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 

S1-01: The journey from student to SpaceX engineer: Juan Vivas

Illustration of Earth with text about a podcast episode featuring Juan Vivas, discussing the journey from student to SpaceX engineer. Includes a photo of a smiling person in a suit.

In this episode, we join Eric Cross as he talks to supply chain engineer Juan Vivas of SpaceX about his experiences growing up as a Latino in STEM. Juan shares his story of moving to the United States to study engineering and becoming successful in his career as a scientist. Juan openly discusses the experiences that made a difference in his life and the teachers that inspired him along the way. He also shares his experience as an engineer in different fields, as well as what it’s like to work in the supply chain during COVID.

Explore more from Science Connections by visiting our main page.

Download Transcript

Juan Vivas (00:00):

But to me, based on my experience so far, I think the best way to put it: An engineer is a technical problem-solver.

Eric Cross (00:28):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Juan Vivas. Juan is a supply chain engineer for SpaceX. His career in STEM has pivoted from chemical engineering to working on foods like Cinnamon Toast Crunch to his current role at SpaceX, where he’s responsible for his work on Starlink, a technology that uses low-orbit satellites to provide internet access across the world. In this episode, Juan shares his story of how he became an engineer and how a thoughtful teacher used robotics to inspire him. I hope you enjoy this great conversation with Juan Vivas. Juan, thanks for being here.

Juan Vivas (01:14):

Yeah, yeah, of course! Super-excited to be here.

Eric Cross (01:19):

Hey, and starting off, I kind of like to ask your origin story. We were talking earlier about Marvel, and your journey of one working for…what I consider the closest thing that we have to SHIELD in the Marvel stories is SpaceX. Like with my own students, we talk about SpaceX like it’s a fictional thing, and we watch the rocket launches together and we watch the recovery and it’s so cool.

Juan Vivas (01:45):

Yeah.

Eric Cross (01:46):

And so when I knew that we were gonna be able to talk to you, I was excited. Like, I felt like I was a kid.

Juan Vivas (01:51):

<Laugh>

Eric Cross (01:51):

So I’d love to hear your origin story of you ultimately landing at SpaceX. And begin wherever kind of seems most natural to you.

Juan Vivas (01:59):

Yeah, yeah, of course. You know, I wasn’t one of those kids at from a young age I said “Oh, I’m gonna be an engineer.” Right? “I want to go and build all these things.” Where I grew up, and the social circle that I had, a lot of people were like doctors or lawyers. Just figured, you know, I’ll go to med school and go down the same path that 90% of like everyone else was gonna take. But in high school, I actually got into robotics. And, kind of like I mentioned, I wanted to do med school, that is what I figured I would end up doing. And then I got into robotics in high school. And I think that was what really kind of like changed my perspective of what I wanted to do, because basically these competitions were just—it was full-on driven by students. So we designed, programmed, and manufactured, like, the entire robot itself. And so through that I ended up doing a summer engineering program at the University of Maryland, the summer before going into my senior year in high school. And there we worked on a competition with underwater robots. And so we spent the entire summer, kind of similar scenario, designing a robot, manufacturing it, programming it. And then in the end it was like a competition in the buoyancy tank with different teams. And, you know, I think one thing that was really neat about that experience is that I got to hear Dr. John C. Mathers, who is a Nobel Prize physicist, speak to us in a room with, like, only 10 high school students. And just hearing his experience of where he started and the accomplishment that he’s been able to do, down in the STEM path, was really neat. And that summer was my final decision that I’m “OK, I know I want to be an engineer.” What’s interesting is I ended up choosing chemical engineering, instead of mechanical, which a lot of people, you know, based on all the experience that led me up to be an engineer, they asked me why I didn’t choose mechanical engineering. And I think one of the reasons why I chose chemical engineering is it’s very process-based. So one thing needs to happen, and there’s different inputs to that one step, and that step has an end-to-end reaction to it, right? So certain things need to happen in step one in order for step two to occur. And however the inputs happen in step one, it’s gonna affect the rest of the process. Honestly, very different than what I thought it was really gonna be. But what’s neat about chemical engineering is that it’s one of the most versatile engineering majors that you can have. Chemical engineering, because you work with a lot of process bases. Everything has a process, right? Everything needs to start with step one, and with, you know, step 10, whatever. And it’s all about optimization and improvement along those processes. So you can really take chemical engineering principles and apply ’em to different areas of a career, which is essentially the experience that I had in college. I had three internships with Dow Chemical where I did environmental health and safety, production, and supply-chain improvement. I then did research and development with Clorox. And then I did manufacturing engineering with General Mills. So really different job roles, different aspects, but same methodology applied.

Eric Cross (05:36):

I feel like there’s so much that you just said, <laugh> and I was trying to always, “I wanna ask him about that!” And in there, what I heard was there was a real pivotable, pivot moment in your life. Was the club…or was it a club, the robotics program? Or was that a class?

Juan Vivas (05:53):

You know, it was actually…it was VEX Robotics, specifically.

Eric Cross (05:56):

It was VEX! OK. Yeah, yeah. Really popular. And they still have it; I think we actually have some downstairs. So it was a club, and not necessarily a formal environment, where you were able to build. And it’s both collaborative and competitive, right? Like, there’s both aspects.

Juan Vivas (06:11):

Yep. Yep.

Eric Cross (06:11):

And, and then you had access to one of the only two facilities in the country that have these…were they buoyancy tanks?

Juan Vivas (06:20):

Buoyancy tanks, yep.

Eric Cross (06:21):

And there’s this book, Malcolm Gladwell’s Outliers, and then another similar book called Balance. It talks about how some of these innovators, like Steve Jobs and, and Bill Gates, they had access to things that other people didn’t. So, like, Bill Gates, I think at the University of Washington, had a computer that, you know, no one else did. And Jobs had one at, like, Hewlett-Packard. So it gave you this awesome headstart, where you’re able to test things in a real-life environment that kind of transfers into real-world skills. And then a few internships, so like, internships and mentors. So you had these people in the industry or people who were front-runners that were able to pour into you and give you these opportunities. And so it’s really neat to see how a program that starts as a club, kind of a competitive thing that introduced you to it and hooked you, then led to unfolding all of these opportunities that ultimately led you up to being here. And there’s one part—in looking at your LinkedIn profile, there’s a couple of really cool things that stand out. There’s a lot of cool things, but there’s two that really stood out. So one, working at SpaceX, and we’ll talk more about that, but I wanna go to General Mills and Cinnamon Toast Crunch. Because Cinnamon Toast Crunch is amazing.

Juan Vivas (07:39):

Yeah.

Eric Cross (07:39):

And you were part of the supply chain for that. In my head, I’m thinking, OK, like, what is he like responsible for? Like, getting the cinnamon and sugar?

Juan Vivas (07:51):

<Laugh>

Eric Cross (07:51):

What was, what did your job entail, when you were running that?

Juan Vivas (07:55):

There, I didn’t even know what I was gonna be doing until my first day. It was just, whatever the business need is, that’s where you’re gonna be put. So this was actually a high-priority plan for General Mills. And the production line that made Cinnamon Toast Crunch was split up into processes. So you have, they call it the process-process side, which is like literally raw materials, like making the cereal from scratch, baking it, adding the sugar, and then sending it to be packaged. And then you have the packaging-process side. so I was then placed as a packaging process lead, for the packaging side of that production line. So I was accountable for two packaging lines that packed out Cinnamon Toast Crunch. And that is where—that was actually my first real, you know, call it “real job,” like graduated college, going straight into the industry. I was a process lead for the packaging side of Cinnamon Toast Crunch.

Eric Cross (08:54):

So you went from cereal to rockets, <laugh>, which which is an amazing trajectory to have.

Juan Vivas (09:03):

Yeah. Yeah.

Eric Cross (09:04):

And when you kind of mentioned, back in your story about medical school, and, you know, it’s kinda like, what you see people doing, and you’re “OK, this is what I think I wanna do.” And then we have a perception in our mind about what a certain job’s gonna be like. And then reality hits. I think a lot of—when I ask my students, “What do you wanna do?” They think, like, “lawyer!” and when they think “lawyer!” they’re like, “I’m good at arguing!” Right? And until they find—until they talk to some lawyers and they find out like what that career can look like.

Juan Vivas (09:28):

Yeah.

Eric Cross (09:28):

You’re not just in the courtroom showing off your arguing skills. But, like, an engineer, when I talk to my students about what does it mean to be an engineer, often it’s very linear. It’s “I build bridges,” or, you know, maybe cars, but you’re a supply chain engineer. And, and that’s something that I think, now more than ever, it’s probably an incredibly critical role, especially considering that all of these supply constraints. Can you—what is a supply chain engineer? And what does it look like in your day-to-day? How is engineering rolled into that?

Juan Vivas (10:03):

Yeah, yeah. I think that’s an excellent question. I, too, once thought that engineering was just “I’m gonna be actually making something physical,” and like being super engineer-y about it. But, to me, based on my experience so far, I think the best way to put it: An engineer is a technical problem solver. As a supply chain engineer, specifically right now in my role at SpaceX…you know, as you can guess, the supply chain in the entire world is crazy. There’s no raw materials anywhere, and nothing can ever get on time. And so what I work on is I help our suppliers develop processes to meet the design criteria that we set up for like a specific part. As my job as a supply chain engineer, it’s “Can I take this design and make it manufacturable?” Right? “Can I go to any supplier and can they actually make this to the tolerance that the design engineer set them to be?” Nine out of 10 cases, the answer is no, essentially, is the best high-level way to put it.

Eric Cross (11:10):

When you’re solving these problems, is it this iterative process of going back and forth? Or is it just this aha-moment when you finally figure things out? ‘Cause I imagine they’re coming up with a design; you’re going back and saying, “Can this be manufactured?” or “Can it be done?” They’re saying no 90% of the time. And then are you the one responsible for kind of iterating on this, or changing it and then going back to them and telling them, asking them, until you get a yes? Is that—

Juan Vivas (11:33):

Yep. Yep, yep. Exactly. So we go through a process called Design for Manufacturing, DFMing. And where I essentially take, you know, the design engineer’s proposal, and then I have conversations with the suppliers, and then, that’s where the iteration begins. Where we go back and forth, back and forth, until we kind of meet in the middle to have something that can be manufacturable. Most of the times, in my experience, suppliers will always tell you no, just because they always want something that is manufactured really easily. And so you just gotta learn through experience. Like, when are they actually telling you something that’s a fact, versus when they’re just trying to you know, get out of a tolerance, or that “all right, all right, they mentioned that would just like make their jobs a little bit more difficult.”

Eric Cross (12:17):

So I’m hearing like there’s soft skills that are woven into the technical skills that you also need to be able to have.

Juan Vivas (12:23):

Oh, yes, absolutely. Yeah. I think, you know, as an engineer—and this is something, again, that I feel like you can only learn through experience—you’re gonna see that it’s not just you working to solve this one problem. Especially for a supply chain engineer. You’re talking with marketing; you’re talking with an industrial design team; you’re talking with logistics; you’re talking with procurement, materials management—just a whole set of people that don’t necessarily have technical background. Right? So sometimes, depending on the audience that I’m targeting, I’m always very, very peculiar on what is my target audience, right? How can I—how deep in my technical knowledge do I need to go? Because if I just, you know, talk straight Engineer, they either don’t care or they’re gonna be really confused about what I’m saying. So there is a stronghold of soft skills that definitely go into engineering, which I think are really important to communicate, you know, to, let’s say, students that are really interested in engineering. So you can be extremely smart and intelligent and really good at problem-solving, but if you don’t have those soft skills that you apply in the real world—’cause in the real world, you’re never only gonna be working with engineers, no matter like where you’re at—so having those soft skills to be able to manage with different backgrounds and different sort of people and different ways of thinking, it’s, I feel, really critical, for, for an engineer in the real world.

Eric Cross (13:50):

No, I think that’s a great point. It reminds me of teaching! And so many other professions where your ultimate goal is to really pour into this person in front of you and help develop them and create a sense of inquiry and wonder and personal growth and inspiration. But you’re also working within constraints and people and relationships. You know, you have your other teachers, you have parents, you have administrators, you have a district, you have communities, stakeholders. You have all of these different dynamics that you have to kind of navigate in order to ultimately help this child thrive. Versus just, like, being in the classroom: “OK, I just got <laugh>, the hundred or 200 students, just you and me. That’s it.” But that’s not the real world. And there’s this report that came out, I think Google ran it, Project Oxygen and Project Aristotle, and they asked the question, “What are the most effective traits of a good team and a manager?” And the top seven skills were all soft skills. So it is like exactly what you’re saying, where, yeah, it’s great that you have this technical aptitude, but if you’re not able to work with other people, problem-solve together, work with people of different backgrounds and perspectives, then you’re gonna run into some roadblocks. And that kind of dovetails, like, looking at things like if you looked at education from the perspective of an engineer. So you’re all about optimizing, right? Optimizing, working with what you got. When you look at education, are there any things that you would optimize to help improve the experience of students? Like, looking back, that you would fine-tune, that you think could provide better outcomes in the classroom?

Juan Vivas (15:28):

You know, I feel…I don’t know. Obviously I’m not a teacher. And I’m sure teachers just have so much stuff going on. But I think just like, finding…giving a chance to those students that you see a lot of potential in and really taking the time to mold them. You know, I did have a teacher who was able to mold me and give me that kind of one-on-one personal experience, right? I think honestly to me it just comes down to mentorship, and motivating students on what, you know, they’re passionate for. Like, putting them in front of engineers, right? Like finding engineers to come volunteer and explain to them. I genuinely believe it just takes one spark to really get a student on a trajectory where they can make an impact in the future. So to me, it comes down to, really, exposure. How much are you really exposing your students to…you know what, something I’ve learned, when I joined SpaceX, is that Elon doesn’t believe—well, you know, there there’s a lot of things that Elon believes and not believes in; there’s a whole different type of conversation!—but he doesn’t think that you can just take a curriculum, let’s say, and just apply it massively to everyone and expect like everyone to be it. That’s just naturally not how it works, right? Students learn at different paces; they have different sort of interests. This is actually why he created his own school for his kids in LA, called Ad Astra. You know, if you take that mentality, what that school is doing is that they’re working at the students’ pace and at the student’s interests, right? And I actually have a coworker who has his kids in that school. And I mean, these are one of the most brilliant kids I’ve ever known. Like, they are taking differential equations in the eighth grade. And I didn’t know what differential equations was until I was in college already and they told me, “This is a class you have to take.” <Laugh>. But it’s finding that crossway where, where is the curiosity of the student? What are they really interested in? and exposing them to that.

Eric Cross (17:51):

Yeah. And what I’m hearing of that is, in teacher-speak, a lot of personalized learning. Like you were talking about…is it Ad Astra?

Juan Vivas (17:59):

Ad Astra? Yep.

Eric Cross (18:01):

Ad Astra. You know, every student learns in their own way and they develop knowledge in their own way. And being able to personalize learning according to the students’ abilities and needs, and then accelerate or slow down, really produces some amazing effects. I know this is something that we as teachers try to do with the classroom. Scaling it is the challenge. But it’s great because even with people who are in charge of policy or people who have decision-making ability, hearing people from the top down saying, “Hey, look, this is what worked for me. This is how I was able to become successful. I had a teacher that was able to be a mentor to me because they knew me, they had a relationship with me, they were able to tap into my passions and use those passions to drive me to do or put me in programs that I might not have known about because they, they knew who I was.” And it’s not one-size-fits-all for everyone. So having—maybe it’s curriculum or learning experiences that are kind of modular, where students are able to maybe try on different things and get that exposure, I’m a big, big believer, like you are, in mentorship. That was a huge, huge thing in my life. Having mentors. It’s the reason why I became a science teacher. In seventh grade, I had a mentor who had us doing college-level science, you know, at UC San Diego. And it completely changed the trajectory of my life, in a direction that I wouldn’t have had without him. So I think that’s great. And it’s something that we as teachers would appreciate hearing. Going back to what you said…earlier you said your wife is a supply chain engineer as well. And so that means that there’s two people who are process-minded in the household. And this is kind of a lighter question, but I gotta wonder, do you have the most optimized flow for grocery shopping? <Laugh> Because…

Juan Vivas (19:49):

Yeah, I think we don’t spend more than like 20 minutes at a grocery store. Mind you, we only shop at Trader Joe’s and we have a very specific list before going in. And if you ever shop at Trader Joe’s, you just know where everything is ’cause it’s always there and it’s small, right? But yeah, like we’re, we’re in and out in like 15, 20 minutes. It’s great.

Eric Cross (20:11):

I love it. I love it. I feel like I’m that way by design. I go in with a purpose and this is exactly what I want. I know where the cookie butter is, <laugh>, I know where my coffee is, and then, OK, I’m in and out. Apple Pay or whatever I’m using. And then we’re good to go. Do you think…so as someone listening to this or some people even just becoming aware of supply chain engineering, what advice would you give someone that’s interested in pursuing this career path? If you maybe reverse-engineered your process, knowing what you know now, you were gonna give advice, you were that mentor, what are just some kind of tips or ideas or thoughts or trajectories that you’d think that they should aim for? I’m assuming like robotics….

Juan Vivas (20:56):

Yeah. You know, I think I would say definitely finding some sort of program that exposes you to a lot of things that you won’t be exposed to, like on a day-to-day basis, or something that you just can’t be exposed to naturally at school. And mentorship, honestly. I was born in Colombia and my parents were both—they’re still both professionals, but they were both professionals in Colombia. And when we moved to this country, this was like December of 1999. My parents started from scratch, and so they didn’t really grow up in the States, right? So when it was my time to go to college and do all of this stuff, it was just like me on my own figuring this stuff out. And, you know, they definitely made some mistakes when it came to college applications and whatnot. But once I was in college, I knew that the best way for my success was gonna be through mentorship. And that’s when I joined the, Society of Hispanic Professional Engineers, which is a nationwide organization. And each college, well, most college campuses, have their own chapter. In joining that, I was exposed to resume workshops, mock interviews—basically how do you even talk to a recruiter? Which is so critical, right? And personally that that organization was really what molded my actual professional career.

Eric Cross (22:19):

There’s this theme that I’m hearing, kind of weaving through this. And in addition to—as we’re talking about STEM and technical skills, in addition to that, there’s this thread that I’m receiving of…being able to form relationships with other people, for our students, is an important skill to teach and should be taught explicitly. Which isn’t…it’s not really a curriculum, right? Like, you don’t get tested on your ability to….conflict resolution or how to write an email or how to develop a relationship. And then the other part in I think what you just said is the aspect of community. Through this organization, you learned kind of some of these hidden rules, maybe I would call it.

Juan Vivas (23:04):

Yep.

Eric Cross (23:04):

It’s not that you didn’t have the…you had the aptitude. You had the drive. But there were these kind of hidden rules, and from moving to the US, you needed a community to be able to show you, so that you can kind of go through the proper steps.

Juan Vivas (23:16):

Exactly.

Eric Cross (23:17):

And so that created a lot of value for you.

Juan Vivas (23:19):

Yep.

Eric Cross (23:20):

Well, the last question that I have is, is just kind of a wondering. You have this awesome story, and the story continues to unfold. I gotta say, <laugh> I’m gonna be following your LinkedIn profile, because I think you just have kind of the coolest trajectory of going from, you know, General Mills, working in chemical engineering, and then ultimately it’s SpaceX. And every time I see the rocket taking off and landing, I’m gonna be thinking, thinking about you. So cool!

Juan Vivas (23:47):

Yeah. Yeah.

Eric Cross (23:49):

And personally, I have a hope that one day, one of my students will be at a company, you know, like SpaceX or Tesla or wherever, and one day I get to interview them and talk to them and see what they say. But the last question I want to ask is, is there, is there a teacher who inspired you, or a memorable experience that you have that made an impact on you?

Juan Vivas (24:16):

Yeah, yeah, of course. It was kind of you know, middle school going into high school. The way my school worked, everything was divided from pre-kindergarten, whatever, first to sixth grade, and then seventh grade to 12th grade. So I had a high school science teacher, Ms. Brown, Ms. Velda Brown, who, came from a small little island town on the east coast of Canada. Somehow landed, in the high school that I went to, to teach science. Going back to the beginning of the story where I mentioned that I figured whatever, I’ll go to med school. I played soccer, basketball, and, you know, I said, “I’ll figure it out once I graduate.” It might have been like life science in the eighth grade or something like that. But then she went on to teach me chemistry and physics as well. And when I was in the 10th grade, she approached me and she asked me if I wanted to join the robotics club. And I remember saying robotics? I don’t know. You know, naturally, in school, it’s different sorts of crowds: people that play sports and people that are like in like STEM clubs or whatever. And I was, “Ah, I don’t know; I don’t know how I feel about robotics; not really my thing….” But somehow she convinced me to join robotics. It’s me, coming into this group of kids that already knew each other, and they were all working on robotics. And I’m, “Yeah, I mean, I guess I’m just here to try this thing out.” It was a thing where we met every single Saturday at like seven in the morning. And there were times where I literally had to choose, “Do I go to like a soccer game or do I go to you help my team with robotics?” And I completely loved it. Like, I fell in love with the aspect of building something from scratch, and just making it operative. And she ended up just being a huge mentor for me in high school, actually. With her, with the help of her, I ended up opening the robotics club at my school. And before I left, we opened it up to middle schoolers. And then, you know, later, years later down the road when I was in college, I found out that it was now a whole-school thing. So there was an elementary robotics club at the school, the middle school one, and then the high school one were still a thing like years after I left. And that was like just so amazing to hear. But yeah, it was Ms. Velda Brown, my high school science teacher, that really took her time to mold me and get me into robotics, and really mentor me. And honestly, I’m sure you as teachers, you guys probably hear about it a lot, but you can have a lot of power in shaping a kid by just telling—believing in them, right? She believed in me so much that I would go on to be a successful engineer. And I’m. “OK, yeah, yeah, you’re just saying it.” But she spoke life into her students up to this day. I still speak about it with my wife, and when I’m in conversations about this, that if it wasn’t for my high school science teacher, I would not—well, no, I would probably not be an engineer right now.

Eric Cross (27:38):

Wow. Shout out to Ms. Velda Brown <laugh>. Would you say she spoke…I think one thing that just resonated with me is when you said she “spoke life” into you.

Juan Vivas (27:46):

Yeah.

Eric Cross (27:46):

That was really powerful. And I think we as teachers have that power and we don’t realize it. Because, you know, we get so we’re so familiar and living day-to-day, but we do have the power of life, speaking life, into our young people. And, yeah, that was—

Juan Vivas (28:03):

Absolutely, yeah. You know, I think obviously people grew up with different backgrounds, different communities, life situations, right? So imagine having like a student that is similar in that environment and then they just hear someone at their school, like, “Hey, you’re really good at this. why don’t you consider doing this?” And that’s when I feel teachers have that power. Where like they don’t necessarily know the background, but they can make that opportunity, or make that decision in the moment, to really shape a student’s life.

Eric Cross (28:37):

And we need to hear that. And I think, I hope that other teachers listening to this will be reminded that many times we don’t get to reap the harvest. We don’t get to see the <laugh> Juan Vivases at SpaceX. They just kind of go, and they disappear, and we hope for the best, and we get a new group. But every once in a while they come back, and we get to see what our watering or seed-planting was able to produce. And so, just know that you sharing your story for educators, and for definitely Ms. Brown, makes a huge difference and is a huge encouragement. So.

Juan Vivas (29:11):

You know, I think we touched on earlier, you know, how do I end up going from cereal to rockets, right? And I think it ties along with what I mentioned earlier of just taking—as an engineer, you’re really a critical problem solver, right? And you think that methodology. And if you find a way, you can apply it to different sectors. When I was doing a lot of like the packaging process stuff at General Mills, being a lead on a high-volume manufacturing line, what I do for SpaceX specifically, right now, I’m actually on the Starlink project. So if you’re up to date with Starlink, it’s, it’s essentially high reliable, fast internet that we’re providing to areas where usually people don’t have access to internet, right? Or maybe they do, but it’s extremely expensive. Because to an internet provider company, the benefit is not there, if they extend an entire internet fiber line out to their place because it’s only directed to them, right? So that’s, that’s essentially what Starlink is trying to solve. And this is the first time that SpaceX is facing a consumer packaging scenario. Before it was just rockets. And now they’re selling a product to consumers. They had never done that before, especially in a high-volume manufacturing setting. And so I am the supplier development engineer for all the consumer-facing packaging for the Starlink product itself. And that’s essentially how all those thoughts connected, where I had this experience coming from General Mills and packaging high-volume manufacturing. And then when Starlink started, they’re all, “Right, well, who knows anything about packaging?” Right? “We know so much about rockets, we need someone with this technical background.” And that’s essentially how I bridge over to SpaceX.

Eric Cross (31:11):

And so while you’re working at SpaceX, you’re working on Starlink, which I know you mentioned that—you said that it’s providing internet globally, which in and of itself, we—especially those of us that live in major cities—we kind of take for granted. Internet is like a utility. But we don’t maybe realize that in many parts of the world, internet is not reliable or even accessible.

Juan Vivas (31:33):

Right. Right.

Eric Cross (31:34):

I see every once in a while, I think, the StarlinK satellites sometimes are visible?

Juan Vivas (31:38):

Yep.

Eric Cross (31:39):

Low orbit?

Juan Vivas (31:39):

Yeah. Yeah. You can go—they’ll kind of be like a little train of bright stars that move along together. Yep.

Eric Cross (31:46):

And that must—that must feel…I mean, we all have jobs and we’re all doing different things, but you’re working on a project and you’re engineering something that actually can provide a lot of opportunities or close a gap in some parts of the world where they don’t have access to internet. They’re gonna be able to have access and be connected all over. I dunno, the word would be “existential.” Existential value. Like, what you’re doing is actually providing a service for people. Humanity. Like, addressing a critical need in many, many places around the world.

Juan Vivas (32:26):

Yeah. We’ve had stories where we have sent Starlink kids to a small school in a village in rural Chile, right in South America. And for the first time ever, they’ve had internet. We have supported disaster relief in Europe. I think this past summer, Europe had really bad floods. We sent Starlink kits out there. You know, the vision of working at an Elon Musk company and SpaceX and Starlink—this is all stuff that is being done for the first time in history. We have never, ever done anything like this before until now. And to be able to provide those that don’t have the access to—to your point, it’s kind of wild, right? Like we, we just take it for granted. “Oh yeah, I just have internet. Let me log on.” There are people on Earth right now that have never been on the internet. Or don’t even know what the internet is. And that’s essentially the, the gap that Startlink is starting to close.

Eric Cross (33:26):

Yeah. We think about that while my students are doing TikTok dances. <Laugh> And there are people who, you know, never, never been connected. And, it kind of makes me more like, just inside, if I can ask: What’s it like working at SpaceX? I showed my students what it’s like working at some of the Silicon Valley companies. ‘Cause just to show them there’s slides and food and, you know, they kind developed this ecosystem inside so that it’s really kind of homey to kind of keep you there, you know. When you’re working and there’s bikes and things like that. And that’s a very Silicon Valley type of thing. But, you know, in listening to you talk about SpaceX and Elon, you know, you’re with a really visionary kind of company, and when I hear you talk about it, there’s I can hear this passion, this, “we’re doing something.” Is that culture, like, pervasive everywhere? Are you around folks that kind of are on that same wavelength? Because I definitely get it from you as you talk about what you do.

Juan Vivas (34:28):

Yeah, yeah. Definitely. I think, as an engineer, you know, going to SpaceX and working at SpaceX, it’s essentially—personally, I believe right now in the US it’s like the mecca of engineering, right? Like, it is where engineering in this most, you know, shape and manner, it’s being applied. I think what’s really interesting is that the way that Elon looks at it is just iterate, and iterate fast, right? Like, fail and fail fast. I think as an engineer, you always want to have things perfect, right? And so you spend a lot of time in making a decision or investigating something or whatever. And working at SpaceX is the complete opposite. It’s just you know, “Assume, state your assumptions—like, what are you assuming right now? What are the risk at it? And just make a decision and then see what the result is.” You know, so it’s an environment where you learn, really quick.

Eric Cross (35:28):

You said something that I think was powerful and I hope, I think <laugh>, this is definitely, I’m gonna get a clip of this <laugh> of you saying it. Because it speaks directly to, I think, what a lot of students struggle with in the classroom, is there’s this competition or feeling that you always need to be right. And you need to be right the first try, on the first time. And a lot of times it’s because students will compare themselves to each other, or there’s a tremendous amount of pressure to be successful. But you said, “Fail and fail fast, iterate, state your assumptions.” And it sounds like this critical part of being an engineer or in what you do, like there’s no room for ego or attaching your identity or your sense of value or worth or ability to whether you’re able to solve a problem in the first try.

Juan Vivas (36:13):

Yep.

Eric Cross (36:14):

Like, you have to be OK with the cycle, is kind of what I’m hearing from you. Is that, is that right?

Juan Vivas (36:19):

Yep. Exactly. It only took six months to develop the product from scratch and launch it to the public, which is insane. Nowhere in the world will any company ever iterate that fast and come up with a brand-new project. But it’s because of that mentality—like you’re saying, it’s not about like just trying to make it perfect and have all this information. And I think Elon has learned this personally, you know, through Tesla and the beginning of SpaceX. It’s, “I can wait to have all this information, and most likely I’m still gonna be wrong after I make the decision.” So it’s, “Might as well take the risk, do the decision, and then just see where you learn from it, right?” And then you keep applying that, applying that. So it’s like you iterate, iterate, iterate, iterate until you get what you want.

Eric Cross (37:00):

I think this is even, like, great advice. I’m taking this personally because I get paralysis by analysis <laugh>.

Juan Vivas (37:06):

Yep.

Eric Cross (37:07):

You know, I’ll research something to death but then not actually execute. Like, I need to make a decision and do it and then course-correct along the way. Somebody once told me it’s a lot easier to turn a moving car than it is a car that’s sitting still. And so as you’re kind of flowing, you’re just making these adjustments along the way until you end up on the path that you want to be. So I think that there’s so many gems in the things that you’re saying right now. What I’m thinking through the lens of my seventh graders that want to work in any STEM field—I mean, really, any field in general, but especially engineering, especially the STEM fields—knowing that, pick it, make a decision, move forward, and then course-correct along the way. That’s what science looks like in the real world.

Juan Vivas (37:49):

Yep. Exactly. Yep. And definitely most important—and I feel like this is sometimes where, not necessarily education in general, but it’s just, we want students to, “OK, you need to get it right the perfect time, right?” But it’s like, every student is gonna think differently. A student is gonna take a different assumption based on their background and experiences. And I mean, you know, we can go a lot deeper in that, but the way a student is shaped, they’re gonna take certain assumptions. So that’s where it gets interesting. OK, why are you assuming that? Where’s your thought process in this?

Eric Cross (38:25):

And we all come from different backgrounds and mindsets and filters and biases that cause us to look at something a certain way. And it’s not just like calling it out, just going, “Hey look, this is what it is.” Like autopsy without blame, this is what I’m working with. Let’s discuss it openly. Right? And if we started that process earlier, you know, younger, in classrooms, we can de-stigmatize the right answer being the best answer more, as opposed to focusing on process as opposed to outcome. And then you kinda get used to wanting to go through the process. I look at it like video games and I talk to my students. I say, “You know, you don’t pick up a video game that’s brand-new and then play it and then you die once and you’re ‘Ah, I’m never gonna play this game again.’ You know, it just doesn’t work that way. You’re going through this iterative process, and no matter what you play, you’re trying things differently. You’re data collecting. And then you’re making new decisions based on the data that you collected.” And for some of my kids, they’ll just raise their hands, say, “No, I just get mad and throw the controller across the room.” <Laugh> But I go, “Yeah, and then you’ll try it again.”

Juan Vivas (39:33):

The best way to know how not to do something is to fail. And so you already…I mean, what is that famous quote? I think that’s why Thomas Edison’s, “Oh, I, did not fail 99 times. Right? I only found 99 times…” I mean, that is that is true. And I feel like at work in a SpaceX, that is something that probably the core of it comes from there. It’s you know, any failure, quote unquote, that you may take it as a failure, it’s really not. You’re just “OK, we, we tried that. It didn’t work. Like what are we gonna do next?” So it’s just like taking that learning and like moving off with it quickly.

Eric Cross (40:09):

I heard a couple of teachers say, “Things fail: First Attempt In Learning: F A I L.” And then another teacher, one of my mentor teachers, she said, “There’s no such thing as failure, just data, in science.”

Juan Vivas (40:20):

Mm-hmm. <affirmative>. Exactly. Yep.

Eric Cross (40:23):

And so I’ve always taken that to heart. And I share that with my own students, just, “A ‘no,’ a lot of times, will tell you more information than a ‘yes.’” ‘Cause if something works in the first try, you may not exactly know why it worked. It just did.

Juan Vivas (40:34):

Yeah. Yep.

Eric Cross (40:37):

So yeah. Well, I went on your time, brother. Dude. <laugh>. The time flew. It was…

Juan Vivas (40:46):

Yeah.

Eric Cross (40:47):

There were so many things I was trying to write out as you were talking, that I just felt like, “This guy is sharing so many gems!” But yeah, I want to thank you for taking time outta your day and for sharing that information for your passion for what you do. And, I don’t know, I think that students and teachers that listen to this will get an insight from a perspective that really matters. ‘Cause ultimately we’re, we’re trying to really prepare our students for real life. Maybe I’ll email you privately if I order a Tesla, if you can move me higher up the Cybertruck line. <laugh>

Juan Vivas (41:22):

Yeah. No promises.

Eric Cross (41:24):

<laugh>

Juan Vivas (41:25):

Yeah. No, I appreciate you guys having me, having me here, and be able to speak on my experience. And hopefully it sparks a couple, one, even if it’s just one teacher that will spark another student, that is already success there. So.

Eric Cross (41:42):

Well I know, I know what you said resonates with me and it fills my cup. And I’m excited. So I’m already thinking of some ideas of things that I can do, just because of this conversation, and I know other people will as well. And, again, this is Juan Vivas, who’s a supply development engineer at SpaceX. He’s worked at some amazing places. And someone who believes deeply in not only the power of the technical skills, but the heart skills, and how community makes a huge impact in his life. It made a huge impact in him ultimately becoming a scientist, and now working on a project at SpaceX, Starlink, that is going to provide access to the world, to the web. And that’ll ultimately help us solve more problems and innovate and create some solutions that will benefit everybody. Thank you, sir. Appreciate you.

Juan Vivas (42:30):

Yeah, thank you. Thank you so much, Eric. Appreciate it.

Stay connected!

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What Juan Vivas says about engineering

“Based on my experience so far, I think the best way to put it… an engineer is a technical problem solver.”

– Juan Vivas

Supplier development engineer, SpaceX

Meet the guest

Juan Vivas is a chemical engineer currently working as a Supplier Development Engineer at SpaceX. Juan got his start at the University of Florida, where he led the Society of Hispanic Engineers (SHPE) as vice president. He’s worked for companies like Clorox, Dow Chemical, and General Mills. Juan lives in Los Angeles, California with his wife and two dogs.

Man in a suit and tie smiling at the camera with a blurred green background.

About Science Connections: The podcast

Welcome to Science Connections: The Podcast! 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.

What’s included in our Spanish language arts curriculum

Amplify Core Knowledge Language Arts® (CKLA) is available in both English and Spanish. Amplify Caminos al Conocimiento Esencial, our robust Spanish language arts companion for grades K–5, supports multiple teaching models, including dual language immersion and transitional classrooms.

A laptop screen displays a kindergarten instructional webpage in Spanish, showing lesson categories with illustrated thumbnails and navigation options.

Year at a glance

The program’s intentional Knowledge Sequence from K–5 connects knowledge and vocabulary within a grade level and across grade levels, for deeper reading comprehension and preparation for college, career, and life. Instead of “activating prior knowledge,” Amplify Caminos helps you build it in the classroom from day one, for every child, expanding each student’s knowledge base long before they transition to reading to learn.

Curriculum flowchart showing reading themes and activities from Kindergarten to Grade 5, organized by grade level and literary theme, with interconnected boxes for each topic.

Units & domains at a glance

Each Knowledge Domain in grades K–2 and Unit in grades 3–5 varies in the number of days based on instructional purpose. Just as with our top-rated Amplify CKLA program, the Amplify Caminos materials engage and delight young learners with resources that are both appealing and original.

Una mujer rubia con un vestido azul cuida ovejas blancas y negras, sosteniendo un bastón de pastor. Un cerdo vestido de azul corre y un hombre de negro toca el violín en una valla. Al fondo hay una casa.

Domain

Nursery Rhymes and Fables/Rimas y fábulas infantiles

Start learning about literature with these classic Mother Goose rhymes.

Ilustración de tres personas en un paisaje cubierto de hierba, una tratando de atrapar mariposas con una red, otra escondiéndose detrás de una escultura alta y frondosa de una mano y otra con binoculares.

Domain

The Five Senses/Los cinco sentidos

Learning about the body starts with learning about how we experience the world.

Una ilustración que representa a un gran lobo con sombrero de copa liderando un desfile de animales y personas con instrumentos musicales a través de un paisaje montañoso.

Domain

Stories/Cuentos

Learn about the parts of a book and some of the stories that go in one.

Una ilustración vibrante de una escena rural con colinas, una granja, una mariposa, un sol brillante, varias verduras como tomates y lechugas, y un gusano en el suelo.

Domain

Plants/Plantas

Discover the lifecycle of plants and the history of George Washington Carver.

Ilustración de una escena de granja que muestra un camión rojo que transporta verduras, campos de cultivo, vacas pastando en una colina, un granero y un molino de viento contra un cielo azul.

Domain

Farms/Granjas

Now we know how plants make their food… but what about animals?

Ilustración de un nativo remando en una canoa en un río con búfalos pastando en un campo, tipis al fondo y pájaros volando en el cielo bajo un sol brillante.

Domain

Native Americans/Los nativos americanos

Who were the first people in America? A look at the Lenape, Wampanoag, and Lakota Sioux.

Una ilustración muestra un rey y una reina en tronos, un castillo en un acantilado y una mujer con enanos cerca de un árbol. Cortinas rojas enmarcan la escena.

Domain

Kings and Queens/Reyes y reinas

To understand fairy tales, it’s best to first understand royalty.

Ilustración que muestra las cuatro estaciones: primavera con flores, verano con árboles verdes, otoño con hojas que caen e invierno con nieve y gente en trineo. Un niño lee debajo de un árbol.

Domain

Seasons and Weather/Las estaciones y el tiempo

The study of natural cycles continues with the weather and why it happens.

Un velero de madera con símbolos de cruz roja en sus velas navega cerca de una isla tropical con exuberante vegetación y palmeras. A lo lejos se ven otros dos barcos en el agua.

Domain

Columbus and the Pilgrims/Colón y los peregrinos

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

Una escena histórica muestra gente afuera de una gran mansión de estilo colonial con dos chimeneas. En primer plano se ve un carruaje tirado por caballos y a la izquierda se ve una casa más pequeña.

Domain

Colonial Towns and Townspeople/Las colonias y sus habitantes

Before the War for Independence, how did the town and country depend on one another?

Ilustración de personas clasificando materiales reciclables en un parque cerca de un río contaminado. Las fábricas emiten humo al fondo, mientras que las mariposas, las flores y los árboles están presentes en el primer plano.

Domain

Taking Care of the Earth/Cuidar el planeta Tierra

We only have one Earth—here are some ways to help care for it.

Ilustración del Monte Rushmore con los rostros tallados de cuatro presidentes de Estados Unidos. Un águila vuela en primer plano.

Domain

Presidents and American Symbols/Presidentes y símbolos de los Estados Unidos

Start learning about government through the lives of five presidents.

Una ilustración caprichosa que muestra animales de granja alrededor de una casa en un árbol junto a un río. Un zorro, un conejo y una oveja interactúan mientras la gente acampa junto a una fogata al fondo. Una araña cuelga del árbol.

Domain

Fables and Stories/Fábulas y cuentos

Learn some of the key elements of a story through classic fables.

Ilustración que presenta anatomía humana, actividades de estilo de vida saludable, profesionales médicos, símbolos dietéticos, una ambulancia y microorganismos, destacando la conexión entre salud, nutrición y ejercicio.

Domain

The Human Body/El cuerpo humano

What are germs? What are the organs? And what does it all have to do with health?

Una ilustración que presenta varias escenas de cuentos de hadas y folclore, incluida una calabaza grande, un tigre, Caperucita Roja, personas con atuendos tradicionales y una pagoda roja con una montaña de fondo.

Domain

Different Lands, Similar Stories/Tierras diferentes, cuentos similares

A world tour of storytelling, and the stories that stay the same across the world.

Ilustración que muestra el antiguo Egipto con pirámides, la Esfinge, agricultores arando un campo con bueyes y ganado pastando bajo un cielo soleado.

Domain

Early World Civilizations/Antiguas civilizaciones del mundo

Rivers, farming, writing, and laws: just what does it take to build a civilization?

Escena ilustrada de la antigua Mesoamérica con maíz, un río, agricultores y pirámides al fondo. En primer plano se ve a una persona con traje tradicional.

Domain

Early American Civilizations/Antiguas civilizaciones de América

What will we find in the great temples of the Aztec, Maya, and Inca civilizations?

Ilustración de la exploración espacial: se lanza un cohete, un astronauta se para cerca de un módulo de aterrizaje, una persona usa un telescopio y aparece un planeta distante con anillos sobre un fondo estrellado.

Domain

Astronomy/Astronomía

How the Earth relates to the moon, the sun, and the rest of the planets.

Dos paleontólogos en un paisaje volcánico examinan fósiles en primer plano, mientras un volcán emite humo y lava al fondo.

Domain

The History of the Earth/La historia de la Tierra

Just what lies beneath the Earth’s surface, and what can it teach us about the past?

Una escena de vida silvestre diversa que presenta un cactus del desierto con un pájaro, un conejo, elefantes, un león, un oso polar sobre el hielo y montañas distantes bajo un cielo nublado.

Domain

Animals and Habitats/Los animales y sus hábitats

A look at the connection between how animals live and where they make their homes.

Una princesa con un vestido rosa sostiene una rana junto a un arroyo con un castillo, árboles y gente al fondo. En primer plano camina un zorro con un sombrero con una pluma roja.

Domain

Fairy Tales/Cuentos de hadas

What do fairy tales have to teach us about how stories are told?

Ilustración que muestra una escena histórica con soldados, veleros y hombres con atuendo colonial discutiendo en el interior.

Domain

A New Nation: American Independence/Una nueva nación: la independencia de los Estados Unidos

The story of the birth of the United States out of the 13 Colonies.

Los pioneros con carros cubiertos y caballos señalan hacia un valle con tipis nativos, fogatas y humo elevándose. Un oso se encuentra sobre una roca y se ven montañas al fondo.

Domain

Frontier Explorers/Exploradores de la Frontera

The story of the journey west from the newborn U.S.A. to find the Pacific Ocean.

Un hombre con un hacha se encuentra entre paisajes exagerados con un castillo, un tren con humo, un buey azul y una persona con un mono observando la escena.

Domain

Fairy Tales and Tall Tales/Cuentos de hadas y cuentos exagerados

Learn about exaggeration and characterization on the frontier.

Ilustración de un paisaje vibrante que presenta diversos monumentos culturales, incluidos templos, palacios, pirámides, una escena de elefantes, montañas distantes y fuegos artificiales en el cielo.

Domain

Early Asian Civilizations/Antiguas civilizaciones de Asia

Tour the world of classical civilization, starting with India and China.

Ilustración que muestra la antigua Grecia con un anfiteatro, estatuas, soldados con armadura, un barco y un templo en una colina rodeada de vegetación.

Domain

Ancient Greek Civilization/La civilización griega antigua

The tour continues with the philosophy and politics of Greece.

Illustration of various mythological scenes including greek gods, a flying horse, and roman architecture under a sunny sky.

Domain

Greek Myths/Mitos griegos

Dive deep into the characters and storytelling of classic myths.

Ilustración de una batalla entre barcos británicos y estadounidenses cerca de un fuerte. El barco británico está a la izquierda con soldados, mientras que el barco estadounidense está a la derecha. La gente porta una gran bandera estadounidense en primer plano.

Domain

The War of 1812/La guerra de 1812

Learn about America’s “Second War for Independence.”

Un paisaje nevado con un zorro durmiendo en una madriguera, gente corriendo y andando en bicicleta por un sendero y árboles que muestran los cambios estacionales.

Domain

Cycles in Nature/Los ciclos de la naturaleza

Introducing the natural cycles that make our lives possible.

Ilustración de carros cubiertos tirados por caballos a lo largo de un sendero en el desierto, con un coyote aullando sobre una alta formación rocosa y un tren de vapor al fondo.

Domain

Westward Expansion/La expansión hacia el oeste

Why did pioneers go west? What happened to the people who were there?

Ilustración de un jardín vibrante con flores, abejas, mariposas, una oruga en una hoja, una crisálida y un apicultor que maneja una colmena junto a un estanque.

Domain

Insects/Los insectos

Lay the grounds for animal classification by looking at solitary and social insects.

Ilustración de una escena histórica con gente escuchando el discurso de un hombre en una plataforma. Al fondo se ve un río y una procesión de personas. En primer plano hay un documento de proclamación.

Domain

The U.S. Civil War/La Guerra Civil de los Estados Unidos

Begin to grapple with U.S. history’s central crisis over slavery.

Una escena en la que aparece una persona explicando un diagrama anatómico humano, otra persona haciendo ejercicio, una cadena de ADN, campos y un microscopio de fondo.

Domain

Human Body: Building Blocks and Nutrition/El cuerpo humano: componentes básicos y nutrición

A deeper dive into the digestive system and the nutrition process.

Un grupo diverso de personas se encuentra en un muelle con vistas a un bullicioso puerto con barcos y un gran barco, un avión volando por encima y la Estatua de la Libertad al fondo.

Domain

Immigration/La inmigración

Why did people immigrate to the United States, and what did they find here?

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.

Domain

Fighting for a Cause/Luchar por una causa

How people can do extraordinary things to make the world better for everyone.

Dos ratones antropomórficos en un bote de remos, uno de ellos remando, navegan por un río tranquilo rodeado de exuberante vegetación y árboles. El ratón que rema lleva una chaqueta azul y el otro ratón parece conversar.

Unit 1

Classic Tales: The Wind in the Willows/Cuentos Clásicos: El viento en los sauces

A deep dive into character, theme, and POV in classic stories from around the world.

Ilustración de un jaguar, una garza, una rana roja, una tortuga y un pez en un paisaje vibrante con montañas y vegetación bajo un cielo soleado.

Unit 2

Animal Classification/La clasificación de los animales

How do we classify different animals by their appearance and behavior?

Ilustración de una figura humana que muestra la anatomía interna, incluidos el cerebro, los pulmones, el corazón, el sistema digestivo y una articulación de la cadera resaltada sobre un fondo degradado.

Unit 3

The Human Body: Systems and Senses/El cuerpo humano: sistemas y sentidos

Let’s take a closer look at how the skeleton, muscles, and nervous system all work.

Un ángel se arrodilla ante una mujer sentada en un sofá dorado encima de un templo en una noche estrellada. Unas escaleras conducen al templo en un paisaje montañoso.

Unit 4

The Ancient Roman Civilization/La civilización romana antigua

What is Rome’s greatest cultural contribution? In this unit, your students decide.

Ilustración de un perro saltando bajo un árbol, persiguiendo una abeja, con una mesa en primer plano sosteniendo una jarra y vasos de limonada. El sol brilla intensamente en el cielo.

Unit 5

Light and Sound/La luz y el sonido

The science behind all the ways we see and hear the world.

Un barco vikingo con una proa en forma de dragón navega en el océano bajo un cielo azul con nubes. El barco tiene una sola vela grande y varios escudos recubren sus costados.

Unit 6

The Viking Age/La era vikinga

An immersive narrative experience about what life was like in Viking communities.

Ilustración de una escena espacial con varios planetas y anillos sobre un fondo de estrellas. Dos planetas grandes dominan el primer plano y se ven planetas más pequeños al fondo.

Unit 7

Astronomy: Our Solar System and Beyond/Astronomía: nuestro sistema solar y más allá

More about our universe, including a writing project about daily life on a space station.

Una persona sentada en el borde de un acantilado con vistas a un vasto paisaje desértico con nubes arremolinadas en el cielo.

Unit 8

Native Americans: Regions and Cultures/Los nativos americanos: regiones y culturas

How did Native American nations change their way of life in different parts of the world?

Ilustración de un velero en el océano con la costa este de América del Norte visible a la izquierda.

Unit 9

Early Explorations of North America/La exploración europea de América del Norte

What was it like to sail to North America with the early European explorers?

Una pintura representa una escena del siglo XVII con colonos, un velero al fondo y un hombre conduciendo un carro tirado por caballos cargado de mercancías. Se ve a otras personas descargando y trabajando cerca.

Unit 10

Colonial America/La época colonial en los Estados Unidos

A study of the very different ways of life in the different pre-U.S. colonies.

Ilustración que muestra el ciclo de la vida: un esqueleto en el suelo, un pájaro posado en una cerca, otro pájaro en una planta y un ave rapaz más grande arriba, todos conectados por flechas circulares.

Unit 11

Ecology/Ecología

Students keep ecologist’s journals to learn about our world and how best to protect it.

Una mano alcanza una manzana verde en una rama. Cerca hay una brújula, un termómetro, un lápiz, notas musicales y un granero rojo sobre un paisaje cubierto de hierba.

Unit 1

Personal Narratives/Narrativas personales

Read stories of personal experience… and learn to reflect on your own.

Ilustración medieval que representa un grupo de figuras con armadura a la entrada de un alto castillo gris con puente levadizo, adornado con banderas y rodeado por un paisaje decorado y fondos ornamentados.

Unit 2

Empires in the Middle Ages/Los imperios en la Edad Media, parte 1 & Los imperios en la Edad Media, parte 2

Explore the medieval history of Europe and the Middle East.

Ilustración dorada de un dragón con alas sobre fondo beige, rodeado de diversos elementos decorativos como estrellas, hojas y estampados abstractos.

Unit 3

Poetry/Poesía

Study the poetry of many nations using licensed text anthologies, and begin to write your own.

Vintage styled illustrations of a microscope, an old telephone, and a clock on textured background with geometric patterns.

Unit 4

Eureka! Student Inventor/¡Eureka! Estudiante inventor

Transform the class into a lab for students to build and present inventions.

Formaciones rocosas en un paisaje desértico con capas vibrantes y arremolinadas de arenisca roja, naranja y amarilla bajo un cielo parcialmente nublado.

Unit 5

Geology/Geología

Plate tectonics, volcanoes, erosion: all the forces that shape the Earth.

Una imagen abstracta y colorida que representa varias formas geométricas de edificios sobre un fondo azul estampado.

Unit 6

Contemporary Fiction with excerpts from The House on Mango Street/Ficción Contemporánea con Fragmentos de La Casa en Mango Street

Explore The House on Mango Street… and write a book while doing it.

Cuadro que representa a un hombre y un niño tocando una gran campana en una torre, con espectadores al fondo y un cartel de "LIBERTAD" visible.

Unit 7

American Revolution/La Revolución estadounidense

Why did America seek independence? Let’s investigate the causes and effects.

Un pequeño bote de remos con tres personas navega por mares agitados mientras dos grandes barcos luchan al fondo, con humo y fuego visibles.

Unit 8

Treasure Island/La Isla del Tesoro

How dSeek the treasure of plot in this detailed study of a classic fiction adventure.

Unit 1

Personal Narratives/Narrativas personales

Through writing and sharing their writing, students begin to identify themselves as writers.

Unit 2

Early American Civilizations/Las primeras civilizaciones americanas

Students craft a codex to explain the rise and fall of the Maya, Aztec, and Inca people.

Dos jinetes medievales a caballo, uno de ellos con la espada en alto, avanzan por un terreno rocoso. El fondo presenta un paisaje brumoso bajo un tono violeta.

Unit 3

Poetry/Poesía

Students close read many forms of poetry… and learn to write them.

Collage ilustrado con un paraguas, un cuervo, un sextante náutico, estrellas, una luna creciente y una brújula sobre un fondo beige texturizado.

Unit 4

Adventures of Don Quixote/Las Aventuras de Don Quijote

Was Don Quixote right to fight the windmill? In this full-length novel study, students decide.

Unit 5

The Renaissance/El Renacimiento

Exploring the art and literature of the Renaissance through the works of its masters.

Tres hombres vestidos con ropa de época examinan una gran hoja de papel dentro de una imprenta. Un hombre parece llevar un delantal, mientras que otro señala el papel y el tercero observa de cerca.

Unit 6

The Reformation/La Reforma

How did the printing press transform the religion and society of Europe?

Patrón botánico morado y lila con hojas, plantas y formas abstractas, incluida una luna creciente y estrellas, sobre un fondo violeta oscuro.

Unit 7

William Shakespeare’s A Midsummer Night’s Dream/Sueño de Una Noche de Verano de William Shakespeare

Students enter the world of Shakespeare by reading, designing, and acting out his work.

Retrato en tonos sepia de una joven de pelo largo, con un collar de pedrería y un chal drapeado.

Unit 8

Native Americans/Los nativos americanos

How did the policies of the U.S. government impact Native American culture and lives?

Una lupa sobre documentos que contienen una pintura de paisaje de montañas, un dibujo con la etiqueta "Raptor Claw" y una nota adhesiva con la "Pista n.° 2". También se ven un sobre y una insignia exterior.

Unit 9

Chemical Matter/Química

Students use knowledge of chemistry to solve a mystery.

Print & digital 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 (Conocimientos) Teacher Guides (K–2)

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 and digital

Knowledge Image Cards (K–2)

Amplify Caminos includes Image Cards for each Knowledge Domain to bring each topic to life through vivid visuals.

Print and digital

Knowledge Flip Books (K–2)

Projectable Flip Books are provided to accompany the read-alouds in each Knowledge Domain.

Digital

Teacher Guides (3–5)

Teacher Guides for grades 3–5 units are based on content-rich topics and incorporate reading, writing, speaking, and listening skills in the context of background knowledge. There is one Teacher Guide per unit.

Print or digital

Teacher Resource Site (K–5)

The program includes a one-stop-shop website for lesson projections, digital versions of all Amplify Caminos materials, lesson planning resources, multimedia (such as eBooks), and more.

Digital

Professional Learning Site (K–5)

The Professional Learning site includes training materials, best practices, and other resources to develop program expertise. Access professional development anywhere, anytime.

Digital

Component

FORMAT

Knowledge (Conocimiento) Activity Books (K–2)

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

Print

Student Readers (3–5)

Student Readers serve as content-rich anchor texts for each unit. Units such as Poetry and Contemporary Fiction feature authentic texts originally written in Spanish.

Activity Books (3–5)

Activity Books in grades 3–5 provide daily opportunities for students to hone reading and writing skills within the context of each unit.

Print and digital

Explore more programs

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

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 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

Website Terms of Use

Description of Site Services; Acceptance of Terms of Use

Welcome to www.amplify.com (together with any successor sites and the Site Services and Company Content (each as defined below), in whole and in part, the “Site”). The Site is operated by Amplify Education, Inc. (“Company” or “we”). The services that Company makes available on or through the Site include education-related articles, information and instructional services, purchasing functionality, support chat functionality and any other features, content, services, functionality and applications offered from time to time by Company on or through the Site (collectively, “Site Services”).

BY ACCESSING OR USING THE SITE, YOU REPRESENT AND WARRANT THAT YOU ARE OF LEGAL AGE TO ENTER INTO THIS TERMS OF USE AGREEMENT (“AGREEMENT”) AND YOU AGREE TO BE BOUND BY THE TERMS AND CONDITIONS OF THIS AGREEMENT. BY PURCHASING GOODS AND SERVICES ON THE SITE, YOU ARE ACCEPTING THE PRACTICES DESCRIBED IN THIS AGREEMENT AS WELL AS ANY ADDITIONAL TERMS OF USE THAT MAY BE ASSOCIATED WITH THE PARTICULAR GOODS AND SERIVICES YOU ARE PURCHASING.

Please read this Agreement carefully. If you are an employee or other representative of a school or other organization who is accessing or using the Site on behalf of such organization, then you are agreeing to this Agreement on behalf of yourself and such organization. We may modify this Agreement at any time in our discretion, and we may provide such modifications to you by any reasonable means, including by posting the revised version of this Agreement on the Site. You can determine when this Agreement was last revised by referring to the “LAST UPDATED” legend at the top of this Agreement. Your access to or use of the Site following any changes to this Agreement will constitute your acceptance of those changes. Notwithstanding the foregoing, any changes to this Agreement shall not apply to any dispute between you and us arising prior to the date on which we posted the revised version of this Agreement incorporating such changes or otherwise notified you of such changes. If you do not agree to be bound by this Agreement, you must not access or use the Site. Your access to and use of certain parts of the Site may require you to accept additional terms and conditions, and may require you to download certain Software or Content (each as defined below).

Jurisdictional Issues

The Site is controlled and operated by Company from the United States, and is not intended to subject Company to the laws or jurisdiction of any state, country or territory other than that of the United States. Company does not represent or warrant that the Site is appropriate or available for use in any particular jurisdiction other than the United States. In choosing to access and use the Site, you do so on your own initiative and at your own risk, and you are responsible for complying with all local laws, rules and regulations. You are also subject to United States export controls and are responsible for any violations of such controls, including any United States embargoes and other federal rules and regulations restricting exports. We may limit the Site’s availability to any person, geographic area or jurisdiction we choose, at any time and in our discretion. Not all products or services described on the Site are available in all states or territories.

Company content

The Site contains information, text, files, images, video, sounds, musical works, computer code, works of authorship, applications, and other materials and content (collectively, “Content”) of Company or its licensors (“Company Content”). The Site (including the Company Content) is protected by copyright, trademark, trade secret and other laws, and as between you and Company, Company owns and retains all rights in the Site. Company hereby grants to you a limited, revocable, non-sublicensable license, during the term of the Agreement, to access, display and perform the Company Content (excluding any computer code) solely for your personal, non-commercial use and solely as necessary to access and use the Site. Except as expressly permitted by Company in this Agreement or on the Site, you may not copy, download, stream, capture, reproduce, duplicate, archive, upload, modify, translate, create derivative works based upon, publish, broadcast, transmit, retransmit, distribute, perform, display, sell or otherwise use or transfer any Content. You may not, either directly or through the use of any device, software, online resource or other means, remove, alter, bypass, avoid, interfere with or circumvent any copyright, trademark or other proprietary notice on the Content or any digital rights management mechanism, device, or other content protection or access control measure associated with the Content.

User content

You may not access or use the Site for any commercial purpose. You are responsible for all Content that you post, upload, transmit, e-mail or otherwise make available on, through or in connection with the Site (collectively, “User Content”). Please choose carefully the Content that you make available on, through or in connection with the Site. Company does not control any Content other than Company Content, and as such you may be exposed to offensive, indecent, inaccurate or otherwise objectionable Content by accessing or using the Site. Company is not responsible or liable for any Content or the conduct of any Site user. If you become aware of any misuse of the Site, please report such misuse immediately to Company at general@amplify.com. Company reserves the right (but has no obligation) to monitor the Site, including for inappropriate Content or conduct, and to remove any Content in Company’s discretion and without liability to you or any third party.

Your proprietary rights

You retain any ownership rights that you have in your User Content. You hereby grant to Company and its affiliates, licensees and authorized users, a perpetual, non-exclusive, fully paid-up and royalty-free, sublicensable (through multiple tiers), transferable (in whole or in part), worldwide license to use, modify, excerpt, adapt, create derivative works and compilations based upon, publicly perform, publicly display, reproduce and distribute such User Content on, through or in connection with the Site and/or any other commercial or non-commercial endeavor of Company or any of its affiliates, including in connection with any distribution or syndication thereof to Third Party Services (as defined below), on and through all media formats now known or hereafter devised, for any and all purposes including promotional, marketing, trade and commercial purposes. The exercise of such rights shall not require any further permission or notice, payment or attribution to you or any third party. Company reserves the right to limit the storage capacity made available for User Content.

You represent and warrant that: (a) you own the User Content made available by you, or otherwise have the right to grant the license set forth in this Section, and (b) the posting of such User Content through or in connection with the Site does not violate the privacy rights, publicity rights, copyrights, contract rights or any other rights of any person or entity. You agree to pay for all royalties, fees and any other monies owing to any person or entity by reason of the use of such User Content.

Use of the site

You agree not to:

  • Post, upload or otherwise transmit or link to Content that is: unlawful; threatening; harmful; abusive; pornographic or includes nudity; offensive; harassing; excessively violent; tortious; defamatory; false or misleading; obscene; vulgar; libelous; hateful; or discriminatory.
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  • Use technology or any automated system, such as scripts or bots, to collect user names, passwords, e-mail addresses or any other data from or through the Site, or to circumvent or modify any security technology or software that is part of the Site.
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  • Solicit, collect or request any information for commercial or unlawful purposes.
  • Post, upload or otherwise transmit an image or video of another person without that person’s consent.
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  • Frame or mirror the Site without Company’s express prior written consent.
  • Use the Site in a manner inconsistent with any applicable law, rule or regulation.
  • Use any robot, spider, site search/retrieval application or other manual or automatic device to retrieve, index, “scrape,” “data mine,” or in any way gather content of the Site or reproduce or circumvent the navigational structure or presentation of the Site without Company’s express prior written consent. Notwithstanding the foregoing, Company grants to the operators of public search engines the permission to use spiders to copy material from the Site for the sole purpose of, and solely to the extent necessary for, creating publicly-available searchable indices of such material, but not caches or archives of such material. Company reserves the right to revoke these exceptions either generally or in specific cases.
  • Attempt, facilitate or encourage others to do any of the foregoing.

Company reserves the right to investigate and take appropriate legal action against anyone who, in Company’s discretion, violates this Agreement or attempts to do so, including terminating or suspending a user’s Account or access to or use of the Site, or reporting any User Content or conduct to law enforcement authorities.

You (and not Company) are responsible for obtaining and maintaining all telecommunications, broadband and computer hardware, equipment and services needed to access and use the Site, and for paying all charges related thereto.

User disputes

You are solely responsible for your interactions with other users of the Site, providers of Third Party Services (as defined below) or any other third parties with whom you interact on, through or in connection with the Site.

Purchases

Company may make available products and services for purchase through the Site, and may use third-party suppliers and service providers to enable e-commerce functionality on the Site. You may only purchase products and services that appear on the Site and that are delivered to an address located in the United States. You may only purchase products and services for personal, non-commercial use by you, your educational institution or students of your educational institution. We may limit quantities or refuse any order for any reason or no reason, including if we have reasonable cause to believe an order is for onward sale or resale other than through distribution channels approved by us. We make no promise that products or services available on the Site are appropriate or available for use in locations outside the United States, and purchasing products or services for delivery to or use in territories where their contents are unlawful is prohibited. If you choose to purchase products or services from locations outside the United States, you do so at your own risk. It is your responsibility to ascertain and obey all applicable local, state, federal and international laws (including minimum age requirements) in regard to the possession, use and sale of any product or service made available through the Site.

If you wish to purchase any product or service made available through the Site, you may be asked to supply certain information relevant to your transaction, including your credit card number, the expiration date of your credit card, your billing address and your shipping information. YOU REPRESENT AND WARRANT THAT YOU HAVE THE LEGAL RIGHT TO USE ANY CREDIT CARD(S) USED IN CONNECTION WITH ANY TRANSACTION. By submitting such information, you grant to Company the right to provide such information to third parties for purposes of facilitating the completion of transactions initiated by you or on your behalf. Verification of information may be required prior to the acknowledgement or completion of any transaction. While it is our practice to confirm orders by e-mail, the receipt of an e-mail order confirmation does not constitute our acceptance of an order or our confirmation of an offer to sell a product or service.

Details of the products and services available for purchase are set forth on the Site. All prices are displayed exclusive of all taxes and shipping/freight charges. Available payment methods, methods of shipping and shipping charges (including charges for expedited shipping, if available) are detailed on the Site. Company may also collect and remit sales tax on your purchase as required by United States law. If you are a tax-exempt entity, please enter the appropriate information where requested on your order form and we will not collect sales tax on your purchase.

Generally, credit and debit cards are not charged until we either ship the product(s) or confirm store availability (at which time you will be charged only for the products we have actually shipped along with any applicable taxes and shipping charges). However, we may pre-authorize your order amount with your credit or debit card issuer at the time you place the order, which may have an effect on your available credit line. When paying for a preorder with a debit card, you will be charged at the time you place your preorder. Please contact your credit or debit card issuer for more information. If you ordered a special delivery product, you will be charged once a delivery time is confirmed. For digitally delivered orders, your credit or debit card will be charged at the time that you initiate the download of the product.

All purchases made through the Site are made pursuant to a shipment contract. As a result, risk of loss and title for products purchased through the Site pass to you upon delivery of the products to the carrier. You are responsible for filing any claims with carriers for damaged and/or lost shipments. Please note that all shipping addresses must be compliant with the shipping restrictions contained on the Site.

Products, services and specifications

All products and services described or depicted on the Site, and all related features, content, specifications and prices, are subject to change at any time without notice. Certain weights, measures and similar descriptions are approximate and are provided for convenience purposes only. Packaging may vary from that shown. We make reasonable efforts to accurately display the attributes of our products, including the applicable colors; however, the actual color you see will depend on your computer system, and we cannot guarantee that your computer will accurately display such colors. The inclusion of any product or service on the Site at a particular time does not imply or warrant that such product or service will be available at any time. Occasionally, the manufacture or distribution of a certain product or service may be delayed for a number of reasons. In such event, we will make reasonable efforts to notify you of the delay and keep you informed of the revised delivery schedule. By placing an order, you represent that the products and services ordered will be used only in a lawful manner. All DVDs and similar products are sold for private, non-commercial home use (where no admission fee is charged), non-public performance, or classroom or instructional use only, and may not be duplicated.

Return and exchange policy

Unless otherwise specified in the terms associated with a particular product, you may return or exchange any product purchased through the Site within fourteen (14) days of receipt, by calling our customer service hotline, 1–800–823–1969, in the event that the purchased product is defective or you received the wrong product. Except for the foregoing, you may not return, cancel or exchange any product or service. Certain jurisdictions may provide additional statutory rights. Nothing herein is meant to limit your return or cancellation rights under local law. In the event that a return or exchange is due to an incorrect order or faulty product, we will be responsible for the shipping costs associated with such return. We will ship a replacement product upon receiving your defective or incorrect product and verifying the reason for the return or exchange.

Accuracy of information

We attempt to ensure that information on the Site is complete, accurate and current. Despite our efforts, the information on the Site may occasionally be inaccurate, incomplete or out of date. We make no representation as to the completeness, accuracy or currency of any information on the Site. For example, products or services included on the Site may be unavailable, may have different attributes than those listed, or may carry a different price than that stated on the Site. If an item’s correct price is higher than our stated price, we will, at our discretion, either contact you for instructions before shipping or cancel your order and notify you of such cancellation. Items in your “Shopping Bag” reflect the current price displayed on the item’s product detail page. Please note that this price may differ from the price displayed when the item was first placed in your Shopping Bag. In addition, we may make changes in information about price and availability without notice.

Chemicals, agricultural materials, and other hazardous materials

Certain products made available through the Site may include chemicals, agricultural materials or other material that may be subject to regulations or restrictions with respect to import or export, or to whom we may sell such material or where or how such material may be used. It is your responsibility to read and abide by all warning notices that accompany any products that you purchase. In addition, we reserve the right to request additional information from you, verify your identity, limit sales to certified educational or research institutions, or cancel or delay your order if required by law or if we believe it is necessary or advisable. Due to special shipping and handling requirements, freight companies routinely impose a surcharge on each package of hazardous material shipped. In such event, we will add such surcharge to your order.

Registration and account security

You may have the ability to create an account on or through the Site (an “Account”). If you submit registration information to create an Account, you represent and warrant that all information submitted to Company in connection with such registration is complete and accurate, and that you will update such information if it changes. If you create an Account, you are responsible for all use of your Account, and for maintaining the confidentiality of the information used to access your Account (including user name and password). You agree not to share your user name or password with anyone, or use anyone else’s Account at any time. You agree to notify Company immediately if you suspect any unauthorized use of, or access to, your Account (including your user name and password). You acknowledge that the reuse of your password in connection with accounts on other websites increases the risk that the security of your Account may be compromised.

The Site may make available, or third parties may provide, links to other websites, applications, resources, advertisements, Content or other products or services created, hosted or made available by third parties (“Third Party Services”), and such third party may use other third parties to provide portions of the Third Party Service to you, such as technology, development or payment services. When you access or use a Third Party Service, you are interacting with the applicable third party, not with Company, and you do so at your own risk. Company is not responsible for and makes no warranties, express or implied, as to the Third Party Services or the providers of such Third Party Services (including the accuracy or completeness of the information provided by such Third Party Service or the privacy practices of any third party). Inclusion of any Third Party Service or a link thereto on the Site does not imply approval or endorsement of such Third Party Service. Company is not responsible or liable for the content or practices of any Third Party Service or third party, even if such Third Party Service links to or is linked by the Site, and even if such Third Party Service is operated by an affiliate of Company or a company otherwise connected with us or the Site

Feedback

Unless we expressly agree otherwise in writing, if you provide us with any ideas, proposals, suggestions or materials (“Feedback”), whether related to the Site or otherwise, you hereby acknowledge and agree that (a) your provision of any Input is gratuitous, unsolicited and without restriction and does not place Company under any fiduciary or other obligation; and (b) any Feedback is not confidential and Company has no confidentiality obligations with respect to such Feedback.. You hereby grant to us a world-wide, royalty-free, fully paid-up, exclusive, perpetual, irrevocable, transferable and fully sublicensable (through multiple tiers) license, without additional consideration to you or any third party, to reproduce, distribute, perform and display (publicly or otherwise), adapt, modify and otherwise use and exploit such Feedback, in any format or media now known or hereafter developed, and you hereby represent and warrant that you have all necessary rights to grant the foregoing license. We may use Feedback for any purpose whatsoever without permission or notice, compensation or attribution to you or any third party. You are and remain responsible and liable for the content of any Feedback.

Privacy

Please review the Privacy Policy for the Site, available at http://www.amplify.com/privacy, to learn about our information collection, usage and disclosures practices with respect to information collected by us through the Site. Please note that certain products or services made available by us, other than the Site, may be subject to different privacy policies. In addition, the Site’s Privacy Policy does not address, and we are not responsible or liable for, the information collection, usage and disclosures practices of any third party or Third Party Service.

Disclaimers

THE SITE, USER CONTENT, THIRD PARTY SERVICES, AND ALL PRODUCTS AND SERVICES SOLD THROUGH THE SITE (COLLECTIVELY, THE “SITE PRODUCTS”) ARE MADE AVAILABLE “AS-IS” AND “AS AVAILABLE” AND COMPANY DOES NOT GUARANTEE OR PROMISE ANY SPECIFIC RESULTS FROM USE OF THE SITE PRODUCTS. COMPANY AND ITS AFFILIATES EXPRESSLY DISCLAIM ANY WARRANTIES AND CONDITIONS OF ANY KIND, WHETHER EXPRESS OR IMPLIED, INCLUDING THE IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN PARTICULAR, COMPANY AND ITS AFFILIATES MAKE NO WARRANTY THAT THE SITE OR USER CONTENT OR THIRD PARTY SERVICES, OR YOUR ACCESS TO OR USE THEREOF, WILL BE UNINTERRUPTED, TIMELY, SECURE, ERROR-FREE, ACCURATE OR RELIABLE. UNDER NO CIRCUMSTANCES SHALL WE BE LIABLE FOR ANY CONSEQUENCES OF ANY UNAUTHORIZED USE OF THE SITE PRODUCTS THAT VIOLATES ANY APPLICABLE LAW OR REGULATION. CERTAIN STATE LAWS DO NOT ALLOW LIMITATIONS ON IMPLIED WARRANTIES OR THE EXCLUSION OR LIMITATION OF CERTAIN DAMAGES. IF THESE LAWS APPLY TO YOU, SOME OR ALL OF THE ABOVE DISCLAIMERS, EXCLUSIONS, OR LIMITATIONS MAY NOT APPLY TO YOU, AND YOU MIGHT HAVE ADDITIONAL RIGHTS.

Under no circumstances will Company or its affiliates be responsible for any loss or damage, including property damage, personal injury or death, resulting from use of the Site, Products, problems or technical malfunction in connection with use of the Site, Products, attendance at any Company event or the conduct of any Site users, whether online or offline. Your use of the Site, Products is solely your responsibility and at your own risk. The User Content and Third Party Services do not necessarily reflect the opinions or policies of Company or its affiliates.

Limitations on liability

IN NO EVENT WILL COMPANY OR ITS AFFILIATES BE LIABLE TO YOU OR ANY THIRD PARTY FOR ANY INDIRECT, CONSEQUENTIAL, EXEMPLARY, INCIDENTAL, SPECIAL OR PUNITIVE DAMAGES, INCLUDING LOST PROFIT DAMAGES, ARISING FROM YOUR USE OF THE SITE PRODUCTS, EVEN IF COMPANY OR ONE OF ITS AFFILIATES HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. NOTWITHSTANDING ANYTHING TO THE CONTRARY CONTAINED HEREIN, THE TOTAL LIABILITY OF COMPANY AND ITS AFFILIATES TO YOU FOR ANY CAUSE WHATSOEVER AND REGARDLESS OF THE FORM OF THE ACTION, WILL AT ALL TIMES BE LIMITED TO THE AMOUNT PAID, IF ANY, BY YOU TO COMPANY FOR THE SITE PRODUCTS.

Indemnity

You agree to indemnify and hold harmless Company, its affiliates, subcontractors and other partners, and each of their respective officers, agents, partners and employees, from any losses, costs, expenses (including reasonable attorneys’ fees), liabilities, claims or demands, due to or arising out of your use of the Site, your breach or alleged breach of this Agreement, your violation or alleged violation of any rights of another, or any Content that you post or otherwise submit on, through or in connection with the Site.

Termination

This Agreement remains in full force and effect while you access or use the Site. If you create an Account, you may terminate your Account at any time, for any reason, by contacting us at general@amplify.com. Company may terminate or suspend your Account and/or your access to or use of the Site at any time, for any or no reason, with or without prior notice or explanation, and without liability. Upon any such suspension or termination, your right to access and use the Site will immediately cease, and Company may immediately deactivate or delete your Account and all files and other information associated with it, and/or bar any further access to such files and other information. Company shall not be liable to you or any third party for any suspension or termination of your Account or of access to or use of the Site or any such files or other information, and shall not be required to make such files and other information available to you after any such suspension or termination. Sections 2, 5, 13, 17, 18, 19, 22, and 26 shall survive any expiration or termination of this Agreement.

U.S. export controls

All software made available in connection with the Site (“Software”) may be subject to United States export controls. No Software may be downloaded from or through the Site or otherwise exported or re-exported in violation of U.S. export laws.

Governing law

The terms of this Agreement are governed by the laws of the State of New York, U.S.A., without regard to its conflicts of law provisions, and regardless of your location.

Arbitration

EXCEPT FOR DISPUTES THAT QUALIFY FOR SMALL CLAIMS COURT, ALL DISPUTES ARISING OUT OF OR RELATED TO THIS AGREEMENT, WHETHER BASED IN CONTRACT, TORT, STATUTE, FRAUD, MISREPRESENTATION OR ANY OTHER LEGAL THEORY, WILL BE RESOLVED THROUGH FINAL AND BINDING ARBITRATION BEFORE A NEUTRAL ARBITRATOR INSTEAD OF IN A COURT BY A JUDGE OR JURY, AND YOU AGREE THAT COMPANY AND YOU ARE EACH WAIVING THE RIGHT TO TRIAL BY A JURY. YOU AGREE THAT ANY ARBITRATION UNDER THIS AGREEMENT WILL TAKE PLACE ON AN INDIVIDUAL BASIS; CLASS ARBITRATIONS AND CLASS ACTIONS ARE NOT PERMITTED AND YOU ARE AGREEING TO GIVE UP THE ABILITY TO PARTICIPATE IN A CLASS ACTION.

Arbitration procedure

Any arbitration under Section 23 above will be administered by the American Arbitration Association under its Commercial Arbitration Rules and Supplementary Procedures for Consumer-Related Disputes (“Supplementary Procedures”), as amended by this Agreement. The Supplementary Procedures are available online at http://www.adr.org/aaa/ShowPDF?doc=ADRSTG_015820. The arbitrator will conduct hearings, if any, by teleconference or videoconference, rather than by personal appearances, unless the arbitrator determines upon request by you or by us that an in-person hearing is appropriate. Any in-person appearances will be held at a location which is reasonably convenient to both parties with due consideration of their ability to travel and other pertinent circumstances. If the parties are unable to agree on a location, such determination should be made by the AAA or by the arbitrator. The arbitrator’s decision will follow the terms of this Agreement and will be final and binding. The arbitrator will have authority to award temporary, interim or permanent injunctive relief or relief providing for specific performance of this Agreement, but only to the extent necessary to provide relief warranted by the individual claim before the arbitrator. The award rendered by the arbitrator may be confirmed and enforced in any court having jurisdiction thereof. Notwithstanding any of the foregoing, nothing in this Agreement will preclude you from bringing issues to the attention of federal, state, or local agencies, and, if the law allows, they can seek relief against us for you.

Employment opportunities

Company may, from time to time, post Company employment opportunities on the Site and/or invite users to submit resumes to Company. If you choose to submit your name, contact information, resume and/or other personal information to Company in response to such employment listings, you are authorizing Company to use this information for all lawful and legitimate hiring, employment and other business purposes. Company also reserves the right, at its discretion, to forward such information to Company’s affiliates for their legitimate business purposes. Nothing in this Agreement or contained on the Site will constitute a promise by Company to review any such information, or to contact, interview, hire or employ any individual who submits such information.

The Digital Millennium Copyright Act of 1998 (“DMCA”) provides recourse for copyright owners who believe that material appearing on the Internet infringes their rights under U.S. copyright law. If you believe that any material residing on or linked to from the Site infringes your copyright, please send (or have your agent send) to Company’s Copyright Agent a notification of claimed infringement with all of the following information: (a) identification of the copyrighted work claimed to have been infringed, or, if multiple copyrighted works are covered by a single notification, a representative list of such works; (b) identification of the claimed infringing material and information reasonably sufficient to permit us to locate the material on the Site (such as the URL(s) of the claimed infringing material); (c) information reasonably sufficient to permit us to contact you, such as an address, telephone number, and, if available, an e-mail address; (d) a statement by you that you have a good-faith belief that the disputed use is not authorized by the copyright owner, the copyright owner’s agent or the law; (e) a statement by you that the above information in your notification is accurate and a statement by you, made under penalty of perjury, that you are the owner of an exclusive right that is allegedly infringed or are authorized to act on such owner’s behalf; and (f) your physical or electronic signature. Company’s Copyright Agent for notification of claimed infringement can be reached as follows: Copyright Agent, Amplify Education, Inc., 55 Washington Street, Brooklyn, NY 11201; Facsimile: 212-796-2311; Attn: Legal. Company’s Copyright Agent for notification of claimed infringement can also be reached electronically at: legal@amplify.com. Company reserves the right to terminate infringers’ and suspected infringers’ Accounts or their access to or use of the Site.

Notice for California residents

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Other terms

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Please contact us at legal@amplify.com with any questions regarding this Agreement.

What’s included in our Spanish language arts curriculum

Amplify Core Knowledge Language Arts® (CKLA) is available in both English and Spanish. Amplify Caminos al Conocimiento Esencial, our robust Spanish language arts companion for grades K–5, supports multiple teaching models, including dual language immersion and transitional classrooms.

A laptop screen displays a kindergarten instructional webpage in Spanish, showing lesson categories with illustrated thumbnails and navigation options.

Year at a glance

The program’s intentional Knowledge Sequence from K–5 connects knowledge and vocabulary within a grade level and across grade levels, for deeper reading comprehension and preparation for college, career, and life. Instead of “activating prior knowledge,” Amplify Caminos helps you build it in the classroom from day one, for every child, expanding each student’s knowledge base long before they transition to reading to learn.

Curriculum flowchart showing reading themes and activities from Kindergarten to Grade 5, organized by grade level and literary theme, with interconnected boxes for each topic.

Units & domains at a glance

Each Knowledge Domain in grades K–2 and Unit in grades 3–5 varies in the number of days based on instructional purpose. Just as with our top-rated Amplify CKLA program, the Amplify Caminos materials engage and delight young learners with resources that are both appealing and original.

Una mujer rubia con un vestido azul cuida ovejas blancas y negras, sosteniendo un bastón de pastor. Un cerdo vestido de azul corre y un hombre de negro toca el violín en una valla. Al fondo hay una casa.

Domain

Nursery Rhymes and Fables/Rimas y fábulas infantiles

Start learning about literature with these classic Mother Goose rhymes.

Ilustración de tres personas en un paisaje cubierto de hierba, una tratando de atrapar mariposas con una red, otra escondiéndose detrás de una escultura alta y frondosa de una mano y otra con binoculares.

Domain

The Five Senses/Los cinco sentidos

Learning about the body starts with learning about how we experience the world.

Una ilustración que representa a un gran lobo con sombrero de copa liderando un desfile de animales y personas con instrumentos musicales a través de un paisaje montañoso.

Domain

Stories/Cuentos

Learn about the parts of a book and some of the stories that go in one.

Una ilustración vibrante de una escena rural con colinas, una granja, una mariposa, un sol brillante, varias verduras como tomates y lechugas, y un gusano en el suelo.

Domain

Plants/Plantas

Discover the lifecycle of plants and the history of George Washington Carver.

Ilustración de una escena de granja que muestra un camión rojo que transporta verduras, campos de cultivo, vacas pastando en una colina, un granero y un molino de viento contra un cielo azul.

Domain

Farms/Granjas

Now we know how plants make their food… but what about animals?

Ilustración de un nativo remando en una canoa en un río con búfalos pastando en un campo, tipis al fondo y pájaros volando en el cielo bajo un sol brillante.

Domain

Native Americans/Los nativos americanos

Who were the first people in America? A look at the Lenape, Wampanoag, and Lakota Sioux.

Una ilustración muestra un rey y una reina en tronos, un castillo en un acantilado y una mujer con enanos cerca de un árbol. Cortinas rojas enmarcan la escena.

Domain

Kings and Queens/Reyes y reinas

To understand fairy tales, it’s best to first understand royalty.

Ilustración que muestra las cuatro estaciones: primavera con flores, verano con árboles verdes, otoño con hojas que caen e invierno con nieve y gente en trineo. Un niño lee debajo de un árbol.

Domain

Seasons and Weather/Las estaciones y el tiempo

The study of natural cycles continues with the weather and why it happens.

Un velero de madera con símbolos de cruz roja en sus velas navega cerca de una isla tropical con exuberante vegetación y palmeras. A lo lejos se ven otros dos barcos en el agua.

Domain

Columbus and the Pilgrims/Colón y los peregrinos

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

Una escena histórica muestra gente afuera de una gran mansión de estilo colonial con dos chimeneas. En primer plano se ve un carruaje tirado por caballos y a la izquierda se ve una casa más pequeña.

Domain

Colonial Towns and Townspeople/Las colonias y sus habitantes

Before the War for Independence, how did the town and country depend on one another?

Ilustración de personas clasificando materiales reciclables en un parque cerca de un río contaminado. Las fábricas emiten humo al fondo, mientras que las mariposas, las flores y los árboles están presentes en el primer plano.

Domain

Taking Care of the Earth/Cuidar el planeta Tierra

We only have one Earth—here are some ways to help care for it.

Ilustración del Monte Rushmore con los rostros tallados de cuatro presidentes de Estados Unidos. Un águila vuela en primer plano.

Domain

Presidents and American Symbols/Presidentes y símbolos de los Estados Unidos

Start learning about government through the lives of five presidents.

Una ilustración caprichosa que muestra animales de granja alrededor de una casa en un árbol junto a un río. Un zorro, un conejo y una oveja interactúan mientras la gente acampa junto a una fogata al fondo. Una araña cuelga del árbol.

Domain

Fables and Stories/Fábulas y cuentos

Learn some of the key elements of a story through classic fables.

Ilustración que presenta anatomía humana, actividades de estilo de vida saludable, profesionales médicos, símbolos dietéticos, una ambulancia y microorganismos, destacando la conexión entre salud, nutrición y ejercicio.

Domain

The Human Body/El cuerpo humano

What are germs? What are the organs? And what does it all have to do with health?

Una ilustración que presenta varias escenas de cuentos de hadas y folclore, incluida una calabaza grande, un tigre, Caperucita Roja, personas con atuendos tradicionales y una pagoda roja con una montaña de fondo.

Domain

Different Lands, Similar Stories/Tierras diferentes, cuentos similares

A world tour of storytelling, and the stories that stay the same across the world.

Ilustración que muestra el antiguo Egipto con pirámides, la Esfinge, agricultores arando un campo con bueyes y ganado pastando bajo un cielo soleado.

Domain

Early World Civilizations/Antiguas civilizaciones del mundo

Rivers, farming, writing, and laws: just what does it take to build a civilization?

Escena ilustrada de la antigua Mesoamérica con maíz, un río, agricultores y pirámides al fondo. En primer plano se ve a una persona con traje tradicional.

Domain

Early American Civilizations/Antiguas civilizaciones de América

What will we find in the great temples of the Aztec, Maya, and Inca civilizations?

Ilustración de la exploración espacial: se lanza un cohete, un astronauta se para cerca de un módulo de aterrizaje, una persona usa un telescopio y aparece un planeta distante con anillos sobre un fondo estrellado.

Domain

Astronomy/Astronomía

How the Earth relates to the moon, the sun, and the rest of the planets.

Dos paleontólogos en un paisaje volcánico examinan fósiles en primer plano, mientras un volcán emite humo y lava al fondo.

Domain

The History of the Earth/La historia de la Tierra

Just what lies beneath the Earth’s surface, and what can it teach us about the past?

Una escena de vida silvestre diversa que presenta un cactus del desierto con un pájaro, un conejo, elefantes, un león, un oso polar sobre el hielo y montañas distantes bajo un cielo nublado.

Domain

Animals and Habitats/Los animales y sus hábitats

A look at the connection between how animals live and where they make their homes.

Una princesa con un vestido rosa sostiene una rana junto a un arroyo con un castillo, árboles y gente al fondo. En primer plano camina un zorro con un sombrero con una pluma roja.

Domain

Fairy Tales/Cuentos de hadas

What do fairy tales have to teach us about how stories are told?

Ilustración que muestra una escena histórica con soldados, veleros y hombres con atuendo colonial discutiendo en el interior.

Domain

A New Nation: American Independence/Una nueva nación: la independencia de los Estados Unidos

The story of the birth of the United States out of the 13 Colonies.

Los pioneros con carros cubiertos y caballos señalan hacia un valle con tipis nativos, fogatas y humo elevándose. Un oso se encuentra sobre una roca y se ven montañas al fondo.

Domain

Frontier Explorers/Exploradores de la Frontera

The story of the journey west from the newborn U.S.A. to find the Pacific Ocean.

Un hombre con un hacha se encuentra entre paisajes exagerados con un castillo, un tren con humo, un buey azul y una persona con un mono observando la escena.

Domain

Fairy Tales and Tall Tales/Cuentos de hadas y cuentos exagerados

Learn about exaggeration and characterization on the frontier.

Ilustración de un paisaje vibrante que presenta diversos monumentos culturales, incluidos templos, palacios, pirámides, una escena de elefantes, montañas distantes y fuegos artificiales en el cielo.

Domain

Early Asian Civilizations/Antiguas civilizaciones de Asia

Tour the world of classical civilization, starting with India and China.

Ilustración que muestra la antigua Grecia con un anfiteatro, estatuas, soldados con armadura, un barco y un templo en una colina rodeada de vegetación.

Domain

Ancient Greek Civilization/La civilización griega antigua

The tour continues with the philosophy and politics of Greece.

Illustration of various mythological scenes including greek gods, a flying horse, and roman architecture under a sunny sky.

Domain

Greek Myths/Mitos griegos

Dive deep into the characters and storytelling of classic myths.

Ilustración de una batalla entre barcos británicos y estadounidenses cerca de un fuerte. El barco británico está a la izquierda con soldados, mientras que el barco estadounidense está a la derecha. La gente porta una gran bandera estadounidense en primer plano.

Domain

The War of 1812/La guerra de 1812

Learn about America’s “Second War for Independence.”

Un paisaje nevado con un zorro durmiendo en una madriguera, gente corriendo y andando en bicicleta por un sendero y árboles que muestran los cambios estacionales.

Domain

Cycles in Nature/Los ciclos de la naturaleza

Introducing the natural cycles that make our lives possible.

Ilustración de carros cubiertos tirados por caballos a lo largo de un sendero en el desierto, con un coyote aullando sobre una alta formación rocosa y un tren de vapor al fondo.

Domain

Westward Expansion/La expansión hacia el oeste

Why did pioneers go west? What happened to the people who were there?

Ilustración de un jardín vibrante con flores, abejas, mariposas, una oruga en una hoja, una crisálida y un apicultor que maneja una colmena junto a un estanque.

Domain

Insects/Los insectos

Lay the grounds for animal classification by looking at solitary and social insects.

Ilustración de una escena histórica con gente escuchando el discurso de un hombre en una plataforma. Al fondo se ve un río y una procesión de personas. En primer plano hay un documento de proclamación.

Domain

The U.S. Civil War/La Guerra Civil de los Estados Unidos

Begin to grapple with U.S. history’s central crisis over slavery.

Una escena en la que aparece una persona explicando un diagrama anatómico humano, otra persona haciendo ejercicio, una cadena de ADN, campos y un microscopio de fondo.

Domain

Human Body: Building Blocks and Nutrition/El cuerpo humano: componentes básicos y nutrición

A deeper dive into the digestive system and the nutrition process.

Un grupo diverso de personas se encuentra en un muelle con vistas a un bullicioso puerto con barcos y un gran barco, un avión volando por encima y la Estatua de la Libertad al fondo.

Domain

Immigration/La inmigración

Why did people immigrate to the United States, and what did they find here?

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.

Domain

Fighting for a Cause/Luchar por una causa

How people can do extraordinary things to make the world better for everyone.

Dos ratones antropomórficos en un bote de remos, uno de ellos remando, navegan por un río tranquilo rodeado de exuberante vegetación y árboles. El ratón que rema lleva una chaqueta azul y el otro ratón parece conversar.

Unit 1

Classic Tales: The Wind in the Willows/Cuentos Clásicos: El viento en los sauces

A deep dive into character, theme, and POV in classic stories from around the world.

Ilustración de un jaguar, una garza, una rana roja, una tortuga y un pez en un paisaje vibrante con montañas y vegetación bajo un cielo soleado.

Unit 2

Animal Classification/La clasificación de los animales

How do we classify different animals by their appearance and behavior?

Ilustración de una figura humana que muestra la anatomía interna, incluidos el cerebro, los pulmones, el corazón, el sistema digestivo y una articulación de la cadera resaltada sobre un fondo degradado.

Unit 3

The Human Body: Systems and Senses/El cuerpo humano: sistemas y sentidos

Let’s take a closer look at how the skeleton, muscles, and nervous system all work.

Un ángel se arrodilla ante una mujer sentada en un sofá dorado encima de un templo en una noche estrellada. Unas escaleras conducen al templo en un paisaje montañoso.

Unit 4

The Ancient Roman Civilization/La civilización romana antigua

What is Rome’s greatest cultural contribution? In this unit, your students decide.

Ilustración de un perro saltando bajo un árbol, persiguiendo una abeja, con una mesa en primer plano sosteniendo una jarra y vasos de limonada. El sol brilla intensamente en el cielo.

Unit 5

Light and Sound/La luz y el sonido

The science behind all the ways we see and hear the world.

Un barco vikingo con una proa en forma de dragón navega en el océano bajo un cielo azul con nubes. El barco tiene una sola vela grande y varios escudos recubren sus costados.

Unit 6

The Viking Age/La era vikinga

An immersive narrative experience about what life was like in Viking communities.

Ilustración de una escena espacial con varios planetas y anillos sobre un fondo de estrellas. Dos planetas grandes dominan el primer plano y se ven planetas más pequeños al fondo.

Unit 7

Astronomy: Our Solar System and Beyond/Astronomía: nuestro sistema solar y más allá

More about our universe, including a writing project about daily life on a space station.

Una persona sentada en el borde de un acantilado con vistas a un vasto paisaje desértico con nubes arremolinadas en el cielo.

Unit 8

Native Americans: Regions and Cultures/Los nativos americanos: regiones y culturas

How did Native American nations change their way of life in different parts of the world?

Ilustración de un velero en el océano con la costa este de América del Norte visible a la izquierda.

Unit 9

Early Explorations of North America/La exploración europea de América del Norte

What was it like to sail to North America with the early European explorers?

Una pintura representa una escena del siglo XVII con colonos, un velero al fondo y un hombre conduciendo un carro tirado por caballos cargado de mercancías. Se ve a otras personas descargando y trabajando cerca.

Unit 10

Colonial America/La época colonial en los Estados Unidos

A study of the very different ways of life in the different pre-U.S. colonies.

Ilustración que muestra el ciclo de la vida: un esqueleto en el suelo, un pájaro posado en una cerca, otro pájaro en una planta y un ave rapaz más grande arriba, todos conectados por flechas circulares.

Unit 11

Ecology/Ecología

Students keep ecologist’s journals to learn about our world and how best to protect it.

Una mano alcanza una manzana verde en una rama. Cerca hay una brújula, un termómetro, un lápiz, notas musicales y un granero rojo sobre un paisaje cubierto de hierba.

Unit 1

Personal Narratives/Narrativas personales

Read stories of personal experience… and learn to reflect on your own.

Ilustración medieval que representa un grupo de figuras con armadura a la entrada de un alto castillo gris con puente levadizo, adornado con banderas y rodeado por un paisaje decorado y fondos ornamentados.

Unit 2

Empires in the Middle Ages/Los imperios en la Edad Media, parte 1 & Los imperios en la Edad Media, parte 2

Explore the medieval history of Europe and the Middle East.

Ilustración dorada de un dragón con alas sobre fondo beige, rodeado de diversos elementos decorativos como estrellas, hojas y estampados abstractos.

Unit 3

Poetry/Poesía

Study the poetry of many nations using licensed text anthologies, and begin to write your own.

Vintage styled illustrations of a microscope, an old telephone, and a clock on textured background with geometric patterns.

Unit 4

Eureka! Student Inventor/¡Eureka! Estudiante inventor

Transform the class into a lab for students to build and present inventions.

Formaciones rocosas en un paisaje desértico con capas vibrantes y arremolinadas de arenisca roja, naranja y amarilla bajo un cielo parcialmente nublado.

Unit 5

Geology/Geología

Plate tectonics, volcanoes, erosion: all the forces that shape the Earth.

Una imagen abstracta y colorida que representa varias formas geométricas de edificios sobre un fondo azul estampado.

Unit 6

Contemporary Fiction with excerpts from The House on Mango Street/Ficción Contemporánea con Fragmentos de La Casa en Mango Street

Explore The House on Mango Street… and write a book while doing it.

Cuadro que representa a un hombre y un niño tocando una gran campana en una torre, con espectadores al fondo y un cartel de "LIBERTAD" visible.

Unit 7

American Revolution/La Revolución estadounidense

Why did America seek independence? Let’s investigate the causes and effects.

Un pequeño bote de remos con tres personas navega por mares agitados mientras dos grandes barcos luchan al fondo, con humo y fuego visibles.

Unit 8

Treasure Island/La Isla del Tesoro

How dSeek the treasure of plot in this detailed study of a classic fiction adventure.

Unit 1

Personal Narratives/Narrativas personales

Through writing and sharing their writing, students begin to identify themselves as writers.

Unit 2

Early American Civilizations/Las primeras civilizaciones americanas

Students craft a codex to explain the rise and fall of the Maya, Aztec, and Inca people.

Dos jinetes medievales a caballo, uno de ellos con la espada en alto, avanzan por un terreno rocoso. El fondo presenta un paisaje brumoso bajo un tono violeta.

Unit 3

Poetry/Poesía

Students close read many forms of poetry… and learn to write them.

Collage ilustrado con un paraguas, un cuervo, un sextante náutico, estrellas, una luna creciente y una brújula sobre un fondo beige texturizado.

Unit 4

Adventures of Don Quixote/Las Aventuras de Don Quijote

Was Don Quixote right to fight the windmill? In this full-length novel study, students decide.

Unit 5

The Renaissance/El Renacimiento

Exploring the art and literature of the Renaissance through the works of its masters.

Tres hombres vestidos con ropa de época examinan una gran hoja de papel dentro de una imprenta. Un hombre parece llevar un delantal, mientras que otro señala el papel y el tercero observa de cerca.

Unit 6

The Reformation/La Reforma

How did the printing press transform the religion and society of Europe?

Patrón botánico morado y lila con hojas, plantas y formas abstractas, incluida una luna creciente y estrellas, sobre un fondo violeta oscuro.

Unit 7

William Shakespeare’s A Midsummer Night’s Dream/Sueño de Una Noche de Verano de William Shakespeare

Students enter the world of Shakespeare by reading, designing, and acting out his work.

Retrato en tonos sepia de una joven de pelo largo, con un collar de pedrería y un chal drapeado.

Unit 8

Native Americans/Los nativos americanos

How did the policies of the U.S. government impact Native American culture and lives?

Una lupa sobre documentos que contienen una pintura de paisaje de montañas, un dibujo con la etiqueta "Raptor Claw" y una nota adhesiva con la "Pista n.° 2". También se ven un sobre y una insignia exterior.

Unit 9

Chemical Matter/Química

Students use knowledge of chemistry to solve a mystery.

Print & digital 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 (Conocimientos) Teacher Guides (K–2)

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 and digital

Knowledge Image Cards (K–2)

Amplify Caminos includes Image Cards for each Knowledge Domain to bring each topic to life through vivid visuals.

Print and digital

Knowledge Flip Books (K–2)

Projectable Flip Books are provided to accompany the read-alouds in each Knowledge Domain.

Digital

Teacher Guides (3–5)

Teacher Guides for grades 3–5 units are based on content-rich topics and incorporate reading, writing, speaking, and listening skills in the context of background knowledge. There is one Teacher Guide per unit.

Print or digital

Teacher Resource Site (K–5)

The program includes a one-stop-shop website for lesson projections, digital versions of all Amplify Caminos materials, lesson planning resources, multimedia (such as eBooks), and more.

Digital

Professional Learning Site (K–5)

The Professional Learning site includes training materials, best practices, and other resources to develop program expertise. Access professional development anywhere, anytime.

Digital

Component

FORMAT

Knowledge (Conocimiento) Activity Books (K–2)

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

Print

Student Readers (3–5)

Student Readers serve as content-rich anchor texts for each unit. Units such as Poetry and Contemporary Fiction feature authentic texts originally written in Spanish.

Activity Books (3–5)

Activity Books in grades 3–5 provide daily opportunities for students to hone reading and writing skills within the context of each unit.

Print and digital

Explore more programs

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

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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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.
 
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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.

Join the Math Teacher Lounge Facebook group to continue the conversation, view exclusive content, interact with fellow educators, participate in giveaways, and more!

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.

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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!
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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.

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.

Welcome, Amplify Math families and community to Amplify Desmos Math!

Amplify welcomes you and your learner to Amplify Math for the new school year. We are very excited to provide you with exceptional learning opportunities through math. Below are resources and helpful guides for enabling your student to have the most productive experience with our platform throughout the year.

math illustration of Amplify Math programs

What is Amplify Math?

Amplify Math is a core math curriculum built for grades 6, 7, 8, and Algebra 1. It features a full suite of products for teachers and students that includes lesson plans, instructional materials, practice, assessments, and support to meet all learners’ needs. Amplify Math is built upon the highly rated curriculum, Illustrative Mathematics’® IM K–12 Math™, which was heavily researched and field-tested and has earned an all-green score on EdReports, the nationally recognized non-profit curriculum evaluation organization.

Read the review on EdReports.

Amplify Math helps students learn math in a way that is engaging and relevant to the world around them using student-centered instruction, which has been proven to increase students’ motivation, engagement, and enjoyment of math. Students using the program are active participants in their learning, solving problems while working with their classmates.

The digital experience allows your student’s teacher to monitor your student’s work in real time and make sure they get the exact support that they need at every part of the lesson. Amplify Math’s open-ended tasks provide engaging challenges for students of all levels, preparing them to solve all types of problems. The parts of Amplify Math work together to help students master the key skills of a 21st century learner!

Features

Some of the unique features of Amplify Math include:

  • Narrative connections: Exciting stories that help students to make connections between the math they learn in class and their everyday lives, making math class more engaging for your student.
  • Amps: Interactive digital activities (included in every lesson) let your student can explore the math and collaborate with their peers.
  • Power-ups: Additional activities that teachers can use to identify when your student needs support and help your student improve on the most important skills.
  • Featured mathematicians: Stories of important mathematicians that help your students see themselves mirrored in the history of math.

Why student-centered instruction?

A diverse group of students, one wearing a unicorn headband, looks at a teacher pointing to an amplify math bar graph on a board.

Student-centered instruction may look different from the way students have learned math for decades, and maybe even the way you learned math. Student-centered instruction instead emphasizes student-led discovery. When students explore and discover strategies, they are more engaged and make longer lasting connections.

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 to remember what they learn in class and apply their knowledge to new situations. Students who experience student-centered instruction have been shown to perform better on standardized tests and have more growth in their grades than their peers who learn through other methods. Your student will also learn to communicate in writing and verbally, understand and challenge the opinions of others, and build confidence in solving new problems. With student-centered learning, students will begin to 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 does an Amplify Math lesson look like?

Four illustrated icons represent phases of a lesson: Warm-up, Activities, Summary and Reflection, and Exit Ticket and Practice, each with related instructional graphics.

Students using Amplify Math will be active participants in their learning and get practice solving interesting and new types of problems. Here’s what a typical Amplify Math lesson includes:

  • Warm-up: A short, attention-getting problem to get students interested in the lesson
  • Activities: 2-3 mini-activities that challenge students’ problem-solving skills
  • Summary: Discussion to review and bring together the important concepts from the lesson
  • Exit Ticket: Questions for students to show what they know from the lesson
  • Practice: Additional problems your student’s teacher may assign for classwork or homework

Check out lessons from Grade 6Grade 7Grade 8, and Algebra 1, and watch this video of a typical Amplify Math lesson:

Materials overview

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. In addition, depending on the district, your student may also have a print Student Edition to use instead of the digital lesson if they do not have a device or internet. The Student Edition is a workbook that students can use to complete their work on problems and practice within the lessons.

Students can access the digital curriculum in school and at home with login information provided by their teachers. You can contact your student’s teacher to learn more about how they log in. Here are some key resources of the digital platform for students:

  • Digital activities to allow students to explore and make sense of math, leading to increased engagement and understanding
  • Digital supports such as a calculator and manipulatives to support all students where they are
  • Power-ups to give students just-in-time practice with key skills
  • Ability to access instructional materials in English or Spanish

Unit Caregiver Letters

Click a unit below to download the caregiver letter for that unit, in both English and Spanish.

How to support your student

Amplify Desmos Math Support
  • Review the unit caregiver letters to understand the key concepts in each unit. You can walk through the worked examples with your student, asking them to explain the strategy shown and asking if they know any other strategies to solve the problems. 
  • 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. 
  • 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. 
  • 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.

Want to learn more?

Interested in learning more about Amplify Math? These resources will help you dig deeper:

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.

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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.

Families & Caregivers — Welcome to Amplify Desmos Math New York for grades K–5!

This is the initial version of the Caregiver Hub for Amplify Desmos Math New York. Para la versión en español, haga clic aquí.

Welcome to the Amplify Desmos Math New York K–5 Caregiver Hub for grades K–5. We’re so excited your student’s school has chosen our program! We designed this space to help you support your student in their math journey this year. Your hard work plays an essential role in your student’s math experience.

We hope your student enjoys using technology to explore math, working with friends to solve problems, and learning all sorts of new and interesting concepts. And we hope you love experiencing it with them!

Excited to learn together,
—The Amplify Desmos Math team

A math activity interface instructs to determine platform heights using a tube length. A student workbook titled "Amplify Desmos Math, New York, Volume 1" featuring children playing is also visible.

Introducing Amplify Desmos Math

Amplify Desmos Math is a core math curriculum built for kindergarten through grade 5. We developed the program around the idea that a structured approach to problem-based learning builds on students’ curiosity to develop lasting grade-level understandings for all students. Each lesson offers opportunities to develop students’ understanding; connect their ideas; grow their skill fluency; and empower them to ask questions, explore, and make discoveries.

Amplify Desmos Math uses a student-centered approach to instruction, which has been proven to significantly increase math learning. Our mission is for your students to learn math—and to love learning math!

In every lesson, the Amplify Desmos Math curriculum poses engaging and relevant problems to solve, giving students daily opportunities to think critically, work collaboratively, and actively participate in their own learning.

Screenshot of the Amplify Desmos Math New York, K-5 section on the Desmos Classroom website displaying a list of ADM lessons for different grade levels.

About student-centered math instruction

Student-centered instruction may look different from the way students have learned math in the past, and perhaps from the way you learned math. Instead of memorizing formulas and tricks, student-centered learning focuses on giving students opportunities to figure out how math works. Research shows that students and teachers alike prefer this method, and teachers report that student-centered instruction has helped their students learn more math.

A diverse group of students, one wearing a unicorn headband, looks at a teacher pointing to an amplify math bar graph on a board.

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. All Amplify Desmos Math K–5 lessons are available in a write-in Student Edition book. Many of the lessons are designed to include hands-on activities with manipulatives. An age-appropriate number of lessons are designed for students to use digital devices like laptops or tablets. These include enhanced digital experiences that teachers can assign to students.

Three animated women of diverse ethnicities smiling and discussing a math curriculum around a laptop at a table, with colorful abstract shapes in the background.

Here’s what you can expect for your students from Amplify Desmos Math:

  • Lessons that drive classroom discussions so students can work toward a shared understanding and sense of community.
  • Responsive feedback that interprets student responses in context and encourages perseverance and revision.
  • Easy-to-follow lesson plans tested in classrooms across the country, with clear teaching suggestions, strategies, and Math Language Routines.
  • Practice problems to support fluency and help students review previous topics.
  • Recommended differentiation suggestions for teachers so that they can meet the needs of diverse learners.
  • Formative assessments that provide information on student understanding so that they can adjust their instruction to meet the needs of all students in their class.
  • Summative assessments that help teachers understand what students know about the math content they have been learning.
  • Daily lesson-level assessments so that teachers can frequently check for understanding.
  • A caregiver resource for each unit that includes explanations of key math concepts and problems to try with your student.

When students use devices, teachers can monitor students’ 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. Here is a sample of what a teacher sees on their dashboard to help them monitor thinking and support student learning.

Screenshot of a digital class attendance and activity tracker with student names and checkboxes indicating their participation in various New York math tasks.

Students are also able to access their digital work at home. Here’s an article on how to navigate the student home page.

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.

Two students, one male and one female, are sitting at a desk with a laptop, discussing a project under a "math club" sign, with speech bubble icons above them.

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: 1-2 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 the teacher to assign in 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.

Here’s what is available after the lesson to support, strengthen, and stretch students’ learning:

  • Differentiation: Mini-lessons, Centers, extensions, personalized learning, and fluency practice.
  • Practice: Additional problems your student’s teacher may assign for classwork or homework.

How can caregivers support math learning at home?

Use our Unit Support for Caregivers

We’ve created a Caregiver Resource for every unit of the program that provides a summary of key concepts, plus a problem from the lesson practice set you can work through with your student. Within each of the grade-level links below, you’ll find a Caregiver Resource document for each unit, in both English and Spanish.

Grade 1
Unit 1: Adding, Subtracting, and Working With Data
English
Spanish

Grade 3
Unit 1: Introducing Multiplication
English
Spanish

Grade 5
Unit 1: Volume
English
Spanish

Review practice problems together

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 your student to walk you through how they solved each problem, or talk about any parts that were challenging for them. Ask your students 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?”

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.

Find the math in everyday life.

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 ten dollar bill. Encourage your student to point out ways that you use math in daily tasks.

Read the Unit Story with your student.

Each unit in Amplify Desmos Math K–5 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 rest of the unit.

Access our Featured Collection of free K–5 Lessons and Activities.

Explore our latest free K–5 content in our Desmos Classroom Featured Collection. With our free collection, you can access:

  • Digital Lessons: Engaging interactive lessons
  • Mini-Lessons: A mix of print and digital activities designed for small-group instruction
  • Math Routines: Short digital activities to kick-start instruction and encourage math discussions
  • Bite-Sized Math Moments: Digital practice activities that use Polypad virtual manipulatives, designed to be used flexibly

Click here to access the collection and sign up for a free account.

How do caregivers 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 orange Login to Amplify Desmos Math button below.
  • Select Log in with Amplify.
  • Enter your student’s username and password provided by your student’s teacher.
  • Select your student’s grade level.

Illustrative Mathematics-NEW

To view this protected page, enter the password below:



Desmos Math 6–A1 correlations with Carnegie Math Texas

To view this protected page, enter the password below:



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.

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.

What is Amplify Math?

Amplify Math is a core math curriculum built for grades 6, 7, 8, and Algebra 1. It features a full suite of products for teachers and students that includes lesson plans, instructional materials, practice, assessments, and support to meet all learners’ needs. Amplify Math is built upon the highly rated curriculum, Illustrative Mathematics’® IM K–12 Math™, which was heavily researched and field-tested and has earned an all-green score on EdReports, the nationally recognized non-profit curriculum evaluation organization.

Read the review on EdReports.

Amplify Math helps students learn math in a way that is engaging and relevant to the world around them using student-centered instruction, which has been proven to increase students’ motivation, engagement, and enjoyment of math. Students using the program are active participants in their learning, solving problems while working with their classmates.

The digital experience allows your student’s teacher to monitor your student’s work in real time and make sure they get the exact support that they need at every part of the lesson. Amplify Math’s open-ended tasks provide engaging challenges for students of all levels, preparing them to solve all types of problems. The parts of Amplify Math work together to help students master the key skills of a 21st century learner!

Features

Some of the unique features of Amplify Math include:

  • Narrative connections: Exciting stories that help students to make connections between the math they learn in class and their everyday lives, making math class more engaging for your student.
  • Amps: Interactive digital activities (included in every lesson) let your student can explore the math and collaborate with their peers.
  • Power-ups: Additional activities that teachers can use to identify when your student needs support and help your student improve on the most important skills.
  • Featured mathematicians: Stories of important mathematicians that help your students see themselves mirrored in the history of math.

Why student-centered instruction?

A group of people and a unicorn amplify math skills as they listen to a presenter showing a bar chart with "Yes" and "No" on the screen.

Student-centered instruction may look different from the way students have learned math for decades, and maybe even the way you learned math. Student-centered instruction instead emphasizes student-led discovery. When students explore and discover strategies, they are more engaged and make longer lasting connections.

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 to remember what they learn in class and apply their knowledge to new situations. Students who experience student-centered instruction have been shown to perform better on standardized tests and have more growth in their grades than their peers who learn through other methods. Your student will also learn to communicate in writing and verbally, understand and challenge the opinions of others, and build confidence in solving new problems. With student-centered learning, students will begin to 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 does an Amplify Math lesson look like?

Icons represent four classroom activities in Amplify Math: Warm-up (student at laptop), Activities (two students discussing), Summary and Reflection (teacher at board), Exit Ticket and Practice (student at laptop).

Students using Amplify Math will be active participants in their learning and get practice solving interesting and new types of problems. Here’s what a typical Amplify Math lesson includes:

  • Warm-up: A short, attention-getting problem to get students interested in the lesson
  • Activities: 2-3 mini-activities that challenge students’ problem-solving skills
  • Summary: Discussion to review and bring together the important concepts from the lesson
  • Exit Ticket: Questions for students to show what they know from the lesson
  • Practice: Additional problems your student’s teacher may assign for classwork or homework

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. 

Check out lessons from Grade 6Grade 7Grade 8, and Algebra 1, and watch this video of a typical Amplify Math lesson:

Materials overview

Your student will have access to all learning, practice, and assessment materials through the Amplify platform. In addition, depending on the district, your student may also have a print Student Edition to use instead of the digital lesson if they do not have a device or internet. The Student Edition is a workbook that students can use to complete their work on problems and practice within the lessons.

Students can access the digital curriculum in school and at home with login information provided by their teachers. You can contact your student’s teacher to learn more about how they log in. Here are some key resources of the digital platform for students:

  • Digital activities to allow students to explore and make sense of math, leading to increased engagement and understanding
  • Digital supports such as a calculator and manipulatives to support all students where they are
  • Power-ups to give students just-in-time practice with key skills
  • Ability to access instructional materials in English or Spanish

Unit Caregiver Letters

Click a unit below to download the caregiver letter for that unit, in both English and Spanish.

How to support your student

A person inside looks out a window at someone holding up a chart with intersecting lines and arrows, aiming to amplify math concepts. There are plants on the windowsill.
  • Review the unit caregiver letters to understand the key concepts in each unit. You can walk through the worked examples with your student, asking them to explain the strategy shown and asking if they know any other strategies to solve the problems. 
  • 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. 
  • 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. 
  • 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.

Want to learn more?

Interested in learning more about Amplify Math? These resources will help you dig deeper:

Students take on the role of a scientist or engineer every day.

Amplify Science is a blended curriculum developed to align with the New York City PK–8 Science Scope and Sequence that meets the New York State Science Learning Standards.

Amplify Science for grades K–8 has been rated all-green by EdReports.

Read the review on EdReports.

Check out the New York City Resource Site for supporting resources designed for the New York City Department of Education Amplify Science adoption for grades K–8.

An illustration of a whale with jellyfish and turtles from Amplify Science

Begin your review

What sets Amplify Science apart?

  • Aligned to the New York City PK–8 Science Scope and Sequence, and meets New York State Science Learning Standards.
  • State-of-the-art, highly-engaging curriculum that invites students to take on the role of a scientist or engineer in every unit to solve relevant real-world problems.
  • Flexible, truly blended program that combines comprehensive print components and compelling online content with hands-on learning in every unit.
  • Robust teacher support for ease of use by a wide range of teachers in diverse classroom contexts, with carefully crafted lessons, standards alignment, differentiation strategies, and ELL supports throughout the program.
  • Embedded assessments throughout the program, including both formative and summative assessments for every grade level.
  • Authored by the industry-leading science curriculum team at U.C. Berkeley’s Lawrence Hall of Science, who have 50 years of experience in K–12 science education and who will continue to enhance and update the program for years to come. To learn more about how the Lawrence Hall of Science collected research, designed the curriculum, and field tested the program with teachers, download our research base document.

The Amplify Science approach

The scope and sequence of the program is designed to show that scientific concepts are interconnected and multifaceted. Each unit focuses on a specific learning goal in the form of an overarching unit question. Rather than following linear steps in an experiment, the program leaves room for students to make connections across concepts and make their own discoveries. In this way, Amplify Science replicates the realities and ambiguities of scientific research and thinking.

Each course in Amplify Science K–5 consists of 3–4 units, with each unit containing 22 lessons. Each lesson in grades K and 1 is written for a 45-minute session, while lessons in grades 2–5 are written for 60-minute sessions. Teachers can always expand or contract the timing to fit their needs.

Each course in Amplify Science 6–8 consists of 7-9 units, with each core unit containing 19 lessons, each launch unit containing 11 lessons, and each engineering internship containing 10 lessons. Each lesson in grades 6–8 is written for a 45-minute session. Teachers can always expand or contract the timing to fit their needs..

Download the K–5 unit sequence

Download the 6–8 unit sequence

Components overview

Amplify Science blends physical materials with a suite of digital tools, presenting students with the resources they need to investigate real-world problems, and empowering and supporting teachers as they lead instruction and gain insight into student growth and progress.

Grades K–5

  • Student Investigation Notebooks (K–2) for every unit allow students to interact with content while taking notes, answering questions, and conducting investigations. Review a sample from the Grade 2 Plant and Animal Relationships unit.
  • Student Books enhance science topics and allow students to practice reading within the science content area.
  • Instructional materials for teachers. The Amplify Science curriculum website hosts all lesson content, media, digital simulations, and more, and is the primary tool “open” for teachers during class time. Print Teacher’s Guides are included. You can view complete unit samples by accessing the curriculum at the bottom of this page.
  • Robust digital simulations and digital applications, developed exclusively for the Amplify Science program. Supported devices include: iPad 3+, Chromebook, Windows PC, and MacBook.
  • Unit Kits for each unit in the program including consumable and nonconsumable hands-on materials, printed classroom display materials, and the students books.
  • Embedded formative and summative assessments are meant to support and guide student instruction.
  • Pacing guides have been developed for teachers to support the implementation of the program.

Grades 6–8

  • New York City Student Editions enhance science topics and allow students to practice reading within the science content area.
  • Special “NYC Companion Lessons” directly target the additional standards in NYSSLS not found in the NGSS.
  • Instructional materials for teachers. The Amplify Science curriculum website hosts all lesson content, media, digital simulations, and more, and is the primary tool “open” for teachers during class time. Print Teacher’s Guides are included. You can view complete unit samples by accessing the curriculum at the bottom of this page.
  • Robust digital simulations and digital applications, developed exclusively for the Amplify Science program. Supported devices include: iPad 3+, Chromebook, Windows PC, and MacBook.
  • Unit Kits for each unit in the program including consumable and nonconsumable hands-on materials and printed classroom display materials for 5 uses of a class of 40 students.
  • Embedded formative and summative assessments are meant to support and guide student instruction.
  • Pacing guides have been developed for teachers to support the implementation of the program.

Review grades K–5

Amplify Science K-5 is an elementary science curriculum that provides teachers with the tools and practices necessary to meet the expectations of the NYSED P–12 Science Learning Standards. The program also aligns to the new NYCDOE PK–8 Science Scope and Sequence. Learn more about Amplify Science K-5 by reviewing the following::

Click the orange button below to access the digital Teacher’s Guide and begin your review.

Review grades 6–8

Amplify Science 6–8 New York City Edition is a new blended curriculum developed to align to 100 percent of the New York City PK–8 Science Scope and Sequence 2018 that meets 100 percent of the New York State Science Learning Standards. Learn more about Amplify Science 6-8 New York City Edition by reviewing the following:

Click the orange button below to access the digital Teacher’s Guide and begin your review.

Watch an overview

Watch curriculum experts walk through the Amplify Science K–5 and 6–8 programs and share information on how you can start to make the shifts to the NGSS with a literacy-rich approach to science instruction.

Ready to order?

When you are ready to place an order for Amplify Science, please reference the ordering checklist on the Core Curriculum Ordering Guide, and then head to:

Making the most of a science education conference

A typical science education conference such as NSTA may offer hundreds of booths, sessions, and new people to meet—and, most of the time, a typical science educator can’t do it all! So how can you maximize these opportunities to learn even more about teaching science … without maxing out? Middle-school educator and Science Connections podcast host Eric Cross is here to offer his tips. Here’s what he shared with us: 

Proven tips for capitalizing on science education conferences

  • Fuel up: Good food and good coffee are essential for me. Before you arrive, do some pre-trip research into local coffee shops and restaurants near the conference center. Avoid the long lines and overpriced food at the conference venue; instead, support local businesses to keep your energy levels up. Also important: comfy shoes, a reusable water bottle, and extra snacks.
  • Make a plan: Once registered, head to the conference website to build your agenda. Phone apps are handy, but I often find the desktop version works better for planning.
  • Narrow it down: NSTA, as just one example, offers more than 1,132 sessions! So it’s crucial to zero in on your options. Use a session schedule filter to focus on the sessions most relevant to your interests and needs.
  • Go where you’re fed: If you’re torn between sessions, go to one to collect resources, then move onto the other. Usually presenters list their session resources on the schedule or in the beginning of their session. Don’t hesitate to leave a session if it’s not meeting your needs, either—you’re there on behalf of your students. Presenters get it.
  • Divide and conquer: If you’re attending with a team, collaborate on a shared document for session notes and resource links. This way, everyone in your department and administration can benefit from the resources gathered at the conference.
  • Visit the expo hall: I recommend visiting right when it opens. You’ll find the booths fully stocked and the energy levels high.
  • Embrace downtime: Remember, conference venues are huge, and you’ll be on your feet quite a bit. Make sure to schedule 30–45 minutes of downtime. Use this break for a bit of mindless relaxation or to catch up on emails and reflect on earlier sessions. This brief pause can be a game changer for your overall conference experience.
  • Revisit next-day plans: Schedules can shift at the last minute. After dinner, I like to give the lineup a fresh look for any speaker or time changes. Being prepared allows me to have a game plan, but flexibility is also key.
  • Network: I especially find value in connecting with educators who teach content or student populations similar to my own and learning about their best practices in science instruction. Sometimes, these new connections can be just as enriching as the sessions themselves.

Note: Amplify will be at NSTA (March 20–23) at Booth #713. Stop by to experience real Amplify Science lessons; gain access to exciting, free resources and activities; and pick up fun swag. You’ll also hear from product experts and real educators about how they use Amplify Science to benefit all students.

Can’t wait? Check out our Amplify Science success stories to see how our K–8 curriculum is helping students everywhere read, think, and talk like scientists.

More to explore

S2-02: Developing your own teaching style: Tips from a veteran teacher.

Poster for "Science Connections" podcast with an image of Marilyn Dieppa, featuring a logo of an atom and text promoting season 2, episode 2 about veteran teaching styles.

In this episode, Eric Cross sits down with veteran educator and former Miami-Dade County Public Schools (M-DCPS) Middle School Science Teacher of the Year, Marilyn Dieppa. During the show, Marilyn shares tips for new teachers, ways to inspire students, and how she utilizes her journalism background to develop literacy skills within her science classroom. She also shares her experiences developing a robotics academy, and the VEX IQ World’s Competition. Explore more from Science Connections by visiting our main page.

Download Transcript

Marilyn Dieppa (00:01):
I think my favorite thing is their success. Whether it’s robotics, whether it’s in the classroom, that they pass a test for the first time, those are my moments of success. And that’s what makes me happy.

Eric Cross (00:15):
Marilyn Dieppa is a veteran middle-school science educator at Miami-Dade County public schools. Dieppa launched her school’s STEM Academy in 2016 and developed professional development through the STEM Transformation Institute of Florida International University. Dieppa’s coached numerous new teachers and was the 2018 Miami-Dade County public schools’ middle-school Science Teacher of the Year. In this episode, we discussed her transition from a career in journalism to the science classroom and the value of personal and professional support systems for teacher longevity. And now, please enjoy my conversation with Marilyn Dieppa.

Marilyn Dieppa (00:52):
Nice to meet you, Eric.

Eric Cross (00:53):
Nice to meet you too. Thank you for being willing to come on the podcast.

Marilyn Dieppa (00:58):
Not a problem.

Eric Cross (00:59):
So you’re out in, you’re out in Florida. In Dade County. I’m out here in San Diego. So I’m like literally on the other side of the country. Have you—were you born and raised in Florida?

Marilyn Dieppa (01:09):
I’ve been here for 40 years, so I’ve been here most of my life. Yeah. I’m Puerto Rican, but I was, you know, my young childhood, I was in New Jersey. And then when I was 15, I came down.

Eric Cross (01:23):
I looked at like your—some of your accolades, which are really impressive. The things that you’ve done for students with robotics, and all the education, or, kind of like teacher enrichment, a lot of mentoring and coaching that you do now.

Marilyn Dieppa (01:35):
I am part of leadership team for the district. I do a lot of training. I work on curriculum. I help with pacing guides to make sure that everything is based on what the state wants, what the district wants. I have done a lot for the district in the last, probably 20 years.

Eric Cross (01:52):
What got you into teaching initially? What was your…like, why middle school science? We’re like a unique group.

Marilyn Dieppa (01:57):
This is the second career choice for me. So I’ve only been doing this for 24 years. I was a journalism major and then I got married and then I had my child and I wanted to do something. My thing was that I wanted to go to Iraq. I wanted to cover the news. I have a minor in Middle Eastern culture. so there was a lot of things that were in my mind when I was young, pre-married. and after, you know, you have children, priorities kind of change. So I totally changed, pretty much had to start from scratch, with my degree, because nothing kind of transferred over from journalism to teaching. So before I actually did that, I started subbing just to see if I liked it. And I fell in love with teaching right away. And that’s how I got into it. So my degree is really in elementary.

Eric Cross (02:45):
Now, when you were subbing, you were doing elementary school.

Marilyn Dieppa (02:47):
Yes. Pretty much elementary.

Eric Cross (02:48):
How did you go from there to like, middle-school science?

Marilyn Dieppa (02:50):
My thing was writing, not necessarily math and science. But I ended up with my cooperating teacher, my CT, she was a math and science teacher. So I was put with her, and who knew that I liked science and I liked math? So I ended up with that and I infused a lot of labs. So in elementary you tend to—I think teachers are a little bit afraid of the labs, so I infused a lot of literature with my labs. I infused all my—I did it like a whole-group type thing, everything I did with my labs, I incorporated the math. I incorporated the science. I incorporated, you know, the reading with it. And from there, I just—you know, they ended up putting me in a lot of leadership roles with science. And then my principal was opening up the school where I’m at now, my former principal. And she, you know, she took me with her. And so her dissertation was in looping, on how following your students, did that really make a difference in test scores? So I was part of her like test study, and I had students that I followed for two years in a row. And she would look at data and that was part of her dissertation. So that really made a difference. So I ended up moving with my students and my first group of middle-school students, I had them for four years.

Eric Cross (04:10):
Oh, wow.

Marilyn Dieppa (04:10):
And that was—those were my children. I, like, boohooed when they left. And I ended up, you know, literally following them from fourth grade all the way to more than four years. Because it was all the way until they left eighth grade.

Eric Cross (04:21):
What did you think of that model of looping with students?

Marilyn Dieppa (04:24):
I think it’s a great model, depending on the kids that you have. I love, you know, the school that I’m at. I’m very blessed, because it’s a great school. It’s really a wonderful school. I’ve had really good relationships with students. They always come back, and they always come back when they wanna tell me that they’re in something in science, right? They’re an engineer or they’re a nurse, or they’re, you know, doctors at this point. So I’ve seen a little bit of everything with my students. And it’s very rewarding.

Eric Cross (04:52):
That’s super-exciting, right? When they come back and they’re either telling you about their college major or what career they’re in. And I like to recruit them at that point and ask them to come talk to my students. Because Google photos gives you unlimited storage, if you have a teacher account, I actually have photos of students from like 10 years ago.

Marilyn Dieppa (05:09):
Oh, wow.

Eric Cross (05:10):
And I’ll put their middle school picture next to their—and then their current picture.

Marilyn Dieppa (05:14):
Oh, that’s awesome. I’ve never done that.

Eric Cross (05:17):
Yeah. You could see, like, they could see the younger version of them.

Marilyn Dieppa (05:19):
And it’s funny because even with the STEM Academy, which I have now, I have the same group of kids for three years. So I’ve had already few groups that have gone by, and those kids come back to me, they come back to our competitions, they help out, you know, they’re very integrated with the robotics. So I’m getting those students back as well. So I’ve maintained that relationship with them as well.

Eric Cross (05:46):
How do you develop your own classroom management style? How did you figure out where your—where you fit and what works for you? What was your process like for that?

Marilyn Dieppa (05:55):
You know what I think, just by teaching, teaching them to respect. And one thing that I’ve developed that—I don’t scream in my classroom; I just talk to the kids. I have very good one-on-one communication with them. I show them respect. I treat them as an equal.

Eric Cross (06:12):
And what grade are you teaching currently?

Marilyn Dieppa (06:14):
Eighth grade. So I do science. I teach high school science. I teach comprehensive, which is like our regular students. I have kids who are inclusion. I have kids that are ESL. So I teach all, you know, dynamics of students. And then I have the academy, which is something separate. But I infuse a lot of physics and of course that they need in order for them to be competitive.

Eric Cross (06:38):
So tell me about that. What is the STEM Academy?

Marilyn Dieppa (06:40):
It is an enrichment program. So it is an advanced enrichment program, because they do follow like the math enrichment. so they have to be really good at math in order for them to be accepted into the program. So, one day we got like a grant, and we got a little robot, the VEX. I don’t know if you’re familiar with VEX. I know it’s big in California. So I was told, “Here, this is for you. See what you can do with it.” So I started with an after-school club, the following year. It kind of hit off. We went to our first little competition. The kids did really well. And then the following year, they told me, “Hey, we need an academy, make it happen.” So it’s not like I had a curriculum. I kind of do my own thing. But we do a lot of different types of things. Our big portion is the VEX, but I also do sec me, we do Future City. We do a whole bunch of competitions within the district. You know, Math Bowl. So I get my kids prepared for anything that really has to do competitive-based. I do that with those students.

Eric Cross (07:38):
What age range or which grade range?

Marilyn Dieppa (07:40):
Sixth to eighth. We have kids who stay the three years and then we have kids that after, you know, sometimes it’s more the parents that want them to be part of the engineering. but sometimes we lose kids after the first year and you know, that’s fine because we wanna really have kids who really wanna be there and are, you know, committed to it. Because there’s a lot of commitments to that program.

Eric Cross (08:01):
Those types of programs, there’s so many like outside-of-the-classroom things that you need to take care of. If you’re going to competitions, and weekends, and all those types of things. Is there a team of teachers that are doing this or is it just you?

Marilyn Dieppa (08:10):
Team of one! .

Eric Cross (08:11):
A team of one! Right? Like, yeah. And how long have you been running this yourself?

Marilyn Dieppa (08:16):
This is probably like my sixth year.

Eric Cross (08:19):
OK.

Marilyn Dieppa (08:20):
So we’ve been very successful. That program is totally inquiry. It’s totally on them. I don’t know how to use a little, you know, remote control. I don’t know how to do anything. I’m there for troubleshoot and to make sure that they’re on task, but they have been very successful because I do put everything on them. And I go, “It’s not my robot. This is your robot.” So they build everything

Eric Cross (08:40):
And that seems to be the theme, especially with, a lot of times, with science teachers. And encouraging them to say, “You don’t have to be the expert in everything.” Teachers tend to be more like risk-taking and innovative when they’re willing to like, not have to be—I don’t have to know everything in order to do something.

Marilyn Dieppa (08:54):
Exactly. So we’ve been very successful. Very proud of my students because you know, we’ve, gone to Worlds twice. We’ve qualified three times in the six years. Actually, I had two teams that went last year.

Eric Cross (09:07):
What is, what is Worlds? That sounds like a big deal.

Marilyn Dieppa (09:10):
It’s a huge thing. And it’s teams from all over the world. You can actually look it up online. It’s—from this year, there were teams, although they said China was not gonna be in there, there were actually some teams from China. There were teams from New Zealand. There were teams from South Africa, the UK, a lot of teams from, from Europe. And then there are teams from here. We are the host country. We’ve been the host country for a while. But it’s amazing. The first time we went, the first team that we were paired up with was a Russian team. So, you know, there was Google Translate and the kids—and it’s, they didn’t need to know the same language because they communicated with the robots. So it was really amazing. They work collaboratively. So it’s not like a battle box. So they work two teams together and whatever, they both get together, they both earn the same points. So it teaches leadership, and there’s so much more to it than just a robot. They have to know how to communicate, because they do get interviewed. They do online challenges. It’s so many things. It’s just—I think it’s one of the best things that our district has really invested in, because these kids are so into it, and they love it so much. For the last year and this year I have the same kids that are in the robotics. I’m also gonna be teaching them physical science. So I have to teach them that separation between what we’re doing in our science classes versus what they’re doing in the class. So there has to be a separation. So they see one side of me in this class where it’s very laid back. It’s very chill. No, no, you, you guys do it. There’s no sitting down. It’s like organized chaos, I call it all the time. But then in the classroom, it has to be a little bit more organized.

Eric Cross (10:53):
Is that something that, as far as getting the parts—like people do, like, GoFundMes and donations and Donors Choose. Can you—

Marilyn Dieppa (11:00):
We get grant money, grant money from the town of Miami Lakes, the town that I work in. So the town actually sponsors us. Without them, we could not do that. It is a very expensive activity to do. If you go online and you look up the prices, you’ll be, “Oh my gosh, goodness, it’s very expensive.” You know? But the smiles on their faces when they come back and they have those little certificates, it means nothing, you know, it’s a little piece of paper. But that, to me, to them, it means the world.

Eric Cross (11:27):
Well, teachers, if you’re looking for ways to get that stuff funded, be fearless on behalf of asking for free things for your kids. Find a local business that somewhat connects to even robotics and say, “Hey, look, I’ve got 50 kids that really want to get after it. And we need X amount of dollars so we can buy those robotics kits. We’ll put your banner up somewhere. We’ll do all these other things. But come support our students. Come to the competition. Donate whatever you can for our students.” And many organizations will say, will say yes. Many just aren’t asked.

Marilyn Dieppa (11:57):
Right. And a lot of towns do have, like, education advisory boards. You wanna reach out to those people. ‘Cause those are the communities where they have money set aside in order to assist things like this.

Eric Cross (12:09):
Do you notice any carryover between the students that do get involved with these extracurriculars into the regular science classroom?

Marilyn Dieppa (12:16):
For sure. They’re more, they’re more disciplined. They tend to care more about the sciences because they see that link in the science. I mean, my kids are talking about gear ratios. They’re talking about, you know, mass accelerations. They had—they infuse all these things. And when they see it in the science class, they’re making that connection, which is really wonderful.

Eric Cross (12:41):
It seems like there’s a high level of engagement because this is an authentic thing. It’s almost, this should be science.

Marilyn Dieppa (12:46):
Yes. And not only that, the writing skills that have to be interpreted because part of the program is that they, they don’t necessarily have to have it, but in order for them to go far and make it to Worlds, they have to have an engineering notebook. So our strength sometimes is not the robot, but the engineering notebook.

Eric Cross (13:02):
his is where the journalism major shines.

Marilyn Dieppa (13:05):
Yes. And I go, “Guys, this is your Ikea manual. You have to explain what you’re doing, what pieces you’re using, what’s going right.” You know, and then they have to interpret and see what didn’t work. How can they fix it? So there’s so much problem-solving. It’s real life, it’s what they’re doing there. More so than sitting and learning rote, you know, vocabulary or whatever the case might be, ’cause they’re actually applying what they’re learning.

Eric Cross (13:31):
Yeah. And that’s, that’s so critical, the communication piece. Because seems like now in society, more than ever, even just being able to communicate something with bad science is convincing to people. Versus if you have great science, but you can’t communicate it, you’re not gonna be able to get it out into the public. It’s so great to see a program that exactly brings together this literacy aspect, in addition to kind of this content and skills aspect of doing the science.

Marilyn Dieppa (13:57):
And that’s what really, you know, since I started, that’s pretty much what I’ve done. My strength, believe it or not, when I was growing up, was not the science. I think I didn’t really have a really good science background. But I remember reflecting and saying, “I don’t want my students to feel like I felt when I was a child.” I wanna make sure that I give them everything, you know, give them the hands-on experience. I think I had one teacher when I was growing up and I still remember him. He was my second-grade teacher and he was just so amazing with the science. And it was just like the only really good experience I had. And I think that always stayed in the back of my mind. And when I started teaching and I go, “I wanna give these kids these experiences.” You know, sometimes I see kids in eighth grade and I go, how sad! They see water boiling and they’re just, like, in a lab room. And they’re just like, in awe, because there’s water boiling. And I go, “You guys haven’t seen water boil before?” And he goes, “No, no, no, not like this!” And I go, oh wow.

Eric Cross (14:58):
Even if it’s simple, everyday phenomena, everyday things that people deal with in a science classroom, or when you’re a teacher in that setting, it’s just—it just hits different, right? Like you, you know, you drop dye into water and watch it diffuse. And it’s like, whoa! Because they’re looking at it through that different lens. And that’s why one of the reasons why—I’m super-biased, but as science teachers, we get to do the coolest stuff.

Marilyn Dieppa (15:21):
Yeah, we do.

Eric Cross (15:22):
We just do. It’s so much fun. And basically anything that happens, that’s cool, like in, innovation and things like that, we can figure out ways to incorporate into our classroom. Now, as a coach and as a mentor, you’ve had multiple student teachers in your classroom. And we have, you know, huge need for new teachers. I teach teachers who are getting their CR, getting their credential. And the landscape of education is, is constantly shifting. You’ve watched it shift over the years. What are your biggest tips that you give to new teachers?

Marilyn Dieppa (15:49):
Well, I just had an intern last semester. I’ve had a few interns where, you know, not only are they doing this, but they’re also learning robotics too. So they’re really getting aspect in how to incorporate that. You don’t have to have everything separate. You can include everything together. But I think, I think it just comes from the foundation where they’re not exposed. Even me, when I went to college, I don’t remember doing so many labs as I should have. And I think it’s just a fear of them trying new things and failing. And I go, you know what? I, sometimes my first class is my guinea pig class, because I always change my labs. I don’t like to do the same thing over and over again. If I see something online, I go, “Oh wow. You know what, I’m gonna try it.” And I go, “Hey guys, this is the first time; we’re gonna do this together.” And it’s really—it’s just for them not to be fearful. And I think especially for science teachers or like even elementary, to give the kids the foundation that they need, they’re afraid. They’re afraid of failing and not trying something new, and say, “Hey, it’s OK. There’s other ways of doing this.” You know? So I always say, “My first class is always my guinea pig class, ’cause that’s the class I’m gonna try this on.” And then, you know, when you have to tweak, reflect, then we do that.

Eric Cross (17:06):
What are some of the things that you’ve seen or encouragements that you give to teachers who are teaching, kind of, in this kind of newer landscape, where as teachers, you become more than just a science teacher. I mean, you’re a mentor. You’re an encourager. Sometimes you’re a counselor for students. And then there, there are things that happen externally that impact teachers as well. It’s a tough job.

Marilyn Dieppa (17:24):
So I always say, you know, when you have a child, we have to be very aware of what’s happening with our children. Especially after these two years of the pandemic. That was kind of crazy. Last year was a really tough year, I think, for most educators that were back in the classroom. But I always tell ’em, you have to be really aware of what’s going on with these kids outside. When you see somebody who’s not doing anything and then you have the parents are there supporting. There’s something going—I mean, there has to be something going on. Kids are not just going to be so, so defiant. You’re gonna have very few that will be like that. But most of them it’s just gotta see and read those kids and see what’s going on, and don’t be afraid to—and I always say, I’m not there to really be your friend, but I’m there to help you. And you gotta tell ’em, you know, if you need to talk, come talk to me. Have an open-door policy with those kids.

Eric Cross (18:16):
What’s been your favorite part of the job? Something you really enjoy about the job? Especially having been teaching for as long as you have.

Marilyn Dieppa (18:23):
I think my favorite thing is their success. Whether they have struggled all the year and they’ve had that one piece of success or they don’t realize what they got out of middle school until they get to high school and they come back to you and they tell you it’s, you know, seeing my kids, whether it’s robotics, whether it’s in the classroom, that they pass a test for the first time, those are my moments of success. And that’s what makes me happy.

Eric Cross (18:52):
So you get those ahas, you get those wins, those turnarounds. And it’s like, “Ah, this keeps me going. This is so good!” But there’s something that I say to myself when I do get challenges in the classroom is teaching seventh grade, I say, “They’re 12. They’re 13. They’ve been on earth for 13 years. And for the first five or six, like, you know, they’re just kind of coming online at that point. And they’re going through all these changes.” And it grounds me in the fact that ’cause sometimes the things that you experience can be really, really challenging kind of interpersonally. And I remind myself, “Well, it’s like—you’re not 28 years old. Like, you’re, 12 and 13, and you need me to not be Mr. Cross, the science teacher. You need me to be, you know, Mr. Cross, the mentor, or Mr. Cross, the coach.” Like you were saying, open door. Keeping that open door, keeping that relationship. Because so much of what we’re doing is like life coaching in addition—and that connects to their success in the classroom. There’s a direct relationship.

Marilyn Dieppa (19:45):
Yes, yes, yes, absolutely.

Eric Cross (19:46):
Now what gets you back each fall? Because at the end, you know, every school year it’s like, “That was a tough one!” Especially with the last couple years. Right? So what’s been something, what gets you back in the classroom every fall, so that you’re ready for your students?

Marilyn Dieppa (20:02):
I think the support I get at home. I have a husband who is the most supportive person ever. He always tells me, “Your kids are grown up.” You know, my kids are adults now. “Enjoy these kids, what they’re doing. You don’t know how much they need you.” So he does tell me that. He goes, “And don’t complain! You love it!” And also my administration, they back me up. And that’s what I think what keeps you coming back. I love my administration. Whatever I ask for, they don’t tell me no. They tell me I’m crazy, but they don’t tell me no. You know, we have these huge competitions once a year at our school, administration has to be involved ’cause they have to be there, and they go, “We do this because we love you! But you know, you’re crazy!”

Eric Cross (20:48):
It’s interesting, ’cause both of these things, they involve human connection. And one is your support system at home, which is incredibly valuable. Shout out to your husband; I don’t know if he’s around. And then the culture, like, feeling supported. Teachers, you know—and it’s not just in education, but people, I’ve experienced—will work harder, longer, be more committed, when they have that intangible. When they feel like they’re connected to something bigger than them. Or on a team, not in a silo. And one person can really create or break whether that happens. And just like us in the classroom as a teacher, right? Like, “What makes you like this teacher’s class?” “Well, I feel connected. I feel safe. I feel it’s fun. It’s the culture!” I like to end with asking this question and you kind of alluded to an answer earlier, but who is one, or it could be multiple teachers, that you’ve had in your own life as a kid growing up or young person in kindergarten through 12th grade, could even be college, that has inspired you? Or made a difference in your life one way or another? Like, who pops out? I feel like we all have somebody.

Marilyn Dieppa (21:58):
One was my second grade teacher, as I mentioned before. Mr. Fernandez, never forget him. And my other teacher was my high school teacher, Mr. Velazquez. It was in New Jersey as well. And he was the one that really got me into the love of writing. He was my Spanish teacher, actually. He wasn’t even, you know—he was like an elective teacher. But he just made me believe like, “Wow, you’re like a really good writer!” To me, those two gentlemen really stood out. Very fond memories of being in school and really enjoying what I was doing.

Eric Cross (22:33):
There are so many teachers that we all have been impacted by. And many of us now who are teachers, we sit in that same seat. We fill those same shoes. And going back to what you had said earlier, one of the most rewarding things is when those kids come back to you. And I’m thinking about all the work that you’ve done, all the students you’ve poured into, all the competitions you’ve done. The ones that have come back to you are a small fragment of the ones that you’ve impacted.

Marilyn Dieppa (22:59):
Mm-hmm, yeah.

Eric Cross (23:00):
‘Cause we think about our own story, right? Like you’ve gone on and paid dividends for that one teacher in second grade. You know, Mr. Fernandez or Mr. Velasquez like, they went and they just gave you exposure to something or helped you fall in love with something. And you went on this trajectory. And if we could see the timeline of, like, this teacher created Marilyn, and Marilyn went and did this, and then what do all those students do? And that, I don’t know, there’s so many jobs that are gonna be hard work and that are gonna be challenging and stressful. But that is the thing that I think fills me when I listen to your story. I just think about like all the students throughout Florida that you have—you probably will never hear from, but have gone on to do amazing things or become great people who would go back and talk about you and say you were an inspiration for them. Marilyn, thank you for taking the time out to be on the podcast and for not only teaching students, but inspiring and coaching younger teachers and new teachers. It’s so critical. And for being willing to spend so much of your time beyond the classroom to create these opportunities for students to do this awesome, fun, engaging science, and go to Worlds. I wish you a great school year.

Marilyn Dieppa (24:11):
Thank you. You too.

Eric Cross (24:12):
We hope you make it to Worlds again and crush, in a competitive, collaborative type of environment. We’ll be checking out—I’m sure other teachers will check out Vex Robotics. Thanks for being on the podcast.

Marilyn Dieppa (24:23):
Thank you. You too, Eric.

Eric Cross (24:26):
Thanks so much for listening. Now we want to hear more about you. Do you have any educators who inspire you? You can nominate them as a future guest on Science Connections by emailing STEM@amplify.com. That’s S T E M at amplifycom.wpengine.com. Make sure to click subscribe wherever you listen to podcasts. And join our Facebook group, Science Connections: The Community. Until next time.

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What Marilyn Dieppa says about science

“I think as science teachers, we’re afraid of failing and not trying something new, and I say, ‘Hey, it’s okay!’ You have to tweak, reflect.”

– Marilyn Dieppa

STEM Academy Coach/Teacher, 2018 Miami-Dade County Public Schools (M-DCPS) Middle School Science Teacher of the Year

Meet the guest

Marilyn Dieppa is a long-time educator and STEM Academy coach at Miami Dade County Public Schools. Currently in her 24th year, Marilyn teaches 8th grade science and coaches the STEM Academy at Bob Graham Education Center. She launched the Science, Technology, Engineering and Math (STEM) Academy during the 2016-2017 school year, and the teams compete in VEX IQ World’s Competition representing both the district and the state. She has been the middle school department chairperson since 2003, attends the district department meetings and Instructional Capacity-building Academy (ICAD), and trains her science department.

Dieppa holds a bachelor of science in Elementary Education and a master of science in reading education. She is also a Nationally Board-Certified Teacher in Science.

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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!

Desmos Math

Desmos Math 6–8 and Algebra 1 is based on the highly rated IM K–12™ curricula from Illustrative Mathematics. What’s more, our 6–8 curriculum also received a perfect, all-green rating by EdReports.

Read the full review on EdReports.

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Desmos Math 6–A1 delivers the instructional power of student-centered learning packaged in a lesson format that is teacher-friendly and manageable.

With easy-to-follow instructional supports, implementing a problem-based program becomes more effective and enjoyable for both you and your students. Delivered through the Desmos Classroom digital experience, math class becomes fun and dynamic, with plenty of opportunities for students to talk through their reasoning, work with their peers, and gain new understandings.

Desmos Classroom technology

Math lessons should be powerful in their ability to surface student thinking and spark interesting and productive discussions. The Desmos Classroom platform brings this vision to life. It even includes a complete library of interactive, collaborative lessons made by your math colleagues.

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Engaging student experience

Relevant content and interactive math tools create an intuitive and engaging student experience. Plus, working together in real-time allows students to see that communicating their ideas and learning from each other are important parts of math class.

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Visibility into student thinking

Imagine having more visibility into your students’ mathematical thinking. Now imagine students have access to this same information. With our collaborative lesson interface and teacher dashboard, students can’t hide. What’s more, they have visibility into the thinking of their peers—exposing them to a wider variety of approaches to solving the same problem.

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Ready-to-teach lessons

Each grade-level includes 150 ready-to-teach lessons complete with slides, step-by-step teaching notes, suggested student and teacher responses, tips for incorporating instructional routines, support for developing mathematical language, and links to useful resources. Teachers can also control what slides students see, giving teachers the ability to control the pace of the lesson to suite the needs of the class.

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A Lesson with Dr. Dan Meyer

Desmos Math has been extensively tested by math educators across the nation…including Dr. Dan Meyer.

In this 8-minute video, Dr. Dan Meyer puts a Desmos Math lessons to the test, and shares how the Desmos Math teacher tools empower all teacher to deliver engaging and interactive lessons.

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Looking to speak directly with your local Account Executive? Get in touch with a California team member to learn more about Desmos Math or to request a demo account.

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wgarcia@amplify.com

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S2-03: Building meaningful student connections in the science classroom

Promotional image for a podcast episode titled "Sharita Ware: Building meaningful student connections," featuring Sharita Ware and "Science Connections" branding.

In this episode, Eric Cross sits down with Indiana State Teacher of the Year, Sharita Ware, to talk about how to successfully build meaningful student connections in the science classroom. Sharita shares her journey from a corporate career to becoming Indiana’s 2022 Teacher of the Year, and her passion for creating project-based lessons for her students. Together, Eric and Sharita discuss how educators can teach students to love science content by building strong relationships, adding in other content areas, and supporting students’ imagination. Explore more from Science Connections by visiting our main page.

Download Transcript

Sharita Ware (00:00):
I try to create that equal playing field where there’s nobody’s voice, that’s more important than anyone else’s and try to make them all feel that what they have to say is important.

Eric Cross (00:14):
Welcome to science connections. I’m your host Eric. My guest today is Sheta where Sheta is the 2022 Indiana state teacher of the year. And in her 10 year career, as an engineering and technology teacher, she has dedicated herself to helping students build knowledge and skills for high school and life. Beyond. In this episode, we discuss how she inspires her seventh and eighth grade students to build problem solving and critical thinking skills through hands on real world and collaborative projects. She is as humble as she is knowledgeable and through our conversation, it was easy for me to see why her students feel successful under her guidance. And now please enjoy my conversation with Sharita Ware.

Eric Cross (00:59):
Can I start off by saying congratulations on teacher of the year. Thank you for the state of Indiana. Um, that’s amazing. So I, I, I did watch, uh, your videos, uh, short interviews, and then you spoke, was it Purdue? Yes. You were there. And so, uh, to see if fellow seventh grade, eighth grade science teacher out there being celebrated, like I was so excited, so yeah, I wanted to congratulate you on that and, and just kind of talk to you about like your teaching journey and ask you, uh, maybe just kind of start off with your story about what brought you into, into the classroom, especially the middle school.

Sharita Ware (01:29):
Classroom. So what happened is when I was working in industry as an engineer and when my husband and I got married, we decided that I was gonna, um, stay home with the kids because, you know, we wanted, um, our influence to be greater on our kids than, you know, the people that would be watching them, you know, because they would ultimately spend more time with them than they would with us. And, and so, um, I stayed home and when my youngest was going to be going to kindergarten the next year, I was like, okay, what am I going to do? Cuz I really don’t necessarily feel like I need to stay at home. Mm-hmm <affirmative> but um, I knew going back to industry would be a challenge just because in my field, I, I was traveling a lot before I got married and had kids.

Sharita Ware (02:14):
And so I knew that that wouldn’t really be conducive to again, raising children. So I, I get this email, my inbox for Woodrow Wilson, teaching fellowship at Purdue. And they were just looking for people in stem fields to go into teaching. And I was like, okay. And it was a national search, you know, I filled out the application, we had to go in and do some sample teaching mm-hmm <affirmative>. And I was picked as, as one of the, the teachers to go through the program. And I started off thinking I wanted high school. And the really cool thing about this, uh, program is that we had long observation periods at high school and at middle schools. And so we would go to a school and we’d stay there two or three weeks. And so it, it kind of gave you right. A little bit more insight to what happened on a daily basis. And after those observations, I was like, I like middle school better than I, uh, like high school. And so I just kind of went that direction and you know, the rest is history. So

Eric Cross (03:19):
I feel like our stories are similar because I went into teaching thinking I wanted to do high school because I like the maturity and you a little bit more sophistication, advanced things, but yes, middle school, I felt like I can, I could get them more upstream before and kind of help shape mm-hmm <affirmative> that experience for them? Because I feel like at middle school is really where they kind of decide like what they can do based on their experiences.

Sharita Ware (03:39):
I found in the middle school that the kids, I mean, they just, they clamor around you and they’re like, what are we doing today? You know? And they get so excited and, um, they’re, they’re just, I don’t know, I guess in some ways, just more hungry in the sense of like they’re willingness to, um, now sometimes they’re a little reluctant, but you know, their willingness just to try new things. And I think, um, my students really what I have found over the years that they have found a safe space and I hear the kids, you know, say to me so many times that, you know, it it’s safe. I feel, I feel safe in here. And, and it’s not something that in my mind I’m thinking about, oh, I need to make this a safe place. It’s just, I guess part of just who I am as a person has created this environment of, of safety and, and the kids recognize that, you know, I don’t play favorites. You know, everybody starts out mm-hmm, <affirmative> on equal footing. I, I don’t care what your backstory is. I don’t care how many times I see you in the hallway when I’m walking during my prep. You know, when you hit my room, I’m, I’m gonna treat you the same way on day one, that I treat everybody else.

Eric Cross (04:54):
You really understand how to build culture with, in, with your classroom, with your students. And, and you said they feel safe, but is there anything that you do that someone could like apply? And like you found that you’ve gotten a lot of just relational capital through doing these things, or is it just your personality? Like how, how do you build those connections?

Sharita Ware (05:12):
You know, growing up being a, a very quiet person. I, I think a lot of times my voice was ignored because I was the quiet kid in the back of the room. And oftentimes I became seen or heard because of my work, you know, in the beginning it was kind of like, oh, she’s just this quiet girl in the back of the room. And then, you know, the first essay was due or the first project was due. And then it was like, oh, you know, then you’re the person to be on, you know, people’s teams. And, and that, I don’t know, that always kind of bothered me because, you know, I’m thinking just because you’re not the loudest person in the room doesn’t mean that you don’t have something to say, mm-hmm <affirmative>, you just might not be talking all the time. You know? And, and so for my students, I just, I try to create that equal playing field where there’s, nobody’s voice, that’s more important than anyone else’s and try to make them all feel like that what they have to say, or what they have to contribute is, is enough, is good.

Sharita Ware (06:14):
Enough is important as…

Eric Cross (06:16):
It is, as it is. And there’s probably a lot of things that you do. But in addition to building these relationships, what do you do? Like how do you make your learning fun for students?

Sharita Ware (06:25):
I think, um, I’m also a little bit on the silly side. Um, we do a, a Barbie prosthetic leg project, and this was after trial and error of having the kids make full size prosthetic legs. And I try to make it as real world as possible, but with none of the children being amputee or, you know, having access to someone, it was really hard for them to really visualize what needed to happen. Mm-hmm <affirmative>. And so, um, I found this Barbie that had a prosthetic leg and I was like, well, LA, so I just started collecting Barbies and chopping their legs off <laugh>. And so I have this jar of Barbie legs. And so, and I said, you’re gonna make prosthetic legs. And I lay this jar of legs on the counter and the kids are like, like they gasp and then they crack up and then they’re like, okay, this lady’s crazy. So…

Eric Cross (07:22):
That’s when you take off your scarf and there’s this necklace of just Barbie legs that are just around and you’re like, I’m a middle school teacher and they go, oh, okay. I understand. Yeah. Yeah. It’s totally fine. Is this a lesson that someone that you made up or is it something that you’ve re remixed? Is it something that someone could do if they looked it up anywhere?

Sharita Ware (07:38):
Um, so I think teach engineering has the, the full size leg that the kids make. And that’s where I initially got it from.

Eric Cross (07:47):
Is that the website teach engineering?

Sharita Ware (07:49):
Yes. And, um, I, in fact, I get lots of ideals from there. Um, and I, I always usually tweak them, but it’s, it’s one of those things that kind of gets your brain going. And so it was kind of a mixture of, uh, project lead the way gateway to technology and the teach engineering. And I think the project lead the way had us making like braces, uh, for, um, kids with, um, like cerebral palsy or, or something like that. And the kids did okay with that project. Uh, but I wanted to go just a little bit, uh, deeper with it because part of what I was wanting them to do is that context and that connection, that human connection, because for me, it’s not just enough for them to make a project. Uh, before we start this prosthetic leg, I read them a story out of a Scholastic magazine, and it’s a, a teenage girl that lost her leg in a boating accident.

Sharita Ware (08:42):
And she was super active, um, playing sports and running. And, and so I was, you know, trying to get the kids to, you know, make that connection, someone close to their age. Um, and then how it’s not, it’s, it’s more than about her physical healing. It’s also about her mental healing and how she had to, you know, talk to herself to say that she could, you know, recover and, and come back from this and still go on to do all of the things that she was doing before. Um, and in some ways it’s kind of cool because, um, you know, she has a running prosthetic, she has a, a swimming prosthetic, and she has her every day with the pain and toils prosthetic. So just trying to, you know, help them to see that it’s more than just the, you know, the biomedical mechanical engineering aspect of the project.

Sharita Ware (09:30):
And so they have to design for comfort. They have to design for, um, swelling. And then, um, they also can, if they, if they want to, they don’t have to, if they want to, they can create their own backstory. So when they get there, um, we have a day where they are introduced to their client, so they get to meet their Barbie and, and then they get to decide if they want a backstory and, and then do their research based off of that. So if it’s someone that was a runner, then they can design a prosthetic running blade. So just, they have lots of, uh, flexibility.

Eric Cross (10:04):
The, that aspect of adding the narrative. It does so much for like listening to it on the outside. It one, it adds this humanity to, you know, what can sometimes just feel like it may be cold, logical stem. We’re just, we’re just doing things. We’re fixing things. We’re, you know, we’re discovering things, but really the stem has value when we’re actually applying it to, to, to serve humanity or our ecosystem or whatever it is. There was a, a coding, uh, class I was doing with my students and I showed them this app called be my eyes. And it’s for people who are visually impaired and it pairs them with a volunteer. And when they call, and there’s a whole huge pool of volunteers and I’m one of them. And when my, when it happens in class, I answer and it uses the FaceTime. So the person who’s visually impaired is holding up their phone and you see what they see and you tell them and real time what’s happening.

Sharita Ware (10:54):
Oh, wow. That’s so cool.

Eric Cross (10:56):
These are, these were the things I think for students that the story, the, the human part of it, mm-hmm, <affirmative>, it must bring in so many more students into engagement.

Sharita Ware (11:05):
Yeah. I, I feel like it does because I, I think, um, and, you know, along the journey, they kind of lose, um, they lose sight a little bit because, you know, they get out in the lab and they have access to all of these different materials. And I think, you know, truly making it, you know, project based for me is I try not to control the materials too much. Um, I try not to make it so wide that they just get lost, but I try to throw a few curve balls in there, you know, of, of materials that really don’t make sense to use, but they kind of think they make sense to use. Um, because the, the, the meat of it is that the prosthetic leg is a similar size of the original leg and that the, the knee functions. And so I don’t limit, and I grade them off of efficient use of materials.

Sharita Ware (11:59):
So, and that just throws them off because I think, well, how many Popsicle sticks can I use? And I’m like, you can use as many as you like, but remember, this is a prosthetic leg that, um, your Barbie, which is one six scale, um, is going to be wearing all day. So you could think that a Popsicle stick, if you chose to use a Popsicle stick is kind of like dragging around a two by four <laugh>, you know? So do, is that what you really want to use as your material? And some of the kids really think about it and saying, okay, I’m, I’ve got this aluminum rod, okay. This is probably what I would use for my bone structure, because it’s lightweight, but yet it is supportive. And then sometimes they come up with their own ideas in terms of materials, like one student brought in his, um, 3d doodle pin mm-hmm <affirmative> and he made joints and everything with this pin.

Sharita Ware (12:54):
And I’m, and I had delayed buying one, cause I’m like, I, how do you have control over that thing? Mm-hmm <affirmative> he brought that in and he did probably two or three iterations of it and, and got it to work where even the knee where it bit back 90 degrees, but it stopped. He made like, so that it didn’t bend forward. It blows my mind. I’m like so many UN unexpected things have, have happened just from my, um, teaching style. Now I did have, my first few years, I had a, a teaching coach, um, come in and, um, I asked her to come into my room because I just wanted to make sure because I was not a traditional teacher. She said, this classroom is amazing. And, and I think the one thing that she helped me with was, was purpose and consistency and the sense of making sure that with the standards that all of these cool things and ways of being, um, that I was doing in my classroom, that, that I kept it purposeful and intentional. So many times as educators, I know in having student teachers again, ask yourself the question, what is the big picture I want the kids to take away. And once you ask that question, then everything that you have them do will lead to that big picture. Well, it should lead to that big picture.

Eric Cross (14:22):
So it sounds like they’re, you’re starting with this end goal in mind and then kind of backwards planning to get there. Yeah. Do you think you would’ve been the same type of teacher if you would’ve gone straight from college into the classroom? No. And if, if, no, as you’re shaking your head, what do you think it is about? Cause I’ve been asking myself these questions, like just over the years, what is it about coming from industry and going into the classroom? Do you feel like, is how has that impacted you in how you teach?

Sharita Ware (14:45):
Well, I think it’s twofold cuz I was older. I already had three children. I think the combination for me, I think is I was already a mom and I had worked in industry. So the behavior aspect of kids and, and then having that real world experience. And I, I just feel like whether it’s in the classroom, um, marriage, kids, to me, it’s 90% relationship, you know, and the rest will work itself out. That’s, that’s just my, my take on it. But I, I feel like having kids, so some of the behavioral things I kind of was aware of, you know, and just learned many times just not to react to some of the things that they did.

Eric Cross (15:31):
Which is huge. Right. Especially in middle school is controlling your reactions.

Sharita Ware (15:35):
Yes. Cuz that’s what they want. You know? And, and I had this student last year as well. She’s brilliant. And so if she cannot wrap her mind around the purpose of what you’re doing and, and you’re pushing her to do something that she doesn’t think is necessary, mm-hmm <affirmative>, she kind of has these meltdowns. And, and so we just had this, you know, I don’t know, we just came to this understanding and it, and it works to control the meltdowns. I tried to make sure. And, and I used her as a gauge because I knew she wasn’t, she wasn’t getting upset because she didn’t understand. She didn’t understand the why mm-hmm <affirmative>. And so I felt like if she got the why then so would everyone else. So when she, if she was okay with it, then I was like, okay, then I must have explained it well enough.

Sharita Ware (16:25):
And so in my mind that I really need to make sure they understand the, again, going back to that purpose <laugh> and intention, making sure that that is clear. And then I think that’s what gets lost. Sometimes mm-hmm <affirmative> uh, with us as teachers, we, we know where we want the kids to go and we want us to trust the process, you know, just do it because I said so, but sometimes, you know, empowering your children to under to understand the why, because that again is what allows them to be able to do bigger and greater things on their own. So on that next project comes along. They’re starting to tell you, well, first we need to make sure we understand what, um, we’re being asked to do to do. So we have to define the question. We have to make our driving question that will help us stay focused. And, and you’re just standing up there going, okay, now you don’t need me. I’ll go here and sit down. <laugh> so it’s, uh, it is really cool.

Eric Cross (17:28):
Now I’m thinking about my own kids. Like, do my students know the why behind the lesson we did today? It’s one area of growth that I wanna make sure I do this year with my students. And so I really appreciate that. So the, and you just hit on something that is, has been in the forefront of my mind lately and math and English as you know, tend to be prioritized in schools everywhere because it’s what state tested. And it’s what, you know, this is a whole other conversation, but I’ve been talking to math teachers frequently about one of the challenges that they experience or they’ve been telling me is that math is kind of taught. Like it’s just computational, you’re solving these problems, but it’s really separated from any real life application. A lot of times, you know, it’s pizza or gumballs or, or just fictional scenarios and students don’t perform well many times. And some of the reasons why is cuz just no connection. I don’t want to solve puzzles. Like it’s not my jam. Do you have any just inside or, or perspective on how math is, is taught in maybe a way that you think it would students would benefit more?

Sharita Ware (18:32):
You know how kids learn in elementary school, you’ve got this, the same teacher teaching all of the subjects. And so wouldn’t that be an awesome opportunity for you to have like these, these projects where I feel like you could, a class could legit work on the same project for a whole entire year. And so couldn’t the English be writing your persuasive letter to the mayor, asking him to do this or do that. And the process of doing that they’re, they’re, they’re writing with a purpose with a true purpose. Um, and then when they’re doing math, you know, they want, they want a new neighborhood park. So, you know, well how much is this gonna cost? Well, math, what size is it gonna be math? Let’s see what it looks like, art, you know, you just, you have all of this things. And then of course then science.

Sharita Ware (19:32):
So if it’s on a heel, how can we, you know, deal with erosion? And you know, you can just pull so many different things into that. And so not only are they learning, but they’re narrowed in and focused on a project, they’re, they’re able to dive deep into, you know, learning more of learning, how to express themselves and communicate with real people. So it’s more of taking these compartmentalized learning that we do in middle school and high school. Mm-hmm, <affirmative> where you’re almost learning apprenticeship style. Mm-hmm <affirmative>, you know, you have these master educators and it’s not about them being the best at math or being the best at this or that. Cuz there’s so many tools now that could help you through that. But you’re, you’re giving, you’re teaching them so many life skills and so many ways to think and problem solve that, that we’re just that the kids just don’t have.

Eric Cross (20:27):

I think that that is amazing. And I think that in that situation, what I’m hearing is we’re going deeper, not wider because there are a lot of different concepts that kids are expected to learn. Or I should say there are several concepts that teachers are expected to teach doesn’t necessarily mean that our kids are learning, but we’re teaching them. And this way you’re embedded it into an authentic context. Students are able to go through this cycle just like real life. And then they’re also able to build these kind of really transdisciplinary skills. Not only am I learning the math, the English, the the, but I’m also learning the interpersonal skills of being able to sell myself and present myself in a way that’s winsome. And it’s especially powerful coming from someone from industry. Last question, even just listening to you, I know you, you are this for a lot of people, but I wanted to ask you who inspires you?

Sharita Ware (21:14):
I think there have been lots of people over the years. Like I’m thinking of my shop teacher who has since, uh, the last few years passed away. Um, he was one of those people, I think similar personality to me, super quiet person, but he was always in the background on my journey and his name was Joe Mo and we called her Madam Carol was my 10th grade English lit teacher. And she was the one that started reading my work out in front of the class. And you know, and that just gave me courage, not so much to be seen. Uh, but that the work I was doing was, was good. And, and I think I needed that kind of encouragement. Lastly, my students inspire me because when I look at their faces and see the excitement, I think of those students for the first time and, and, and think about this seventh and eighth graders for the first time feeling like they really have something to say, they really have something to contribute of value. And, and I do it for them. You know, the reason why I am here in this moment is because of them. Um, without them, you wouldn’t be talking to me <laugh>

Eric Cross (22:37):
This is, this is true. This is, this is true. You would probably never say this about yourself, but you just exude a humility and a service in how you talk about your students and yourself. And I just wanna thank you for using your gifts, but I don’t wanna just call them gifts because it makes it sound like you didn’t earn ’em and your skills that you’ve earned and worked very hard to acquire over the years to go back into the classroom and leave industry, cuz you, you could have gone back to industry too, but you decided not to. And you could have worked in the industry and your hours were a little different pay is a little different, but you came back to serve the kids of Indiana and because of you and because of that choice, those students have a brighter future and believe in themselves and they’re finding their voice. And I want to thank you for that and for representing all of us stem teachers who are in middle school and being that leader. So thank you for that and thank you for being on the podcast.

Sharita Ware (23:24):
You’re welcome. Thank you for having me.

Eric Cross (23:28):
Thank so much for listening. Now we wanna hear more about you in the amazing work you’re doing for students. Do you have any educators who inspire you? You can nominate them as a future guest on science connections by emailing stem, amplifycom.wpengine.com. That’s ST E M amplifycom.wpengine.com. Make sure to click, subscribe wherever you listen to podcasts and join our Facebook group science connections, the community until next time.

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What Sharita Ware says about science

“Sometimes, empowering your students to understand the why is what allows them to be able to do bigger and greater things on their own.”

– Sharita Ware

Engineer and Technology Teacher, 2020 Indiana Teacher of the Year

Meet the guest

Sharita Ware, a Purdue University graduate, is in her 10th year of teaching engineering and technology education to middle school students in the Tippecanoe School Corporation. Ware challenges her students with real-world, problem-based design scenarios that will help them contribute to global technology and integrated STEM. Follow her on Twitter and Instagram.

A woman with curly black hair, glasses, and a white turtleneck smiles at the camera.

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!

S1-06: Supporting students with a creative twist: A conversation with Kentucky Science Teacher of the Year, Shad Lacefield

In this episode, Eric sits down with the Kentucky Science Teacher of the Year, Shad Lacefield. Shad shares his experience teaching during the first year of the pandemic, where Shad dressed up in over 100 costumes to create a unique and engaging online learning experience for his students. Shad also explains ways he connects with his students to celebrate student success, as well as large-scale efforts he leads within his school to cultivate the love of learning science content. Explore more from Science Connections by visiting our main page.

Download Transcript

Shad Lacefield (00:00):
When you stay relevant, it’s being engaged with your students and figuring out, or what are, what are they liking? And every year it’s gonna be different. And that helps you stay relevant. When you have conversations and you build relationships with your kids,Eric Cross (00:13):
Welcome to science connections. I’m your host. Eric Cross. My guest today is Shad Layfield. Shad is a teacher at garden Springs elementary and a part-time professor at Asbury University in Kentucky during the first year of the pandemic, Mr. Layfield dressed up in over a hundred costumes to create a unique and engaging online learning experience for his students. He also created Vader visits, where he visited students at their homes, dressed as Darth Vader to celebrate their online successes and keep them encouraged. During a challenging time. In this episode, we discuss how creativity impacts engagement, transferring lessons learned from distance teaching back to in-person instruction, and how upper grades can apply the same principles to improve student learning. I hope you enjoy this discussion with shad lays field. So you’ve been in fourth grade for four years, and then you were in second grade and fifth grade. And so like how long have you been teaching for like total?

Shad Lacefield (01:09):
So this is my 15th year teaching.

Eric Cross (01:12):
Really? Yeah. You’ve been in the game for a while.

Shad Lacefield (01:15):
Yeah. Yep. It, it doesn’t, and it’s always surprising to parents too during that, that first like, come in and meet your teacher. And I walk in, I’m like, yeah, I’ve been teaching for 15 years and every time it gets ’em, they’re like no way. And I’m like, yeah,

Eric Cross (01:28):
That’s, that’s a good thing though. That’s a good thing. Right?

Eric Cross (01:31):
You know? So like, well the energy and then, and you’re just how you’re perceived. Like you’re, they’re just, I don’t know. It’s something about work with young people. Like it keeps you young.

Shad Lacefield (01:39):
That’s what it is. Absolutely.

Eric Cross (01:41):
So how did, how, like, what’s your origin story? Like, how did you become a teacher? Like what, what was it? Was it something like you knew second career, like right outta school? Like how did you end up in the classroom?

Shad Lacefield (01:53):
Yeah. No, and I love this question cause I’m a big Marvel and, and superhero. So origin stories are all, I love a good origin story. So I grew up on a 13 acre farm in a little bitty town called Gustin, Kentucky, and very early on, like we were instilled my parents, amazing, amazing parents. But they really instilled like a, a super important work ethic in our lives of like, it’s, it’s all about hard work and it’s important that you’re working hard in whatever it is that you do. And I’m one of six kids as well in my family.

Eric Cross (02:24):
Where are you in the–

Shad Lacefield (02:25):
I’m second to last.

Eric Cross (02:26):
Second to last. Okay. So you’re the second youngest.

Shad Lacefield (02:29):
Yes. Okay. And and so, and so growing up, like with that, like, you know, I worked in tobacco, I worked in hay, you know, we did things being on the farm and stuff like that. And within my family as well, there’s four boys. And so when I decided to go to college I was the first guy in my family to go to college. And the first and only boy that ended up going to college. And so it was like this big deal, like, oh, you know, we got one of our boys gonna go to college. So what is he gonna be? And I was like, well, if I’m gonna put forth the, the time and effort and then the financial strain that it would cause cuz we were not poor at all. My dad worked two jobs to make sure, but I really felt the responsibility of like, if I’m gonna go, I’m gonna work in a profession.

Shad Lacefield (03:09):
That’s gonna make a lot of money. And here I am as a teacher now. So I didn’t go to college to be a teacher. I actually was pre dentistry. I thought, now here’s a profession. You can, a lot of money. You don’t work weekends or holidays, you know, I can still be the doctor thing. And so I’m gonna be pre dentistry. But like all good origin stories. There was a, there was a flip. So in my first year I started working at the most majestic place that you will ever go. It’s called Squire, boon, caverns. It’s a cave in Southern Indiana. And it’s an amazingly beautiful little place. You have to like one lane highway, like road to go back there up and down. Like you, you think you’re never gonna make it. And if it rains too much, the bridge will flood and you actually can’t even get back there.

Shad Lacefield (03:52):
So that’s how we’re talking like way back in the sticks. But once you get back, back there totally worth it. And as part of the job you were a tour I also did grist mill demonstrations and gym mining adventures, or, you know, as they’re gym mining and stuff like that. And within that, I started working with school aged kids and on very large tours and stuff. And my manager at the time, Claudia, I’m still great friends with and we still take our kids back there. Every summer she, to me, you’re really good with kids. Like you’re really good with kids. We have this scout program that’s on the weekends. And then during the summers and you would be teaching kindergarten through eighth grade kids, geology and forestry. What do you think about doing that? And I said, well, right, let’s try that out. And then I got the teaching bug and it hit and I was like, oh my gosh, like I don’t wanna spend my life doing something that is all about money or, or that is like, this is where it’s at. Like, I love this, I enjoy this. I enjoy the response that I get when I’m talking. And kids are excited about learning and getting new information and learning new stuff. And so then I change my major and here I am now, all these years later teaching instead of being a dentist,

Eric Cross (05:04):
Are there, are there days, do you ever have days where you’re like, you know, dentistry, it’s still an option. Like I can, I can go back.

Shad Lacefield (05:12):
Oh, rare, rare occasions. Rarely. Yeah.

Eric Cross (05:16):
Okay. Yeah. All right. All right. Fair enough. I, I, I always joke and say that like we have, you know, sometimes I have my, my alternate job on the hard days, which is for me, it’s working at the gap where I just want to fold clothes and go home at the end of the day, you know, on those really rough days. And you know, it’s never the kids, right. It’s always other things. The kids are like the great part. And then there’s all these other things. And I just wanna work at the gap. I just wanna work at the gap. Fold some clothes. Yes, sir. Yes. Ma’am absolutely. I can find that size for you. And then I just go home cause about their job when they go home at the end of the day, when you work at the gap, at least sorry, gap workers. I’m sure hard of that, but my perception in my mind is that you close up shop and then you’re done. Yeah,

Shad Lacefield (05:52):
Absolutely. Like you said, they can turn it, like it’s a turnoff at the end. Exactly. As teachers we know, like you don’t ever turn it off, it’s always there.

Eric Cross (06:00):
Yeah. So one of the things that I was super excited about when I, when I first heard about you is I went on your website and there’s so many things I feel like I can just talk about your website and just the, the content that you’ve produced. I, I, there’s so many directions I can go. But one, one of the things I want to ask you is, is about that. Now, one of the things that’s on there, and this is coming from a fellow star wars, Fisha who finished Bobba FET and the Mandalorian recently and is Jones in four OB one to come out.

Shad Lacefield (06:33):
Oh, so yes,

Eric Cross (06:35):
I live in Southern California next to Disneyland visited Galaxy’s edge star wars. You have these things called VA Vader visits. And so what do you do in those? And like, where did you get the idea for these Vader visits?

Shad Lacefield (06:50):
So the costumes were bringing the kids into the classroom. But when they left my room because you would, we only had them for a certain amount of time. There was still a lot of extra work that they needed to get done. And what I was seeing was I could get them to come in and they were really engaged during my lesson. But then afterwards, when it came to work completion or getting things done, there was, it was starting to fall off. As you know, we were experiencing, you know, more and more craziness of what’s going on. So then as an incentive, I decided if you have everything turned in, by the end of the day, I’m gonna dress up in my Darth Vader outfit, full costume, the, you know, the, the full helmet, like everything. And I’m gonna show up to your house and we’re gonna hang out and play any game at all that you wanna play.

Shad Lacefield (07:34):
So then it was a way of rewarding. My kids for getting everything turned in. But same time I felt like it would also help me build a relationship with them. That was a very challenging part of online learning. Like, again, I want you to feel like you’re a part of my classroom. I wanna feel like I’m invested in you and wanna learn about you. And it was a commitment because some of those kids put me through the ringer, whether it was we’re gonna do gymnastics on a trampoline. And again, I’m in full costume doing gymnast on the trampoline, or we’re doing soccer drills with their soccer coach at their house playing football games. I mean, all kinds of stuff. I made a Yachty game for a kid that loves Harry Potter. And it was really a big part of getting work turned in because, and it’s the crazy thought they wanted to spend time with me. Like that’s what it was. And so it was like, yeah, absolutely. I’ll keep dressing up. I did over 50 plus Vater visits. It wasn’t just for my homeroom. It was for all of fourth grade. So I went over 50 visits and it was cool to see kids in their home and talk to them and meet their parents. It was a great opportunity for me to engage with parents as well. How is online learning, going, what can I do to support you? Do you guys have any questions and stuff like that? So

Eric Cross (08:39):
This thing of relationships is like leading to work completion, which isn’t, which isn’t always the, the thing that we think to as educators of like how, you know, work completion. A lot of times we think of like structures or you know, certain protocols that you do in class get work completion, but here you are addressing as Darth Vader. And, and you said students were turning in more work because they’re connected to, you saw an increase in, in yeah. Engagement.

Shad Lacefield (09:07):
And absolutely. And, and I remember even saying that to myself, like this is, this is what’s getting them. But it, it was, and as part of the Vader visit as well with the videos we recorded all of them and I said, I’m gonna make you a YouTube star. And so I would, I, I recorded them. I put ’em on my YouTube channel. And so a lot of the videos that are on my website, all those Vader visits are like the kids showing off and playing against the teacher. And I promise you, I didn’t take it easy on any one of those kids. Like when it was like a verse match, I went all out and I told ’em. I was like, if you beat me, you know, it’s gonna be like, you earned it.

Eric Cross (09:38):
What a great way to leverage, just what, what is relevant to our students? Like you used your platform and then now you’re showcasing them on your, you know, your platform or what you were using. And then they’re seeing each other. And I could just see, regardless of the grade level, like just students, like beam from, from getting that kind of positive praise through, through, you know a medium that doesn’t, that tends to be more of a, just content consumption, but you’re kind of watching other folks do stuff, but now it’s about them. Like, and they’re, they’re getting that attention directly. Now I have to ask about the Vader costume. Did you, did you buy it for this event or did you already have that Darth Vader costume in your closet?

Shad Lacefield (10:19):
I had parts of the costume, but not the complete costume. And honestly, the very first Vader visit I had, I had the Vader mask that makes sounds, and like you could talk and it makes you sound like Vader.

Eric Cross (10:29):
My dark saber is on order. Yes. And it keeps getting delayed from best buy. It’s supposed to arrive in April, but I do have dark staple and order that I ordered back in November. So the best to your point, I don’t know who doesn’t have one, I’m waiting for mine though.

Shad Lacefield (10:42):
There you go, come on. Best buy come through for us. So

Eric Cross (10:44):
You, you did all this investment in time and, and you created all this content, but then we went back in person. Were, were you able to bring this back into the classroom or any of the things that you had generated during distance learning back in the classroom? Or are you, are you using some of the things that you learned? Like what, or is it just completely separate and you’re just doing something completely different. Now

Shad Lacefield (11:04):
That’s a great question. So I still try to dress up at least once every week, if not once every other week just to make whatever we’re doing fun, cuz I already have costumes that were connected to the content that I was doing. So had I had made a character called captain Soundwave that will use when I’m teaching my amplify lessons over sound. And so then I, you know, I have that or I would have, you know, specific characters that were designed for certain lessons that I would do. And so I still

Eric Cross (11:32):
Lemme interrupt you real quick. Where did you get these character ideas from? Cause they are super creative. I clicked on one random one. And you have had like a, a knitted like skull cap and like some blue shiny like cloak and I like who is this guy? I think, is that him? Is that captain sound wave? That’s

Shad Lacefield (11:48):
That’s hilarious. That was, that was my attempted Elsa. Oh, that was yeah. Started buying more and more costumes and and making characters and putting costumes together. And so yeah, it just ends up being this thing where you never know when I’m gonna show up in a completely random costume and be like today, we’re getting ready to learn about how sedimentary rocks form. And I dressed in my rock outfit, which is the old school rock with the turtleneck and the gold chain with,

Eric Cross (12:16):
Wait, do you have a Fanny pack too?

Shad Lacefield (12:17):
I have a Fanny pack. Yes you have. Yep. You nailed it. And they’re like, what does this guy

Eric Cross (12:22):
Do? He raise the one eyebrow. Can you do the, the rock eyebrow? Oh yeah, you got this. Oh, people on the podcast. Can’t see. Chad’s got it down. He’s got it down. He’s got the, he’s got the eyebrow going. Okay, so you, so I feel like I can go on a tangent and talk about all your costumes that you have, but the thinking about this. So tons of engagement, younger people now taking like some of the principles that you’ve learned from this, how can, how can upper grades like bring this joy to their classroom? Like middle school students, you know, older kids sometimes, you know, they can, they’re still kids, but you know, they might not be the same thing as fourth graders. Like would you, do you have any ideas of like how teachers and upper grades can kind of take these elements that you’ve done and, and apply them?

Shad Lacefield (13:04):
Absolutely. So some of the things that you had talked about, like with YouTube can also be applied to like TikTok videos and things like that, that kids are, are willing to watch and, and be engaged in. And so those things, I feel like I’ve seen other middle and high school teachers really utilize in their classroom. But honestly, and this is a new initiative that we’ve started in our district. Minecraft has been something that a lot of kids play and are really engaged in and has shown an amazing engagement for all of our kids when it comes to science engagement, particularly. And so with that, so there’s 126 million active Minecraft players right now in the world. And Minecraft is one of the largest selling video games. The average age, cuz they’re always like, oh, Minecraft is for kids who actually the average age is like 24.

Shad Lacefield (13:51):
So a lot of the older kids are playing Minecraft as well with the younger kids. And with that in mind, it was a way when I looked at Minecraft and specifically like Minecraft educational edition came out and it was during COVID and it was free. So if you had a school email or it’s like the, what the go 365 account, you could get it for free and all of our kids got it for free. And so then, then we went from playing Minecraft on the computer as like a fun game to me looking at it and saying like, wait a minute. I feel like when I’m doing energy conversions, we can take Redstone and Minecraft and kids can now show how a simple system using different parts and devices can work and understand even more con creates how energy is converted from one form to another.

Shad Lacefield (14:39):
And so let’s make this a, a, a, an actual activity. Let’s take what I’m teaching in the classroom. And if they get done early as an enrichment piece, because there’s not a ton of science and enrichment activities at times for kids to be able to do, like, what do I do when I’m done, Minecraft ended up being that. And so I could have these elaborate worlds that I would build for them that they could then go and play and be super engaged in and show me way more on this Minecraft world, what they knew than what they were writing on paper sometimes, cuz I, you know, you’d get like a sentences out of them on paper, but then all of a sudden when they would build this elaborate system and you just had them record and talk, it was like, oh my gosh, you understand way more than I was thinking that you did with that last exit slip, an assessment that we did.

Shad Lacefield (15:25):
And so like, this is awesome. So then I went to my district and I actually proposed an idea what if we did tire Minecraft build challenges for the whole district? So our district has 37 elementary schools and I was like, I think this could be something that, you know, as we’re looking for science, curriculum engagement and making kids excited about learning science and stuff again, cuz that was always the hard part. I feel like sometimes with COVID everything kids lost this love of, of being in the classroom and, and, and learning and that it was like, you know, getting them to come back into the classroom and, and finding, learning fun again. It was like this, this started to get ’em excited and like, yeah, I get to play in Minecraft and I’m learning at the same time. And it was working for all kinds of content areas.

Shad Lacefield (16:07):
We’re doing a blast off to, to Mars. We it’s called blast off to us. We’re partnering with CLO of the future. They’re working with SpaceX. Our kids will actually get to send postcards to space and yes, it’s, it’s a super cool thing. And I love my district and all of the office of technology, individuals, Ashley Josh and Kelly for putting this together. And so it asks this question if you could a community in space, what would it be like? And the goal is that kids will write on the back what they want. And then we send this postcard off to space, they stamp it saying it’s been in space and the kids get to have it back and, and be able to use it. But what, what we decided, what we could do with Minecraft is what if they actually built the colony on Mars, like really research put time and effort into reading scientific articles about plants and how plants would grow and, and water and, and structures and apply all of that in a massive build challenge. And then that be, you know what we’re doing? That can be the answer to the question. And so it’s not just a couple sentences on a postcard, but it’s like a week or two week unit that pulls all this scientific content and standards that we’re working with and really allows kids to show so much creativity like on my Twitter I’ve been posting like pictures and stuff like that of some of the students builds. And I’m gonna continue to do that throughout the build challenge.

Eric Cross (17:26):
Now, are you using Minecraft EDU?

Shad Lacefield (17:28):
Yes. That is correct.

Eric Cross (17:29):
I love Minecraft EDU. Like it, it, you talking about it inspires me to, to try to dive back into it. One of the things sometimes I feel limited by is the time that I have and the things that we’re trying to cover. And it’s almost, it almost feels like we’re doing something wrong using a video game to teach, but it’s such a great educational tool. Like you said, you just said that students are able to show what they know in, in a way by creating something that’s different than if they would’ve just written it, but they’re actually creating, and this is one of the things, I guess you kind of hit on this, but I wanted to probe it a little more. Is do you have your students creating content like you do? Cause I kind of heard that they, you were, did you say that they were explaining or doing a video recording or describing it? How are they, how are they, how are they doing that work?

Shad Lacefield (18:17):
Yeah. So what they actually do is they’ll write a script and they will use Screencastify to record and then upload to Flipgrid. And then that way they can actually show their build to all of fourth grade. Since we weren’t allowed to be in the same class, like we were all departmentalized, so then we will have voting challenges. So after you record, you get to see everyone’s videos, you get to like and comment and leave feedback on their builds. So you can see what the other kids created. And then then from those initial videos and voting, we selected a certain of kids that then go on to the district level for our Minecraft build challenge. And then those videos are viewed by administration and other teachers to vote again. And then you end up having grade level winners and then an overall winner, which shout out to my boy in fourth grade, who was our overall winner, Eli, super proud of him.

Shad Lacefield (19:07):
He, he made this really, really space saving system, which was hidden stairs that ran off of Redstone and used motion, energy. And again, in his video, he talks about like how motion energy has changed to electrical energy and then back into motion through the process of how this hidden staircase would be in the wall. And then you’d be able to use this lever to then release that staircase. So you could go up and down but it was just, and again, when you, when you let kids talk about energy conversions and you let them build all of a sudden, you have kids making security systems for banks. Another kid that made a feeding system for kids for animals at the zoo, and it was just like, oh my gosh, I had no idea that this was what you guys could run out and do. When I, when I taught you how energy conversions work, that this is what you could produce and come over, like this is mind blowing. I love it,

Eric Cross (19:56):
What our kids can do and what they can create always kind of blows us away when we give them an opportunity to kind of have that freedom to, to create and take their knowledge and actually do something with it versus channel it into what, show me what, you know, but only do it like this. This is, this is the lane that you have to stay in. How do you get these ideas and, and stay, stay relevant? Like so many of the things like you’re touching, like pop culture, you, you have this hand in education technology, you have you’re, you’re doing video editing. Like where are you drawing from? Cause I’m just thinking like, as a teacher listening to this, that might be newer. And they go to the side like, oh my gosh, this, this guy is doing these so many things like where are you drawing from for inspiration or ideas?

Shad Lacefield (20:39):
I think a lot of it is like you say, when, when you stay relevant, it’s being engaged with your students and figuring out, or what are, what are they liking? And every year it’s gonna be different. And that helps you stay relevant. When you have conversations and you build relationships with your kids to figure out, you know, what’s going on. Because I was not a big Minecraft person. It was the group that came in that really challenged me to do Minecraft because it, it showed up on their Chromebooks one day and all of a sudden it’s like, oh, we can play Minecraft all the time. And I said, no, you can’t play Minecraft until that I’ve had training. And I know what’s going on because I’m super nervous about this new thing. And I wanna make sure you guys aren’t doing something that you’re not supposed to.

Shad Lacefield (21:13):
And like, they hounded me hardcore about you better do you need to do that training, Mr. Lacefield, you need to, we wanna play Minecraft. You better be doing this. Right. And so I was like, all right, man, I’ll, I’ll invest. I’ll, I’ll put some time into this training. And I’m so glad that I did yeah, again, that’s it just like building relationships and having those conversations help you realize like, what’s, what’s what are they interested in? What what’s going on and what would be really funny, even connecting that back to the costumes. What would it be really funny if I showed up in you know, today, princess Jasmine.

Eric Cross (21:42):
Yeah.

Shad Lacefield (21:43):
Been yes. Done that. That’s a great one. I,

Eric Cross (21:45):
I, I just went to the social studies page. I, and I stop laughing while you were talking. Cause I saw the princess Jasmine.

Shad Lacefield (21:52):
Oh yeah. Folks.

Eric Cross (21:53):
I’m telling you, you have to go, you have to go to his videos and see what he’s done. I mean, they’re just, they’re just amazing with my middle school students. They, I, I find myself having to be into things that I’m not normally into. And we have these intergenerational relationships, right? Like I think teachers are unique in this I aspect where I can connect with a 12 year old with what 12 year olds are in no matter where this 12 year old’s from. Cuz I get 12 year old culture. But sometimes when I go back into my adult world, like I forget that like, Hey yeah, haven’t watched a new anime you know, or, or whatever, you know, up

Shad Lacefield (22:26):
That. Yeah. No said too. And a kid will show up wearing a, a shirt to school and I’m like, I wasn’t the world’s that like, I’ve never even seen that before. And you’re like, okay, I’m gonna have to learn what that is cuz that yeah.

Eric Cross (22:38):
And then the next student asks you about, Hey, do you like, do you like these this game? I’m like, yeah, yeah, let me go Google that game real quick. Yeah, I’m totally into it. I’m downloading on my phone real quick. And, and now I’m connected to all kinds of obscure random interests, but to your, to what you said, it like, it helps keep us fresh, right? With I, with ideas, there, there is something that is super practical that you’ve done that you’ve created that I’ve encouraged teachers to do. And I think you really nailed it. On your site, you have these video tutorials. When I look at those, I, I think about how much time you must have saved yourself of not having to explain the same exact thing multiple times. Because you’ve created this virtual help section that allows students to log in amplify earth, check, Flipgrid, whatever. Like do you, when you’re, when you’re teaching students, do you, do you use those in direct students there so they can kind of support themselves? Or is that, what, how did that come to be when you, when you made these, these virtual tools? Because I could just imagine these are time savers for you.

Shad Lacefield (23:49):
Absolutely. Cuz again, like you said, it’s it saves on time. So a lot of when you have kids that are already visual learners as well, and they love watching YouTube and they learn stuff from YouTube, why not? I mean, make the video and then attach it to my Google classroom, keeping everything online. Everyone always has access. And by still having those videos, it allows kids to hear the directions multiple time, but on their time and at their pace. So then it’s posted on the assignment. So even though I probably still will give those directions verbally out loud if a kid forgets and maybe they feel a little nervous about asking in front of their peers, like, oh, how do I do this again? Or, oh, I don’t remember how to do that. That video is linked on there. So that way they can go back and watch it.

Eric Cross (24:28):
It’s almost like a little co-teacher that you have like a little aide that’s like, but it’s you, but it’s like a mini you who’s helping you out. I found that putting sometimes those tutorial videos on ed puzzle, where at different points in time, you can set it up so that at a certain timestamp, it asks a question and you can control it. So they can’t move faster past it until they respond to the question and you have the question be about whatever you just said. And then it, it syncs with Google classroom. So you can import all the grades and you can see how far through the video they got. But that was one other layer that I was able to do. So I can have some accountability and make sure that okay, everybody watched it and they answered all five questions of like, how do you do this?

Shad Lacefield (25:07):
Oh, see, now you’re sharing stuff with me, Eric, because I, I’m not as familiar with ed puzzle. I’ve used like near pod and per deck, but I mean just you saying that I’m like, okay, I need to check out ed puzzle and, and see what, what this is all about. Cause that sounds awesome.

Eric Cross (25:20):
Hey, I shared something with Chad and it it’s useful. I’m I’m feeling good right now. I’m feel I’m feeling good. So as we, as we kind of wind down one, couple questions I wanna ask. One of ’em is you’ve been in teaching for, for 15 years and I, I talk to you like right now and I get this energy and this vibe that’s just so upbeat, so positive. How do you stay fresh, fresh. And how did you stay fresh during a time when things have been so hard, you know, and it, and still is for so many educators, how do you stay encouraged? Like what, what have you done and, and to stay in, in education for, for this long,

Shad Lacefield (26:00):
I think it, it even goes back to like when I made my initial decision to switch my major to education, like I, I really felt like I found so thing that I thoroughly loved and enjoyed, and I always feel like you go through seasons. Like, and I definitely, when, when COVID hit, like you went through a season of where you start to feel again, that pressure like do I really like doing this as much as I thought that I like doing this and am I ready for this next thing? And then I just go back to just the, well, why did I do this to begin with? And, and it gets me, you know, excited to be like, I did it for the kids, like, and it’s about the kids. And I get joy when they’re laughing and smiling. So again, with the videos, it’s like, how can I make ’em laugh and smile because if they’re laughing and smiling and having a good time, I’m gonna get, you know, jacked and ready to start teaching again.

Eric Cross (26:48):
And I just hear that so much in what you’re saying is you’re serving your kids is, is being more than that building the relationship, that connection. And then through all that, the learning happens. The last question I wanna ask you is who’s one teacher that created a memorable experience for you or inspired you. Is it someone that you remember when you were in school or learn experience that just, that stands out to you to this day? Cuz as teachers, we remember thi like our kids remember us and it’s weird to be in that position to think that we’re gonna be that person. So is there anybody or anything that stands out to you that you remember from a, a teacher and experience?

Shad Lacefield (27:27):
Gosh, I have, I have a lot that you know, from my fifth grade science teacher, Mr. Goodman, who we did the ecology meet and the ecology team, and we went to OT Creek park and we competed against other schools about science, connected materials to my physics teacher in high school that let us build boats out of cardboard and take it to the only hotel in our town and the pool. And we had like boat races with the cardboard boats that we did. But really I, I go back to Squire boon and Claudia my manager and I remember not only was, she’s such a, a pivotal like getting me into teaching. But I remember the, the curriculum that we were using at the time that I was. And again, it goes back to what if I was to teach that curriculum, I would not still be a teacher because again, as sometimes you experience with curriculum, it can be boring and not engaging. And I was already putting my own flare on it at SQUI boon during the scout lessons. And I said, what if I just completely rewrote this curriculum? What if I made it really fun and put my own, spin on it? And, and she was like, absolutely, absolutely do that. And I feel like that encouragement as teachers, when we encourage kids to be creative when we encourage kids to, to take risk and to try new things we end up getting such amazing results that we didn’t even expect

Eric Cross (28:45):
Thought I out to Mr. Goodman for the ecology meet the physics teacher for the, the boat races, which are hilarious, by the way, if you’ve ever been able to watch students, did you make ’em at a cardboard?

Shad Lacefield (28:53):
We did. Yep.

Eric Cross (28:54):
Yeah. Those are hilarious to watch. And Claudia for giving the freedom to let you be a educational DJ and remix things to make it fun. Thanks for being on the podcast. Thanks for your inspiration and for sharing your stuff like publicly and letting other people see it and, and get ideas. It’s, I’m sure there’s more people than, you know, and more teachers than, you know, that are looking at that and getting their own ideas and coming up with their own. It might not be star wars, but coming up with their own inspiration, maybe it’s like Harry Potter or Lord of the rings or some like that.

Shad Lacefield (29:26):
Yeah. Whatever. You’re passionate about. Pull that in.

Eric Cross (29:31):
Thanks so much for joining me and Shad 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. That’s STEM@amplify.com and make sure to click, subscribe wherever you listen to podcasts until next time.

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What Shad Lacefield says about science

“It’s about being engaged with your students and figuring out what are they liking. Every year it’s going to be different…when you have conversations and you build relationships with your kids.”

– Shad Lacefield

4th Grade Science Teacher, District Elementary Science

Meet the guest

Shad Lacefield is a teacher at Garden Springs Elementary and part-time professor at Asbury University in Kentucky. Mr. Lacefield leads professional development in his district, and has been a guest speaker for Eastern Kentucky University, Campbellsville University, and Amplify Education. His topics include classroom managment, integrating techology, and student engagement. He earned his bachelor’s degree in elementary education from Campbellsville University in 2007, and his master’s in science from Southwest Baptist University in 2011. Shad has either taught or coached every grade K-12, and in his 14 years in education he has served as a lead teacher in literacy, math, science, and social studies. He currently coordiantes with the FCPS Office of Instructional Technology to plan Minecraft build challenges for elementary students, and is working on setting up a science field trip that turns a golf course into a STEM lab. During the first year of the pandemic, Shad dressed up in over 100 costumes to create a unique and engaging online learning experience for his students. He also created Vader Visits where he visited students at their homes dressed as Darth Vader to celebrate their online successes, and keep them encouraged during a challenging time. His creative teaching style, and over 50 “Vader Visits” with students, have been featured on WKYT-TV, LEX-18, Spectrum 1 News, and several local and college news publications. Shad lives in Lexington Kentucky with his wife Whitney Lacefield and their three children.

Check out his websiteYouTube channel, and Facebook account!

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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!

S2-01: How teachers are really feeling this school year

science connections S02-01 Episode Cover

In this special solo episode, Eric Cross starts the season by sharing his personal journey as an educator, and how the difficulties of the last few years have shaped his mindset going into the upcoming school year. Eric also addresses teacher burnout and what inspires him to continue working as a classroom educator. Explore more from Science Connections by visiting our main page.

Download Transcript

Eric Cross (00:02):

Welcome to Science Connection, Season Two. As we begin the next season, I thought it would be a good time to share my story. As the host, I get to ask people questions about their journey, but I’ve actually never shared much about my own. So I’ve taken some of my most frequently asked questions to guests and asked them to myself. I hope you enjoy.

Eric Cross (00:23):

So the origin story question, I think really gets to the heart of why a person does what they do, because so much of who we are, especially as adults and teachers, is a result of experiences that we had in our lives when we were kids or in school with other teachers. And my life’s no different. I was born to a 19-year-old single mom. And when you’re a young boy growing up, especially with a young single mom, you often look to older men in different positions as kinda like a surrogate or like a mentor. And you may not even tell them that they are that to you. You kind of keep it close to the chest. And that’s what I did growing up. One of the ones that really stood out to me is, in seventh grade, I went to a middle school here in San Diego that was called Keiller Middle School. And we were a magnet program that specialized in science. And they had this program that brought professors from the local universities and they did this high-level enrichment. They would even take us to the college campus and we would work in these labs as seventh graders. It was amazing. And one of the people there, his name was Dr. Tress, and he was a professor. And Dr. Tress took a liking to me. I reminded him of his son. We were doing this great embryology experiment. We would take purple sea urchins. And we would inject them with potassium chloride, which would cause them to spawn. And we would fertilize these eggs, and then we would run different experiments using them. And these were things that I had never done before. I had always loved science. I’d always loved tinkering and building things. But this was my introduction, really, to high-level biology and to higher levels of education. I didn’t—I didn’t have many figures like that in my life growing up. I mean, I’m a first-generation, you know, high school, college graduate. Many of these are first generations for me. So, this was a new experience. And so Dr. Tress really unlocked a core memory and was one of my first mentors, as far as academics are concerned. And during my seventh-grade year, I entered the science fair and won first place, which was a huge deal. They took us out to Balboa Park. We got to miss school for a week. We got to go to all the museums for free. It was the best. And I think at that point in time, it really solidified something in me that would lay dormant until later on in my adult life. High school, I was really fortunate: the high school I went to was Morse High School, not too far from Keiller, and they had an aeronautics program. So I was able to enroll in that aeronautics program. And I learned how to fly before I learned how to drive. And I had this great instructor named Mr. Klon, who was this like 6′ 4″, 250-pound hippie guy. And he—we would get in the plane and we would have these like philosophical conversations. And through that, especially looking back now as a teacher, I realized that he was making connections with me and investing into who I was as a person. And it was something that I so needed at the time. Because at home I didn’t have that. You know, my safe place, a lot of time, was school. It was my only structure. It was where I knew I would get encouragement. It was where I knew things were reliable and consistent. For a lot of people, and a lot of kids, their home life isn’t like that. School was that for me. So Mr. Klon, I mean, he was this authentic, you know, consistent person in my life and made a huge difference at this time.

Eric Cross (03:23):

After I graduated high school, I left home just to get away from a difficult environment. And I was homeless for a little while and that was a huge moment in my life. And around that time, an aunt found out and she said, “You’re gonna come stay with us.” And this was like this three-year process of me living with them in this, like, functional family that ate dinner together. And they went to the zoo. They had family passes. And they took family photos at Christmastime. This was all weird stuff. Like, I didn’t know—I didn’t know who did these things. It was—I felt like a puppy that like lived in a home that was like…it was a home that was just always kind of like violent or like just really toxic. And then it gets put into a healthy home and doesn’t know how to act. That’s how it felt. And this was around like 19, 20 years old. During that time I started putting myself through school. So I went to community college and I was broke as a joke. And so I couldn’t afford the textbooks while I was going. So I would just go to the bookstore, the Barnes and Noble bookstore in Mira Mesa here in San Diego. And I would stay there all night using the textbooks or using the books there for doing my work. And then I would just put the books back on the shelves. Because let’s just face it. Textbooks are expensive, brother wasn’t trying to pay for all that. So I really had to earn that time. So I was working full-time. I was going to school. And, eventually I got a job in working in finance with a really great friend who mentored me during my younger twenties. And I didn’t wanna be broke and finance made sense.

Eric Cross (04:44):

And so I did that for a little while, until I got to a point in my career where I was watching an episode of The Office, the UK version, the Ricky Gervais version, and a character said, “I’d rather be at the bottom of a ladder I want to climb than halfway up one I don’t.” And I realized, working in finance, that I was halfway up a ladder I never wanted to climb. So I wanted to move into something that, if I was gonna spend eight hours a day or 10 hours a day doing something, I wanted it to be something that actually filled me up inside. And this is how I got into teaching. So I had always been working with young people, specifically 12- to 18-year-olds, like a non-profit or volunteering, mentoring, after-school programs. And I’ve always managed to rationalize my job in the finance world as meaningful because it let me do the real work that fulfilled me. So the real work was working with the kids. But my day job, my, like, Clark Kent-type job, was just, you know, doing the finance thing of like helping people that have a lot of money make more money. Which at the end of my life, I look back and I said, “That’s not what I want my legacy to be.”

Eric Cross (05:43):

And when the finance crash happened in 2008, that’s when I think I started looking back on it and said, “If I’m gonna spend all my time doing something and spending 40 or 60 or 80 hours of my day of my week doing things, I want it to matter. And that’s when I decided to pivot and leave that field and go and get my master’s in education and get my teaching credential, teaching science specifically. Now, one of the questions we get asked a lot and I’ve been asked is, is “How has teaching changed as a result of the pandemic?” And I feel like this could be several podcasts in and of itself, and it’s also regional, because everybody’s experienced it differently, And we’re still experiencing it! That’s the crazy thing! It’s like, it’s not over, we’re still in it. And some places have innovated and pivoted and some places just did what they needed to and they are trying to go back to business as usual. But if anything has happened, the pandemic revealed how much more, how much schools are more than places of just content learning. For many students it’s where they have their only community, their structure, their emotional wellness. They get regular meals, access to tech, and adults that care about them that are outside of their family. The schools are so much more than that. I mean, my school, they were a place, like a hub, that was giving out food every single day during the pandemic to families that would kind of drive by. So for a lot of schools, they became places like that. It also…the pandemic revealed the intensity of the educator workload. I mean, being able to manage your family, having the capacity, to be a content expert, you need to be a counselor, a trauma-care specialist, a coach, an encourager, a tech expert.

Eric Cross (07:23):

I mean, the term mental health is now more common and starting to become prioritized. Now we’re focusing so much more on the whole child. And we know from research that how a child feels about themselves and their safety and their security impacts their ability to learn. So the more comfortable and safe a student feels in the classroom with teachers and with friends, the better they’re gonna be able to learn. And ultimately the higher they’re gonna be able to achieve. You can’t, you can’t have one without the other. In addition, I think less teachers, see themselves teaching into retirement. I think that’s a big thing. I read these articles about teacher shortages and I think the reality is it’s actually teacher exodus. It’s teachers leaving. And that’s been really difficult. I’ve had many friends who’ve left for the private sector. And I get it, especially if you’re one that has—if you’re the first in your family to graduate from college, with a STEM degree, to them taking a teaching position can mean walking away from a salary in the private sector that pays two or three times more.

Eric Cross (08:23):

And in many places around the country, in order to be a teacher and maintain a median standard of living, you need either dual income, multiple jobs, or a multi-generational household. For a lot of people it just doesn’t make sense. And even right now, today, as I’m recording this, I’m reading articles and getting text messages…and I received a text message three days ago from a teacher that said, “My goal this year is to just not resign.” And that’s where a lot of teachers are feeling right now: isolated, challenged, and under-appreciated. And Plato said, “What’s honored in a country is cultivated there.” And I’ve been looking at how teachers are honored and one of the ways is just, like, practical. Like, look, I gotta pay my bills. You know, love the Starbucks gift card. Love the CPK, the gift card. The cards, all those other things…but brother got a car payment. And at the end of the day, if we care about our kids, we need to take care of the people that take care of them. And there’s very practical ways for that to happen. And everybody in different sectors around the country is dealing with that in different ways. I think the pandemic also revealed, now the public can see how our kids don’t receive the same quality of education. And once you’re aware of that, you can’t put the genie back in the bottle. So once you see on Zoom or once you see in a meeting, or once you see on the news, that students in different areas, whether it’s the rural South or a suburb in Seattle, are not getting equitable educations, well, ultimately that impacts all of us. Now. It’s not all doom and gloom. Good things have come from, as a result of, the pandemic. Many schools have made progress towards narrowing the technology gap, ’cause they had to! ‘Cause you can’t do Zoom and you can’t do Google Meet and all that stuff with a packet! You gotta get those Chromebooks. And Chromebooks and the internet and access to tech is not a new thing. It’s been out for a long time. The technology gap is not a new thing. It’s been written about extensively, but all of a sudden districts and schools started figuring out how to close that gap. And that’s awesome. We didn’t want a pandemic to be the catalyst for that to happen. But at the end of the day, we started closing it. A lot of schools did an amazing job and districts did an amazing job with deploying the hardware, sending out buses with wifi, putting lessons and videos on USB sticks and dropping them off to parents who live in sparsely populated areas. I mean, there were so many stories that I’ve heard about schools and teachers just doing amazing things, going above and beyond what they needed to on behalf of kids.

Eric Cross (10:51):

I think in addition to that, there’s also been students and families are now having more options to personalize their learning. So we have this in-person model, we have this Zoom or kind of online model, and this hybrid model, and it hasn’t all been perfect, you know, at all. But some families have come out and said, you know what actually doing this hybrid model is better for my son or better for my daughter or better for my student, because they’re able to get the socialization, but also able to focus better at home than they are in a classroom of 36. And that’s legitimate. You know, we talk about personalized learning, but it’s not exactly personalized when everybody has to wake up at the same time, same schedule, go to the same, the same classroom of, you know, up to 40 kids, and do the same lesson. I mean, we have to be honest about our limitations with personalizing learning for students. And when we can provide more options and we give teachers the infrastructure to be able to use different platforms, then we’re able to personalize learning a lot more.

Eric Cross (11:51):

There’s also been an emphasis on the whole-child wellness. I think the spotlight on mental well-being heavily impacts their academic success, but counseling teams, social workers, school psychologists—I think more than ever we’ve realized the value that they bring to the schools. And unfortunately many of them have caseloads of 200 students or more. And they’re seeing students most often that are in crisis. And especially after the pandemic, we’re realizing how valuable they are and how much we need to, one, honor them and give them the support that they need, and also recruit more. Because as we start recognizing how our brains are impacted by the things that we’re dealing with, we’re also gonna see how that’s gonna impact our students’ performance. And we need the specialists in those positions to be able to support our kids. I think, last, I think more innovation and lesson design and how we assess students. And so we’ve been talking about in education just kind of critiquing: how do we assess what a student knows? How do we make what a student actually does at school relevant to real life? I mean, so many times I have students who’ve graduated that are like, “I feel like the things I learned in school, like, they’re not always transferable to real life. It helped me on a test, but like, I don’t know how to do my taxes.” Or “I memorized these facts, but I don’t really apply it in my job.” Or “The facts that I learned I could have actually learned on the fly in my job. I wish I would’ve actually focused on the skills or had an earlier opportunity to get some experience because when I’m trying to apply for a job, <laugh> they ask for experience and I’m 22 years old.”

Eric Cross (13:28):

And so all these things kind of come up. And so I think there’s been some great conversations around “how do we rethink what education looks like?” And there’s different pockets around the country that have been doing that, I think, really well. And I think it’s important for us as teachers to stay connected to those people who are kind of pushing the boundaries and thinking outside the box, because when we get siloed, it’s really easy to get calcified and cynical. I get it. And it impacts me too. But when we’re around those people who have those fresh ideas, who are really pushing the limits, it inspires us. And that’s something I think during the pandemic that I’m grateful that I was intentional about, is staying connected with other teachers. There’s a big question; Why do you continue your work in the classroom and what keeps you motivated? And I was thinking really hard about this question, because depending on <laugh>, depending on my day, I feel like my answer’s gonna be a little bit different. So I’ve had to step back from this 30-foot, thousand-foot perspective and answer the question. And my answer is this: I think because I still feel like I can be effective to influence positive change in my classroom with my students and within the larger education system as a whole. I think if I lost either of those two, then I’d rethink my profession. Look, I’m an innovator. I like asking “why” questions and things like that. And I’m not always the most popular person when you do that. But education is like just a huge ship. It doesn’t pivot on a dime. And asking why questions and pushing for change on behalf of kids isn’t easy, fun, or glamorous, but it’s it’s necessary. And I feel like over the last few years, I’ve been able to see these kind of glimmers of a trajectory change, at least where I am locally. And that’s something that has given me a lot of hope. I’m very fortunate to be connected to educators and people in leadership that are really about making a difference beyond just kind of the cliched platitudes. They actually wanna make systemic change, in a way that’s positive. And that’s been really helpful for me. So as long as I feel like I’m useful in the classroom for students, and as long as I feel like I’m bringing, I think change, on behalf of teachers and students and administrators and our community in a way that moves the ball down the field, that’s what keeps me motivated. And what I like to ask teachers when I close in the podcast is. “What teacher or teachers have inspired you?”

Eric Cross (15:54):

And for me, I think it would start off with the teachers who cared about me when they didn’t have to, in elementary school all the way through college. And there are numerous teachers. My science-teacher community of practice. For the last two years, I’ve been fortunate to spend every month, once a month, meeting with just a core group of science teachers that really care about some of the things that we are impacted by in the classroom. And when the pandemic was going on, we still met regularly. And because we’re not all teaching in the same place, we kind of were able to bring different perspectives to the table. I think the current classroom teachers and former classroom teachers that I have in my community really inspire me. The ones who are dedicated to opening doors for students. The graduate students that I teach at the University of San Diego, they keep me fresh. I love leaving teaching my 12- and 13-year-olds, and then driving down the street to the university and teaching 20somethings who are all about to be in the classroom. They come with new ideas, they’re asking questions, and I get to actually share things that I just did three hours ago. I think that’s one thing that continues to inspire me. And it’s one of the reasons why I love teaching at the University of San Diego. Their energy and enthusiasm is super-refreshing. And then all the teachers that are willing to take risks and fail forward, to try things different, to ask hard questions, to push the envelope. Teaching’s hard. It’s easy to point out the problems in education as a whole. But after we do that, it’s important to figure out the practical ways we can make the changes that we wanna see.

Eric Cross (17:23):

Now, that’s to say that if you have the capacity for it and the resources and the support. Some of us, we don’t. Some of us, we are on an island, and that’s a really, really difficult place to be, especially when you have family and kids to take care of. And you have to make decisions on what’s best for you and for your own students. We do this work on behalf of kids. And it’s one of the most honorable services a person can provide to our community. But one area for growth that I think we have kind of as a society, is teachers spend their lives, daily, on behalf of the future of our country. For other people’s children. They fall asleep at night worrying about other people’s kids. They spend their own money to create opportunities and experiences that students might not otherwise have. And it’s important that we collectively, and I know I’m preaching the choir when I say this, but this is one of my messages, is that we honor them in turn. We create programs that allow them to be able to afford housing. We create opportunities for them to be able to generate wealth. We create ways for them to be able to find rest, to get connection. And then internally we create systems where they can just work on themselves, fill themselves, get trained, and be whole, so they can bring their best self to the kids in front of them. That’s one of my personal platforms. It’s something that I think is vital. We gotta take care of the people that take care of our kids. So there’s a saying that says, “It’s better to light a candle than to curse the darkness.” And it takes one person to blow out a candle, but one candle can light thousands of other candles, without diminishing its own light. And that’s what we have to be. So my encouragement, teachers, as you’re going into this new school year, and you’re thinking about what’s going on, you’re thinking about all the challenges—and they’re there, and they’re real, and trust me, it’s not like some Pollyanna, like, “Hey, just be positive!” mindset and everything’s gonna be great—no, no, no, no, no. It’s not that. But my encouragement…if I can tell you one thing that’s helped me more than anything else, it’s being connected to other people who are candle-lighters. Because there are a lot of places that are gonna blow out the candle. It could be the staff lounge. It could be Twitter, it could be Reddit. It could be Instagram. It could be TikTok. It could be, you know, anybody. Someone next door to you. There’s a lot of folks that are gonna be willing to point out and say, “Look, this is what’s wrong.” But find the helpers. Find the people that are candle-lighters. And stay connected with them. Find that community. I can tell you for me, that’s been the thing that’s been able to help me sojourn through all of this—I couldn’t do this by myself—is being able to share my story with other teachers and knowing that I’m doing this work alongside of other folks who are doing this work, and I can share my story with them and listen to their stories, is something that’s been able to fill my cup. And so I hope I can do the same for you and for other people listening to other people I come in contact with.

Eric Cross (20:08):

Teachers, I wish you a great school year. Hang in there. Be those candle-lighters and bring your best self on behalf of the students. Thanks so much for listening. Now, we wanna hear more about you. If you have any stories you wanna share about the classroom, please email stem@amplify.com. That’s STEM at amplifycom.wpengine.com. And make sure to click subscribe wherever you listen to podcasts. And join our Facebook group, Science Connections: The Community. Until next time.

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 Eric Cross says about science

“We do this work on behalf of kids, and it’s one of the most honorable services a person can provide to our community.”

– Eric Cross

K–8 Science teacher, Host of Science Connections: The Podcast

Meet the guest

Eric Cross is a 7th grade science/technology teacher, grade level lead, and digital learning innovator for Albert Einstein Academies, International Baccalaureate schools. He is also an adjunct professor of learning and technology at the University of San Diego and a Google certified innovator. Eric earned a bachelor’s degree from Azusa Pacific University and a Master of Education from the University of San Diego. He had 17 years of experience working with at-risk youth and underserved populations before becoming a middle school teacher. By building relationships with students, colleagues, and the community, he has become an empowered leader in and out of the classroom. Through meaningful learning experiences centered around student agency, STEM has become accessible to students through highly engaging lesson design, thoughtful integration of digital tools, and culturally relevant pedagogy.

Smiling person with short hair and a beard, wearing a collared shirt and sweater, against a dark background. Small star icon on the top left of the circular frame.

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!

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.

Season 10, Episode 14

Your comprehension questions answered, with Nathaniel Swain, Ph.D.

In this episode of Science of Reading: The Podcast, returning guest Nathaniel Swain, Ph.D., joins Susan Lambert to close out the season by answering thoughtful and thought-provoking comprehension questions submitted by listeners. Nathaniel and Susan answer questions about comprehension strategies, the relationship between comprehension and memorization, and how to shift the mindset among your teaching colleagues to help them understand comprehension.

Second Mockup Episode 14: Your comprehension questions answered, with Nathaniel Swain, Ph.D.

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Season 10, Episode 14

Your comprehension questions answered, with Nathaniel Swain, Ph.D.

In this episode of Science of Reading: The Podcast, returning guest Nathaniel Swain, Ph.D., joins Susan Lambert to close out the season by answering thoughtful and thought-provoking comprehension questions submitted by listeners. Nathaniel and Susan answer questions about comprehension strategies, the relationship between comprehension and memorization, and how to shift the mindset among your teaching colleagues to help them understand comprehension.

Mockup Episode 14: Your comprehension questions answered, with Nathaniel Swain, Ph.D.

To view this protected page, enter the password below: