this…just pretend nothing ever happened, and everything’s fine!” You know, she really talks about making time for reflection. And I kind of got mad that anytime I thought about math, or math schooling came up. Or, you know, whatever, any time that came up that I just felt UGH about it. And I felt like a failure. And I’m like, “You know what, what if I took a math class? And I’m an adult at this point. I’ve graduated. I have—I’ve left college. I have my degrees. But I said, “What if I took a math class?” So I went down to, the city college and I found out that you have to take this exam, like a placement exam. And I went and took the placement exam. And I remember it’s one of the responsive tests where if you get it right, the next question’s a little harder. And so I’m taking it, panicking, because it’s getting more like…I just, you know. And I remember it placed me in like, whatever, Algebra Something, this class that was far more advanced than I thought I should be in. And I was like, there’s been a mistake! You know, and I went to the counselor and said, you know, “I got these results, but I couldn’t answer a lot of the questions on the test.” She’s like, “No, no, no, that’s how it works.” So I go take this class and the class was hard. And I decided that I was just gonna keep showing up. And every day before class, I kid you not, they had a little math…it was like a math center where you could go in and they had a bunch of tables and you’d sit at the table and you could sit and do your work or whatever. If you had a question, you walked up and put your name on a clipboard and then somebody would come and help you. So I did that, every single—like before every single class I would go in. I’d sit there. I’d do the work. I’d go. And I’d get help. Like somebody would walk over and you know, some kid for whom they’re like this…you know, they’re math—it might be you, Dan! It could be you! It could have been you! You know, would walk over and be like—

Dan Meyer (34:38):

Yeah, I was in Help like that. Naw, it’s awesome. Love, love those people. Yeah.

Bethany Lockhart Johnson (34:42):

And you know, I did it. And I did so well in the class. I did exceedingly well in the class. And I said—

Dan Meyer (34:50):

Take that! Take that, everything! Every other math experience!

Bethany Lockhart Johnson (34:53):

I said, what?

Dan Meyer (34:55):

Yeah!

Bethany Lockhart Johnson (34:55):

Wait a second.

Dan Meyer (34:56):

Yeah.

Bethany Lockhart Johnson (34:57):

And it was that I was present. I was not afraid to look at what didn’t make sense. And if something didn’t make sense, it didn’t mean there was something wrong with me. Whaaaaat?

Dan Meyer (35:10):

Yeah. Yeah.

Bethany Lockhart Johnson (35:10):

So I was just in such a different space. And then I took another math class and that class was even harder. And I did the same thing where I went to the little lab and, you know, and it just buoyed me. And it made me realize that, like, this story, that my experience with it was very powerful and that was a real lived experience, but that it didn’t have to define my relationship with math. But then! I decided I wanted to go back to school to become a classroom teacher. And I totally—this was a couple years after that math class experience. So now, you know, I’m healing my relationship with math through basic positive experiences, da, da, da, you know, doing other work. But fast-forward, for a whole number of reasons, decided to become a classroom teacher. And I freaked out. All of my—like, I’m studying for the GRE and the CSET and all the things you have to the hoops you have to jump through to apply to the masters program and the credential program. And I freaked out. I was so close to quitting, Dan. Because I was convinced that the reason I couldn’t be a classroom teacher is because I wasn’t capable in math. Like I was—it was all that resurfaced. And even though I now had evidence to say something different, to the contrary, it was still so visceral. And I was so scared. But I passed that Math CSET.

Dan Meyer (36:47):

Get it.

Bethany Lockhart Johnson (36:47):

I did well enough on the GRE—

Bethany Lockhart Johnson (36:50):

Yes!

Bethany Lockhart Johnson (36:50):

You know, I finished my credential. I worked really, really hard. I had to work so hard in my student placement, when I was student teaching for a fifth-grade class, ’cause I felt like, “Oh my God!” I mean, now I could do the mathematics, but I couldn’t TEACH it to someone, you know? But I had amazing professors at UCI, and my math professors really like just—and my mentor teacher! shout out to Jennifer! shout out to Phil!—these amazing mentor teachers who just loved teaching and who loved—like you said, you have these teachers in your life who you got to see the way that they listened to students. They taught me about that love of listening to students. And then I fell in love with, you know, CGI, cognitively guided instruction, and started learning all about all of these educators who just wanna learn from students’ thinking. And it was just so powerful. And I realize as a kindergarten teacher that I have this really special role in helping to create space for a positive school experience. Like we get to talk about—I talk about my students as mathematicians; they’re writers; they’re thinkers; they’re problem-solvers. And I also want to make space for parents. Some of them, this is their first kid in kindergarten, and they brought all of their experiences, a lot of it negative, that they had had with mathematics. So I felt like it was such an exciting opportunity to help show parents how they could have conversations about math with their students. That also, I hope helped heal their own anxiety with mathematics.

Dan Meyer (38:41):

Right, right.

Bethany Lockhart Johnson (38:42):

Like, I’ve not even scratched the surface of math learning. But I just have such a changed perspective and relationship with math. And I just fell in love with the sense-making. And I fell in love with the journey of it. I still experience math anxiety about a wide variety of things, but I do love it. And I feel like there’s a space for me in relationship with math. And that really excites me.

Dan Meyer (39:09):

Yeah. Wow. Listen to that folks. We, we don’t deserve her! Bethany Lockhart Johnson! She got some math game and could have gone off there and, you know, become an accountant or something. And she chose to hang with kids and their parents. That’s so wild that you’re like rehabbing parents and their self-conception about mathematics at the same time. I think that is so cool.

Bethany Lockhart Johnson (39:32):

Well, thanks Dan Meyer. I gotta tell you, I don’t know when or if I’ve ever shared that much of my math story. So there is a certain amount of vulnerability there. But thanks for listening. And I’m glad that, you know—I think there’s space for us to talk about these things that we care deeply about, but that can be really complicated.

Dan Meyer (39:56):

Yes. Yes. And I love how you you’ve really sharpened the point on what I feel like I know in my brain, but not my body all the time: That individual teachers are huge. Like, individual teachers, and individual moments of teaching, are just not something to play with. You know, like that kid that’s in fifth grade having a tough time, like there could be a month or a day-long period where all of a sudden, like, you’re just like, “Oh yeah, I’m back in the mix; like, me and math are still buddies.” And there’s also like moments that you had, where like one casual word from a teacher can just really put a huge wedge between you and a discipline that needs and wants you and your intellect in it.That’s a really powerful testimonial. Not just for math, but for teaching, your teaching bio.

Bethany Lockhart Johnson (40:43):

I agree with you. And I also, I also…you know, I think we can’t put this—we are human. Teachers are human. And so I’m sure there’s things I’ve said to students. Twenty-second story: a student stapled his finger in my class. <Laugh> And I remember holding his hand and saying, “Why did you do that?” And I wasn’t yelling at him, but it was like, I am sure the panic in my face…like, that’s what he’s gonna remember about kindergarten. Right? <Laugh>.

Dan Meyer (41:19):

Yeah.

Bethany Lockhart Johnson (41:20):

That. He will remember that. He won’t remember the really cool city project we did. He’s gonna remember his teacher holding his hand, in his face: “Why did you do that?”

Dan Meyer (41:30):

Yeah. Yeah.

Bethany Lockhart Johnson (41:30):

You know, so we’re human. And yes, it was awful that that teacher said that to me. There were a thousand other ways that he could have said whatever it was he was thinking. And that did deeply wound me. But despite his influence—because teachers do have a lot of power and I think they need to examine that power, ongoing—it still doesn’t have to define us. So I don’t wanna put this pressure, like—

Bethany Lockhart Johnson (41:55):

Sure.

Bethany Lockhart Johnson (41:56):

“So never ever say anything negative!” You know, we’re human.

Dan Meyer (42:00):

I feel like that kid is currently on some office-supply podcast talking about “your office-supply bio” and saying, “Let me tell you how I first got really freaked out by staples. Here’s the deal: I only use paper clips. And here’s why.”

Bethany Lockhart Johnson (42:15):

“Here’s why.” But then—callback!—he’s going to stumble upon THIS podcast and think, “And because I’m so adept with paper clips, I can beat that record!”

Dan Meyer (42:30):

Though—aaay! whoa! Settle down!

Bethany Lockhart Johnson (42:31):

BOOM.

Dan Meyer (42:31):

Don’t get any ideas, kid. No way. Uh-uh. I don’t like that at all. That’s not what—that’s not what I want to have happen here. No, thank you.

Bethany Lockhart Johnson (42:41):

Well, I’m spent, Dan. I need a nap.

Dan Meyer (42:45):

Yeah. I need a box of Kleenex. I need a nap. I need a—yeah, for sure, a baba. Uh-huh. Definitely. Hey, so look, I’m not expecting you folks out there in the lounge to kind of give us the same depth or breadth. You know, we are here, of course, for your entertainment. Feast on our stories and dramas. But I would love to know at some point, like, what are a few, a few moments that really came to define you mathematically? Came to influence you as a teacher? I think we would do really well for each other to understand that about all of our processes. So yeah, I would just toss in a plug in for Twitter, @MTLShow, or Facebook, Math Teacher Lounge; it would be fantastic to hear from you.

Bethany Lockhart Johnson (43:24):

Thanks so much for listening.

Dan Meyer (43:25):

Thanks, folks. Bye now.

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What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer, or don’t offer, now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

Winter Wrap-Up 02: Mathematizing Children’s Literature

Promotional graphic for Math Teacher Lounge podcast, episode 2, featuring Allison Hintz and Antony Smith, discussing how mathematizing children's literature can build math fluency.

While we’re hard at work producing the exciting fifth season of Math Teacher Lounge: The Podcast, we’re continuing to share some of our favorite conversations from our first four seasons. This time around, we’re revisiting our popular episode that connected literacy and math!

In this episode, we sit down with Allison Hintz and Antony Smith, authors of Mathematizing Children’s Literature, to talk about what would happen if we were to approach children’s literature, and life, through a math lens–and how we can apply those same techniques to classroom teaching!

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Bethany Lockhart Johnson (00:02):

Hi, I’m Bethany Lockhart Johnson.

Dan Meyer (00:04):

Hi, I’m Dan Meyer.

Bethany Lockhart Johnson (00:05):

And we are so excited for another episode of Math Teacher Lounge. And as you know, podcast format; you’re listening now. I think one beautiful thing about the podcast format is that it gives us a little bit more time to have these rich conversations. And I promise I won’t do it, but I could talk to our guests for hours, hours! Authors Allison Hintz and Tony Smith have just released Mathematizing Children’s Literature: Sparking Connections, Joy, and Wonder Through Read-Alouds and Discussion. And today we get to talk to the authors. Allison, Tony, welcome. Welcome to the lounge.

Allison Hintz (00:53):

Thank you. We’re so grateful to be here.

Bethany Lockhart Johnson (00:55):

We’re so excited to have you here. And I wanna say that my very first—was it my first math conference? Maybe it was my first math conference—up in Seattle, the CGI conference, and I’m all like, you know, wide-eyed and just like, “Can this be a place for me, this math community?” Re-envisioning my relationship with math and thinking about myself as a math teacher, what? And I went to your session on mathematizing children’s literature, and I was just so fired up. I was so wowed by your ideas, your energy, and your passion for students’ thinking. And I feel like as I read this book, I felt like I was hanging out with you. Like you were just so encouraging all the way through. Of educators, of other folks working with young people, and really guiding us how to listen with joy and with an open curious mind.

Dan Meyer (02:03):

Yeah. I would love to hear a bit about the genesis of this book for you folks. Like, I’m coming at this from a secondary educator lens. I’ve got small kids, so that’s also part of my interest here. But I love any book, any idea that seeks to merge what seems like two disparate worlds. Like it’s often the case that we feel like, well, there’s approaches for ELA and approaches for math, and they’re kind of separate disciplines. And these poor elementary teachers have to learn all of them and be experts at all of them. And here you both come along and say, “Hey, what if they are the same kind of technique?” Can you just speak to how this came about?

Allison Hintz (02:38):

Definitely. Tony, do you wanna take a try? Do you want me to start us off?

Antony Smith (02:42):

I can start. We oftentimes present and talk together and so we kinda switch back and forth. So that’s just how we are. So probably about eight or nine years ago, Allison and I, our offices were next to each other on our small campus. We’re both professors and we just happened to have a few children’s books that we looked at together and we were just thumbing through the pages. We really liked children’s literature. And we noticed that I would stop at certain points wondering about character motive or plot or sequence of events or language use. And Allison would stop at very different points in the book and notice number and concepts or something about mathematics. And that’s when we started to wonder, what would it be like if we were sharing a children’s book with a group of children and we put our ideas together? Where would we stop? What would we talk about? What would we ask children about in terms of their thinking and what they notice?

Allison Hintz (03:42):

And so we started playing with these questions that we had and started approaching stories with multiple lenses to see what kinds of things would children notice and what kinds of things might they say. And we were also on our own journey in trying to understand how to plan for and facilitate lively discussions and classrooms that surface really complex mathematics. And it felt like stories were a place where that might be a fruitful context for hearing children’s thinking. We’ve worked with a lot of teachers and students in our region. We live in the Seattle area and we’ve applied for some funding over time that’s really helped us be in a lot of community-based organizations and educational contexts and libraries and pediatricians’ offices and classrooms, various classrooms, and see what’s interesting about this and what might teachers and children do with stories that would surface complex mathematics to think about together.

Antony Smith (04:41):

Over time, we came to the realization that if we wanted to hear children’s ideas, we had to stop bombarding them with questions. <laugh> Yeah. And at first it made it worse that we were asking them math and literacy questions at the same time. And so we realized that what we needed to do was to back off and to ask children what they noticed and wondered.

Bethany Lockhart Johnson (05:01):

Can you say more about that and how that kind of evolved into mathematizing children’s literature?

Antony Smith (05:07):

We did work with a number of very thoughtful, talented classroom teachers and children’s librarians in public library systems who were just so masterful at asking open-ended prompts and questions, rather than kind of like the de facto reading quiz, that a read-aloud can become, which I’ve always disliked as a literacy educator. And we realized in our observing these read-alouds or interactive read-alouds or shared reading experiences that given the opportunity in the space and an adult who was actually listening, that children came up with all of the ideas we would have asked them about and more. So we didn’t have to be bombarding them with questions. They were already much more thoughtful than what would’ve been sufficient to answer our questions.

Allison Hintz (05:58):

And much like mathematics, it was really an iterative process. You know, we had some clunky read-aloud discussions where we were trying to accomplish so much and toggling multiple chart papers and different colored pens and all sorts of “how do we capture these ideas” and “do we separate ’em? do we keep ’em together?” And so it’s really been over time that with partners, we’ve learned these ways of having multiple reads of the same story that allow us to hear what children notice and wonder, and then to delve more deeply into their questions and their ideas through multiple reads where we might spotlight literary ideas that they notice; we might spotlight mathematical ideas that they notice. We might make purposeful integrations between those. But we found it to be most productive—and Kristin Gray really help us think about this—to have an open Notice and Wonder, get everything out much like an open-strategy share. We welcome here, record all the ideas, and it goes all over everywhere. You know, it can be a really not math-y noticing! And those are amazing! So there’s a lot of, um, yes, there is a ladybug on this page! The grandma is wearing green triangle earrings! Oh, your grandma wears green earrings! I mean, it all comes out.

Bethany Lockhart Johnson (07:27):

Wait, have you been in my classroom? ‘Cause that’s exactly— <laugh>

Allison Hintz (07:29):

<laugh> And then, you know, we think of it a lot like if math teachers might use the 5 Practices for selecting and sequencing, or if you might move from an open-strategy share to a targeted share, how can we get out all the questions that children are asking and then step back from them, take some time to really think about what they’re telling us they’re curious about, and plan some purposeful, intentional subsequent discussions that can delve more deeply into their ideas.

Dan Meyer (08:02):

I’d love to go into that a little bit more if that’s all right. Um, I’m gonna speak from someone who doesn’t have an elementary background and I’m gonna voice some worries that I had, some anxiety. One anxiety I have like in a classroom or a curriculum is when there’s no room for student ideas. Right? When it’s like, oh, there’s just room for the curriculum author or the teacher here. That is a sadness. But I when I see an instructional environment like you’re describing here, where there is openness to all kinds of different student ideas, of different levels of formality, from different kinds of cultural fonts of knowledge or wherever, I also get a little bit nervous because that, like, increases the risk that a student might come to understand that “my ideas are not good enough,” whereas in the class with no room for their ideas from their home or their language or their hobbies, like, they’re not gonna internalize the message that, “that wasn’t good enough.” And so I’m really curious as you move from the open Notice and Wonder where kids share all of themselves with you, and then you move to a targeted focus on some sort of disciplinary objective, how do you navigate that tension and help students feel like their contributions are valuable, even though we aren’t taking them up per se?

Allison Hintz (09:18):

That’s such an important question. I mean, I think we’ve grappled with this broadly in math education. I think any time we’re thinking about which ideas we choose to take up to pursue to consider, we have a responsibility to think carefully about whose ideas are being taken up and heard and considered. And so one of the tensions I hear you naming, I think, Dan, is when we engage in lively discussion where children’s thinking’s at the center, how do we make sure to upend and interrupt kinda status norms that run the risk of being deepened? Um, and I think by paying attention to whose ideas are taken up as much as which ideas are taken up, and what’s the mathematics we wanna explore is one tension. Um, another tension I might hear you naming is, you know, the complications that teachers face with time and pressure and coverage, and which mathematics ends up getting worked on. And, um, you know, it’s something we’ve really had to struggle with in mathematics education, where we move to more discussion-oriented classrooms that are really centered in sense-making to know that it takes a lot of time to do this thoughtful, thoughtful work. Um, does that begin to get at some of the tensions you’re raising? Is there, is there more you’re thinking about?

Dan Meyer (10:53):

I think it’s really helpful that you kind of broadened the scope of the question beyond your book to “this is an issue that we are, you know, really challenged by and focused on broadly in math education.” And, um, I appreciate you bringing the element in of whose idea—not just which idea is taken up, but whose idea is taken up—is an opportunity where, let’s say, multiple people raise an idea that is towards an objective the teacher has, they have the opportunity to disrupt certain kinds of status, like ideas about status, in that moment. From your perspective, like, are there techniques to say, I don’t know, parking-lot certain kinds of questions and say like, “Hey, like these are awesome”? I don’t know. I just know that I see kids at like ninth grade. They are very reticent, often. They’ve internalized totally this sense of like, “I’m not gonna just, like, share about the pants the grandma’s wearing, you know; that will not be received well.” And so I’m just kinda wondering how that happens and like, what are the ways we can disrupt that? That process?

Antony Smith (11:54):

So thinking about that, Dan, from the teacher’s perspective, in those kinds of scenarios where you wanna honor each child’s contribution, a couple of things that come to mind: One is that by, you know, initially by modeling what I as a teacher, something that I notice or wonder about, helps kind of set the expectation for what kind of response would be encouraged. And it’s broad, but it gives an example. And then also we really try to record or to chart all of the ideas that are shared so that we can revisit and honor those together. And then either later or on another day, if we choose one or two of those to explore in some way within a more focused read, then another thing that we do is have the idea investigation afterward that continues that thought, but goes back to being as open-ended as possible, so that those students or children who maybe didn’t have their idea as the one that was focused on by the group could go back to that or explore some other idea of their own, so that the idea investigation isn’t a lockstep extension activity, which is why we don’t call it that. So they could again bring in their own perspective. But I have to say from the teacher’s point of view, there is that moment of potential panic <laugh> because there is that power transfer when you’re asking children to help steer where this is going. And if you really mean it, you have to let them steer a little bit. And that can be terrifying. And, um, I always think of one teacher, Ashley, we worked with who read an adorable book, Stack the Cats, by Susie Ghahremani. And in that book, there’s a point where there are eight cats and they’re kind of trying to be a tower of cats and they fall and they’re sort of in the air on that page. And she asked her first graders—she stopped, and she asked, “How, do you think, how will the cats land?” And for about a minute and a half, the entire <laugh> class, was silent. They had their little papers; they had chart paper; they had clipboards; they had everything they needed. But that unusual phenomenon of a group of six- and seven-year-olds actually just sitting and thinking and not being peppered with activities was really stressful, but amazing. And then, after about the 90 seconds, they started out into their exploration of how the eight cats might land. They just needed a minute to think. And it’s so rare that we’re able to let children have that.

Allison Hintz (14:40):

In that same moment, Ashley, who’s a learning partner to us, she turned to us kind of quietly, like, “Should I pose a different question?” And <laugh>, we’re like, “No, let’s stick with it. Let’s see what happens.” So I think it creates this space too, this thinking culture, right? And this culture of “what does that mean to really pose a rich task?That’s open-ended, where there’s multiple access points?” Those eight cats could land in so many different ways. And there was broad access, there was a wide range of all the cats landing, and one’s on their feet, ’cause cats always land on their feet <laugh>, and there was every combination. And so, um, I think what’s really interesting—and to me, this brings back to your wonder, Dan—is, you know, “What’s the risk in openness?” And there’s always risk in openness. Um, it’s scary as a teacher, right? If I’m not the authority of knowledge and I don’t have control over where we’re gonna go, it might get into places that I didn’t anticipate. Or I don’t really feel as solid in the math as I want to. Or I don’t know what it sounds like to stick with silence and wait time, to know if my students are really in productive struggle or if that question was a flop. And so, um, I think this is some practice space for young mathematicians and teachers of mathematics, and just teachers, to explore with that openness and kind of the risk of the openness required for complex thinking to emerge.

Bethany Lockhart Johnson (16:12):

You know, it feels like the way you’re both describing this, it really is a culture shift, right? I kept feeling like I was given permission to be a beginner as I read this book. Like I was really…I loved how you said, I believe it was you, Allison, when you were in the class, you had a couple index card that you kept on your clipboard and that as you walked around, you were like, “Hey, if I don’t know what to ask, I ask one of these questions.” You know? And just this idea that, that, like Dan was saying, there is that loss of control, but that’s also a way to create this culture where students ideas are valued and we are allowing students to really generate the questions, which I thought was such an important idea to explore.

Allison Hintz (17:00):

We started this work long ago, super-excited about math-y books. And we saw a lot of potential in them and we still do. But the limitation we saw is that math-y books, they, they put forth a certain mathematics to be curious about. In some ways they tell you what mathematics to think about. So we started asking ourselves what would happen if we considered any story a chance to engage as mathematical sense-makers. And we started playing with non-math-y books and we got to a place where we could consider every story an opportunity to engage in mathematical thinking. And so we started noticing things over times, oh, these books tend to be really math-y. We call those text-dependent. We’d have to pay attention to the mathematics to understand the story. Whereas this pile of stories, these, they’re not overtly math-y. You could really enjoy the story and not pay attention to mathematics and have an amazing conversation. But what would happen if we thought of about this story as mathematical sense-makers and how might it deepen our understanding of the story? And then this other teetering pile of books, these are books where, you know, children didn’t tend to engage as overtly as mathematicians in it, but there’s opportunities in this story to go back to something—to a moment, to an illustration, to a comment—and think as mathematicians. And those were more about illustration exploring. And so, as we notice these different kinds of books, we really broaden what we thought about. And I think one of the things we really wanna think about in community through this book is what happens if we approach any story, every story, as mathematical sense-makers, because stories are alive in children’s lives, in homes and communities and in schools. And it’s a broad opportunity that we wanna take up. I was thinking, as I stay in this strait for just a moment about book selection, before we move into that process, um, Bethany in a previous MTL, you talked about representation.

Bethany Lockhart Johnson (19:12):

Mm, yeah.

Allison Hintz (19:14):

And do you remember when you shared the image of hair braiding?

Bethany Lockhart Johnson (19:19):

Yes. Vividly, yes. <laugh>.

Allison Hintz (19:22):

Yeah. And can you say just what that meant to you? What that….

Bethany Lockhart Johnson (19:27):

Yeah. Well, it was from a conference; Sunil Singh had used it and was talking about the artistry in mathematics and beauty in hair braiding. And, um, particularly, he was showing this particular image of this Black woman with her hair braided in profile and looking at the angles and the symmetry. And I shared that, you know, I spent so many hours in the beauty shop with my aunties and my mom and my grandma and continue to, to this day, that it just, it struck me immediately as familiar. And it struck me immediately as seeing an image that was reflective of my lived reality, projected as valuable and worthwhile for consideration in the world of mathematics. Which is not what I felt as a student of mathematics as a young adult or child. So it was this beautiful moment of, for me, the power of when we see images and we allow opportunities for re-envisioning what may be a common practice for that student, or may be something that they see every day.

Allison Hintz (20:44):

And in that same way, that image that was put up, we wanna think really carefully about representation in the stories that we select. And when we think of stories as mirrors or windows, we really wanna be mindful in story selection of whose stories are told and whose stories are heard. And when you said that you would sit down to listen to a story and you felt at ease or that you saw an image and you saw yourself that can be and should be something we really think carefully about when we select the stories that we select.

Dan Meyer (21:21):

It’s a wider path for representation of different kinds of people in literature, because people’s stories seem so much more present and towards the surface of their lives, versus, say, the abstractions and numbers and shapes in mathematics. It feels like more of a struggle to find ways to show people, hey, like you’re here, this, this place belongs to you. So in all these reasons, I think it’s really great you folks are using literature, which has this history of humanities, literally humanities, as a vehicle for mathematics. That seems pretty special here.

Antony Smith (21:56):

We both go to libraries and bookstores and look through books as often as we can, but also our partner, a children’s librarian, Mie-Mie Wu, helped us go through—when we would meet, she would bring three or four hundred books at a time.

Bethany Lockhart Johnson (22:13):

When you described her wheeling in the cart, oh, I wish I been in that room! <Laugh>

Antony Smith (22:18):

And the cart was, you know, probably three or four times bigger than she was sometimes. And we would go through hundreds of books and look at them and listen to her thoughts as a skilled librarian sharing with families, diverse families, and what catches the attention of a three-year-old sitting with her grandfather. And that was really a valuable, helpful experience. And it’s a partnership that continues. So in Last Stop on Market Street—and this is in the book; we talk about this, this children’s book quite a bit—in this story, CJ with his Nana, his grandmother, are riding the bus to the last stop on Market Street in San Francisco, to go, as we will find out, to help serve in a soup kitchen to help the community. And the teacher, Susan Hadreas, had the children record their ideas. She charted them in an open Notice and Wonder read. And one of the ideas that a young boy noticed was that CJ on the bus…a man with a guitar starts playing the guitar on the bus and CJ closes his eyes and it says CJ’s chest grew full. And he was lost in the sound and the sound gave him the feeling of magic. So this boy said, “I wonder, what does that feel like if you’re feeling the magic? What’s that?” And that was one of many ideas in the open Notice and Wonder, and Allison will talk about the math lens read, but first Susan went back and read with them. She had that idea, she circled it on the chart paper, and another day that week, she said, let’s go back and visit this story we really liked. And remember, we wondered what feeling the magic was like. Let’s go back through and let’s keep track of all the feelings and emotions that CJ had across the journey to the soup kitchen in this book. And so they did another read of the story; they were very familiar with it, of course, but they noticed new things and they also, every few pages, stopped and she helped chart all of the emotions that CJ experienced from envy to excitement to sadness. There’s a huge range in this book. And it was fascinating.

Allison Hintz (24:36):

I think one of the things that the children noticed was that CJ’s feelings were shaped by community. And that he shaped and shaped…he was shaped by and helped shape his community. And so the ways that he felt across the story were impacted by the other characters that he comes across. The guitar man on the bus. The bus driver who can pull a coin out from behind someone’s ear. The lady with the butterflies in the jar. Nana helping him to see the rainbow. And the students started, you know, being curious about that. How do we shape and how are we shaped by community? What communities are we a part of? This class is one community. I’m in many communities across my life. And they started to quantify the number of people in the story. So Mrs. Hedreas went back for a math lens read, and she said, let’s just keep track of and pay attention to how many people are in CJ’s life in this day. Because I can hear you starting to think about quantity. This class at the same time in other areas of the day had been working on counting collections, how to keep track, so they got out their tools. Some people pulled out ten frames, some people pulled out clipboards. They had a wide range of things they could use to help them keep track. They developed their own strategy, keep track however you want. She did a quicker read through it, flipping the pages, and then they get into these debates: <laugh> “We already counted that person!” “But they took their hat off and put it down to collect money!

Antony Smith (26:10):

“What about the dog?”

Allison Hintz (26:11):

“That’s the same person!” “Yeah, there’s a dog pound in his community!” <laugh> “Do animals count in our community?”

Bethany Lockhart Johnson (26:17):

I love it!

Allison Hintz (26:17):

“Yes, they count!” Uh, and so we went through and quantified and there was really this understanding as you saw these people throughout the story that communities can be of different sizes, but community has impact. And you have responsibility in your community to show up and to lean in and to know that bringing your full, authentic, vulnerable self, you shape people and they shape you. And what communities are people a part of. And it turned into this really interesting discussion about quantity and helped us think more about quantity and community. I think a really important moment for us and for that class was the transition from being people who almost did mathematics to a story, like counted things on a page, um, count acorns on a page in an autumn book, to being mathematicians who thought within the story.

Antony Smith (27:17):

And then two idea investigations that came from that —not at the same time, of course, but with the same group of children—one was they identified an emotion of their own and wrote and drew about that. And also, who helped them address or get out of or acknowledge that emotion. And then the other idea investigation was that all of the children drew or kind of mapped out a community that they were part of. Whether it was their neighborhood or their classroom or their soccer team or whatever it was. And so then those investigations strengthened the connections of those concepts to the lives of those children.

Bethany Lockhart Johnson (28:05):

Well, I, actually wanted to ask you about idea investigations. Because I feel like that was such an important invitation in your book. And the way I understood the idea investigation is you’re really paying attention to what’s coming up in your other reads. Right? And then these are opportunities to extend the thinking, or like you said, to extend a particular aspect: What’s your community? Can we map your community? Or what’s a particular emotion? And it was in such contrast to what I think I have probably done in my classroom more than once, which was like, “Oh, we read this story about seals. So now my story problem is gonna be about seals, right? <laugh> Like in the story, you know, Jojo, the seal had five balls. <laugh> So if Jojo still had five balls and two of them bounced away…” You know, or whatever. Right? But that’s not what an idea investigation is. Right?

Allison Hintz (29:03):

Yeah. I think this is where we also had some stumbles and can totally relate to what you’re saying as previous classroom teachers as well. We have come to a place where we are pretty in favor of a super open-ended idea investigation that takes up the things that have surfaced in the multiple reads and making sure it’s a rich task with many, many ways children can engage with that. There’s many, many, many right answers or ways to engage. Less is more there. So we moved way away from, like, even a worksheet that might have an idea from it to blank paper and math tools and places to get into some productive struggle around some of the complex things that were raised.

Antony Smith (29:59):

A challenge with worksheets is that they put a frame around children’s ideas. So either there are only three lines to write on, or there’s only a small box to draw in. Whereas a blank page really opens up the possibility. Um, and so—is it Ann Jonas who wrote Splash!? sorry, I don’t have it in front of me—the book Splash!, about animals that end up in and out of the pond, including a cat that is not happy about ending up in the pond, an idea investigation after that for very young children was, with the list of the different creatures displayed at the front of the room: On blank paper, hey, draw your own pond and decide how many of which and each type of animal you want in your pond and then write about it. Just on blank paper. And so that allowed some children to draw, like, three giant goldfish. But other children drew 17 frogs and three cats. And, and just, it lets children follow—

Bethany Lockhart Johnson (31:02):

It was theirs, right? It was theirs.

Antony Smith (31:04):

Their idea. <laugh> And that comes partly from, I think, as Allison mentioned, we both were classroom teachers before moving into academia. And I remember giving children worksheets, particularly math worksheets, where they weren’t necessarily bad, but right at the bottom, it says like, explain your strategy. And it gives two lines.

Bethany Lockhart Johnson (31:23):

Right! <laugh>

Antony Smith (31:25):

The only thing a seven-year-old can write there is “I thought.” Or “I solved it.” <laugh> And that’s not where we need to go.

Dan Meyer (31:34):

Yeah. If I could just ask the indulgence of the primary crowd here, like, I’m trying to make sense of all this. And I just wanna like, offer my perspective. My summary statement of what’s going on here. I’m trying to—I love how you both came here—

Bethany Lockhart Johnson (31:45):

<laughs> How ya doin’, Dan? How ya doin’?

Dan Meyer (31:47):

<laughs> I’m, ah, A, I’m loving this a lot. Um, B, I came in here loving how you folks are broadening the work of primary education to kind of find commonalities between these sometimes seemingly disparate kinds of teaching in ELA and math. Love that, I wanna say. But I think you folks are describing, with all these teachers you observed and your own work, is the work of attaching meaning to what students might not realize yet has meaning. Or they might think it only has one kind of meaning. But you, the teacher, with their knowledge, realizes that there are many more dimensions of meaning that can be attached to those thoughts. And I’m hearing that from you folks, when you describe A, what math is and the power of a teacher to name a thing as mathematical. Like, “Oh, you didn’t think math was that, but math is noticing; math is wondering; math is asking questions,” for one. But also this work you’re describing of how, like, first the task has to invite lots of student thoughts and then to say like, “Oh, I see that there’s a similarity to these two.” And to raise those up for a conversation or to ask a question like to extend one person’s, one student’s question a little bit more. But it’s always…I’m just hearing you folks attaching more meaning than the student might have originally thought. I appreciate the conversation. That’s really interesting.

Bethany Lockhart Johnson (33:03):

Well, and now that the book is out, I think it’s gonna keep evolving, right? Now that it’s gonna be in the hands of teachers and librarians and educators and caregivers, it’s exciting to see kind of where it goes next. Which actually brings us to our MTL challenge. Dan Meyer, do you wanna share?

Dan Meyer (33:22):

Math Teacher Lounge, we have a challenge for the folks who listen and we’d love for them to hop into the Facebook group Math Teacher Lounge, or hit us up on Twitter at @MTLShow and just, like, kind of exercise beyond listening, exercise the ideas you folks are talking about, some kind of a challenge that can help us dive deeper into your ideas. So what would you folks suggest for our crowd, for our listeners?

Allison Hintz (33:42):

I would love to invite people to playfully experiment with a favorite story, with a story that’s new to you. I would love to invite listeners to sit with a story maybe on your own, and just ask yourself as a mathematician: What do you notice and wonder in this story? Don’t feel any pressure. Maybe sit with a child or some children and listen to what they notice and wonder. Like, really listen! Don’t ask questions! But hear their questions and place children at the center and consider multiple reads. Consider continuing to pursue their questions. And we have a planning template that might support people in kind of sketching out some ideas if you’re open to playing with that too.

Bethany Lockhart Johnson (34:34):

And we will post—

Dan Meyer (34:36):

That’s awesome.

Bethany Lockhart Johnson (34:36):

—a link for that planning template in our Facebook group and on Twitter as well. So thank you so much for that resource, because I think it’ll definitely help. It could help you, like you said, it could help you kind of organize your thoughts or help you think about this work in a new way. So thank you for that resource and thank you for the amazing resource that is Mathematizing Children’s Literature. I am so excited to continue to engage with you both and with listeners as they dive into this book. If folks want to engage with you more, where can they find you? How can they reach you?

Allison Hintz (35:12):

Well, we’re on Twitter.

Bethany Lockhart Johnson (35:14):

Great.

Dan Meyer (35:15):

What’s your home address? <laugh>

Bethany Lockhart Johnson (35:24):

Wait, let me try that again. <laugh> ‘Cause it does sound like I’m like, <fake ominous voice> “Where can they find you?”

Allison Hintz (35:29):

4-2-5…. <laughs>

Antony Smith (35:32):

At the bookstore!

Bethany Lockhart Johnson (35:34):

Y’all, if folks want to continue this conversation or share these ideas or the math challenge, how can they tag you? How can they, they reach you on the World Wide Web, besides the Math Teacher Lounge Facebook group?

Antony Smith (35:50):

Yeah. Well, we are both on Twitter, and we’ve been trying to promote the hashtag #MathematizingChildrensLiterature. It’s very long, but once you type it once, your phone or computer…

Bethany Lockhart Johnson (36:01):

Easy. Yeah, those click, right? Is that what it is now?

Antony Smith (36:03):

<laugh> The other is that we do for our project, we have an Instagram account that is @MathematizeChildren’sLiterature.

Allison Hintz (36:11):

We care really deeply about hearing from people. You know, we think our ideas are constantly evolving and that there’s such exciting room to grow. And we just felt compelled to share what we were learning now so that together we could learn and build vibrant experiences for young children and teachers and families through stories. So we want to hear from people! We wanna learn about stories that are important in your lives and what children say, and grow these ideas together.

Bethany Lockhart Johnson (36:42):

And credit to Dan, you told me you went and ordered a bunch of the books they have on the suggested read list.

Dan Meyer (36:48):

Oh my gosh.

Bethany Lockhart Johnson (36:49):

You read ’em to your son.

Dan Meyer (36:50):

I got such a side-eye from my significant others around here for what I dropped on Amazon in one night! <laugh> Uh, all these books I didn’t have. Some of them I did. We are not fully illiterate around here! We do love the written word at the Meyer household! But there were a bunch that that I grabbed. I’m morseling them out day by day.

Bethany Lockhart Johnson (37:09):

Wait, at bedtime I read my one-year-old One Is a Snail, Ten Is a Crab. <laugh> And let me tell you, he had vigorous pointing and “Da? Da da da da?”

Allison Hintz (37:22):

<laugh> Aww, da da!

Bethany Lockhart Johnson (37:22):

So hey, we’re on the road. <laugh> <music> Deeply grateful, not only for your work and your beautiful book and your work, but also for the invitation to dive into the world of children’s literature in a way that many of us have not before. And it’s fun! Thank you, Tony. And thank you, Allison. And thanks for hanging out in the lounge.

Allison Hintz (37:48):

Thanks for having the lounge!

Antony Smith (37:49):

It’s been fun!

Allison Hintz (37:52):

Thank you both.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Allison Hintz says about math

“We started asking ourselves, “what would happen if we considered any story a chance to engage as mathematical sensemakers”.”

– Allison Hintz

Author and Associate Professor, University of Washington Bothell

Meet the guest

Allison B. Hintz: Dr. Hintz’s research and teaching are in the area of mathematics education. Her focus on mathematics came about during her years as a fifth grade teacher – it was alongside her students that she developed her own positive identity as a mathematician! Today she studies teaching and learning, specifically facilitating engaging discussion. Her research and teaching happen in partnership with educators and children in formal and informal settings and focuses on beliefs and practices that support all children in lively mathematics learning. She is a co-author, with Elham Kazemi, of Intentional Talk: How to Structure and Lead Productive Mathematical Discussions.

Twitter: @allisonhintz124

Antony T. Smith: Antony T. Smith is an associate professor of literacy education at the University of Washington, Bothell. He works alongside teachers to create engaging literacy-mathematics learning experiences through exploring and discussing children’s literature. He is committed to the concepts of motivation, engagement, challenge, and creativity in literacy teaching and learning.

 Twitter: @smithant  Instagram: mathematizechildrensliterature

Two people appear in separate circular frames; the woman is smiling and wearing headphones, while the man stands in front of bookshelves, perhaps discussing Mathematizing Children’s Literature.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

San Diego Caregivers — Welcome to Amplify Desmos Math!

Welcome to the Amplify Desmos Math Caregiver Hub for San Diego USD. We’re excited to partner with San Diego USD teachers, principals, and district leaders to provide your student with exceptional opportunities to learn math. We designed this hub to help you in supporting your student along their math journey this year.

Introducing Amplify Desmos Math

Amplify Desmos Math is a new core math curriculum built for grades 6, 7, 8. Designed to help students learn math in a way, Amplify Desmos Math uses a student-centered approach to instruction, which has been proven to significantly increase math learning.

In every lesson, Amplify Desmos Math poses engaging and relevant problems to solve, giving students daily opportunities to think critically, work collaboratively, and actively participate in their own learning.

Amplify Desmos Math was built upon the highly rated Illustrative Mathematics curricula: IM K-12 Math™️, which earned an all-green score on EdReports.

About student-centered math instruction

Student-centered instruction may look different from the way students have learned math for decades, and maybe even the way you learned math. Instead of memorizing formulas and tricks, student-centered learning focuses on giving student opportunities to figure out how math works. Plus, research shows that students and teachers alike prefer this method, and teachers report that student-centered instruction has helped their students learn more math.

This way of learning helps students:

  • Understand how math concepts work.
  • Remember what they learn in class and apply their knowledge to new situations.
  • Perform better on standardized tests and have more growth in their grades than their peers who learn through other methods.
  • Learn to communicate in writing and verbally, understand and challenge the opinions of others, and build confidence in solving new problems.
  • Develop key skills for success in college and the workplace, like using technology, completing projects independently and with others, and persevering through difficult problems.

What materials do students use?

Amplify Desmos Math supports blended learning with supportive print materials and a unique digital experience. In addition to a consumable Student Edition, students are invited to use our interactive online platform to solve open-ended tasks and challenging problems.

Here are some key highlights of the digital platform:

  • Digital activities that allow students to explore and make sense of math
  • Digital calculator and virtual manipulatives that support students of all levels
  • Immediate feedback that guides students in understanding challenging concepts
  • Ability to access instructional materials in English or Spanish

With access to their own special online dashboard, teachers can monitor students’ work in real time, making sure they get the exact support that they need at every part of the lesson.

What does a lesson look like?

Students in an Amplify Desmos Math classroom can be seen (and heard!) — asking questions, debating answers, justifying their thinking, grappling with problems, and working together and independently.

In class, your student will spend their time working on challenging problems while the teacher acts as a guide, highlighting different strategies for solving problems and helping students to understand the reasoning behind the math they do in class. Your student will be pushed to think more deeply about the math in their class as the teacher and other students question them on why their ideas make sense. Research has proven that this method helps students become better problem solvers, critical thinkers, and have a stronger conceptual understanding of what they are learning.

Here’s what a typical Amplify Desmos Math lesson includes:

  • Warm-up: A short, attention-getting problem to get students interested in the lesson
  • Activities: 1-3 mini-activities that challenge students’ problem-solving skills
  • Synthesis: Discussion to review and bring together the important concepts from the lesson
  • Exit Ticket and Reflection: Questions for students to show what they know from the lesson
  • Practice: Additional problems your student’s teacher may assign for classwork or homework

How can families support math learning at home?

Find the math in everyday life

Relate math to daily activities at home, whether it be baking, grocery shopping, or planning for a road trip. Your student can help you figure out the price of an item after a coupon, cut a recipe in half, or figure out how much gas you’ll need to make it to your destination. Encourage your student to point out ways that your family uses math in your daily tasks.

Review practice problems together

Your student’s teacher may assign practice problems at the end of each lesson for classwork or homework. Ask your student to walk you through how they solved each problem, or talk about any parts that were challenging for them.

Remember getting stuck is okay

Emphasize that getting stuck is part of the process and a necessary part of learning. Many students (and adults!) fear making mistakes, however, research shows that making mistakes helps your brain grow more. When your student gets stuck on a problem, encourage them to try different strategies, even if they are not sure if they are right.

Use our Unit Summaries for Families

We’ve created a Family Resource for every unit of the program that provides a summary of key concepts plus examples for how to work through problems.

Within each of the grade-level links below, you’ll find a Family Resource document for each unit, in both English and Spanish.

Unit 1: Area and Surface Area

Unit 2: Introducing Ratios

Unit 3: Rates and Percentages

Unit 4: Dividing Fractions

Unit 5: Arithmetic in Base Ten

Unit 6: Expressions and Equations

Unit 7: Rational Numbers

Unit 8: Data Sets and Distributions

Unit 1: Scale Drawings

Unit 2: Introducing Proportional Relationships

Unit 3: Measuring Circles

Unit 4: Percentages

Unit 5: Rational Number Arithmetic

Unit 6: Expressions, Equations, and Inequalities

Unit 7: Angles, Triangles, and Prisms

Unit 8: Probability and Sampling

Unit 1: Rigid Transformations and Congruence

Unit 2: Dilations and Similarity

Unit 3: Linear Relationships

Unit 4: Linear Equations and Systems of Linear Equations

Unit 5: Functions and Volume

Unit 6: Exponents and Scientific Notation

Unit 7: Irrationals and the Pythagorean Theorem

Unit 8: Associations in Data

Note: The below links are for our Volume 2 units, which most students are working in currently. Additional units will be coming soon!

Unit 1: Coming Soon!

Unit 2: Coming Soon!

Unit 3: Fractions and Decimals

Unit 4: Expressions and Equations

Unit 5: Proportional Relationships

Unit 6: Percentages

Unit 7: Positive and Negative Numbers

Unit 8: Describe Data

Note: The below links are for our Volume 2 units, which most students are working in currently. Additional units will be coming soon!

Unit 1: Coming Soon!

Unit 2: Coming Soon!

Unit 3: Coming Soon!

Unit 4: Linear Relationships and Systems of Linear Equations

Unit 5: Functions

Unit 6: Associations in Data

Unit 7: Volume and Surface Area

Unit 8: Exponent and Scientific Notation

Unit 9: Pythagorean Theorem and Irrational Numbers 

Listen to our podcast

Our Math Teacher Lounge is a biweekly podcast created specifically for K–12 math teachers. In each episode, co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with expert guests, taking a deep dive into the math and educational topics.

From time-to-time, the topic of an episode is perfect for families. For example, the episode below features Dr. Marjorie Schaeffer. She discusses what causes math anxiety, math hacks, and how the right math technology can make an incredible impact in children and family members who struggle with math anxiety.

Listen today and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!

Download Transcript

How do families access the program at home?

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. Students can access the digital curriculum in school and at home by following these simple instructions.

  • Click the Amplify Desmos Math button.
  • Select Log in with Amplify.
  • Enter this username and password provided by your student’s teacher.
  • Select the desired grade level.

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Alert: Progress in early literacy is slowing.

The latest middle-of-school-year data from Amplify show that throughout the spring and fall of 2023, schools across the country made some progress increasing the number of K–2 students on track for learning to read. But that progress is slowing.

Between 2021–2022 and 2022–2023, the number of K–2 students on track for learning to read increased by four to five percent across all grades; however, between 2022–2023 and 2023–2024, the increase was only two percent in each grade. Yet this is not the time for slow progress, because literacy rates in the United States are already a concern. Only half of K–2 students are on track for learning to read, and three in ten students are far behind.

To address slowing gains, schools and districts need to act now to accelerate literacy outcomes.

Early reading: Why we need to act now

The decline is especially urgent for students in kindergarten through the second grade. That’s because of what comes next: third grade, known to be the make-or-break year for reading and future academic success. To put it bluntly, students who are not proficient in reading before entering fourth grade are much more likely than their peers to struggle in school, and they are much more likely to drop out.

“The data is clear—literacy rates at the earliest and most critical time for student development are slowing. Changing this course requires schools and districts to act now and review their approaches in all grades,” says Susan Lambert, chief academic officer of elementary humanities at Amplify. “Schools that deliver strong outcomes focus on building a solid foundation at the start and intervening quickly when students need extra support, rather than trying to play catch up later, when it can be more difficult.”

The good news: We know what to do.

When students receive science-based reading instructionliteracy outcomes improve.

Changing these outcomes requires that districts and schools review the processes and practices they have in place at all levels. Schools that deliver strong outcomes focus on getting students on track—and often ahead—in the earliest grades, because it’s easier to get students ahead from the beginning than to catch them up later.

Districts should:

  • Administer universal screening assessments three times per year to monitor levels of risk for reading difficulties.
  • Allocate staff to support students who are at risk, spending additional time in literacy instruction beyond grade-level instruction.
  • Regularly monitor progress for students who are at risk, making adjustments as needed.
  • Ensure that instructional staff gain knowledge about science-based reading instruction and implement high-quality core curriculum with fidelity.
  • Instill a love of reading and books during all school-based programs, with the support of caregivers and the community.

“The good news is that when students receive science-based reading instruction, outcomes improve,” Lambert continues. “And, when that instruction takes place in the earliest possible grades, research shows that most students can be taught to read at or approaching grade level.”

Read the full report.

More to explore

S3-03: Instructional strategies for integrating science and literacy

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

We’re continuing our investigations around science and literacy with Doug Fisher, Ph.D., professor and chair of educational leadership at San Diego State University. We talk about the importance of integrating science and literacy, as well as practical guidance for teachers who want to unite the two disciplines in their own classrooms.

Listen as we discuss how science and literacy can be powerful allies and specific strategy areas to focus on when integrating the two disciplines. And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Douglas Fisher (00:00):

It’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. This season, we’re making the case for our favorite underdog, which of course is science. Each episode we’re showing how science can be better utilized in the classroom, and making the case for why it’s so important to do so. In our last episode, we examined the evidence showing that science and English instruction can support each other. And now on this episode, we want to give you some more strategies for really making that a reality in your own home or classroom or community. So to help me, I’m joined on this episode by Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Dr. Fisher is actually someone who has conducted literacy training at my own school, so I’m excited to be able to share some of his wisdom with all of you. Oh, and just a heads up, Dr. Fisher dropped some gems about the ways teachers can integrate literacy and science in their classrooms. So you may want to have a notepad. Ready. And now here’s my conversation with Dr. Douglas Fisher.

Eric Cross (01:12):

Well, Doug, thank you for your time and for being willing to come and talk about literacy and science. I know you’re busy, all over the place, and so I was super-excited that we were able to lock you in and talk about this. And, on this episode, we’re gonna talk about the ways that science and literacy can support each other. And one of the reasons why I’m really excited for you is because you said some really key things for me as a science teacher, when you talked about literacy and supporting students. That just resonated so deeply in me. And I was like, “I need more Doug!” Because we’re on that same frequency. And I know it’s a subject that you’ve spent a lot of time writing about. So can you tell us a little bit about how this became an area of interest or a passion for you? Just literacy, and all of the work that you’ve put into it?

Douglas Fisher (01:54):

Yeah. So I’ve wanted to be a teacher for a really long time. And I went to San Diego State as an undergraduate, and I was taking English class and we were assigned topics. You know, like, you’ll do an assignment, you’ll write a paper for this English class. And I got the topic “illiteracy,” and I was a freshman at San Diego State reading all of these things about adults who don’t read very well or not at all. And I ended up writing my very first college essay on illiteracy — at the time, you know, called illiteracy, at the time. And so I got super interested in this. And so as I moved through college and into my teaching career, literacy became a really important thing for me to think about, because it’s the gatekeeper. You know, you can be taken advantage of, if you’re not very literate. People can use vocabulary against you, if you’re not very literate. We know that people who have higher levels of literacy have better health outcomes. They have better lifespans, longer lifespans. I mean, there’s just — literacy impacts so much more than “Are you reading your fourth-grade textbook?” It really has lifelong implications.

Eric Cross (03:01):

That part that you said about being taken advantage of … I just got a flyer in the mail yesterday. It was one of these mailers that looked like it was an authentic debt-reduction type of thing, but it was really just like a marketing email. If you read the fine print at the very bottom, it had all of this jargon about “This is a paid, you know, for-profit company.” But when you look at it, it had official stamps all over it. And I could imagine if someone’s receiving that, that probably fools a lot of people. Is that kinda like what you’re talking about, like being taken advantage of?

Douglas Fisher (03:28):

Yes. I had a student turn 18, got a letter from a “credit card company” that was offering her daily compounding interest. And if you don’t know what that means — at 23 percent! — if you dunno what that means, you are gonna be a victim. Literacy really influences a lot of our life. It’s also how our brain works. We have a language-based system in our brain. We read, write, speak, listen, and view. And the things we learn, we learn through speaking, reading, writing, listening, and viewing. From what we know, we are the only species that has an external storage mechanism. Like, we have the ability to store complex information outside of our body, in the form of notes. We can type them. We can write them. And we can then go back and retrieve that information, that complex orthographic information later. And it means the same thing. We can say we have a storage system and we’ve been doing this for a really long time. Way back to, you know, hieroglyphics and messages on cave walls. And throughout the ages of humans learning, how to store information that they can re-access again later. That’s become a super-complicated system. It’s how computers operate. And we send messages to each other and we text each other and we write things down, and we’re really good at putting ideas, information out there. Now, if it’s just speaking and listening, then we can forget it. We can say, “No, you said this,” or “I said that.” But when it’s written, and it’s print literacy, you know, it’s the orthographics there, you can go back to the same message and over and over again. Now, you might change the interpretation of it, but the message is still there.

Eric Cross (05:16):

Right. And that is such a key element, at least of modern education, is this written element of it. It’s what many schools live and die by. They’re quantitatively and qualitatively analyzed by it. It’s public. They can see it. And so there’s this heavy emphasis. And why do you think science and literacy can be powerful allies together?

Douglas Fisher (05:38):

Awesome. Well, it’s hard to learn science if you’re not literate.

Eric Cross (05:42):

This is true.

Douglas Fisher (05:42):

But that’s a one-way direction. And yes, science teachers and scientists do a lot of reading, writing, speaking, and listening and viewing. They use the five literacy processes all the time. When we interview scientists, they spend a lot of their time reading the work of other scientists and writing their findings, writing grant proposals, presenting at conferences, you know. So a huge part of the work of a scientist is not just at a bench conducting experiments. But even if you’re conducting experiments, you’re using your literacy processes to think about what you’re seeing in your experiment. So that’s a one-way direction. And I do think literacy has an influence on science. But since science goes the other way, it influences literacy. As you learn more and you understand more about the world, your background knowledge grows, your vocabulary grows, you become more literate in those different areas. And how you think. So if I’m learning about life science; I’m learning how the world works in a more, biologic physical world. And that knowledge helps me think about when I’m reading a novel, and there’s an appeal to some science knowledge or a concept that gets played with, you know, perhaps time-space continuums … well, if I don’t have the science knowledge of how I think the world works, it’s hard for me to understand what this author is doing. So it does go both ways. They feed each other. And the more literate we become, the more complex science information we can understand. ‘Cause our background knowledge and our vocabulary influence how much we understand about what we read. And as we access more complex science information, it starts to change the way we think about other things in our world.

Eric Cross (07:23):

There was a couple of things that you said in that, but one of the first things that kind of perked my ears is when you said grant proposals. Because I have friends that are scientists — and this is one of the things that when I was in school, they don’t talk about — but how much of their research is reliant upon getting funding —

Douglas Fisher (07:37):

Mm-hmm. <affirmative>,

Eric Cross (07:38):

— which you don’t think about if you’re becoming a chemist or a physicist or a biologist or working in the field, is that that funding, coming from the NSF or anywhere else. And sometimes students ask in class like, “Why am I writing so much? Like, I want to go into science!” Or “I wanna do this!” And this is a real-life example of how the writing could actually apply, in addition to all of the things of collecting data and conclusions and results. But that grant proposal thing just really perked my ears, yeah.

Douglas Fisher (08:01):

And if you can’t write a grant proposal, your ideas and experiments are not gonna get funded. And if you can’t write a strong proposal, that compellingly convinces your readers to fund you, you’re not gonna get funded. But then once you get the grant, you have to write publications. You have to share your work with other people. Make PowerPoint presentations and write journal articles or books or whatever. So it’s a cycle that literacy influences the things we do, including the things we do in science.

Eric Cross (08:31):

Now to get in maybe some data, if you were trying to convince someone that like this happy marriage can exist, what would be like your number one piece of evidence to support this, this back and forth of supporting each other?

Douglas Fisher (08:44):

Awesome. So the quote I’ll often say — and this is from studies from more than two decades ago now — but in general, in high school science, students are introduced to 3000 unfamiliar words, 3000. Each year! Because there are words that are used in a scientific way that are used commonly in other places. And there are discipline-specific words. So 3000 words a year in high school science. The Spanish 1 textbook only has 1500 words in it. So science teachers have double the academic-language vocabulary demand that a typical introductory world-language class has. So just the vocabulary alone should say to us, literacy is gonna be important if you’re gonna learn science. And if you don’t understand these technical words, and you don’t understand the way science uses this particular word in this particular way… . When you say the word “process,” it means something very specific In science. “Division” — cellular division is not the way we think about it in mathematics; there’s a similar concept, but cellular division is different than dividing numbers. And those are words that get used in multiple areas. Then you have all these technical terms that you have to be able to use, to understand the concepts. To share the concepts. To talk to other people. Whether you’re in, you know, fifth grade and talking science, or you’re a university professor, there’s a shared language, appropriate for our grade level, that we have shared meanings of.

Eric Cross (10:22):

And we’re essentially … what I’m hearing you say is … most of the people that are listening to this are science teachers. We’re we’re also language teachers. In a sense.

Douglas Fisher (10:29):

So my frustration is when people say, “Every teacher’s a teacher of reading.” And I don’t like that. I’ve written against that phrase. I don’t think all teachers are teachers of reading, any more than all teachers are teachers of chemistry. Or all teachers are teachers of algebra. But what I will say is the human brain learns through language. And all of us — every teacher that I’ve ever met understands that language is important in my class. If my students don’t have strong listening skills and speaking skills; reading, writing, and viewing skills; I’m gonna have a hard time getting them to learn things. If I can help them grow their speaking, listening, reading, writing, and viewing in my content area, I’m gonna do a service for my learning of my subject and also their more broad literacy development.

Eric Cross (11:16):

  1. So, at a high level, what does it look like to integrate science and literacy? We’ve done education for the last, what, hundred years?

Douglas Fisher (11:24):

Mm-hmm. <affirmative>

Eric Cross (11:25):

—kind of pretty similarly, right? Kind of siloed way. What does this look like at the 30,000-foot level? You’re a professor, department chair. Run schools. Speak everywhere. Like, when you think about this from that high level, what does it look like?

Douglas Fisher (11:39):

A high level? Every time I meet with students in a science class, you know, biology or fifth grade or whatever? They should be reading, they should be writing, they should be speaking and listening. Every class. So what print do you want them to access? And it can be a primary source document, it can be an article, it can be from a textbook. Are they reading something? Are they writing to you? Because writing is thinking. If they are writing, they are thinking. As soon as their brain goes somewhere else, they stop writing. The pen won’t move or the fingers don’t type. And then speaking and listening, of course, is the dynamic of our classes. So every day we should see some amount of reading, writing, speaking, and listening, viewing in our classes. That’s at a high level. There are some generic things that seem to work across the literacy. So, learning how to take notes. Focusing on vocabulary. Using graphic organizers. These are generic things that as educators we can use in our classes. Then there’s more specialized things. So, scientists and science teachers think differently than historians and literary critics and art critics. So scientists, if you look at the disciplinary literacy work, there’s a whole body of research where they interview and study high-end experts in their field: chemistry, physics, biology, et cetera. And there are some characteristics that were more disciplined, specific. Scientists like cause and effect relationships. They look for them when they’re reading. They like sourcing information. “Where this come from?” “What’s the history of this idea?” Scientists have a long view in terms of time. Historians have a shorter view of time. English teachers have even shorter view of time. Scientists tend to think in long periods of time. And so all of that influences how a scientist reads and how we should apprentice young people after they get past the generic “I know how to take notes. I know how to study my vocabulary. I know how to do summary writing for my teacher in my notebooks and things,” there’s some generic tools. Once we get past those, we need to be looking at specifically how do people in science use literacy.

Eric Cross (13:52):

I’ve never had my thought process of reading deconstructed just now, but we just described how scientists read. I was like, “Yeah, that’s pretty much how I read, right there.” I also like how you said how we should apprentice young people. And I feel like you as the literacy guy, you chose that word very specifically, as far as apprenticing young people. That is a view, I think, that’s really important to hold. ‘Cause that’s what we’re doing essentially … is, if we’re doing what we should be doing, we are apprenticing these young people.

Douglas Fisher (14:18):

Yes.

Eric Cross (14:18):

And helping them develop. Now, let’s imagine there’s a listener out there and they’re interested in getting better at integrating science and literacy instruction. They want to start somewhere. Before we dive in, do you have any initial words of encouragement for the person who’s like, “Everything is like a priority right now,” in their classroom or in their world?

Douglas Fisher (14:37):

Yeah. So I’ll talk about elementary for just a moment. When we’re reading informational texts in our literacy block, we should be reading information that is aligned to what kids need to learn in science and history in, in that grade level. Why are we reading things that are gonna be in conflict with what they’re gonna learn in science later that day in fourth grade, for example? So when we look at our standards, our expectations, what is it that third graders need to know in history, science, mathematics, language arts? And when we’re reading text and we’re learning to apply our reading strategies during our literacy block, why aren’t we reading topics that build our background knowledge for our science time? So we’re seeing some synergy there. We should be looking at life cycles in grades that are appropriate for life cycles and knowing there’s more to life cycles than the frog and the plant or the seed. There are all kinds of life cycles. And we call ’em life cycles for a reason. That’s a general concept. Now in science, we’re looking at this particular lifecycle right now. And so that’s a high level. If we could get more connection to the content standards during our literacy blocks, it would be very good. When we talk about the time at which we call “science” in the day, in more of the K–8 continuum, the science needs to include some primary source documents. Some real things that students are reading. Read about a scientist; read about a scientist’s discovery; read about what they discovered. So that we’re building our background knowledge. So when we go to do things, activities, labs, simulations, we have background knowledge and we understand what we’re experiencing. It can’t be like—I watched this awesome lesson on lenses and the teacher had all these different lenses in the room and the students came in and they were brand new. They don’t know anything. They were picking ’em up. They’re exploring them. They’re trying to figure out, and they’re trying to come up with theories about what this is and how it works. And then the teacher gave them a reading, a short reading, on refraction of light. And they read this thing. And the clarity that they had about what these lenses must do, well! All of a sudden they’re putting them up to the lights! They’re asking if they can go get the lights out of the storage unit! ‘Cause there’s — and they’re shining different lights through the lenses to see what happens to the light. Because that little bit of reading turned some focus on for the students. And it allowed them to take what I’m thinking about, what I’m trying to figure out, how this thing works in another direction. That’s the power of using literacy in our classes.

Eric Cross (17:20):

And what I’m hearing essentially is transfer across disciplines, across content areas, ultimately. And in an elementary school classroom, would it be fair to say, probably the teacher has more autonomy to be able to do that, since they’re teaching all the subjects? But secondary, logistically, planning and those types of things … from what you’ve seen, is it fair to say this kind of needs to be like a top-down, full vertical alignment, to teach like this?

Douglas Fisher (17:45):

I think that would be awesome to do that. But if I’m a sixth grade English Language Arts teacher and I’m working with my sixth grade science teacher, the conversation should be, “What units are you teaching?” Because I’m choosing informational text. My job is to teach them how to find central ideas. My job is to teach them how to find the details in the text. My job is to have them make a claim and support that claim with evidence. The stuff I use is generic. Yes, we do read some literature and some narratives, but we also read about 50% of the text in English around informational text. So if I can help you and accomplish my standards as well, fantastic. So let’s have this conversation and say, “Oh, this is what you’re teaching in science in the next three weeks? I’m gonna choose some texts and we’re gonna analyze ’em for central idea. We’re gonna analyze ’em for details. We’re gonna, for mood or tone or whatever that we’re teaching. And by the way, I’m building background knowledge. So when they come to you, they know some stuff about what you’re going to be teaching next.” So I don’t think it’s impossible to say teams of teachers could come together and say, “What do we believe that our students need to know and learn and be able to do? And then how do we choose things that are gonna help them accomplish exactly that?”

Eric Cross (19:01):

And that’s empowering. Because that’s one thing that we can control maybe is this East-West, peer-to-peer, different content areas. A system may not be able to change as quickly, but I can definitely go talk to my English team or math team and check in and kind of see, “Hey, where do we have overlap in that?” And I know the times that I’ve accidentally had overlap with the teams, it’s super-exciting. And the students have been more bought in! Because it’s like, we’ve done something on the human microbiome and we’ve talked about genetics and all these different things, and then when they read The Giver, or they read some book about genetics, they have all this knowledge. And they’re excited. And they talk about colorblindness or they come to my class and they’re like, “Hey, we read about this!” It’s almost like they saw a magic trick, the fact that these things linked up. And the engagement has been so much higher when it’s the same content in different classes, but through different lenses. At least, that’s what I’ve seen in my years of teaching.

Douglas Fisher (19:54):

I saw a lesson on space junk that was so cool. Middle-school students learning space junk. And the history teacher had a part of it, science teacher had a part of it, English Language Arts teacher had a part of it. And these students, I mean, you watch them look up all the time, ’cause there’s space junk up there. Where’d it come from? Why is it there? What are the politics of this? How do we clean it up? I mean, it was just so interesting to watch them when the teachers came together. And the teachers met their standards in this couple-week-long space-junk exploration. Investigation was met. Politics was met. All these different things. Economy. You know, how much does it cost to clean up this problem? So there’s really cool opportunities when teachers come together and realize we can work together and improve the literacy and learning of our students.

Eric Cross (20:50):

Absolutely. So before this recording, we picked your brain a bit. And I know that there were three specific strategy areas that you wanted to touch on. And one of those — which is kind of coming back to the 3000-words language teachers — was vocabulary. So what are the opportunities that you see, as far as the way of educators to approach vocabulary? Because, you know, there’s a lot. We got a lot of it. The 3000 words.

Douglas Fisher (21:14):

Yeah. There’s a lot of it. So the worry is, we make a vocabulary list and have students look up the words in definitional kinds of things. That’s not really gonna help. Students need to be using the words. They need to be using the words in their conversations, in their writing, in how they think about your content in science. So vocabulary is a huge predictor of whether or not you understand things. Vocabulary is also a pretty good predictor if you can read on grade level. So when we think about vocabulary, there’s something called word solving. You show students a piece of text and you’re reading it, you’re sharing your thinking, and you say, “Oh, here’s a context clue!” Or “I know this prefix or suffix or root!” And in science, a lot of the words are prefixed, suffixed, or root words. We tend to add things together with a lot of prefixes and suffixes and have roots and bases in science. So we can help students think about, “Oh, what does geo- mean? We already know what geo- means here. It means the same thing in this word. Let’s apply that knowledge.” So word solving is part of it, showing students how we think about words that we might not know. The second is more direct instruction of vocabulary. As students encounter the words, we work on what it means, how we say it. We practice it a few times. The process is called orthographic mapping. It’s kind of a scientific idea here. But you have the sound and the recognition of by-the-word, by sight, and what it means. And your brain starts to automatically recognize that word in the future. So I don’t have to slow down, disrupt my fluency, and try to figure out what the word is saying. ‘Cause I’ve seen it enough. I’ve heard it pronounced enough, I’ve pronounced it enough, and I know what it means. So teachers should be saying, “What words in sixth grade science, what words in third grade science, do my students really need to know?” And I’m gonna have them encounter those words over and over. I’m gonna have them use the words. I’m gonna have them see the words. I’m gonna have them say the words. I’m gonna say the word and we’re gonna be over and over with these terms, so that students incorporate them into their normal view of, “These are the things I know about the world.” By the way, when they go to read that next thing, and they understand “geology,” you know, for sixth graders, for example, they know how to say it. They don’t stumble on it. And it activates a whole bunch of memories in their brains. “This is what geology is.” There are branches of geology, there’s physical geology, there’s all this thinking that activates as they read.

Eric Cross (23:35):

There was a practice that I participated in and am trying to incorporate — I don’t know what the name of it is. But essentially what happened was we were dissecting a flower. And the instructor had us name parts of the flower. But we got to come up with our own names for it.

Douglas Fisher (23:49):

Ah.

Eric Cross (23:50):

So, for instance, the stamen we call “the fuzzy Cheeto.” And we all used our own words and then everything was legitimized. And so we went through and learned the whole activity using our own vocab words. But then, in the end, after we presented and talked about it, then the words, the actual academic language was attached to our word. And we were able to say, “OK, the fuzzy Cheeto is the stamen,” and this, this, this, and this. But it was such an interesting practice, because it kind of legitimized all of our definitions. But we weren’t stumbling on these long Latin terms and things like that. Is there a name for that? Or. … ?

Douglas Fisher (24:29):

Yes. I don’t know the name for that. I think it’s really smart. So here’s what I would say about that, is: we don’t learn words, we learn concepts. Words are labels for our concepts. So what that teacher did for you was allow you to develop concept, a concept knowledge. “There’s a part of this plant, it goes like this, we’re gonna call it fuzzy Cheeto. Now I have this concept. And look, it occurred in all these plants. And those people called it that and that other group called it that. We called it a fuzzy Cheeto. Here’s the part of it.” And then the concept is in your brains. And the teacher said, “It’s really called stamen.” And it’s an instant transfer, because you already had the concept. What we often see is students are trying to learn a really hard academic word and the concept for the word at the same time. And so it slows down the whole process. And there’s higher levels of forgetting. Because human beings, we don’t learn words; we learn concepts. If you don’t have the concept, if I gave you a word out of the blue that you’ve never seen, never heard, and a week from now I asked you to remember it, you probably would not, because it didn’t register. It wasn’t part of your schema. You didn’t have a way to organize the information. You don’t have a concept. So that teacher? It’s a great idea. Got you to develop concept knowledge. And then said, “Here’s a real label for it: What some other people called it when they had the chance to come up with their own names.”

Eric Cross (25:50):

Shout out to my teacher, who was—

Douglas Fisher (25:51):

Right.

Eric Cross (25:52):

It was learned then. It was a great practice. And the fact that you’re right, like, I just mean from my own personal experience, I agree that learning concepts versus complicated words. And it’s interesting that you said higher levels of forgetfulness, you know. And you often hear that complaint about it: “Students forget! Students forget!” But this complex topic and this complex word that’s new to me, and I have to remember both of those things.

Douglas Fisher (26:12):

That’s right.

Eric Cross (26:13):

And the other neat thing that it did, is it actually honored the background and like the founts of knowledge of all the different groups in the classroom. You just said something about “this group called it this and this group called it this,” and so by letting different groups share all of those names, now we’re starting to build these kind of interesting connections. That’s at least what I remember experiencing. And so this, even this practice of this approach is very layered, beyond just kind of generating new knowledge of things. So I appreciate that aspect of it. Now another area that you mentioned was complex text.

Douglas Fisher (26:41):

Yeah.

Eric Cross (26:42):

And how we can get students into complex text. So what can we do there?

Douglas Fisher (26:46):

I think science is an ideal place to get students reading things that are hard for them. And I do believe that some parts of school should be a struggle. Not all day, every day. But there should be doses of struggle, which are good for our brains. And these complex pieces of texts that don’t give up their meanings easily allow students to go back and reread the text and maybe mark the text and talk to peers about the text and answer questions with their groups. And the whole point of complex text is to say, “We persevere through it. We may not understand it fully on our first read. But we go back and we might underline, we might highlight. We might write some margin notes. Our teacher might say, ‘What did this author mean here?’ And we go back and look at that part and we take it apart. What do we think about that? And we talk to each other. It’s showing that when we read things, we work to understand. We work through our thinking, often in the presence of other people. And our understanding grows as we go into the text over and over and over again.” So I said geology earlier. There’s about a two-page article on “what is geology” that sixth graders often read. And some kids find it super boring. It’s a once-read, “OK, geology, I don’t really understand it. There’s a bunch of words in here that I don’t understand.” But if you go back to it a few times and you start taking apart, “What are the branches of geology? Oh, I’m gonna go reread that.” How are these two branches related to each other?” “What are the subtypes of each branch of geology?” “How do geologists do their work?” You start asking questions where students are going back into the text. You spend a little bit of time. Now, the introduction to geology, the students know so much more. So whatever you do next— video experiments, whatever—they have a frame of reference, because of that deep, complex read. It’s probably better than simply telling them, “Here’s the information.”

Eric Cross (28:45):

Right. And I even feel like as an educator, when I reflect on my own learning in the classroom, and then looking at it through the perspective of an educator <laugh>, you find this difference between how you were taught and then what the data says good teaching is.

Douglas Fisher (28:59):

Mm-hmm. <affirmative> mm-hmm. <affirmative>.

Eric Cross (29:00):

It’s so easy to slide back into how you were taught!

Douglas Fisher (29:02):

Yeah.

Eric Cross (29:02):

Even though, you know, you mentally assent to, “This is the best way. This is the data shows.” And you find yourself kind of sliding back at times.

Douglas Fisher (29:10):

Yep. And there’s good evidence to support what you just said, that most people teach the way they experienced school. And it is very hard to change that. And people have studied this. And it’s very hard to change that. Because it worked for us. And we have an n of 1, and it worked for us. Now, remember, there were a whole bunch of other kids in the class that it may not have worked for. And we chose to be in school the rest of our lives, and some of your peers did not choose to be in school the rest of their lives. In fact, some of them hated school and found no redeeming qualities of their experience. So just because it worked for us in a case of one, n of 1, doesn’t mean it worked for all of the kids, or even the majority of them.

Eric Cross (29:57):

Very well said. It’s that, what is that, the survivor bias? Survivorship bias? Where you were the one that made it. But you don’t think about all the other folks. ‘Cause we’re thinking about ourselves.

Douglas Fisher (30:05):

That’s right.

Eric Cross (30:06):

Great case for empathy too, is thinking about the people left and right. Because my friends are like, “I hated science.” And I say, “Who hurt you? Like, what did they do? It’s so amazing, so much fun!”

Douglas Fisher (30:16):

“What happened to you? Science is the coolest. Right? It’s so amazing!”

Eric Cross (30:21):

But I also had a unique experience in seventh grade with my teacher who did some of these things, and made it accessible for so many of us, in opening opportunities that I wouldn’t have had otherwise. But you’re absolutely right. That was my story. That wasn’t the story of everybody that was around me. And I think that’s really important. Now, I know this is also a big one for you, but I wanna talk about writing. What are the opportunities that you see in terms of writing specifically?

Douglas Fisher (30:51):

So would love it if science teachers had short and longer writing tasks in the science time. Of course, you can integrate some of the science writing, the longer ones, in the English language arts time, especially if you’re the elementary teacher and you can have control of the whole day. But I said this earlier; I’ll say it again. Writing is thinking. While you are writing, there’s nothing else you can do but think about what you are writing. Your brain cannot do something else. So if a science teacher wants to know, do their students really understand the concepts? Have them write. Now some of the shorter ones, I like something called “given word” or “generative sentences”: “I’m gonna give you a word: CELL. C-e-l-l. We’re in science. I want you to write the word ‘cell,’ c-e-l-l, in the third position of a sentence. So it’s gonna go word, word, cell, and then more words.” You could also say, “I want the sentence longer than seven words,” or whatever. But the key is, I’m telling you where I want the word. You will know instantly if your students have a sense of what the word “cell” means in the context of science. If they write “my cell phone,” they don’t get it. If they write about spreadsheet cells or jail cells or whatever, they didn’t get it. But if they talk to you about plant cells and animal cells and the components of those cells, and then once they have that sentence down, you can say to them, “Now write three or four more sentences that connect to that sentence.” It’s super simple. So whatever concepts you’re teaching, put ’em in a specific position. Now you don’t have to only put it in the third position. You can say the first position, the fifth position, the fourth position. But it forces them to think about what they know about the word and then how to construct a sentence for you. That’s a very simple way to get some writing from your students that helps you think about what they understand. Other kinds of writing, you can have quick writes, you can have exit-slip writes. There’s something in the research space called the muddiest part, where halfway through the lesson you have them write so far what has been the least understood or the most confusing part of this lesson. And they do a quick write, right there, at the muddiest part. And as a teacher, you flip through these and you start to say, “Oh, these are the points that are confusing to my students.” So if 80% of them all have the same thing, I gotta reteach that. If these five got, “This is the muddiest part,” If these five thought, “This is the muddiest part,” these seven, “I thought this was the muddiest part,” what do I need to do? Because it’s gonna be hard to move forward if this is their area of confusion. There are also all kinds of writing prompts that have a little bit longer. My favorite one is RAFT. What’s your Role? Who’s your Audience? What’s the Format? And what’s the Topic we’re writing about? Super flexible writing prompt. When you teach something, we don’t want students to only think they write to their teacher. So your role is an atom. You are writing to the other atoms. What do you wanna write about? What’s the topic? What’s the format of it? Is it a love letter? Is it a text message? Is it … so we, we mix it up with students in saying, how do they show some knowledge through a prompt that we give them? And then of course, longer pieces as they get older. More opinion pieces through fifth grade. More claims and arguments starting in sixth grade. So that they’re starting to see, “I have to use the evidence from things I’ve learned, read, listened to, watched, and construct something: an opinion, an argument where I back it up with reasons or evidence.” And those longer pieces, you know, less frequently. The shorter pieces, pretty regularly. So the teacher sees the thinking of the students.

Eric Cross (34:29):

When you were speaking about these really creative writing prompts, there were specific students coming into mind, that were coming into mind … they’re, they’re great science students, but they also have this really strong artsy side drawing, creative writing, and things like that. And when you said something about atoms talking to each other, it elicited, in my brain, certain students that would really love this aspect of creativity in the sciences. And it’s not how we’re typically trained as science teachers, to kind of incorporate this, like you said. A book of props. But I’m imagining, like, as a science teacher, if I took this, this would be a great way to reach more students to be able to show what they know, in a way that might resonate with their own intrinsic “Oh, I get to write creatively!” So I was kind of writing furiously as you were sharing all that information there.

Douglas Fisher (35:12):

So here, I’ll give you another example for elementary people. Again, with RAFT. There’s a book called Water Dance. It’s a pretty popular book for elementary teachers. It’s really about the life cycle of water. For example, you are a single drop of water. You are writing to the land. The format is a letter. And you’re explaining your journey. Now, if they can do this, they’re essentially explaining to you the cycle of water. But you got it in a way that people are now, “Oh, I’m a drop of water. So it’s me. My perspective. Where do I go from? Where do I start?” Because you can start anywhere in the cycle, right? My drop could have started in the clouds. My drop could have started in the ground. My drop could have started in the lake. But it has to show you the journey. So there are many ways of showing you the right answers.

Eric Cross (36:02):

And that’s using the RAFT protocol.

Douglas Fisher (36:04):

That’s RAFT: Role, Audience, Format, Topic. It’s been around 20 or 30 years.

Eric Cross (36:09):

You just gave the name to something a teacher shared in our podcast community, Science Connections: The Community, on Facebook. Teacher shared a Google slide deck and on it were just three slides. And the role that the student had to have is they had to show, then tell, the story of a journey of a piece of salmon being eaten, a piece of starch from pasta being eaten, and then an air molecule in a child’s bedroom. And they had to give the path of travel and the experience from the mouth and then breaking down into protein and all those kinds of things. And this teacher shared it and I wish I knew the teacher’s name because I wanna give ’em credit, but they shared it. And so I used it with my students and then had ’em read aloud their stories and dramatize it. And they were so into it!

Douglas Fisher (36:49):

So cool.

Eric Cross (36:50):

But through it, I was able to see that they understood different parts of the body. They understood cell respiration. The whole thing. And it was fun! To watch them get so into this creative writing. And now I know the name of it. That’s been 30 years they were using RAFT. So you just talked a bit about complex texts and writing. And before we go, I wanted to circle back to something that you said, because I think it’s important, and if you could elaborate on it a little bit, about the value of struggle. Can you talk more about that?

Douglas Fisher (37:21):

Sure. I do believe in a lot of the U.S. we’re in an anti-struggle era of education. And it predates Covid. I think it made it worse during Covid. We front load too much. We pre-teach too much. We reduce struggle. We quote, “over-differentiate” for students. And there’s value in struggle. The phrase, “productive struggle” — if you haven’t heard it, Google productive struggle — it’s an interesting concept, that we actually learn more when we engage in this productive struggle. Now, productive struggle originally came from the math world, and it was this idea that it’s worth struggling through things to learn from it, that you’re likely to get it wrong, and then there was productive success. And there are times when we want students to experience success and we make sure we put things in place for productive success. But there are times where we want them to struggle through a concept. ‘Cause it feels pretty amazing when you get on the other side, when you know you struggled and you get to the other side. If you think about the things, listeners, think about the things in your life where you struggled through it and you are most proud of what you accomplished. I want students to have that. I don’t wanna eliminate scaffolding, eliminate differentiation. But I do want some regular doses of struggle. So if you look at the scaffolding, we have a couple choices. We have front-end scaffolds, distributed scaffolds, and back-end scaffolds. Right now we mostly use front-end scaffolds: We pre-teach, we tell students words in advance, that kind of stuff. But what if we refrained from only using front-end scaffolds, and we use more distributed scaffolds, when they encounter. So there’s a difference between “just in case” and “just in time” support for students. So we tend to plan on the “in advance, here are all the things we’re gonna do to remove the struggle before students encounter the struggle.” What if instead we said, “Let them encounter some struggle. Here’s the supports we’re gonna provide. We’re gonna watch; we’re gonna remove those scaffolds, and allow them to have an experience of success, where they realize, ‘I did it. I got it.’” Every science teacher I’ve ever worked with, when they do an experiment or a lab or simulation, they are looking for productive struggle. They don’t tell the answers in advance. They don’t tell if the answers are right. That’s your data. What does your data tell you? I mean, this is what you do. But then the other part of your day when you move into, like, reading, you don’t do that. You fall into the trap of removing struggle. And so allow them to grapple with ideas. Allow them to wonder what words mean. Allow them to say, “I’m not getting this, teacher! It’s really frustrating!” And you say, “Yeah, this is really hard. This is why we’re doing it at school. ‘Cause it’s really hard. If it was easy, I’d have you do it at home. But we’re doing it here, ’cause it’s really hard and it’s OK not to get it at first.” And create a place where errors are seen as opportunities to learn, and struggling through ideas and clarifying your own thinking and arguing with other people to reach an agreement or reach a place where we agree to disagree is part of the power of learning.

Eric Cross (40:38):

There’s a teacher, who I took this from. My master teacher when I was student teaching. And she said that there’s no such thing as failure in science, just data. And I took that same mantra. And I resonate with what you said about how science teachers, all of us, hold onto that productive struggle, because it’s part of being a scientist. It’s part of the experiments. That genuine “aha” moment. Or it didn’t work out? That’s great! That’s totally fine! Let’s write about it and let’s take photos and let’s publish it and let’s be scientists. That’s totally true. As we wrap up, Dr. Fisher, is there any final message that you have to listeners about bringing science and literacy together? I know you speak everywhere, but for everyone that’s listening, if you can put out your encouragement or message or suggestion … you’ve given so many great tips and practical applications. But, any final thoughts on the subject?

Douglas Fisher (41:32):

I think many science teachers are intimidated because they think they have to be reading teachers. And there’s a knowledge base to reading. And some teachers are reading teachers and science teachers, and I don’t wanna dismiss that. But it’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work. And so as you think about the way in which you are learning and the ways in which you want your students to learn, what role does language play? What role does speaking, listening, reading, writing, viewing, play in your class? And then provide opportunities for students to do those five things each time you meet with them.

Eric Cross (42:12):

Dr. Fisher, thank you so much for being here and for your encouragement, and sharing your wisdom and experience. And then personally serving my city, here in San Diego, and my students, when they make it to your high school and ultimately the alma mater of San Diego State University.

Douglas Fisher (42:30):

That’s right.

Eric Cross (42:31):

Yeah. We really, really appreciate you in serving all kids and lifting the bar and making things more equitable for all students. And encouraging teachers. So thank you.

Douglas Fisher (42:39):

Thank you very much.

Eric Cross (42:42):

Thanks so much for listening to my conversation with Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Check out the show notes for links to some of Doug’s work, including the book he co-authored titled Reading and Writing in Science: Tools to Develop Disciplinary Literacy. Please remember to subscribe to Science Connections so that you can catch every episode in this exciting third season. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. Also, if you haven’t already, please be sure to join our Facebook group, Science Connections: The Community. Next time on the show, we’re going to continue exploring the happy marriage between science and literacy instruction.

Speaker  (43:26):

I had this moment of realization I felt a few months ago: I’m like, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that.

Eric Cross (43:39):

That’s next time on Science Connections. Thanks so much for listening.

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What Dr. Douglas Fisher says about science

“There are really cool opportunities when teachers come together and realize we can work together to improve the literacy and learning of all our students.”

– Dr. Doug Fisher

Professor and Chair of Educational Leadership, San Diego State University

Meet the guest

Douglas Fisher, Ph.D., is professor and chair of Educational Leadership at San Diego State University and a leader at Health Sciences High & Middle College having been an early intervention teacher and elementary school educator. He is the recipient of an International Reading Association William S. Grey citation of merit, an Exemplary Leader award from the Conference on English Leadership of NCTE, as well as a Christa McAuliffe award for excellence in teacher education. He has published numerous articles on reading and literacy, differentiated instruction, and curriculum design as well as books, such as The Restorative Practices PlaybookPLC+: Better Decisions and Greater Impact by DesignBuilding Equity, and Better Learning Through Structured Teaching.

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About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

S1-05: How does coding fit in the science classroom? A conversation with Aryanna Trejo of Code.org

Podcast cover titled "Science Connections" featuring Aryanna Trejo, Season 1, Episode 5. It includes abstract illustrations of a globe and telescope, discussing coding in the science classroom.

In this episode, Eric sits down with Aryanna Trejo, a professional learning specialist of Code.org. Aryanna shares her journey from working as an elementary teacher in New York City and Los Angeles to teaching other educators at Code.org. Eric and Aryanna chat about computer literacy within the science classroom, problem-solving skills, and ways to model productive struggle for students. Aryanna also shares ways to teach coding and computer literacy in schools, no matter the classroom’s technology level. Explore more from Science Connections by visiting our main page.

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Aryanna Trejo (00:00):

I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.”

Eric Cross (00:19):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Aryanna Trejo. Aryanna is a member of the professional learning team at Code.org. Before joining Code.org, Aryanna led computer science professional development for elementary school teachers, and served as an instructional coach for new educators. She also taught fourth and fifth grade in both New York City and in Los Angeles. In this episode, we discuss Aryanna’s journey to Code.org, where she helps educators connect coding to real life, how to use a rubber duck to solve problems, and how coding and computer science principles can be taught to students in areas without access to the internet…or even a computer. I hope you enjoy my conversation with Aryanna Trejo. So I was born and raised here, and I saw that you went to UC San Diego.

Aryanna Trejo (01:11):

I did, I did. I actually just put a deposit down on an apartment in University Heights, ’cause I’m moving back.

Eric Cross (01:16):

You’re coming back?

Aryanna Trejo (01:17):

I’m coming back. Yeah.

Eric Cross (01:19):

So if you need a classroom to visit….

Aryanna Trejo (01:21):

I would love to do more classroom observations!

Eric Cross (01:24):

Are we doing this? Let’s do—we’re making this happen.

Aryanna Trejo (01:26):

We are. Yeah. So I’ll be there. I’m moving there in April. I actually grew up in Orange County too, so I’m like a very diehard SoCal person.

Eric Cross (01:35):

So I feel like I know the answer to, hopefully—Tupac or Biggie? ‘Cause you’re on the East Coast, and you’re on the West Coast.

Aryanna Trejo (01:40):

Yeah. I like Tupac, but I have more Biggie songs committed to memory. Which is not a lot. I have “Juicy” and “Hypnotized” memorized.

Eric Cross (01:53):

All right. So you’re just memorizing, and you have the Biggie songs memorized, but not the Tupac ones.

Aryanna Trejo (01:58):

No, but I do love Tupac songs. You know, it’s like, Biggie has the flow, but Tupac has the lyrics. Nobody’s—they both have something really amazing about them.

Eric Cross (02:06):

You know, I can respect that you broke it down into both of their strengths.

Aryanna Trejo (02:11):

Thanks for buttering me up before this interview. And not….

Eric Cross (02:15):

<laugh> Oh, we already started.

Aryanna Trejo (02:16):

Huh? We already started?

Eric Cross (02:17):

We’re already started. Yeah. We’re already into this.

Aryanna Trejo (02:19):

We’re into it.

Eric Cross (02:21):

You were in the classroom, fourth and fifth grade, and you were doing TFA.

Aryanna Trejo (02:26):

I did. I did Teach For America. I was 2012, New York City Corps. Right after graduation. ‘Cause I graduated UC San Diego in 2012. So graduation was on June 17th, and I touched down at JFK on June 19th.

Eric Cross (02:40):

Even though I wasn’t in TFA, I know a lot of the fellows that are in it. And there’s just some phenomenal teachers in there. How long were you doing elementary school when you were teaching?

Aryanna Trejo (02:49):

Yeah, I taught for—well, I did, three years of teaching fourth grade. Then there happened to be an instructional coach opening in my fourth year. I took that, did some instructional coaching within the same network, and then I moved back to LA and I taught fifth grade for a year.

Eric Cross (03:11):

  1. And what was it like now? Did you go to Code.org right after the classroom?

Aryanna Trejo (03:17):

No, I didn’t. No. I transitioned after teaching fifth grade for a year in downtown Los Angeles, in the Pico-Union neighborhood. I ended up getting this email out of the blue from someone who had actually found me through the Teach for America job site. ‘Cause I was hitting the pavement; I was really looking to transition out of the classroom. And she invited me to interview with this company called 9 Dots. And they taught computer science to kids K–6 throughout Los Angeles and Compton. And I was like, “Sure, no problem. Let’s do it.” So I interviewed, I got the job, and yeah, that’s how I transitioned to 9 Dots. And then after almost four years there, I transitioned to Code.org, with the same person. Actually, she moved over to Code.org first, and then she helped me get this job.

Eric Cross (04:07):

Oh, that’s happened a lot—like, that relationship kinda carries over.

Aryanna Trejo (04:11):

Yeah. We’re meant to be coworkers.

Eric Cross (04:13):

Yeah. Are you still? Is she still there? Are you both still together?

Aryanna Trejo (04:17):

Yeah, we’re on the same team and it’s nice. I saw her last night for Happy Hour, with another coworker who’s in LA. So we’re tight. And she’s a wonderful, wonderful mentor to me.

Eric Cross (04:28):

That’s great. Did you have computer-science background, when you were doing elementary school teaching? Did you have—

Aryanna Trejo (04:34):

No. <laugh> Not at all. When I was teaching in New York City, I had like four desktop computers in my classroom, and we rarely used them. Which was such a shame. And then when I moved to Los Angeles and taught fifth grade there, we were a one-to-one school, and the joys of that are just amazing. It was just really wonderful to, you know, get the students used to typing on the computer, using different software to submit their assignments. Getting creative—as creative as you can get—with Google Slides. You know, to show off what they know. And stuff like that. That’s all I had, though. And you know, when I transitioned to 9 Dots I was like, “Sure, why not? Let’s give a shot.” And I learned a lot. It was really interesting, yeah.

Eric Cross (05:26):

And so now at Code.org you are…well, so my journey with Code.org, I’ve been in the classroom for eight years. Still in the classroom as of…an hour ago, I was there. <Laugh> And I use Code.org, and I feel like I’ve checked it periodically, and I feel like it’s evolved over the gaps. And I’ve seen it. It’s become more robust in the things that they offer, over the years I’ve been an educator. Just to kind of…could you give a thumbnail sketch? Like, what is Code.org? Who’s it for? Who’s the target audience? What resources are there?

Aryanna Trejo (06:00):

Yeah. So it’s for everyone. It is a nonprofit that provides curriculum and training and a platform for teachers and students. We provide curriculum for K through 12. It’s completely free. And it comes with lesson plans, slideshows, all that. We focus specifically on underrepresented groups. So we have targeted measures for Black students, for Native American students, for students who identify as female. That’s a huge part of our mission. But we’re really working to expand access to computer science to as many students as we can.

Eric Cross (06:41):

One of the things I’m hearing in your story is you were teaching in Compton; you were in Bronx, New York. One of the reasons why I got into the classroom is because of educators, and the impact they made on me in exposing me to science and technologies I’d never had access to. And that intentionality, that you’re going about it…are there…not just the code, but how you bring that across to different groups…are there strategies, or are there ways to connect this idea of coding to diverse groups and diverse audiences? Or is it kind of, the curriculum applies for everyone? ‘Cause in science, when I’m teaching, I’m always trying to make what I’m doing relevant to the backgrounds of my students.

Aryanna Trejo (07:28):

Sure.

Eric Cross (07:28):

So I’m teaching biology, and I’m trying to make this kind of connection. Sometimes it’s more organic; sometimes it feels kind of forced. Because it’s just not always a nice fit. But it sounds like Code.org is really about inclusion. And in the numbers that I’ve seen for representation, in especially computer science software engineers, the groups that you’re focusing on are not necessarily represented in the professional workforce. At least disproportionately.

Aryanna Trejo (07:54):

Yeah, absolutely. Yeah, that’s correct.

Eric Cross (07:57):

And so how do you go about being intentional about reaching groups that we don’t see in, you know, the Silicon Valley software engineers? How do you start that? Like, at a young age, do you look for specific schools in specific areas to say, “We are going to bring this to the school. We’re going out to these populations of the cities”? Because we’re just not seeing…you know, on the map, we’re not seeing anybody really doing anything with coding here. Or we’re not seeing the numbers come out of these areas, out of these cities, of students who are going into STEM or going into computer science fields.

Aryanna Trejo (08:41):

Yeah. I don’t necessarily work on the recruitment side of it, is the issue, in my position. But I do work on the professional learning, that is brought out to teachers. And we have a huge focus on equity throughout the workshops that we create from K–12. It’s something we’re really passionate about. We definitely aim to prepare teachers to teach computer science. That’s a huge part of it. Knowing the content, but also thinking through, “What does recruitment look like at your school to make sure that the demographics of your classroom match the demographics of your entire school?” Also, thinking through, “How can we make sure that female students feel included in your classroom? How can we make sure that we are, giving students creativity to think about, or we are setting students up to be creative and think about the problems that are in their community, and how they can use computer science to solve them, or at least work towards them?”

Eric Cross (09:39):

So solving real-world problems and that inclusion aspect…are there things like…you were saying “female or students who identify as female”…are there things that teachers can do to ensure that they’re being more inclusive? Or to recruit, or encourage more female students to take part? One of the things I was thinking of, that I’ve seen, is I’ve seen coding kind of camps.

Aryanna Trejo (10:06):

Sure.

Eric Cross (10:08):

That were specifically for a female audience. And that seemed to help with recruitment. Is that something that you see on your side?

Aryanna Trejo (10:16):

That’s not something that we set up, no. But the curriculum that I work with is CS Principles. And it’s offered as an Advanced Placement course, as well as an AP class. So that’s a curriculum that’s designed for students who are in grades 10 through 12. And so at that point, we can really talk to teachers and ask them what the recruitment strategy is. But in terms of strategies that teachers can use to recruit those students…I mean, I’ve heard over and over from lots of different teachers who identify as female that they didn’t think that computer science was for them, until they saw a role model in that position. And so just being a role model for those students is really wonderful.

Eric Cross (11:00):

And I see it too, with—like, we do “Draw a Scientist” activity, which is like a popular science thing—

Aryanna Trejo (11:05):

Sure, yeah, I’m familiar.

Eric Cross (11:05):

But it’s the same thing, right? Like, it fleshes out. My students don’t draw themselves as scientists. They draw what they perceive, based on what television says. I imagine with computer science, it’s probably really similar, when you think about “What’s a software engineer look like?” Do students tend to draw themselves? Or is it even a mystery? Because I don’t even know what a software engineer looks like.

Aryanna Trejo (11:28):

Yeah, absolutely. Well, one of the things we love to do with our professional learning workshops is talk about understanding yourself, your identities, how they show up in the classroom as biases. And, you know, things like stereotype threat. We see that as really important to understand, and think through, and consider, before you step into the classroom. So that you’re not, you know, coddling certain groups of students because you don’t believe that they are able to be successful in computer science. Holding all the students to the same expectations and believing that they can succeed. And computer science, I think a lot of the times people have this conception of it being this utopian, bias-less, technocratic field. When in reality, everything has bias. And people talk about algorithmic bias and facial recognition, but also the people who created computers and computer languages have their own bias that comes through. And I think it’s really important to show students that. So that they can, one, know what they’re working with, and two, make sure that they can create products that reduce that bias.

Eric Cross (12:50):

It’s like…it’s not objective, just because we’re creating software. Like, once it gets to a point of being so sophisticated…I think, like, AI software, right? With facial recognition? And we’re seeing more and more articles come out about, you know, predicting trends based on historical data.

Aryanna Trejo (13:12):

Sure.

Eric Cross (13:13):

But then, the trends and things that they’re seeing tend to target things that have happened in the past. But it also doesn’t take into consideration a lot of other factors that can lead to certain groups or populations being identified. And I’ve seen some articles lately about how your code is really just representation of what you put into it. And like you just said, your bias—if you have that, conscious or unconscious—you’re gonna put that into your code. And the input is gonna be an impact, is gonna impact the output.

Aryanna Trejo (13:44):

Yeah, absolutely. Or even just—and I’m ashamed to say this, ’cause this is an idea that came to me just recently, through an article that I read—but computers themselves have bias. The hardware assumes that you have vision, that you can see the screen, that you are able-bodied, that you can use your hands to work the keyboard, the mouse, et cetera, and that you don’t have to use assistive technology. You know, there are small things like that, where we think that technology, like I said, is this utopian, futuristic science…but there are biases throughout.

Eric Cross (14:19):

You’re absolutely right. I’ve never even—I’ve never even considered that. Even though I do use assistive tech, and figure it out, I’ve never thought from the ground up, the process is built for an able-bodied, sighted, hearing person.

Aryanna Trejo (14:31):

Exactly.

Eric Cross (14:32):

To be able to engage with the hardware. And then these other things, these tertiary things that we kind of add on, so that you can do this, but it’s not designed from the ground up for people who are, you know, different audiences, physically. So I’m glad you brought that up, though. Now I’ve seen—and I haven’t done this—but I know Hour of Code is a big thing. And this is something that’s ongoing. Can you talk a little bit about what Hour of Code is? I know it’s, it’s a big thing for the classroom teachers.

Aryanna Trejo (15:08):

Yeah. So Hour of Code is really exciting, and it’s just blossomed from something small to something tremendous. This year is gonna be the 10th Hour of Code. So what it is, is it happens during CS Education Week in December, during Grace Hopper’s—or to honor Grace Hopper’s birthday. She was a computer scientist and Navy Admiral. And basically the aim of it is to get as many students on the computer doing an hour of code, and demystify what coding is. You know, to do seed-planting. To show teachers that this is something that you can facilitate for your students. And also to show students like, “Hey, computer science is something you can absolutely do. Not just for an hour, but more if you want.” So, yeah. Now it’s worldwide, and it’s really exciting.

Eric Cross (15:58):

That’s awesome. And I think about teachers and I still hear the apologetic—when I’m helping teachers in the classroom with education technology—the self-deprecating “I’m a dinosaur; I’m not good with tech,” which is never true. Like, they’re better than they even realize. And I feel like sometimes there’s still a stigma, too. It’s like <laugh> The Simpsons’ Comic Book Store Guy. The condescending tech support person—

Aryanna Trejo (16:27):

Sure.

Eric Cross (16:28):

—who has that tone. And so I feel like some people have been so negatively impacted by that person. So I know when I’m helping people, I actually try to go full-spectrum the other side. But I’m thinking about teachers’ barrier to entry. Sometimes code is like, “Whoa.” And I don’t teach computer science. Do you see those barriers to entry, or at least the perception of them? And then, what’s the reality for like someone listening, and going, “I’m a fourth grade teacher,” or “I’m a humanities teacher in ninth grade.” What’s the perception that you see, versus reality, with the teachers that you train? Is it much more accessible than we think? Or is there a level of sophistication that you have to have coming into it?

Aryanna Trejo (17:10):

No, not at all. I know computer science, and that says a lot! <Laugh> You know, I know my own corner of computer science. And you know, that’s me being self-deprecating, too. But I think learning computer science has helped me in so many different ways that I wasn’t expecting. I recently took the GRE in hopes of, you know, getting back into grad school. And I think just the way that computer science teaches you to search for bugs in your code, or errors, and kind of tirelessly look at a problem from multiple different angles, I was able to carry that into the math that I was doing. And I noticed just a huge difference in the way that I approached it, and the way that I was open to it. But you asked a great question, in regards to the barriers to technology. In my position at 9 Dots, I was working directly with teachers to lead professional development with them. Sometimes it would be a full day; sometimes it would be an hour after school. And the one thing that I always had in my back pocket that was really useful is that I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.” You know, it takes some patience and nobody’s gonna get it perfect 100 percent of the time. Have I banged my head against the wall trying to solve one tiny little syntax error in my code? Absolutely! But it feels absolutely phenomenal to fix that. And I was an English major in undergrad, and I had never done computer science before. So it’s something that becomes really satisfying.

Eric Cross (19:07):

Yeah, I imagine. I had someone—a trainer or a presenter—one time bring up the fact that our students rarely get to see us learn in real time.

Aryanna Trejo (19:19):

Yeah.

Eric Cross (19:19):

So we don’t get to ever really model failure. I mean, unless we’re in a classroom situation <laughs> in our failures, with classroom management. Then they see it, they see it! But they don’t get to see us model learning failure. And I don’t mean like failure—and yes, I know, “first attempt is learning,” and “no such thing as failure”—that’s not what I’m talking about. But just when we’re not successful with our code, and then we experience real-time frustration.

Aryanna Trejo (19:42):

Yep.

Eric Cross (19:42):

And they said that is actually a great learning experience for your students to watch you go through productive struggle. And that was really liberating for me. Because now I’m in the classroom, and I’m trying to go through it with my students, and the beautiful thing was, they started helping me. We were all trying to solve the problem. And then we had this authentic problem-solving experience. I think it was like a Scratch program, where we were trying to solve, trying to embed it somewhere, or something. And then, in the background of the class: “Mr. Cross! I got it! I figured it out!” And it was this really neat bonding experience. And I felt that—your ears get red, and you get hot, ’cause you’re not—

Aryanna Trejo (20:19):

Oh yeah.

Eric Cross (20:20):

You don’t know it! And you’re in front of 36 kids! And I said, “OK, I need to tell them how I feel.”

Aryanna Trejo (20:25):

Yeah.

Eric Cross (20:26):

So I said, “Now I feel really frustrated.” Like, “I want to go through this, and here’s my thoughts.” ‘Cause I knew that it would be helpful if they saw and would hear my thoughts. So I just did a quick think-aloud and I said, “In my head, <laugh> I want to just quit,” I said, “But I realize that this is the part where my learning’s happening. So I just want you all to hear what’s going on in my brain.” And now I feel like when I’m doing coding with my students, and it’s just basic coding, I feel much more comfortable, like, not knowing. But I needed someone to release me from that “I have to be the expert in everything” to do it.

Aryanna Trejo (21:06):

And teachers are used to being the experts. Right? And they should be. And coding is just such a different landscape. But I think once you kind of give over to the power of tinkering, I think it’s really gratifying. I love being able to…you can revise a sentence, and then read your paragraph back to yourself in English, and say, “OK, I get it.” But there’s something so gratifying about changing a line of code or a block and then being able to hit play and watch your program come to life, and say, “Hmm, that’s not quite what I wanted. Let’s try something different.”

Eric Cross (21:39):

I love your connection to tinkering. ‘Cause—I had never thought about it—’cause I love tinkering with my hands. But I always think about physical things. But coding is exactly that. It’s tinkering.

Aryanna Trejo (21:47):

It’s exactly that.

Eric Cross (21:47):

That’s exactly what it is.

Aryanna Trejo (21:49):

And a lot of it is, for me, especially when I’m trying something new, it’s guess-and-check. It’s like, “OK, that didn’t work. What if I add a semicolon here? Will it finally work? Or what if I add a ‘for’ loop? Will this get me what I want?” And it’s wonderful because you have that with students as well. Like, you have that record of their thinking, and you can ask them to go step-by-step and tell you, you know, “First, I added this, because I wanted the program to do this,” and so on and so forth. And so you have that record, but you can always get rid of it. Students often wanna get completely get rid of it. That’s something that I’ve noticed a lot as I’ve taught computer science. But, once you can get them to target the specific parts of the program, tinker with that, and continue, that’s a really wonderful learning space. There was also something you said about modeling failure. I love the fact that in computer science you can model failure for your students. You said to your students, “I’m getting frustrated.” I love that, because I never got that in math. Nobody ever showed me what it was like to be frustrated with graphing a parabola. Right? Like, my math teachers were always like, “Doot, doot, doot, here you go, you’re done!” <Laugh> And I would get so frustrated, because it didn’t come that easily to me. And I think there’s two parts to that. So there’s modeling the learning and the thinking and the productive struggle, but also there’s the identity of being a computer scientist and modeling what that looks like. So for me, when I get really frustrated with a program, I walk away. I take five minutes. I take a deep breath. I say, “I’m not gonna think about it in these five minutes.” And I come back to it. And I think once you start teaching computer science, you can facilitate that for students. And there’s so many different strategies that they can pick up. They can pick up rubber ducking, which is where they pick up a rubber duck or a similar object, and they talk to it as if they were a partner and talk through their code. And oftentimes, as you’re rubber ducking, you’re gonna find that error, because you’re explaining it to someone who’s a stand-in for a novice. And rubber ducking is a well-known strategy for computer scientists who make it their career. You know, there’s pair programming. Some students love pair programming; some students hate it. But the students start to build this identity about how they problem-solve. And how they approach failure. And I just love that.

Eric Cross (24:31):

I’m writing this down. Because the rubber-ducking strategy, I love. I just imagine my seventh graders, a bunch of 13-year-olds with, like, rubber on the desk. And not necessarily in coding, but I was thinking in my science class. And they’re working through a challenge, and they’re all looking at this duck, and they’re talking to it. But I just love the the idea of externalizing your thought process and talking through it yourself so that you can hopefully arrive at a conclusion. But it’s such a great practice, and this is something that’s been around for a long time, apparently. So.

Aryanna Trejo (24:59):

Yeah. Yeah. It’s a real thing. And you know, you can go low-fi. It doesn’t have to be a rubber duck. You can have students talk to their pencils or their imaginary friends. That’s not the issue; the issue is, you know, talking to somebody.

Eric Cross (25:10):

I know you support teachers. But I just wanted to…I was just curious about your typical day, what that’s like. And then what you do, how you support ’em.

Aryanna Trejo (25:15):

So, at my previous job at 9 Dots, I was in there with the teachers in the classrooms. I was coaching our internal staff who went out to co-teach with teachers. And I loved that. And I had such a great impact on a local scale. But now at Code.org, I have a much broader impact. But I don’t get to interface with—that’s such a tech-y word!—I don’t get to interact with—

Eric Cross (25:42):

You work at Code.org! You get to—

Aryanna Trejo (25:42):

I know! But I’m a teacher at heart, forever, right? That’s my identity that I forged when I was 22 years old. And a typical day looks like opening up my computer, taking a look at my calendar. I often have meetings to talk about, different things that we’re doing to support our facilitators who go out to our teachers and lead their workshops for them. I recently worked on a product that was designed for CS principles, teachers, to onboard to the course if they weren’t able to get into an in-person workshop. And it’s completely self-paced, so it gives teachers an on-ramp into the course. And now I’m working on some in-person workshop agendas. So I feel really wonderful that my work is going out to thousands of teachers. But at the same time, I really, really miss talking to teachers. Because that’s something that energizes me so much.

Eric Cross (26:46):

When should students start learning computer science? I feel like we see it in this kind of narrow lane. Like, this is computer science if you make an app. Can it be more than that? As far as like the benefit of computer science? And—I guess two-part question—when should students, one, start being exposed to it? And then two, what are some of the benefits beyond just, “I wanna just make an app”?

Aryanna Trejo (27:08):

I taught coding to kindergartners. It can start as early as you as you want it to. And it doesn’t necessarily need to be on the computer. A lot of students that I worked with didn’t have computers at home, were interacting with computers for the first time. And that’s a huge barrier, of course, to a lot of teachers. But there are so many unplugged lessons that you can do to start to start to have students think about algorithms, which is just a series of steps to complete to solve a problem. As long as a student can use a computer, I think they can do computer science. There are products out there like codeSpark, where students—and Code.org has these products too—where students are moving an avatar around a board, kind of like a quadrant to…you know, they feed the directions to a computer and then the computer enacts it for them. And with that, they can learn algorithms. You know, that is computer science. And a lot of people don’t see it that way, but it really is. And it starts to set students up for more complex thinking as they move on.

Eric Cross (28:13):

One of the biggest underserved communities, geographically, are students in rural areas.

Aryanna Trejo (28:20):

Yep.

Eric Cross (28:21):

They can be reservations; they can be places just not an urban area. Is there a way to serve our communities of students and bring these skills in an unplugged way?

Aryanna Trejo (28:32):

Yeah. Yeah. If you typed in “unplugged computer science lessons” to Google, you’ll have a ton of hits. And there are so many students out there—not just in rural areas. But there’s incarcerated students. It hurts my heart to even say those words, but in urban areas too. Like in my classroom, where I only had four desktop computers. Access is a real struggle. And there’s things, like I said, instead of moving an avatar around a grid on the computer, I used to have an actual mat that I would take out to my kindergarten classrooms, lay it out, and it would have a grid on it. And we’d have one of the students act as the avatar and the rest of the students would give them directions to get to a different point on the grid. And there, you’re building an algorithm or just a series of steps. Like I said, it’s not some fancy term to solve a problem. And there’s multiple ways to solve that problem, too. And I think investigating that can be a really good way to stretch those lessons.

Eric Cross (29:32):

It almost sounds like an oxymoron, but this low-tech computer science strategy. Develop these skills and then transfer that once you have access to the tools.

Aryanna Trejo (29:39):

Yeah. Yeah. Absolutely. And I think it’s a good way for students who need kinesthetic means to start to understand something, or just different learning styles, to start transferring that over.

Eric Cross (29:53):

I probably have students in the classroom where those kinesthetic moving things would help be a great way—or WILL be a great way—for them to learn the principles and the fundamentals of coding. Instead of only giving the option to just do the computer, actually giving them some choice. Or giving them a way to be able to manipulate things. We’re still in the system of education that’s still very siloed. It’s been the same way for a hundred years. We got math and then we got science and we got English. I’m wondering, how can a teacher fit this into their daily lessons? And then, do you have any experiences or stories or things that you’ve seen, just really creative ways that you’ve seen teachers incorporate this? Outside the norm of, “This is a computer science class; we’re just gonna code.” But have you seen it branch out? In the trainings that you’ve done?

Aryanna Trejo (30:40):

I’ve seen examples of that. I’ve seen a teacher use Scratch to demonstrate different climates of California, and show the different climates. This past year for Hour of Code, my friend Amy—the one who helped me move to 9 Dots and at Code.org—she created this incredible tutorial called Poetry Bot. And it was a way to get students to match the mood of the poem to some of the elements that were happening in the stage. So they would have different backgrounds show up at different parts of the poem. When the words would show up, they would have different sprites show up. They would have, sometimes, sounds. Or the text would show up with different animations. So there are cross-curricular opportunities everywhere, if you can be creative enough to find them, or if you beg, borrow, steal from other educators who are doing this incredible work out there.

Eric Cross (31:36):

Yeah. I say this all the time, but I’m an educational DJ, not an MC.

Aryanna Trejo (31:44):

Oh yeah.

Eric Cross (31:45):

So MCs write their lyrics and DJs remix with things that other people have done.

Aryanna Trejo (31:48):

Absolutely.

Eric Cross (31:48):

I was like, I’m a DJ. I was like, all day. Sometimes I’ll write a lyric, once or twice, but most of the time I’m remixing things. So teachers, if you’ve been out there and you got an awesome interdisciplinary thing, or you’ve incorporated coding and it’s something that’s traditionally not seen, please send it to us. Share it with us.

Aryanna Trejo (32:03):

Yeah. And there are so many different places where you can find that. We have a forum for Code.org, but there’s also CSTA, the Computer Science Teachers Association. You can join your local chapter and get to know other computer science teachers out there.

Eric Cross (32:19):

I guess…to wrap up, I’ve been using Scratch programming, the MIT website. My students do the basic animated name, CS First, stuff. But over the years, I’ve noticed that my students are coming in with a higher level of sophistication in Scratch to where now the differentiation…some of my students are just doing very basic…and then I have other students who’ve created full-on video games with complex…like, you look at their Scratch page and it’s just an amazing amount of blocks and integrations and things that they have. Is there anything on Code.org that could be a next step? That takes them beyond, maybe like the visuals? And if so, what would be a good next step, to take students to advance them to another platform? There’s so many coding languages out there, I feel like. Or I might not even be thinking about that the right way.

Aryanna Trejo (33:20):

No, I think you are. You know, we have three different curricula out on our website right now. We have CS Fundamentals, which is probably more in line with what you’re talking about. We have a free CS Discoveries curriculum, and that is designed for, grades, I believe, 6 through 10. And that would be a really good entry point, for both teachers and for students.

Eric Cross (33:44):

There’s a lot of new stuff that I hadn’t seen yet, a few years ago.

Aryanna Trejo (33:49):

Yeah.

Eric Cross (33:49):

So I was really excited.

Aryanna Trejo (33:50):

One thing that I do know is that CS Discovery has just added an artificial intelligence slash machine-learning unit, that you can just pick up and give to your students. You don’t have to go in order with CS Discoveries, like you do with CS Principles. And I’ve gone through some of those lessons. They are really rad. And I would’ve loved to have learned that when I was in middle school or high school. So yeah, we’re constantly thinking of how we can make things one, relevant to our students, and two relevant to what’s going on in the world.

Eric Cross (34:20):

So would I be overselling it if I said, “If you go through this, you’ll be able to create an AI or a neural net to do all your homework”?

Aryanna Trejo (34:26):

You would be overselling it.

Eric Cross (34:27):

I would be? OK. So what I’ll do is, I’ll wait until the end of the school year, and then introduce it, and then by the time they’ve realized it’s not true, they’ll be eighth graders.

Aryanna Trejo (34:35):

There you go. Good old bait-and-switch.

Eric Cross (34:37):

You’re amazing. Thank you for serving teachers, and for being part of such a great organization that puts out great stuff. So much free curricula for teachers to be able to use. Especially nowadays we hunt and scour the internet for those types of things. And to be able to bring computer literacy into the classroom, and with your focus of serving communities of underrepresented groups, it feels good to know that not only is it high-quality material, but it’s also trying to raise everyone up. Because ultimately when we have more people trying to solve a common problem, we come up with better solutions. And I was talking to somebody who was a materials engineer somewhere in Europe, and he said one of the things about the U.S., As he was critiquing me on this flight, critiquing the U.S., He said, “One of the things about your country is that you have a heterogeneous group of people who, in a group, when you have multiple perspectives attacking a problem, you come up with more novel solutions.” He says, “That’s one of the great things, is that there’s not necessarily just a hive mind.” And I think that that’s one of the great things. We uplift different communities, and we uplift women, people of color, people who, have backgrounds that parents didn’t go to college but have these amazing qualities and strengths. And we put everybody focusing on the same issue. We come up with novel solutions that we wouldn’t have come up with if only select groups were trying to look at it and solve it. And so—.

Aryanna Trejo (36:22):

Yeah.

Eric Cross (36:23):

And we couldn’t do that without organizations like yours, that help empower teachers. So.

Aryanna Trejo (36:27):

Yeah! You really said it.

Eric Cross (36:29):

You’re coming to my classroom when you’re back in San Diego?

Aryanna Trejo (36:31):

Yeah! I totally will. Yeah. Let’s make it happen.

Eric Cross (36:34):

Last question. If you think back in your schooling, your own schooling, K through college, is there a person or a teacher that had a big impact on you? Or a learning experience that had an impact on you? And it could be, you know, positive or negative. But something that impacted you, even to this day, that stands out to you, that you remember?

Aryanna Trejo (36:56):

This is a big diversion from the topics that we’re talking about. But in grades 10 through 12, my drama teacher, Mr. Byler, who I still talk with, was such a huge impression on me. Really wonderful. And I couldn’t tell you the teaching moves that he did that were wonderful. I don’t know much about his management. But I can tell you that he gave me space to be confident, and grow into myself, through drama productions. They were high school productions, so they weren’t amazing. But I just really came into myself in high school, because I had the confidence to get on stage. And he was just such a wonderful mentor to all of us. So, props to Mr. Byler.

Eric Cross (37:39):

Shout out to Mr. Byler for creating space for Aryanna to fly! Thanks for making time, after your workday, to talk with us and to share Code.org with teachers.

Aryanna Trejo (37:54):

Of course. Happy to.

Eric Cross (37:59):

Thanks so much for joining me and Aryanna today. We want to hear more about you. If you have any great lessons or ways to keep student engagement high, please email us at stem@amplify.com. Make sure to click subscribe wherever you listen to podcasts. And join our brand new Facebook group, Science Connections: The Community for some extra content.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Aryanna Trejo says about science

“I would hear teachers saying things like, ‘Well I just can’t do coding, it’s just too hard for me.’ And I would ask them…Would you say that to your student about math or English? Be as kind to yourself as you would be to your student.”

– Aryanna Trejo

Professional Learning Specialist, Code.org

Meet the guest

Aryanna is a member of the Code.org Professional Learning Team. Before joining Code.org, Aryanna led computer science professional development for K-6 teachers and served as an instructional coach for new educators. She also taught fourth and fifth grade in New York City and Los Angeles. In her spare time, Aryanna loves taking advantage of the California sunshine, creating wheel-thrown pottery, and hanging out with her dog Lola.

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About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

A closer look at grades 3–5

Amplify Science is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the 3–5 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
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Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, students build and deepen their understanding, increasing their ability to develop and refine complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science California to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our 3–5 program to address 100% of the California NGSS in just 88 days.

Scope and sequence

Every year of our grades 3–5 sequence consists of 4 units and 88 lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons for grades 3–5 are written to last a minimum of 60 minutes, though teachers can expand or contract the timing to meet their needs.

Educational curriculum chart showcasing a progression of amplify science lessons from kindergarten to grade 5, categorized by grade and subject areas like plants, animals, weather, and energy.

Unit types

Each unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, while also emphasizing a particular science and engineering practice.

In grades 3–5:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
  • One unit emphasizes the practice of argumentation.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Argumentation units

Argumentation units provide students with regular opportunities to explore and discuss available evidence, time and support to consider how evidence may be leveraged in support of claims, and independence that increases as they mount written arguments in support of their claims.

Units at a glance

Una ilustración de un tren de alta velocidad moderno y aerodinámico que viaja por una vía elevada con un paisaje verde de fondo.
Balancing Forces

Domain: Physical Science

Unit type: Modeling

Student role: Engineers

Phenomenon: The town of Faraday is getting a new train that floats above its tracks.  

Download unit guide

Download lesson planner

An illustration from the Inheritance and Traits unit
Inheritance and Traits

Domain: Life Science

Unit type: Investigation

Student role: Wildlife biologists

Phenomenon: An adopted wolf in Graystone National Park (“Wolf 44”) has some traits that appear similar to one wolf pack in the park and other traits that appear to be similar to a different wolf pack. 

Download unit guide

Download lesson planner

An illustration from the Environments and Survival unit
Environments and Survival

Domains: Life Science, Engineering Design

Unit type: Engineering design

Student role: Biomimicry engineers

Phenomenon: Over the last 10 years, a population of grove snails has changed: The number of grove snails with yellow shells has decreased, while the number of snails with banded shells has increased.  

Download unit guide

Download lesson planner

An illustration from the Weather and Climate unit
Weather and Climate

Domains: Earth and Space Science, Engineering Design

Unit type: Argumentation

Student role: Meteorologists

Phenomenon: Three different islands, each a contender for becoming an Orangutan reserve, experience different weather patterns.  

Download unit guide

Download lesson planner

An illustration from the Energy Conversions unit
Energy Conversions

Domains: Physical Science, Earth and Space Science, Engineering Design

Unit type: Engineering design

Student role: System engineers

Phenomenon: The fictional town of Ergstown experiences frequent blackouts.  

Download unit guide

Download lesson planner

An illustration from the Vision and Light unit
Vision and Light

Domain: Physical Science, Life Science, Engineering Design

Unit type: Investigation

Student role: Conservation biologists

Phenomenon: The population of Tokay geckos in a rain forest in the Philippines has decreased since the installation of new highway lights.  

Download unit guide

Download lesson planner

An illustration from the Earth's Features unit
Earth’s Features

Domain: Earth and Space Science

Unit type: Argumentation

Student role: Geologists

Phenomenon: A mysterious fossil is discovered in a canyon within the fictional Desert Rocks National Park.  

Download unit guide

Download lesson planner

An illustration from the Waves, Energy, and Information unit
Waves, Energy, and Information

Domains: Physical Science, Life Science, Earth and Space Science, Engineering Design

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Mother dolphins in the fictional Blue Bay National Park seem to be communicating with their calves when they are separated at a distance underwater.

Download unit guide

Download lesson planner

An illustration from the Patterns of Earth and Sky unit
Patterns of Earth and Sky

Domains: Physical Science, Earth and Space Science

Unit type: Investigation

Student role: Astronomers

Phenomenon: An ancient artifact depicts what we see in the sky at different times — the sun during the daytime and different stars during the nighttime — but it is missing a piece.  

Download unit guide

Download lesson planner

An illustration from the Modeling Matter unit
Modeling Matter

Domain: Physical Science

Unit type: Modeling

Student role: Food scientists

Phenomenon: Chromatography is a process for separating mixtures. Some solids dissolve in a salad dressing while others do not. Oil and vinegar appear to separate when mixed in a salad dressing.  

Download unit guide

Download lesson planner

An illustration from the Earth System unit
The Earth System

Domains: Earth and Space Science, Physical Science, Engineering Design

Unit type: Engineering Design

Student role: Water resource engineers

Phenomenon: East Ferris, a city on one side of the fictional Ferris Island, is experiencing a water shortage, while West Ferris is not.  

Download unit guide

Download lesson planner

An illustration from the Ecosystem Restoration unit
Ecosystem Restoration

Domains:Physical Science, Life Science, Earth and Space Science, Engineering Design

Unit type: Argumentation

Student role: Ecologists

Phenomenon: The jaguars, sloths, and cecropia trees in a reforested section of a Costa Rican rain forest are not growing and thriving.  

Download unit guide

Download lesson planner

Welcome to Amplify Desmos Math Cherokee CSD!

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A curiosity-driven K–12 program that builds lifelong math proficiency

Amplify Desmos Math thoughtfully combines conceptual understanding, procedural fluency, and application. Each math lesson is designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.

What is Amplify Desmos Math?

Amplify Desmos Math supports teachers in building students’ lifelong math proficiency. The program:

  • Supports social classrooms, invites mathematical creativity, and evokes wonder, creating a welcoming learning space where students are empowered to see themselves and their classmates as having brilliant mathematical ideas.
  • Provides teachers with clear, step-by-step moves to build systematically from students’ prior knowledge to grade-level learning.
  • Connects students to each other’s thinking and to an understanding that they can use math to make sense of the world.
  • Enables access to grade-level understanding for every student, every day.

A powerful suite of math resources

Amplify Desmos Math combines the best of problem-based lessons, intervention, personalized practice, and assessments into a coherent and engaging experience for both students and teachers.

Data informs instruction. Comprehensive student profiles provide full data on students’ assets and skills, empowering teachers to provide just-in-time scaffolds throughout core instruction and targeted intervention when needed.

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Experience Amplify Desmos Math

Click the links below to explore our interactive digital lessons, where you’ll also find print Teacher Edition and Student Edition pages for each lesson.

For helpful navigation tips and more program information, download our Grades K–5, Grades 6–Algebra 1, and Grades 9–12 program guides.

You can also watch a product expert walk through a lesson and the available program components with a lesson walkthrough video.

Diagnostic screening and progress monitoring assessments

Integrated mCLASS® Assessments go beyond accuracy to reveal students’ math thinking through an asset-based approach. This data provides better insights about what students know, what math assets to leverage, and where students need support.

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Personalized learning and support

Amplify Desmos Math includes digital, adaptive practice that provides the personalized support a student needs to access grade-level math every day. Boost Personalized Learning activities target a skill or concept aligned to the day’s core lesson, with each student receiving personalized scaffolds based on what they already know. This technology complements daily learning and provides another layer of support to the in-lesson differentiation and instructional guidance provided to teachers. Click here to try a Boost Personalized Learning activity. More activities coming soon!

The Fluency Practice of Amplify Desmos Math uses an evidence-based approach to memory retention—spaced repetition—for the basic operations. Students around the world have answered more than 120 million multiplication questions within our application. Try it now! 

Contact us

Support is always available. Our team is committed to helping you every step of the way. Contact your dedicated Indiana representative here for program access, samples, and additional information.

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Elizabeth Sillies Callahan

Southern IN
(513) 407-5801

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Jody Kammer

Central IN
(310) 402-7837

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Amanda Knipper

Northern IN
(260) 894-5123

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Paige Lawrence

District enrollment below 1200
(980) 421-2608

Amplify Desmos Math Summer bridge program

This upcoming back-to-school season is sure to be anything but normal. It will be critical to use the summer months to tend to unfinished learning and prepare students for the math to come. 

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Thinking ahead

Amplify is offering free complete middle school and Algebra 1 units that support a number of typical summer school or bridge programs. The lessons are based on the highly rated Illustrative Mathematics program and designed to make problem-based instruction easier for teachers and more exciting for students.

Units available (June 2020)

COURSE UNITS  
6
Expressions and Equations (19 lessons)
Key for algebra readiness (variables)
Rational Numbers (19 lessons)
Key for algebra readiness (negatives)
7
Expressions, Equations, and Inequalities (23 lessons)
Key for algebra readiness
Angles, Triangles, and Prisms (18 lessons)
8
Associations in Data (9 lessons)
Data and modeling skills are critical
Exponents and Scientific Notation (15 lessons)
Understanding exponential behavior in today’s world is critical
Algebra 1
 Introduction to Exponentials (22 lessons)
Understanding exponential behavior in today’s world is critical
 Introduction to Quadratic Functions (23 lessons)
A key connection to physics

Find a complete list of lessons available here.

Materials available June 2020

  • Complete unit Teacher’s Guide available online or for printing
    • Delivery format: Google Docs
  • Complete unit Student Edition pages available online or for printing
    • Delivery format: Google Docs
  • Digital lessons
    • Delivery format: Desmos
  • Pre- and post-assessments
    • Delivery format: Desmos and Google Docs
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Making the materials work for you

We’re offering free, asynchronous professional learning resources to help your teachers quickly get up to speed with the Amplify Desmos Math lessons. These resources include:

  • Quick-start videos for each unit, including a unit overview and a walkthrough of the print and digital lessons.
  • Pacing suggestions for a variety of summer school scenarios.
  • Regularly scheduled office hours in July and August with an Amplify Desmos Math product expert.

Proposed learning models

Icons representing three educational models: in-school lessons, mix of at-home and in-school lessons, and digital lessons, each with brief descriptions.
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Samples

Printable Google Docs

Including Teacher Edition pages, Student Edition pages, and practice

Digital lessons powered by Desmos

mCLASS K–8 Literacy & Math Assessment System | Amplify

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S5-01. Investigating math anxiety in the classroom

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Season 5 is here! This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, we sat down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
 
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:01):
Hey, folks. Welcome back to Math Teacher Lounge. I’m one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:05):
And I am your other host. I’m Bethany Lockhart Johnson. Season five! Hello!

Dan Meyer (00:11):
Bethany, how are you doing? How have you been spending the long break between our recording sessions?

Bethany Lockhart Johnson (00:16):
As much as I loved sharing content from previous seasons, I am so thrilled that we’re back for season five. I have been, you know, chasing a toddler. I think he’s already tired of me saying, “Ooh, can we count that?” He’s like [sighs] “One two, one two.” Like, he’s done already.

Dan Meyer (00:36):
Too much counting. Yeah, I worry about that so much, that my love of mathematics might be perceived by my kids as smothering. Yeah, I worry about the same. We shared with you folks some bangers of reruns, in my humble opinion. Some great guests. But, we’ve been excited—me and Bethany—to hop back on the mics, on the ones and twos, and explore some new ideas together.

Bethany Lockhart Johnson (01:01):
Well, I loved our season talking about joy in mathematics. And personally I could…like, we could turn this whole podcast into joy in mathematics. However, we’re kind of going a different route. Because if you ask folks why they don’t feel joy in mathematics, a lot of times at the root of that is some really intense math anxiety. So this whole season, we’re going to be delving into math anxiety. Exploring what it is, who has it, why do we think it happens, what do we think we can do about it, and how can we navigate through it, so that we can experience that joy in math? These are questions that we’re gonna explore over the course of the season. Dan Meyer, how do you feel about that?

Dan Meyer (01:49):
It feels big and it feels personal. I mean, as we shared in our math stories back from season…whatever it was, math anxiety was a huge part.

Bethany Lockhart Johnson (01:59):
It was last season, Dan.

Dan Meyer (02:00):
Last…? I mean, who can remember? Big part of your journey. I’ve had some very punctuated but intense moments of anxiety in math class. And socially, we have built math up to be this incredibly powerful thing. You know, restricting movement on economic ladders, preventing people from getting into careers they want. Whether or not they have much to do with math class, math anxiety is a really large part of educational but also social life. And yeah, I’m really excited to explore it with you. We’re bringing on some really excellent guests. Some researchers, yes. But not just researchers! Also people who practice in the field and know firsthand what it looks like to resolve issues of anxiety with students.

Bethany Lockhart Johnson (02:45):
Yeah, you’re right, Dan. My math story contained quite a bit of math anxiety, so I am particularly invested in this season. I mean, I still navigate math anxiety. And, you know, many of us do, and let’s talk about it. And let’s—I love that you reminded me. We’re gonna have a lot of great researchers all throughout the season, and a lot of times folks feel like the research happening, there’s sometimes a gap between researchers and what’s actually happening in the classroom. Not in all cases, but a lot of times. Right? And I remember a lot of conversation about the latest research when I was in grad school, but unless you’re actively studying something, sometimes we don’t know what’s happening. Right? We’re really focused on what’s happening right in front of us in our classroom. So let’s take some of that research; let’s break it down; let’s talk to some of the folks who are thinking about this for the bulk of their day, right?

Dan Meyer (03:41):
Yep. So we got our first guest coming up in a moment here.

Bethany Lockhart Johnson (03:45):
So to kick off this season, we’re starting episode one by talking to Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University. And he’s been researching math anxiety for more than a decade. He’s worked with so many amazing folks in the field. He’s worked with students, he’s worked with teachers, with educators…I’m just so excited to talk to him. If you look up math anxiety, you see his name as one of the folks who is really thinking about this at so many different angles, and we get to talk to him. So enjoy our conversation with Dr. Gerardo Ramirez.

Dan Meyer (04:29):
We are so excited to have Dr. Gerardo Ramirez on the show with us. Dr. Ramirez is an Associate Professor of Educational Psychology at Ball State University. Thanks so much for joining us.

Dr. Gerardo Ramirez (04:40):
Yeah, thank you for inviting me to talk about math anxiety.

Bethany Lockhart Johnson (04:43):
So with your interview, Dr. Ramirez, we are actually launching the season. We’re gonna be talking about all different aspects of math anxiety, and it feels pretty perfect that you are first guest of the season, because of the sheer breadth of research and conversations you’ve had about math anxiety. Could you start us off kind of telling us a story of how did you get interested in studying math anxiety? Or why, you know, why did you dive into this topic that, you know, I think a lot of folks might…like, if you’re on a plane, and you say, “Oh, I study math anxiety,” what kind of reaction are you gonna get?

Dr. Gerardo Ramirez (05:24):
Oh, sure. Yeah. I think most people are actually very interested because they all have their own story about feeling anxious about math, or just being anxious about evaluation situations that involve math. And, yeah, they wanna share those stories. People feel quite comfortable talking about their anxiety about math, for some reason. But for me, I started off, when I was in undergrad, I was studying to take the GRE quiz. I was hoping to go into a psych program. But I wasn’t exactly sure what direction yet. As I took some of the practice tests, there’s some situations in which I was very nervous about taking the practice test. And I just noticed that I did really poorly on some of these exams. And so I became very interested in issues like choking under pressure, which means when you underperform relative to what you expected to perform. And so, as I was researching these issues, I started to come across this whole field of math anxiety. And I saw that while there are some people who choke under pressure during tests, there are other people who just have a strong general fear of mathematics.

Dan Meyer (06:29):
That’s really helpful. I can imagine you’re doing a lot of free psychology sessions, free therapy for people on airplanes when they bring to you their own stories of math. So let’s thank you for your service in that sense. I’m super-curious. So Bethany and I have both taught math. We both have seen firsthand what it looks like when a student is anxious in math class, though maybe we don’t have kind of the clinical language to describe it. And I’m curious, from a clinical sense, how do we define math anxiety?

Dr. Gerardo Ramirez (06:57):
Sure. So first off, math anxiety is not something that you would find in the DSM, for instance. But we generally define that as a fear or apprehension to situations that involve math. So it doesn’t have to necessarily be educational situations. It could be someone asks you a math-related question during a party, or you have to calculate the tip at a restaurant, for instance. It doesn’t have to be about schooling situations, although that’s obviously where it seems to matter a lot for many people. So it is basically a fear or apprehension to situations that involve math. And I think distinguishing the term “fear” from “anxiety” is really important here. A lot of times people use those terms interchangeably, and the term “fear” is obviously within our definition of math anxiety. But oftentimes what differentiates anxiety from fear is that, anxiety is—think of it like a recipe. Anxiety is fear plus a little bit of unknown. OK? So if, for instance, if you hated snakes, and they threw a snake at you, you’d be in intense fear. Whereas if you hated snakes and they said, “There is a snake in the room, but I’m not gonna tell you where,” that’s gonna cause anxiety. And so the reason why we call it math anxiety is because a lot of times people experience this fear for a possible unknown future that involves math or possible unknown evaluations that people might have about your competence, because of math. And so for a lot of kids, they feel anxious about how they’re gonna do on a test or whether they’re gonna be able to pass a class or whether they’ll be able to understand what you’re saying in your lessons, for instance. And so the anxiety component really gets at fear of something that’s unknown, but related to mathematics situations.

Dan Meyer (08:47):
Math is somewhere in the ceiling right now. Perhaps I might be surprised with a math situation!

Dr. Gerardo Ramirez (08:52):
Yeah. yep.

Dan Meyer (08:52):
So I have this tendency to assume that every other subject that we teach has it better and easier than math does. It’s not true. I know this is not true. But I’m kind of curious here. Is math anxiety, like, part of a general just set of anxiety around schooling itself? Like, is there a reading anxiety, a writing anxiety, and does that all just flow from the same kind of fount of anxiety around schooling or situations about learning? And what makes math special in this regard? If it is its own special anxiety, for instance?

Dr. Gerardo Ramirez (09:27):
There are different…so some people obviously suffer from generalized anxiety. Right? And so they would, you know, feel anxious both for evaluative and non-evaluative situations. But in the research that we’ve done and that other people have done, there are differences between things like reading anxiety, math anxiety; I’ve also studied spatial and creativity anxiety. A lot of times what we’re trying to do in these studies is we measure all of the above, and we try to show that, look, math anxiety predicts math situations above and beyond these other things. So yeah, we definitely distinguish those things. And so what’s special about math is that, well, I think the symbolic nature is a big part of it. The abstract symbolic nature is just not as tangible to students. They can’t touch it. And so it doesn’t allow ’em to use their full cognitive faculties to play with it, as you might see, for instance, in science. Or it doesn’t allow people to relate math to their own interests the way you might see, for instance, in English. So maybe I hate reading novels, but I’m interested in zombies and you give me a book on zombies, well, ok, great, you’ve connected my personal assets to the topic. Whereas with math, either that’s harder to do or instructors don’t do such a good job of setting that connection up.

Bethany Lockhart Johnson (10:46):
Also, I think, you know, I’ve heard of students being really anxious, let’s say, during a reading session, when teachers used to do—hopefully they’re still not doing it—the popcorn reading, where you just randomly call on a student to read out a sentence. Right? But you don’t really hear students or adults talking about, “Oh, no, no, no, I don’t read; I don’t mess with reading.” You know? Whereas with math, you do hear, “Oh, I’m not a math person. Oh no, no, no, don’t ask me any math questions.” And that is such a distinction.

Dr. Gerardo Ramirez (11:18):
Yeah. And I think a lot of that’s because it’s just so common. As an adult, to be nervous about reading is kind of an uncommon thing. So people feel a stigma around admitting that. But math is something that everyone feels like they’re inadequate in. And so there’s a lot of comfort in telling you how they’re just one of the many people who don’t like math. And that, you know, can have a lot of different consequences and outcomes. I think on the one hand, I think for a lot of kids it becomes a normalized message that if you fear math, that’s OK, join the club. Right? But we have to be careful about that, ’cause a lot of math anxiety researchers will oftentimes say, part of what leads to math anxiety is adults normalizing that it’s OK to be scared of math. So I think a lot of times adults, teachers, for instance, math teachers, they’ll tell kids, “You know, if you’re scared, that’s OK.” And so a lot of the math anxiety community says, “No, no, no, you’re not supposed to do that.” But my recent view is different. I view that as a form of validation. Because math is hard. And so telling kids, “Hey, look, it’s actually easy if you just try,” I don’t think that’s true. It’s actually just hard. And I think even if it was easy, to the kid, it feels hard! And I think something that’s not really well-studied right now in our field is the value of validating people’s math negative math experiences. We don’t want to validate that, ’cause we think that we’re gonna reinforce that. But actually, I think the opposite. I think when you validate people’s negative math experiences, it helps ’em to feel that they can handle it. They can start to take control over their own emotions.

Bethany Lockhart Johnson (12:52):
I love that. And I, I actually, I think that’s so powerful, what you’re talking about, that validation. I taught kindergarten, and I vividly remember being in a parent-teacher conference and that parent saying, “Oh, I wasn’t a math person either,” right? Or, you know, their language and their experience with their own math schooling, their anxiety about math was actually impacting their students’ experience of math. Or the conversation that, when I would go to talk about a math assessment, let’s say, you could see the parent actually tensing up. And there was this moment of validation, that I felt like we needed to make space for that in the conversation with the parents, right?

Dr. Gerardo Ramirez (13:38):
Yeah.

Bethany Lockhart Johnson (13:38):
Like, this is a real thing. And we are working on teaching students that math is something that gets to—your experience with math gets to look all sorts of different ways. And it’s OK if we, you know, make a mistake, or if we kind of only get this part, but we’ve really got that part. Or let’s talk about it; let’s write about it. So I really feel like that that validation is something that’s so missing. And instead of the validation, like you said, you see folks being like, “Oh yeah, me neither. I’m not a math person either.” Right?

Dr. Gerardo Ramirez (14:10):
Yeah. I think…part of the reason why people are comfortable sharing this because they’re looking for validation also. When they say, “Oh, I’m not a math person,” you know, I think they’re hoping that, you’ll say like, “Yeah, me neither,” or “Of course not, ’cause math is terrible.” Right? They’re looking for validation, not to reinforce their perspective, but to feel that it’s OK not to be a math person. And I think that’s one of the techniques that I’m trying to work on in my research right now, is to provide evidence that actually people will work harder when you validate their math experience. You don’t have to tell them a positive story per se. If your current story is “Math is hard and I’m very, very anxious; I’m scared,” then we can just validate that and help you work through that. And it actually will strengthen our relationships. Because if you’re a student and you’re struggling with math and I tell you, “Yeah, it’s hard; it’s OK to struggle with math,” that makes you feel seen. And that’s gonna lead you to want to ask me more for help, because I’m someone who understands you. And that’s a great, you know, remediation opportunity.

Dan Meyer (15:14):
A common thread that I think I’m seeing here in several answers is that math sometimes asks students to disassociate part of themselves. Where success in math oftentimes means working from an a level of abstraction with symbols, like you said, that can feel alien. Like, who am I here? And in the same way, I love that you’re proposing we validate and reassociate people with a very deeply felt part of themselves that is anxious about mathematics.

Dr. Gerardo Ramirez (15:44):
Yeah. I mean, I think that’s what validation’s supposed to do, right? So a lot of us, when we feel these strong emotions, we wonder, “Is this even a real thing? Are other people feeling this? Is there something wrong with me?” So we feel the emotions, but we can’t actually deal with them, because we wonder if they’re legitimate. And so when someone says, like, “Yeah, this is hard,” it crystallizes that emotion. And once something is made real, you can actually choose how you want to deal with it. Some kids are gonna deal with it by staying anxious. But some people are gonna choose to deal with it by saying, “Well, there’s nothing I can do about it now; I have to take this math test, so I’m just gonna think positive.” And that’s great. If the kid can end up saying that to themselves, that’s much more effective than me telling the kid, “Hey, you just gotta think positive. You’re gonna start the test anyway.” And so we want the kid to make meaning of their experience, and the way we do that is by crystallizing their emotions through validation.

Dan Meyer (16:36):
Yeah. I love that. And so what you’re proposing there, I think, sounds like, a solution, like a post-talk solution after students are feeling anxiety.

Dr. Gerardo Ramirez (16:43):
Yes.

Dan Meyer (16:43):
To validate and empathize.

Dr. Gerardo Ramirez (16:45):
Yes.

Dan Meyer (16:45):
And over the course of our season, we hope to explore a lot about solutions to math anxiety that are preventative, that reduce the odds of anxiety arising, through instruction and curriculum, before it arises. And I’m just wondering if you’ve seen anything that would hint at either specific or general words of wisdom you wanna share with the educators, about not just addressing it after the fact, but preventing math anxiety before it arises?

Dr. Gerardo Ramirez (17:14):
To be honest, at this point, I haven’t seen enough evidence for me to recommend anything concretely as an intervention for math anxiety, or an intervention to prevent its development. All I can really do here is rely a lot on the more broad cognitive-behavioral research on anxiety, which says that one of the ways we prevent people from developing anxiety is by helping them to make more positive appraisals of challenge situations. So a lot of times, when kids are challenged, they don’t know how to interpret that. “What does it mean that I’m struggling with this thing?” And so that’s where I think a lot of teachers can help students’ interpretations of that. ‘Cause if you leave kids to their own devices, they’re gonna think, “I’m struggling because I’m stupid. I’m struggling because I’m not good enough. I’m struggling because my dad is right; I’m gonna be a failure.” You know? They’re going to impose an interpretation to a challenge situation regardless. And so, as teachers, one thing we can do is we can help shape that interpretation and say, “What does it mean to struggle with math? People will say it means you’re stupid. That’s one interpretation. What’s another one? It means that your brain is working really hard to think through something. That’s another interpretation. What’s better? What do you think is more helpful?” And then, helping students to see how interpretations matter to how you ultimately feel about something. And that’s a very metacognitive way of thinking about things. So yeah, I would say that one way to prevent it is to help students to take more positive interpretations of their experience. But another way, and I think a more successful way, I think, is to give students early experiences where they feel efficacious dealing with math. One of the ways you do that, for instance, is by obviously making sure that the students understand the material—but that’s obvious; people are trying to do that. One of my favorite recommendations is to keep reassigning assignments, the same exact assignment, for, say, three weeks, back-to-back. So if in week one you do the homework assignment, you do OK, you don’t do so great, when week two you do it, you give the exact same assignment, and now the student can see like, “Wow, OK, this was much easier.” And then, week three, you give the exact same assignment; now the kid’s feeling really confident. And the reason why that’s great is because it helps kids to see that they’re growing in confidence. A lot of times kids don’t get to see that because we’re constantly throwing new assessments at them. And so they’re never seeing that growth. All they’re seeing is a new challenge, a new challenge, a new challenge. So I think we need to set up situations where they can feel that they’re growing, when we keep the assessment static. That can be a formative assessment, for instance—doesn’t have to be a summative assessment.

Bethany Lockhart Johnson (19:55):
That feels so powerful and it feels like it really connects to that validation piece, right? We are actually helping to create a culture in our math classroom where we might struggle with something, but we keep revisiting it. And it’s not so much to reach mastery, but as Dr. Megan Franke — we talked to her about this partial understanding and about pulling on those threads of things that you do understand, so that you can build your confidence…build, not just confidence, but build your…I guess, kind of get your footing, right? You’re saying, “Well, I do understand this. I see how this works.” And if I’m revisiting an assignment, I feel like that would give me permission to like, “Hey, I don’t have to have this figured out on the first pass. You know?

Dr. Gerardo Ramirez (20:44):
Yes, yes. Yeah. I mean, I’m gonna give you a silly analogy, but I think it works. You know, a lot of times people will have nightmares, right? And they’ll keep having the same nightmare over and over again, right? And so one reason that we suspect this happens is because they haven’t worked through whatever that nightmare’s supposed to be about. So if, say, I’m scared of driving, I may be having the same dream about driving and crashing over and over. And we keep having these nightmares. And I think math anxiety is kind of like a waking nightmare, where you keep rehashing something because you haven’t had the chance to finally address that dragon. You know? And so if someone was having a lot of fear over driving, then one behavioral approach would be, you know, to work with a therapist to actually get behind the wheel and maybe drive around the same track over and over until you feel comfortable at that, and then the nightmares stop. Well, the same thing is true, I think, about math, math and math anxiety, is that you wanna give people these opportunities to feel confident by going back to that original experience that caused them to feel anxious, and saying, “This one assignment that we did in week three that really freaked you out, let’s try it again now in week five. How was that?” “Yeah, it wasn’t so bad. It was still kind of annoying.” “OK, we’ll we’ll come back to it.” “Now it’s week seven. Now let’s go back to that assignment. How is it now?” “That’s actually…it wasn’t that terrible.” And that gives people the opportunity to reflect on how they’ve grown past that nightmare.

Bethany Lockhart Johnson (22:05):
I have to say, Dan talked about you being like a therapist. I’m like, wait, “How did you know, Dr. Ramirez? I did have this recurring dream! I did! And I had to face it. No, but I had such intense math anxiety in high school and it was debilitating. And the biggest thing for me, I thought I was the only one. I thought there was something wrong with me. I thought, “Why can’t I figure this out?” There wasn’t a conversation about “Here are some tools,” or “Here are some, some, some…”. Like, “This is OK, for you to feel scared about this or overwhelmed!”

Dr. Gerardo Ramirez (22:41):
Mm-hmm. Mm-hmm.

Bethany Lockhart Johnson (22:42):
You know, I think often when we talk about how widespread math anxiety is, I think a lot of folks automatically jump to high schoolers or college students avoiding math courses. But we see this in really young kids.

Dr. Gerardo Ramirez (22:56):
Yeah. So people are…people are just constantly making meaning of themselves, regardless of the age range. And that’s true even with young kids; they are trying to figure out who they are. Right? And so one of the things you see oftentimes with young kids is you ask ’em, “What are you good at?” And they say, “Everything!” And that’s their attempt to, you know, make meaning of themselves. But sometimes they’re not good at everything. Sometimes they actually struggle in math. And I think even early on, they have to make meaning of that. They say, “Well, I’m good at everything except math.” And how do you make sense of that? Well, why not math? “Oh, because math is terrible. It’s not for everybody. You know, it’s not something that I like.” And so, yeah, in a lot of the studies that we did early on, we basically went into these first-grade classrooms with the purpose of trying to assess whether we can actually show variability in kids’ math anxiety, even early on. In other other words, do kids even report feeling anxious about math situations? Or do they tell us that they’re great at everything? And what we found was that in fact, a good chunk of kids are, again, perfectly willing to tell you that “No, certain situations involving math make me very anxious.” Counting or addition, or doing a problem on the board. And the way we do that is by—I think there are probably more sophisticated ways that can be done, but this is the best we have at this point—is we go in there and we ask them, we show them a bunch of smiley faces and anxious faces. And we say, “I want you to tell me how you feel about these different situations that involve math.” And so we say, “If you feel kind of nervous, I want you to point to this face. If you feel very nervous, point to this face.” And we basically will read to them situations. We’ll say, “How would you feel if your teacher asked you to open up your new math textbook and you saw all the numbers inside of it?” And they’ll point to the really nervous face. So right now, those are some of the more reliable assessments for math anxiety among young kids. And that work showed us that even young kids are self-reporting math anxiety.

Dan Meyer (24:51):

Obviously this is worth our study, because we would hope people would not feel anxious in general, and especially if we have a mandated…kids are mandated to be in math classes for their entire childhood. So I see the need for this study, these studies. I’m curious: What are the consequences, though? Like what, what correlates with math anxiety? What are other reasons why we should care about math anxiety and work to remediate it?

Dr. Gerardo Ramirez (25:16):
Oh, sure. So it correlates with their actual math performance. It can correlate when they choose to do homework. Right? So a lot of times, the parents report having to fight with their kids over math homework a lot. And you also oftentimes see a lot of frustration over mathematics specifically. And so it can, you know, not only affect their academic ongoing outcomes, like math tests and math assignments, but it can also affect their relationship with their parents. So if every time you come home, your dad’s screaming at you because you haven’t done your math homework, and when he asks you to solve the problem in front of them, you don’t remember, ’cause you were checked out, ’cause you’re so stressed out, that’s gonna cause a really negative experience. You know, a lot of times people grow up and they still remember their dad screaming at them over the math homework. You know, it’ll affect your relationship with your teacher. So if you’re making me feel incompetent, if you’re stressing me out, you’re not the kind of person I wanna come to for help. So it can predict relational outcomes as well as academic outcomes. And down the line, of course, when it affects students’ opportunities to get into things like AP classes, it affects students standardized test performance and their choice of colleges, as well as scholarship opportunities.

Dan Meyer (26:29):
Once you show that it correlates to performance, then that opens up a whole range of other correlations that are pretty important, it sounds like. Whether that’s career options or, you know, post-secondary education and the like.

Dr. Gerardo Ramirez (26:40):
Yeah. And a lot of times, when people are choosing a career at college, a lot of times students will make a decision specifically based on what career has less math requirements or less math courses. So I think this finding needs to be verified further. But, there’s some studies showing that, for instance, elementary ed teachers, one factor that feeds into the decision to go into elementary ed is the math requirements are very low in elementary ed. So that can…obviously it’s not what we wanna hear, because these are our first formal math teachers, right? For our kids.

Bethany Lockhart Johnson (27:16):
It feels so powerful, the impact that math anxiety can have, not only while you’re in, let’s say, elementary school, high middle school, high school, but then the impacts beyond that in terms of your career. And I shared this last season, when we talked about our personal math story, but I know when I was navigating the deepest part of my math anxiety, I really felt like, maybe this is a reason I can’t be an elementary school teacher. Because I was so worried that I wouldn’t be able…not that I wouldn’t understand the math for fourth grade, fifth grade, but that there was something about my ability to teach it or understand it or develop a love and passion for it that I wouldn’t be able to do. And I really had to reclaim it in my own way. But, you know, something that I think is so powerful about your research is just the applicability — not only to the field of mathematics, but folks’ everyday lives. And the way that you have talked in the past about math being a gatekeeper…I have a family member who, brilliant American Sign Language interpreter. I mean, amazing. Like a dance with her fingers. I could just watch it all day. And she actually didn’t complete the program because she couldn’t complete the math requirements. And I remember talking to her about like, “Well, have you gone to the free tutoring? Have you gone to, you know, this or that?” But it was a paralyzing fear, you know? So Dr. Ramirez, what do you wish educators understood about math anxiety? Or the research about math anxiety? Or maybe even the general public at large, what do you wish folks understood about math anxiety?

Dr. Gerardo Ramirez (28:58):
Oh, I think that a lot of students, they struggle with math. And I think we wanna normalize that struggle as much as possible. We want to create a culture where it’s OK to do math slow; it’s ok to take your time. And I know that’s not possible with a lot of these requirements that a lot of math teachers have to do. But I think if we want to prevent math anxiety, we have to create opportunities to tell better stories. So that’s ultimately what I tell people is, why do people develop math anxiety? Because they had experiences that challenged their competency and they told a negative story. And so making space to reflect in math classrooms about what does it mean to go slow in math, or what does it mean to make mistakes, and then helping kids to tell better stories, I think it’s really the best thing we can do as math educators. ‘Cause you know, your job is not to be a therapist ultimately. You know, there’s only so much math teachers can do. But I think one of the most powerful things we can create is setting up students’ experiences where they feel confident, and they can tell better stories, so they can have better dreams about math.

Dan Meyer (30:06):
Really appreciate this introduction to math anxiety. It’s been a fantastic kickoff to our season. Dr. Ramirez, thank you so much for joining us.

Dr. Gerardo Ramirez (30:14):
Sure. Thank you.

Dan Meyer (30:16):
Thank you folks so much for listening to that conversation with Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University.

Bethany Lockhart Johnson (30:25):
Dan, OK, if not for your frantic signaling, I would’ve probably asked another 20 questions. I need to know what you thought .

Dan Meyer (30:34):
I found it interesting at all points. And especially I think I started to understand a little bit better where the anxiety comes from for some students. I got a little bit here, which is that I think math, more than other disciplines, involves alienation. Check that word. You like that? Alienation? I’m into it. I’m feeling it. It’s like…to get good at math, to be successful in math, you gotta, as a kid, lose your attachment to the world you understand. And I mean, “got to” as in like, “you are asked to” — many times, unfortunately, by curriculum and instruction. Which is to say, you’re turning things you can hold onto into numerals. Right? You’re turning the world and its patterns that you can see and touch into Xs and Ys. And I just don’t know that other disciplines deal with that as much. Maybe I’m wrong and just guilty of, you know, “grass is always greener” syndrome here. But I think that’s an experience that kids have in math. And I thought that Dr. Ramirez got at that when he’s talking about the need to validate a student’s experience of anxiety. Like, in treating anxiety, sometimes we alienate people further by just like saying, “Oh, no, no, no, it’s just like, you need to, you know, drill yourself more, practice more,” and kind of invalidate that. So this feeling of alienation, I think permeates a lot of math instruction. I’m looking forward to learning more about that with our future episodes

Bethany Lockhart Johnson (32:00):
Alienation. That’s interesting. I definitely felt, I definitely felt isolated and alone many times in my math journey, when I was having my…you know, in high school, when I was feeling like, “Clearly everyone can look at tan, sign, cosign, and that means something to them.” Right? I think it’s really interesting, because I’m thinking about the other disciplines; I’m running through them, and I’m like, even in science, which can seem abstract, so oftentimes there’s these experiments that accompany these concepts, where you’re like, “Look at this concept made real in front of you.” Right? . And so yeah, that’s really interesting.

Dan Meyer (32:39):
You’re always one step away from blowing something up! Or, you know, dissecting something that’s tangible to you.

Bethany Lockhart Johnson (32:46):
Yeah. That’s really interesting. I did really love how he brought up the abstract. And how, I think, even validating it…he talked so much about validation. Which to me was like, YES. If somebody just said, “Hey, it’s not only possible to have math anxiety, but it also doesn’t mean that you don’t belong here.” If somebody had said that, it would’ve literally changed the trajectory, you know? And I wonder what those conversations could look like in our classrooms, where teachers celebrate that. Like, WHOA, this is a new way to think of this. This is a new way. Asking how many, or what do you notice for this image, through a mathematical lens, or looking…we talked to Alison Hintz and Antony Smith, like mathematizing books, like looking through these lenses — it’s an invitation to step into this other world, right? But there’s not only one way to do it. And I think oftentimes it’s like that anxiety of “Am I gonna say the right thing?” or “Am I gonna notice the right thing?” Right? How do we create that space more, where there’s so many possibilities and we want kiddos to notice what they notice, right?

Dan Meyer (33:54):
You gotta become a certain kind of person to be successful in math class. I feel like is part of the implied deal. Where you’ve gotta—like how you said—say a certain thing or think about a certain thing a certain kind of way. You’re trying to become someone who is not necessarily you. Which I think is fundamentally an experience of alienation, separating you from important parts of yourself.

Bethany Lockhart Johnson (34:19):
I will never, ever dive into mathematics on the scale and level that you have with your PhD. You understand math in a way that my brain just…I won’t get there, right? And yet I’m allowed to call myself a mathematician, with all of my deep dives in elementary math and my love of early numeracy and thinking about how we start thinking about counting and numbers. Right? It’s like, if we make more space for what mathematicians can look like, and what is your personal relationship with math…I mean, that to me feels really exciting. ‘Cause I think we both have something to offer each other.

Dan Meyer (35:03):
I think I have never found early math more interesting than when I talk to early math educators. And learn just like all the different ways that students come to understand a concept that I had thought was simple. Like addition of whole numbers. Whoa! There’s a lot of ways kids do that work, and their brains think those thoughts. And, yeah. That’s a good word there you’re offering us and our listeners.

Bethany Lockhart Johnson (35:27):
Yeah. Yeah. I’m really excited about this season. I think there’s — again, there’s no way we’re gonna cover all facets of math anxiety. But I think having the chance to explore it over the course of a season is going to be really fascinating. And really, I hope, destigmatize it and open up the conversation for our listeners. And, you know, if you listeners…we wanna know what you thought of this episode. Do you have any particular questions? Do you have questions related to math anxiety? Questions related to this episode? We are in development for this season, so we’re gonna do our best to get those questions answered. You can keep in touch with us in our Facebook discussion group, Math Teacher Lounge Community, and on Twitter at MTLshow.

Dan Meyer (36:14):
Next time, we’re gonna go deeper into the causes and consequences of math anxiety.

Dr. Erin Maloney (36:20):
It’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you.

Dan Meyer (36:41):
Til next time folks,

Bethany Lockhart Johnson (36:41):
Bye.

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What Dr. Gerardo Ramirez says about math

“A lot of students struggle with math, and we want to normalize that struggle as much as possible. We have to find opportunities to tell better stories and reflect on our experiences.”

– Dr. Gerardo Ramirez

Associate Professor of Educational Psychology, Ball State University

Meet the guest

Dr. Gerardo Ramirez obtained his Ph.D. from the University of Chicago, where he studied the  role of teachers and parents in shaping the math attitudes of their students, as well as reappraisal techniques to help students cope with anxiety during testing situations.

Dr. Ramirez is currently an associate professor at Ball State, where he examines the role of frustration, empathy, and cultural capital in shaping students’ success and persistence.

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!