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

S5-01. Investigating math anxiety in the classroom

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.

Season 5 is here! This season, we’ll be talking all about math anxiety: what it is, what causes it, and what we can do to prevent or ease this anxiety in the math classroom. To launch this very important theme, we sat down with Dr. Gerardo Ramirez, associate professor of educational psychology at Ball State University.
 
As someone who’s been studying math anxiety for more than a decade, he had some interesting research and advice to share on why math anxiety affects so many students (and adults), and tips for how to start reducing it.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page.

Download Transcript

Dan Meyer (00:01):
Hey, folks. Welcome back to Math Teacher Lounge. I’m one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:05):
And I am your other host. I’m Bethany Lockhart Johnson. Season five! Hello!

Dan Meyer (00:11):
Bethany, how are you doing? How have you been spending the long break between our recording sessions?

Bethany Lockhart Johnson (00:16):
As much as I loved sharing content from previous seasons, I am so thrilled that we’re back for season five. I have been, you know, chasing a toddler. I think he’s already tired of me saying, “Ooh, can we count that?” He’s like [sighs] “One two, one two.” Like, he’s done already.

Dan Meyer (00:36):
Too much counting. Yeah, I worry about that so much, that my love of mathematics might be perceived by my kids as smothering. Yeah, I worry about the same. We shared with you folks some bangers of reruns, in my humble opinion. Some great guests. But, we’ve been excited—me and Bethany—to hop back on the mics, on the ones and twos, and explore some new ideas together.

Bethany Lockhart Johnson (01:01):
Well, I loved our season talking about joy in mathematics. And personally I could…like, we could turn this whole podcast into joy in mathematics. However, we’re kind of going a different route. Because if you ask folks why they don’t feel joy in mathematics, a lot of times at the root of that is some really intense math anxiety. So this whole season, we’re going to be delving into math anxiety. Exploring what it is, who has it, why do we think it happens, what do we think we can do about it, and how can we navigate through it, so that we can experience that joy in math? These are questions that we’re gonna explore over the course of the season. Dan Meyer, how do you feel about that?

Dan Meyer (01:49):
It feels big and it feels personal. I mean, as we shared in our math stories back from season…whatever it was, math anxiety was a huge part.

Bethany Lockhart Johnson (01:59):
It was last season, Dan.

Dan Meyer (02:00):
Last…? I mean, who can remember? Big part of your journey. I’ve had some very punctuated but intense moments of anxiety in math class. And socially, we have built math up to be this incredibly powerful thing. You know, restricting movement on economic ladders, preventing people from getting into careers they want. Whether or not they have much to do with math class, math anxiety is a really large part of educational but also social life. And yeah, I’m really excited to explore it with you. We’re bringing on some really excellent guests. Some researchers, yes. But not just researchers! Also people who practice in the field and know firsthand what it looks like to resolve issues of anxiety with students.

Bethany Lockhart Johnson (02:45):
Yeah, you’re right, Dan. My math story contained quite a bit of math anxiety, so I am particularly invested in this season. I mean, I still navigate math anxiety. And, you know, many of us do, and let’s talk about it. And let’s—I love that you reminded me. We’re gonna have a lot of great researchers all throughout the season, and a lot of times folks feel like the research happening, there’s sometimes a gap between researchers and what’s actually happening in the classroom. Not in all cases, but a lot of times. Right? And I remember a lot of conversation about the latest research when I was in grad school, but unless you’re actively studying something, sometimes we don’t know what’s happening. Right? We’re really focused on what’s happening right in front of us in our classroom. So let’s take some of that research; let’s break it down; let’s talk to some of the folks who are thinking about this for the bulk of their day, right?

Dan Meyer (03:41):
Yep. So we got our first guest coming up in a moment here.

Bethany Lockhart Johnson (03:45):
So to kick off this season, we’re starting episode one by talking to Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University. And he’s been researching math anxiety for more than a decade. He’s worked with so many amazing folks in the field. He’s worked with students, he’s worked with teachers, with educators…I’m just so excited to talk to him. If you look up math anxiety, you see his name as one of the folks who is really thinking about this at so many different angles, and we get to talk to him. So enjoy our conversation with Dr. Gerardo Ramirez.

Dan Meyer (04:29):
We are so excited to have Dr. Gerardo Ramirez on the show with us. Dr. Ramirez is an Associate Professor of Educational Psychology at Ball State University. Thanks so much for joining us.

Dr. Gerardo Ramirez (04:40):
Yeah, thank you for inviting me to talk about math anxiety.

Bethany Lockhart Johnson (04:43):
So with your interview, Dr. Ramirez, we are actually launching the season. We’re gonna be talking about all different aspects of math anxiety, and it feels pretty perfect that you are first guest of the season, because of the sheer breadth of research and conversations you’ve had about math anxiety. Could you start us off kind of telling us a story of how did you get interested in studying math anxiety? Or why, you know, why did you dive into this topic that, you know, I think a lot of folks might…like, if you’re on a plane, and you say, “Oh, I study math anxiety,” what kind of reaction are you gonna get?

Dr. Gerardo Ramirez (05:24):
Oh, sure. Yeah. I think most people are actually very interested because they all have their own story about feeling anxious about math, or just being anxious about evaluation situations that involve math. And, yeah, they wanna share those stories. People feel quite comfortable talking about their anxiety about math, for some reason. But for me, I started off, when I was in undergrad, I was studying to take the GRE quiz. I was hoping to go into a psych program. But I wasn’t exactly sure what direction yet. As I took some of the practice tests, there’s some situations in which I was very nervous about taking the practice test. And I just noticed that I did really poorly on some of these exams. And so I became very interested in issues like choking under pressure, which means when you underperform relative to what you expected to perform. And so, as I was researching these issues, I started to come across this whole field of math anxiety. And I saw that while there are some people who choke under pressure during tests, there are other people who just have a strong general fear of mathematics.

Dan Meyer (06:29):
That’s really helpful. I can imagine you’re doing a lot of free psychology sessions, free therapy for people on airplanes when they bring to you their own stories of math. So let’s thank you for your service in that sense. I’m super-curious. So Bethany and I have both taught math. We both have seen firsthand what it looks like when a student is anxious in math class, though maybe we don’t have kind of the clinical language to describe it. And I’m curious, from a clinical sense, how do we define math anxiety?

Dr. Gerardo Ramirez (06:57):
Sure. So first off, math anxiety is not something that you would find in the DSM, for instance. But we generally define that as a fear or apprehension to situations that involve math. So it doesn’t have to necessarily be educational situations. It could be someone asks you a math-related question during a party, or you have to calculate the tip at a restaurant, for instance. It doesn’t have to be about schooling situations, although that’s obviously where it seems to matter a lot for many people. So it is basically a fear or apprehension to situations that involve math. And I think distinguishing the term “fear” from “anxiety” is really important here. A lot of times people use those terms interchangeably, and the term “fear” is obviously within our definition of math anxiety. But oftentimes what differentiates anxiety from fear is that, anxiety is—think of it like a recipe. Anxiety is fear plus a little bit of unknown. OK? So if, for instance, if you hated snakes, and they threw a snake at you, you’d be in intense fear. Whereas if you hated snakes and they said, “There is a snake in the room, but I’m not gonna tell you where,” that’s gonna cause anxiety. And so the reason why we call it math anxiety is because a lot of times people experience this fear for a possible unknown future that involves math or possible unknown evaluations that people might have about your competence, because of math. And so for a lot of kids, they feel anxious about how they’re gonna do on a test or whether they’re gonna be able to pass a class or whether they’ll be able to understand what you’re saying in your lessons, for instance. And so the anxiety component really gets at fear of something that’s unknown, but related to mathematics situations.

Dan Meyer (08:47):
Math is somewhere in the ceiling right now. Perhaps I might be surprised with a math situation!

Dr. Gerardo Ramirez (08:52):
Yeah. yep.

Dan Meyer (08:52):
So I have this tendency to assume that every other subject that we teach has it better and easier than math does. It’s not true. I know this is not true. But I’m kind of curious here. Is math anxiety, like, part of a general just set of anxiety around schooling itself? Like, is there a reading anxiety, a writing anxiety, and does that all just flow from the same kind of fount of anxiety around schooling or situations about learning? And what makes math special in this regard? If it is its own special anxiety, for instance?

Dr. Gerardo Ramirez (09:27):
There are different…so some people obviously suffer from generalized anxiety. Right? And so they would, you know, feel anxious both for evaluative and non-evaluative situations. But in the research that we’ve done and that other people have done, there are differences between things like reading anxiety, math anxiety; I’ve also studied spatial and creativity anxiety. A lot of times what we’re trying to do in these studies is we measure all of the above, and we try to show that, look, math anxiety predicts math situations above and beyond these other things. So yeah, we definitely distinguish those things. And so what’s special about math is that, well, I think the symbolic nature is a big part of it. The abstract symbolic nature is just not as tangible to students. They can’t touch it. And so it doesn’t allow ’em to use their full cognitive faculties to play with it, as you might see, for instance, in science. Or it doesn’t allow people to relate math to their own interests the way you might see, for instance, in English. So maybe I hate reading novels, but I’m interested in zombies and you give me a book on zombies, well, ok, great, you’ve connected my personal assets to the topic. Whereas with math, either that’s harder to do or instructors don’t do such a good job of setting that connection up.

Bethany Lockhart Johnson (10:46):
Also, I think, you know, I’ve heard of students being really anxious, let’s say, during a reading session, when teachers used to do—hopefully they’re still not doing it—the popcorn reading, where you just randomly call on a student to read out a sentence. Right? But you don’t really hear students or adults talking about, “Oh, no, no, no, I don’t read; I don’t mess with reading.” You know? Whereas with math, you do hear, “Oh, I’m not a math person. Oh no, no, no, don’t ask me any math questions.” And that is such a distinction.

Dr. Gerardo Ramirez (11:18):
Yeah. And I think a lot of that’s because it’s just so common. As an adult, to be nervous about reading is kind of an uncommon thing. So people feel a stigma around admitting that. But math is something that everyone feels like they’re inadequate in. And so there’s a lot of comfort in telling you how they’re just one of the many people who don’t like math. And that, you know, can have a lot of different consequences and outcomes. I think on the one hand, I think for a lot of kids it becomes a normalized message that if you fear math, that’s OK, join the club. Right? But we have to be careful about that, ’cause a lot of math anxiety researchers will oftentimes say, part of what leads to math anxiety is adults normalizing that it’s OK to be scared of math. So I think a lot of times adults, teachers, for instance, math teachers, they’ll tell kids, “You know, if you’re scared, that’s OK.” And so a lot of the math anxiety community says, “No, no, no, you’re not supposed to do that.” But my recent view is different. I view that as a form of validation. Because math is hard. And so telling kids, “Hey, look, it’s actually easy if you just try,” I don’t think that’s true. It’s actually just hard. And I think even if it was easy, to the kid, it feels hard! And I think something that’s not really well-studied right now in our field is the value of validating people’s math negative math experiences. We don’t want to validate that, ’cause we think that we’re gonna reinforce that. But actually, I think the opposite. I think when you validate people’s negative math experiences, it helps ’em to feel that they can handle it. They can start to take control over their own emotions.

Bethany Lockhart Johnson (12:52):
I love that. And I, I actually, I think that’s so powerful, what you’re talking about, that validation. I taught kindergarten, and I vividly remember being in a parent-teacher conference and that parent saying, “Oh, I wasn’t a math person either,” right? Or, you know, their language and their experience with their own math schooling, their anxiety about math was actually impacting their students’ experience of math. Or the conversation that, when I would go to talk about a math assessment, let’s say, you could see the parent actually tensing up. And there was this moment of validation, that I felt like we needed to make space for that in the conversation with the parents, right?

Dr. Gerardo Ramirez (13:38):
Yeah.

Bethany Lockhart Johnson (13:38):
Like, this is a real thing. And we are working on teaching students that math is something that gets to—your experience with math gets to look all sorts of different ways. And it’s OK if we, you know, make a mistake, or if we kind of only get this part, but we’ve really got that part. Or let’s talk about it; let’s write about it. So I really feel like that that validation is something that’s so missing. And instead of the validation, like you said, you see folks being like, “Oh yeah, me neither. I’m not a math person either.” Right?

Dr. Gerardo Ramirez (14:10):
Yeah. I think…part of the reason why people are comfortable sharing this because they’re looking for validation also. When they say, “Oh, I’m not a math person,” you know, I think they’re hoping that, you’ll say like, “Yeah, me neither,” or “Of course not, ’cause math is terrible.” Right? They’re looking for validation, not to reinforce their perspective, but to feel that it’s OK not to be a math person. And I think that’s one of the techniques that I’m trying to work on in my research right now, is to provide evidence that actually people will work harder when you validate their math experience. You don’t have to tell them a positive story per se. If your current story is “Math is hard and I’m very, very anxious; I’m scared,” then we can just validate that and help you work through that. And it actually will strengthen our relationships. Because if you’re a student and you’re struggling with math and I tell you, “Yeah, it’s hard; it’s OK to struggle with math,” that makes you feel seen. And that’s gonna lead you to want to ask me more for help, because I’m someone who understands you. And that’s a great, you know, remediation opportunity.

Dan Meyer (15:14):
A common thread that I think I’m seeing here in several answers is that math sometimes asks students to disassociate part of themselves. Where success in math oftentimes means working from an a level of abstraction with symbols, like you said, that can feel alien. Like, who am I here? And in the same way, I love that you’re proposing we validate and reassociate people with a very deeply felt part of themselves that is anxious about mathematics.

Dr. Gerardo Ramirez (15:44):
Yeah. I mean, I think that’s what validation’s supposed to do, right? So a lot of us, when we feel these strong emotions, we wonder, “Is this even a real thing? Are other people feeling this? Is there something wrong with me?” So we feel the emotions, but we can’t actually deal with them, because we wonder if they’re legitimate. And so when someone says, like, “Yeah, this is hard,” it crystallizes that emotion. And once something is made real, you can actually choose how you want to deal with it. Some kids are gonna deal with it by staying anxious. But some people are gonna choose to deal with it by saying, “Well, there’s nothing I can do about it now; I have to take this math test, so I’m just gonna think positive.” And that’s great. If the kid can end up saying that to themselves, that’s much more effective than me telling the kid, “Hey, you just gotta think positive. You’re gonna start the test anyway.” And so we want the kid to make meaning of their experience, and the way we do that is by crystallizing their emotions through validation.

Dan Meyer (16:36):
Yeah. I love that. And so what you’re proposing there, I think, sounds like, a solution, like a post-talk solution after students are feeling anxiety.

Dr. Gerardo Ramirez (16:43):
Yes.

Dan Meyer (16:43):
To validate and empathize.

Dr. Gerardo Ramirez (16:45):
Yes.

Dan Meyer (16:45):
And over the course of our season, we hope to explore a lot about solutions to math anxiety that are preventative, that reduce the odds of anxiety arising, through instruction and curriculum, before it arises. And I’m just wondering if you’ve seen anything that would hint at either specific or general words of wisdom you wanna share with the educators, about not just addressing it after the fact, but preventing math anxiety before it arises?

Dr. Gerardo Ramirez (17:14):
To be honest, at this point, I haven’t seen enough evidence for me to recommend anything concretely as an intervention for math anxiety, or an intervention to prevent its development. All I can really do here is rely a lot on the more broad cognitive-behavioral research on anxiety, which says that one of the ways we prevent people from developing anxiety is by helping them to make more positive appraisals of challenge situations. So a lot of times, when kids are challenged, they don’t know how to interpret that. “What does it mean that I’m struggling with this thing?” And so that’s where I think a lot of teachers can help students’ interpretations of that. ‘Cause if you leave kids to their own devices, they’re gonna think, “I’m struggling because I’m stupid. I’m struggling because I’m not good enough. I’m struggling because my dad is right; I’m gonna be a failure.” You know? They’re going to impose an interpretation to a challenge situation regardless. And so, as teachers, one thing we can do is we can help shape that interpretation and say, “What does it mean to struggle with math? People will say it means you’re stupid. That’s one interpretation. What’s another one? It means that your brain is working really hard to think through something. That’s another interpretation. What’s better? What do you think is more helpful?” And then, helping students to see how interpretations matter to how you ultimately feel about something. And that’s a very metacognitive way of thinking about things. So yeah, I would say that one way to prevent it is to help students to take more positive interpretations of their experience. But another way, and I think a more successful way, I think, is to give students early experiences where they feel efficacious dealing with math. One of the ways you do that, for instance, is by obviously making sure that the students understand the material—but that’s obvious; people are trying to do that. One of my favorite recommendations is to keep reassigning assignments, the same exact assignment, for, say, three weeks, back-to-back. So if in week one you do the homework assignment, you do OK, you don’t do so great, when week two you do it, you give the exact same assignment, and now the student can see like, “Wow, OK, this was much easier.” And then, week three, you give the exact same assignment; now the kid’s feeling really confident. And the reason why that’s great is because it helps kids to see that they’re growing in confidence. A lot of times kids don’t get to see that because we’re constantly throwing new assessments at them. And so they’re never seeing that growth. All they’re seeing is a new challenge, a new challenge, a new challenge. So I think we need to set up situations where they can feel that they’re growing, when we keep the assessment static. That can be a formative assessment, for instance—doesn’t have to be a summative assessment.

Bethany Lockhart Johnson (19:55):
That feels so powerful and it feels like it really connects to that validation piece, right? We are actually helping to create a culture in our math classroom where we might struggle with something, but we keep revisiting it. And it’s not so much to reach mastery, but as Dr. Megan Franke — we talked to her about this partial understanding and about pulling on those threads of things that you do understand, so that you can build your confidence…build, not just confidence, but build your…I guess, kind of get your footing, right? You’re saying, “Well, I do understand this. I see how this works.” And if I’m revisiting an assignment, I feel like that would give me permission to like, “Hey, I don’t have to have this figured out on the first pass. You know?

Dr. Gerardo Ramirez (20:44):
Yes, yes. Yeah. I mean, I’m gonna give you a silly analogy, but I think it works. You know, a lot of times people will have nightmares, right? And they’ll keep having the same nightmare over and over again, right? And so one reason that we suspect this happens is because they haven’t worked through whatever that nightmare’s supposed to be about. So if, say, I’m scared of driving, I may be having the same dream about driving and crashing over and over. And we keep having these nightmares. And I think math anxiety is kind of like a waking nightmare, where you keep rehashing something because you haven’t had the chance to finally address that dragon. You know? And so if someone was having a lot of fear over driving, then one behavioral approach would be, you know, to work with a therapist to actually get behind the wheel and maybe drive around the same track over and over until you feel comfortable at that, and then the nightmares stop. Well, the same thing is true, I think, about math, math and math anxiety, is that you wanna give people these opportunities to feel confident by going back to that original experience that caused them to feel anxious, and saying, “This one assignment that we did in week three that really freaked you out, let’s try it again now in week five. How was that?” “Yeah, it wasn’t so bad. It was still kind of annoying.” “OK, we’ll we’ll come back to it.” “Now it’s week seven. Now let’s go back to that assignment. How is it now?” “That’s actually…it wasn’t that terrible.” And that gives people the opportunity to reflect on how they’ve grown past that nightmare.

Bethany Lockhart Johnson (22:05):
I have to say, Dan talked about you being like a therapist. I’m like, wait, “How did you know, Dr. Ramirez? I did have this recurring dream! I did! And I had to face it. No, but I had such intense math anxiety in high school and it was debilitating. And the biggest thing for me, I thought I was the only one. I thought there was something wrong with me. I thought, “Why can’t I figure this out?” There wasn’t a conversation about “Here are some tools,” or “Here are some, some, some…”. Like, “This is OK, for you to feel scared about this or overwhelmed!”

Dr. Gerardo Ramirez (22:41):
Mm-hmm. Mm-hmm.

Bethany Lockhart Johnson (22:42):
You know, I think often when we talk about how widespread math anxiety is, I think a lot of folks automatically jump to high schoolers or college students avoiding math courses. But we see this in really young kids.

Dr. Gerardo Ramirez (22:56):
Yeah. So people are…people are just constantly making meaning of themselves, regardless of the age range. And that’s true even with young kids; they are trying to figure out who they are. Right? And so one of the things you see oftentimes with young kids is you ask ’em, “What are you good at?” And they say, “Everything!” And that’s their attempt to, you know, make meaning of themselves. But sometimes they’re not good at everything. Sometimes they actually struggle in math. And I think even early on, they have to make meaning of that. They say, “Well, I’m good at everything except math.” And how do you make sense of that? Well, why not math? “Oh, because math is terrible. It’s not for everybody. You know, it’s not something that I like.” And so, yeah, in a lot of the studies that we did early on, we basically went into these first-grade classrooms with the purpose of trying to assess whether we can actually show variability in kids’ math anxiety, even early on. In other other words, do kids even report feeling anxious about math situations? Or do they tell us that they’re great at everything? And what we found was that in fact, a good chunk of kids are, again, perfectly willing to tell you that “No, certain situations involving math make me very anxious.” Counting or addition, or doing a problem on the board. And the way we do that is by—I think there are probably more sophisticated ways that can be done, but this is the best we have at this point—is we go in there and we ask them, we show them a bunch of smiley faces and anxious faces. And we say, “I want you to tell me how you feel about these different situations that involve math.” And so we say, “If you feel kind of nervous, I want you to point to this face. If you feel very nervous, point to this face.” And we basically will read to them situations. We’ll say, “How would you feel if your teacher asked you to open up your new math textbook and you saw all the numbers inside of it?” And they’ll point to the really nervous face. So right now, those are some of the more reliable assessments for math anxiety among young kids. And that work showed us that even young kids are self-reporting math anxiety.

Dan Meyer (24:51):

Obviously this is worth our study, because we would hope people would not feel anxious in general, and especially if we have a mandated…kids are mandated to be in math classes for their entire childhood. So I see the need for this study, these studies. I’m curious: What are the consequences, though? Like what, what correlates with math anxiety? What are other reasons why we should care about math anxiety and work to remediate it?

Dr. Gerardo Ramirez (25:16):
Oh, sure. So it correlates with their actual math performance. It can correlate when they choose to do homework. Right? So a lot of times, the parents report having to fight with their kids over math homework a lot. And you also oftentimes see a lot of frustration over mathematics specifically. And so it can, you know, not only affect their academic ongoing outcomes, like math tests and math assignments, but it can also affect their relationship with their parents. So if every time you come home, your dad’s screaming at you because you haven’t done your math homework, and when he asks you to solve the problem in front of them, you don’t remember, ’cause you were checked out, ’cause you’re so stressed out, that’s gonna cause a really negative experience. You know, a lot of times people grow up and they still remember their dad screaming at them over the math homework. You know, it’ll affect your relationship with your teacher. So if you’re making me feel incompetent, if you’re stressing me out, you’re not the kind of person I wanna come to for help. So it can predict relational outcomes as well as academic outcomes. And down the line, of course, when it affects students’ opportunities to get into things like AP classes, it affects students standardized test performance and their choice of colleges, as well as scholarship opportunities.

Dan Meyer (26:29):
Once you show that it correlates to performance, then that opens up a whole range of other correlations that are pretty important, it sounds like. Whether that’s career options or, you know, post-secondary education and the like.

Dr. Gerardo Ramirez (26:40):
Yeah. And a lot of times, when people are choosing a career at college, a lot of times students will make a decision specifically based on what career has less math requirements or less math courses. So I think this finding needs to be verified further. But, there’s some studies showing that, for instance, elementary ed teachers, one factor that feeds into the decision to go into elementary ed is the math requirements are very low in elementary ed. So that can…obviously it’s not what we wanna hear, because these are our first formal math teachers, right? For our kids.

Bethany Lockhart Johnson (27:16):
It feels so powerful, the impact that math anxiety can have, not only while you’re in, let’s say, elementary school, high middle school, high school, but then the impacts beyond that in terms of your career. And I shared this last season, when we talked about our personal math story, but I know when I was navigating the deepest part of my math anxiety, I really felt like, maybe this is a reason I can’t be an elementary school teacher. Because I was so worried that I wouldn’t be able…not that I wouldn’t understand the math for fourth grade, fifth grade, but that there was something about my ability to teach it or understand it or develop a love and passion for it that I wouldn’t be able to do. And I really had to reclaim it in my own way. But, you know, something that I think is so powerful about your research is just the applicability — not only to the field of mathematics, but folks’ everyday lives. And the way that you have talked in the past about math being a gatekeeper…I have a family member who, brilliant American Sign Language interpreter. I mean, amazing. Like a dance with her fingers. I could just watch it all day. And she actually didn’t complete the program because she couldn’t complete the math requirements. And I remember talking to her about like, “Well, have you gone to the free tutoring? Have you gone to, you know, this or that?” But it was a paralyzing fear, you know? So Dr. Ramirez, what do you wish educators understood about math anxiety? Or the research about math anxiety? Or maybe even the general public at large, what do you wish folks understood about math anxiety?

Dr. Gerardo Ramirez (28:58):
Oh, I think that a lot of students, they struggle with math. And I think we wanna normalize that struggle as much as possible. We want to create a culture where it’s OK to do math slow; it’s ok to take your time. And I know that’s not possible with a lot of these requirements that a lot of math teachers have to do. But I think if we want to prevent math anxiety, we have to create opportunities to tell better stories. So that’s ultimately what I tell people is, why do people develop math anxiety? Because they had experiences that challenged their competency and they told a negative story. And so making space to reflect in math classrooms about what does it mean to go slow in math, or what does it mean to make mistakes, and then helping kids to tell better stories, I think it’s really the best thing we can do as math educators. ‘Cause you know, your job is not to be a therapist ultimately. You know, there’s only so much math teachers can do. But I think one of the most powerful things we can create is setting up students’ experiences where they feel confident, and they can tell better stories, so they can have better dreams about math.

Dan Meyer (30:06):
Really appreciate this introduction to math anxiety. It’s been a fantastic kickoff to our season. Dr. Ramirez, thank you so much for joining us.

Dr. Gerardo Ramirez (30:14):
Sure. Thank you.

Dan Meyer (30:16):
Thank you folks so much for listening to that conversation with Dr. Gerardo Ramirez, Associate Professor of Educational Psychology at Ball State University.

Bethany Lockhart Johnson (30:25):
Dan, OK, if not for your frantic signaling, I would’ve probably asked another 20 questions. I need to know what you thought .

Dan Meyer (30:34):
I found it interesting at all points. And especially I think I started to understand a little bit better where the anxiety comes from for some students. I got a little bit here, which is that I think math, more than other disciplines, involves alienation. Check that word. You like that? Alienation? I’m into it. I’m feeling it. It’s like…to get good at math, to be successful in math, you gotta, as a kid, lose your attachment to the world you understand. And I mean, “got to” as in like, “you are asked to” — many times, unfortunately, by curriculum and instruction. Which is to say, you’re turning things you can hold onto into numerals. Right? You’re turning the world and its patterns that you can see and touch into Xs and Ys. And I just don’t know that other disciplines deal with that as much. Maybe I’m wrong and just guilty of, you know, “grass is always greener” syndrome here. But I think that’s an experience that kids have in math. And I thought that Dr. Ramirez got at that when he’s talking about the need to validate a student’s experience of anxiety. Like, in treating anxiety, sometimes we alienate people further by just like saying, “Oh, no, no, no, it’s just like, you need to, you know, drill yourself more, practice more,” and kind of invalidate that. So this feeling of alienation, I think permeates a lot of math instruction. I’m looking forward to learning more about that with our future episodes

Bethany Lockhart Johnson (32:00):
Alienation. That’s interesting. I definitely felt, I definitely felt isolated and alone many times in my math journey, when I was having my…you know, in high school, when I was feeling like, “Clearly everyone can look at tan, sign, cosign, and that means something to them.” Right? I think it’s really interesting, because I’m thinking about the other disciplines; I’m running through them, and I’m like, even in science, which can seem abstract, so oftentimes there’s these experiments that accompany these concepts, where you’re like, “Look at this concept made real in front of you.” Right? . And so yeah, that’s really interesting.

Dan Meyer (32:39):
You’re always one step away from blowing something up! Or, you know, dissecting something that’s tangible to you.

Bethany Lockhart Johnson (32:46):
Yeah. That’s really interesting. I did really love how he brought up the abstract. And how, I think, even validating it…he talked so much about validation. Which to me was like, YES. If somebody just said, “Hey, it’s not only possible to have math anxiety, but it also doesn’t mean that you don’t belong here.” If somebody had said that, it would’ve literally changed the trajectory, you know? And I wonder what those conversations could look like in our classrooms, where teachers celebrate that. Like, WHOA, this is a new way to think of this. This is a new way. Asking how many, or what do you notice for this image, through a mathematical lens, or looking…we talked to Alison Hintz and Antony Smith, like mathematizing books, like looking through these lenses — it’s an invitation to step into this other world, right? But there’s not only one way to do it. And I think oftentimes it’s like that anxiety of “Am I gonna say the right thing?” or “Am I gonna notice the right thing?” Right? How do we create that space more, where there’s so many possibilities and we want kiddos to notice what they notice, right?

Dan Meyer (33:54):
You gotta become a certain kind of person to be successful in math class. I feel like is part of the implied deal. Where you’ve gotta—like how you said—say a certain thing or think about a certain thing a certain kind of way. You’re trying to become someone who is not necessarily you. Which I think is fundamentally an experience of alienation, separating you from important parts of yourself.

Bethany Lockhart Johnson (34:19):
I will never, ever dive into mathematics on the scale and level that you have with your PhD. You understand math in a way that my brain just…I won’t get there, right? And yet I’m allowed to call myself a mathematician, with all of my deep dives in elementary math and my love of early numeracy and thinking about how we start thinking about counting and numbers. Right? It’s like, if we make more space for what mathematicians can look like, and what is your personal relationship with math…I mean, that to me feels really exciting. ‘Cause I think we both have something to offer each other.

Dan Meyer (35:03):
I think I have never found early math more interesting than when I talk to early math educators. And learn just like all the different ways that students come to understand a concept that I had thought was simple. Like addition of whole numbers. Whoa! There’s a lot of ways kids do that work, and their brains think those thoughts. And, yeah. That’s a good word there you’re offering us and our listeners.

Bethany Lockhart Johnson (35:27):
Yeah. Yeah. I’m really excited about this season. I think there’s — again, there’s no way we’re gonna cover all facets of math anxiety. But I think having the chance to explore it over the course of a season is going to be really fascinating. And really, I hope, destigmatize it and open up the conversation for our listeners. And, you know, if you listeners…we wanna know what you thought of this episode. Do you have any particular questions? Do you have questions related to math anxiety? Questions related to this episode? We are in development for this season, so we’re gonna do our best to get those questions answered. You can keep in touch with us in our Facebook discussion group, Math Teacher Lounge Community, and on Twitter at MTLshow.

Dan Meyer (36:14):
Next time, we’re gonna go deeper into the causes and consequences of math anxiety.

Dr. Erin Maloney (36:20):
It’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you.

Dan Meyer (36:41):
Til next time folks,

Bethany Lockhart Johnson (36:41):
Bye.

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What Dr. Gerardo Ramirez says about math

“A lot of students struggle with math, and we want to normalize that struggle as much as possible. We have to find opportunities to tell better stories and reflect on our experiences.”

– Dr. Gerardo Ramirez

Associate Professor of Educational Psychology, Ball State University

Meet the guest

Dr. Gerardo Ramirez obtained his Ph.D. from the University of Chicago, where he studied the  role of teachers and parents in shaping the math attitudes of their students, as well as reappraisal techniques to help students cope with anxiety during testing situations.

Dr. Ramirez is currently an associate professor at Ball State, where he examines the role of frustration, empathy, and cultural capital in shaping students’ success and persistence.

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About Math Teacher Lounge

Math Teacher Lounge is a biweekly podcast created specifically for K–12 math educators. In each episode co-hosts Bethany Lockhart Johnson (@lockhartedu) and Dan Meyer (@ddmeyer) chat with guests, taking a deep dive into the math and educational topics you care about.

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

S5-03. Cultivating a joy of learning with Sesame Workshop

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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.
 
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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.

Stay connected!

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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.

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

Grade 6

Unit 1: Area and Surface Area

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

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

Unit 2: Introducing Ratios

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

Unit 3: Rates and Percentages

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

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

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

Unit 4: Dividing Fractions

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

Unit 5: Arithmetic in Base Ten

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

Unit 6: Expressions and Equations

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

Unit 7: Rational Numbers

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

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

Unit 8: Data Sets and Distributions

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

Grade 7

Unit 1: Scale Drawings

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

Unit 2: Introducing Proportional Relationships

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

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

Unit 3: Measuring Circles

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

Unit 4: Proportional Relationships and Percentages

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

Unit 5: Rational Number Arithmetic

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

Unit 6: Expressions, Equations, and Inequalities

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

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

Unit 7: Angles, Triangles, and Prisms

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

Unit 8: Probability and Sampling

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

Grade 8

Unit 1: Rigid Transformations and Congruence

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

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

Unit 2: Dilations, Similarity, and Introducing Slope

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

Unit 3: Linear Relationships

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

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

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

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

Unit 4: Linear Equations and Linear Systems

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

Unit 5: Functions and Volume

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

Unit 6: Exponents and Scientific Notation

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

Unit 7: Irrationals and the Pythagorean Theorem

Practice Day 2 (Print available)

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

Unit 8: Pythagorean Theorem and Irrational Numbers

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

S5-05. Math technology & hacks for math anxiety: research-based tips for caregivers

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.

We’ve been very lucky to have so many prolific and brilliant researchers on this season of Math Teacher Lounge, and our next guest is no exception.

Listen as we sit down with Dr. Marjorie Schaeffer to discuss what causes math anxiety, math hacks, and how the right math technology can make an incredible impact in children and caregivers coping 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!

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Marjorie Schaeffer (00:00):

I think the most important thing we know from literature right now is that high math-anxious parents, when they interact with their children, their children learn less math over the course of the school year.

Bethany Lockhart Johnson (00:12):

Welcome back to Math Teacher Lounge. I’m Bethany Lockhart Johnson.

Dan Meyer (00:15):

And I’m Dan Meyer.

Bethany Lockhart Johnson (00:16):

We’re onto Episode 5, Dan, of our series on math anxiety. And I wanna say it feels so lovely to imagine all of these people out there doing work to help combat math anxiety. I dunno, it just makes me feel excited about the possibilities. This work is out there; it’s happening! Kids and teachers and caregivers are being impacted by these conversations. Not just — I mean, I don’t just mean the conversations we’re having on Math Teacher Lounge, but I mean, that these researchers are doing. Like, yes, we can change this!

Dan Meyer (00:53):

This is great. Yeah. We have people who are extremely smart, who have dedicated their professional lives to studying math anxiety and resolving it. And each of them that we’ve chatted with — they share lots of ideas in common, but I’ve loved how they each have their own different flavor or take or area of emphasis on a problem that hits everybody everywhere. It’s in your home, with kids and caregivers. It’s in schools. It’s in our places of teacher preparation and professional learning. Every place is a place where we can focus on resolving issues of math anxiety. It’s exciting.

Bethany Lockhart Johnson (01:26):

Yeah, I feel like … if there could be a course in — we all know that our teacher prep programs, in MOST teacher prep programs, there’s not nearly enough math methods or time to cover <laugh> — it’s like ready, set, go! And depending on who your mentor teacher is or what your math methods course … I mean, it can totally shape the way that you are prepared or really not prepared for going out there to teach math! And so I love that we’re having these conversations.

Dan Meyer (01:55):

What I love about today’s conversation is, one, it’s got a little bit of a technology flavor, so there’s that. But I also love, it’s got one of my favorite features about change, which is that it focuses on change to action, change to routine, rather than change to belief. Rather than saying like, “OK, everybody! Everybody stop thinking bad beliefs about math and transmitting them to your kids!” Instead, it says, “What we’ll do is just, hey, we’ll set that aside for a second and we’re gonna do a certain thing every day and watch as those actions make your beliefs change.” That to me is extremely cool. And I think it has a higher likelihood of success than just, like, me telling parents, “Hey, stop thinking these thoughts!”

Bethany Lockhart Johnson (02:37):

“Ready, set, stop being anxious!”

Dan Meyer (02:39):

Exactly. Exactly. So it’s an exciting conversation we’re gonna have here.

Bethany Lockhart Johnson (02:43):

Right. So it’s not a, you know, “wave the wand and all of a sudden, you’re not anxious about math anymore.” But these incremental changes, these incremental conversations, this validation, can really, really impact change. I’m with you on it, Dan. I hear what you’re saying.

Dan Meyer (03:01):

To help us talk through all of these ideas and more, we’re joined by Dr. Marjorie Schaeffer, Assistant Professor of Psychology at St. Mary’s College in Indiana.

Bethany Lockhart Johnson (03:10):

Enjoy. <Jaunty music> So, yes, Dan, we are so excited to welcome Marjorie Schaeffer. She’s Assistant Professor of Psychology at St. Mary’s College. Dr. Schaeffer, we’re so excited you’re here. Hello!

Marjorie Schaeffer (03:28):

Thank you so much for inviting me.

Dan Meyer (03:29):

Yeah. We are super-lucky to have had so many prolific and brilliant researchers about math anxiety on our show. You’ll be no exception. And every time, we love to find out about how you came to study math anxiety, which winds up being a really interesting glimpse into your backstory bio. So tell us, what is the route by which you came toward studying math anxiety?

Marjorie Schaeffer (03:51):

Oh, I love that question. I’m really interested in how the attitudes and beliefs of parents and teachers influence children, especially around math. And I actually became interested in this idea in college, when no Child Left Behind was actually first starting to be implemented in schools with high-stakes standardized testing. So much so that I actually did my thesis on this thinking about, “Do children understand the importance of high-stakes testing? Do they have anxiety around that idea?” And so that was really my first foray into the anxiety literature. And that was kind of the entry point into math anxiety for me.

Dan Meyer (04:28):

So you started by studying a very high-stakes assessment, like our students connecting with this. And the assessment is once per year. And classroom instruction is every day. So how did you move from the assessments to the everyday instruction?

Marjorie Schaeffer (04:44):

That’s a great question. So, after college, I actually taught kindergarten. And so from that, I saw the day-to-day impact of instruction and the day-to-day impact of children’s individual attitudes and beliefs. And so I really became interested in thinking about, “How do we understand why some children are really successful from the instruction happening in classrooms and why other children need a little bit more support?” And so math anxiety was one way for me to really think about the individual differences I saw in my kindergarten classroom.

Dan Meyer (05:18):

It feels like you headed … you went farther upstream, is what it feels like. Where assessment … there’s like some kind of anxiety around assessment, let’s say. And then you ventured farther up the stream to classroom instruction and then still farther into kids’ homes. It seems like your research invokes a lot of curiosity about the sources of a kind of amorphous, flowing phenomenon called math anxiety. And I’d love to hear a bit about what you know about how caregivers transfer, transmit — whatever the word is — math anxiety to their kids.

Marjorie Schaeffer (05:55):

For parents … we think that the attitudes and beliefs of parents matter. And we see that for lots of areas, not just math anxiety. But I think math anxiety, we see that really clearly. And so, we can think about it both in terms of what kind of input parents provide. So, how do families talk about math with their children? What kind of support do they provide around homework? And those are ones that I think are a little obvious. But we can also think about the offhanded comments that parents say to children when they’re talking about math generally. Right? So, we see lots of memes going around, talking about how hard math homework is. And so, I think when parents say offhanded comments like, “I’m not a math person,” or “We’re just bad at math,” that communicates values to children. I think the most important thing we know from literature right now is that high math-anxious parents, when they interact with their children, their children learn less math over the course of the school year. And this specific mechanism by which that happens is still an area for a lot of research. And so some people think it’s about input. So maybe if I’m math anxious, I’m avoiding math. And so, when I have an option to read a picture book that has math content, I focus on the colors instead. And so, my child is actually getting less math than other children. We can also think it’s about these messages that are provided. So, when I talk about math, I send the message to my child, it’s not for them, and therefore the child wants to engage in it less. And some of my work looks at things like expectations and values. So, thinking about, “Do math-anxious families actually value math less than other families unintentionally?” And so, we have some support for this idea that they expect less of their children. And so maybe when they struggle, they respond in different ways than a family who’s lower in math anxiety.

Bethany Lockhart Johnson (07:53):

This is so fascinating to me. I also was a kindergarten teacher. And I remember a mom who just … she had such like palpable math anxiety. And during one of our conversations, she was talking about these homework sessions with her daughter. And I may have mentioned this on the podcast before. But she was talking about how every night they would sit together and they would do all this math. They’d do, like, extra math together. And it always ended in tears. And despite her math anxiety, she didn’t want her daughter to experience the math anxiety that she did. So she was trying to pile it on, so her daughter was more proficient and comfortable. And instead, it was perpetuating this anxiety about it. And so, it’s a phenomenon then, right? Even if a parent is saying, like you said, maybe completely unwilling, this mother was actually trying to do the opposite. She was trying to help, you know, imbue the love and comfort with math. Right?

Marjorie Schaeffer (09:01):

Absolutely. This is why I think in my research, it’s really important that we find low-stakes, low-stress ways for high math-anxious families to do math. They absolutely can support their children in doing math. But they need a little support. We want it to be a fun, low-stakes environment, right? So maybe that’s the connection back to high-stakes testing, that I want children to have fun math experiences.

Dan Meyer (09:28):

Yeah. This is challenging, because it feels like the more caregivers know about math anxiety, and its pernicious effects on students, and how easily transmitted it is, one could become quite anxious about math anxiety. And, you know, no one makes great decisions when they’re anxious. So if I’m recalling our various episodes we’ve done, we’ve heard from people say, “Well, you need to validate students’ math anxiety. This is not something to just ignore or brush past. But also, not validate it in a way that says, you know, ‘This is OK and generational and inevitable.’” Which presents parents with a very thin path to follow, it seems like. So I love what you’re saying about how we gotta just de-stress the whole process.

Bethany Lockhart Johnson (10:11):

You’re avoiding the whole, “I wasn’t a math person either” kind of thing. <laugh>

Dan Meyer (10:15):

Right, right, right. Yeah. So I’d love to know more. We’re excited about the technology that you have studied and helped develop, presumably, called Bedtime Math, anapp for caregivers. And I’d love to know more about what that is and what it offers parents who know enough about math to know that they don’t want to transmit math anxiety to their children, but also want to support. So what does that offer them?

Marjorie Schaeffer (10:39):

So Bedtime Math is an app. It’s freely available on iTunes or the Apple Store or Google Play. And what it’s designed to do is to provide a nightly topical passage. So one of my favorites is the one about Groundhogs Day. And so it talks a little bit about the history of Groundhogs Day, and then it asks math-related follow-up questions. So starting at a preschool level, going through late fifth grade. And it’s really meant for parents to pick the one that meets their children where they are. And so the preschool-level question asks children to pretend to be a groundhog and walk to the left and walk to the right. So a skill that families might not think about as being math, but we actually think that IS part of understanding math. Understanding left and right directionality. And then the next question can ask questions like, “If it took the groundhog three seconds to climb out of the hole, and then two more seconds to see its shadow, how much time did it take all together?” So a simple addition problem, but it’s phrased in a fun way. And so the hope is that for high math-anxious families, these interactions are fun and playful. They don’t look like fights over homework. They’re just conversations that families can have around topics that are naturally interesting to children. And our hope is that when families have lots of these positive low-stakes interactions, they actually can see that we can talk about math in unstressful ways. In lots of ways, right? We can also do this at the grocery store. We can also do this while we’re cooking in the kitchen. It doesn’t just have to be fights over homework.

Bethany Lockhart Johnson (12:14):

And I actually have the Bedtime Math — one of the Bedtime Math books. And I was so excited to find out that there’s an app. And I think one of the things that I loved about the book is that these are invitations, right? They’re exactly that. Low pressure <laugh>, and they’re invitations to have a conversation. And if we were just to tell parents, “Oh, just count!” or, “Hey, just count wherever you go!” You know? No. It’s, in a way, I think, like you said, it’s retraining the parents on what math could look like. Like, “Oh, I didn’t even think we could just kind of have this conversation and we’re actually doing math together.”

Marjorie Schaeffer (12:55):

Yes, absolutely. I absolutely agree. We want it to be fun and playful and not stressful. And we want it to also be things that are meaningful to children’s lives. So these are topics children are interested in. It’s not that we are using flashcards or making children practice math facts over and over again. These are things children should wanna do that can naturally fit into a child’s routine. So almost all families read books before bed, and what we hope is that math can also be a part of the nighttime routine.

Dan Meyer (13:27):

There’s something really subtle here going on that I just wanna name and ask a question about. First of all, it’s cool that you started with studying high-stakes stuff and now you are developing low-stakes stuff. And I’m really curious what makes a thing low-stakes? Like, a few things I’m hearing from you is that there’s, like … I have a small child that I read literature to on a nightly basis. And I feel very anxiety-free doing that. And it’s almost as though, because each of the — tasks is the wrong word for this, but experiences — involve some reading, it puts me, the parent, in a mode that is comfortable and familiar to me. I’m curious: Are there other, as you design, what, one per day for a year? All these different experiences. What are some of the principles that you lean on that help make a thing low-stakes for kids and for parents?

Marjorie Schaeffer (14:17):

Yeah, that’s a great question. So one thing we wanted to be really intentional about is that our app doesn’t look like a lot of traditional apps. There isn’t noises that go off. You don’t enter an answer. And so one of the things that we thought made it low-stakes is that while there is a right or wrong answer — there is a correct answer — we aren’t giving children upsetting feedback. Instead, what we wanna encourage families to do is, if you struggle to remember how many seconds it took the groundhog to come out of the hole, you can work through that with a parent. So it doesn’t feel like you’re getting negative feedback; you’re being told you’re bad at math; you did it wrong. Instead, you’re just getting natural support moving forward. And so that’s one thing we wanted to be really intentional about, was that it wasn’t going to be a negative experience for children. And we are trying to build on all of the positive interactions families are having around nightly book reading. So many ways this can look very similar. You get to read another story that’s topical and hopefully interesting. And then do these little questions together. And so for a lot of families, their children don’t actually really look at the question. It almost feels like the parent is just asking them on their own. Like, they just came up with it. They just wanted to know what would happen to the groundhog. If there were three more groundhogs? How many groundhogs would we have all together? Not like it’s gonna be like homework or other parts.

Dan Meyer (15:38):

So my understanding is that there isn’t a blank into which people type a number in, press “submit” for evaluation, receive the red X, the green check. That’s a key part of the design here.

Marjorie Schaeffer (15:50):

Yes, absolutely. And for research purposes, we would’ve loved to know what families were saying. But we think it’s really important that it’s fun, interactive, that families are working together to get to the right answer, that it’s not a test for children.

Bethany Lockhart Johnson (16:03):

In your research, when you were — maybe you could walk us through the study a little bit. But I’m also curious if you heard from parents that it was carrying over beyond the bedtime routine. Because I would imagine, if I am building these skills and reading these questions and learning that I could talk to my kid like this about math in a fun way, that’s gonna happen then, like you said, when I’m in the grocery store. Or when I’m waiting in line for at the bank. Or whatever, you know? People go into banks now still, right?

Marjorie Schaeffer (16:35):

Yeah, absolutely. So in our study, we recruited almost 600 families and we randomly assigned them. So they had an equal chance of getting both our math app and what we call our control app. And that’s really just a math app without the math. We think of it as a reading control app. And that’s because we wanna make sure that families are having a similar experience, that it’s not just that having high-quality, fun interactions with your child is actually impacting children’s math achievement. And so what we then did is followed those children over the course of early elementary school. And so we worked with them in schools in the fall and spring of first, second, and third grade, really to look at their math learning. And so what we find is that children of high math-anxious adults, when they have the reading app, so what we think of as what’s happening in the real world, we see that really classic gap between children of high math-anxious adults and children of low math-anxious adults. So if you have a high math-anxious parent, you’re learning about three months less math over the course of first grade. But for children who receive this math app, we see this gap as closed. Those children look no different than a low math-anxious parent. And so that’s leading us to think that we’ve helped families talk about math in fundamentally different ways. We did a little bit of just talking to families to see a little bit about what might be going on. And a lot of families do report exactly what you’re describing, where they say this did help them talk about math in different ways they were doing it other times.

Dan Meyer (18:10):

That’s a really extraordinary study design. I don’t know … I love that you folks gave the control group not nothing. Like it’s possible that just parents and kids bonding over a thing regularly would be enough to provoke some kind of academic gain. But you gave the control group a thing that had them interacting socially, bonding, and still this large common gap between high-anxious and low-anxious parents, their kids shrunk together. Is that what I’m gathering here?

Marjorie Schaeffer (18:41):

Yeah, absolutely. So we’re basically seeing we can no longer, when we look at children’s data, say that parents’ math anxiety explains individual differences. So these children look really similar. They’re learning more than children who has a high math-anxious parent and just got our reading control app.

Dan Meyer (19:01):

just diving into the study a little bit more here, what is the time commitment? Or, did you guide parents to say, “All right, we’re gonna do this do this delightful story about a badger for an hour”? Or did people do it for five minutes? And what was the time commitment, roughly, for people?

Marjorie Schaeffer (19:17):

So we tell families to do it however they see fit. Because it is an app, we are able to get some sense of how long, and we are talking about three to six minutes for many families. For a lot of families, they’re reading a paragraph, the paragraph and a half, and then answering one or two questions. They’re not going through every possible question. They’re just doing a little bit, really meeting their kids where they are.

Dan Meyer (19:39):

Roughly how many times per week was that?

Marjorie Schaeffer (19:41):

So we asked families to do it as much as it fit. But we’re seeing about two and a half on average in the first year. And so families are fitting it in a couple of nights a week. It’s not every night.

Bethany Lockhart Johnson (19:52):

So what it sounds like you’re saying is what really was powerful about this app is that it was the space and time and prompts between the caregiver and the child, that chance to really sit down and have some of these meaningful and positive math interactions. How did it shift those relationships?

Marjorie Schaeffer (20:12):

So one of the things I think that makes the app effective is the changing of expectations. After a year, families are really using the app a lot less. And I think that’s OK, that they have found other ways to incorporate math into their lives. And we find that we don’t see an impact on their math anxiety, that they aren’t becoming less math anxious from this experience. Which I think makes sense, because they have had a lifetime of math anxiety. But we do see a change in parents’ expectations and value of math. So they expect their children will be better at math, and they also report that math is more important in their children’s lives. And so I think that’s an important part of it, which is, we can change these values for families, even if we aren’t able to change the math anxiety of the adults in children’s lives.

Bethany Lockhart Johnson (21:01):

I want to for a second before — because I’m loving this idea of the app, and I’m excited to find out more ways to cultivate these conversations in my home and also share this with other folks. Because even folks who don’t even maybe realize they have math anxiety … like you said, so often it’s unconscious. So often we’re putting these little snippets into our everyday conversation, like, “Oh yeah, I’m not a math person.” And we don’t even realize how much is impacting our kiddos and ourselves, right? So I am really curious: What do you think … in your research, what were some other takeaways that you feel like are really strategies that we can think about for combating math anxiety in general?

Marjorie Schaeffer (21:47):

So I’m particularly interested in thinking about how math-anxious adults can help tone down their anxiety so that they can have high-quality interactions with their children, that they interact with. And so one of the big takeaways for my research, I think, is that math-anxious families can help their children with math. They just need support. And so I think there are lots of ways for that support to look like. One, I think it can be an app, but I also think reading a little bit about math can be really helpful. So it’s not new. So the first time you aren’t thinking about some of these ideas is as your child has their homework open in front of you. And so you can process your own feelings separately before you have to do it with a child. I also think reminding parents that math is everywhere and that math is actually lots of things that we all love to do. Math isn’t just calculus. Not that calculus isn’t wonderful. But that math is measuring, math is counting ducks at the park. Math is talking about how many times did I go down this slide. And talking about math in this way, I think reminds families that they are great at that. That even if maybe they’ve had bad math experiences before, they can do math. Especially the way their preschool or early childhood, early elementary school student needs them to. And I think that can then set the foundation for being really successful later.

Dan Meyer (23:13):

So is your research then, your subsequent studies, your line of inquiry, is moving more towards how to support parents, then? Is that what I’m hearing?

Marjorie Schaeffer (23:22):

Yeah. So I’m really interested in both understanding how the math anxiety of parents and teachers influences children. And so math anxiety is really common and we know that it’s particularly common in early elementary school teachers. And so it’s very likely that children are interacting with a highly math-anxious adult. And so I’m really interested in thinking about how we can support those individuals in doing it. And so both, I think, things like Bedtime Math, which provide fun, unscripted ways to do that, but I’m also interested in the teacher equivalent. So, thinking about whether having things like a math coach can help teachers have more positive experiences with math. So if you see someone else play math games with your students, can that help you do it as well?

Dan Meyer (24:09):

It makes me wonder a lot about an app for teachers or an app for parents, one that’s not designed to be co-consumed with kids and their parents. But what that would look like … yeah, that’s really interesting.

Bethany Lockhart Johnson (24:21):

If we have a parent who, let’s say they have a third grader, fourth grader, fifth grader, or a middle schooler, right? Outside of early education. And they say, “OK, but what do I do? I’m with my kiddo; I don’t remember this math.” And they’re realizing that their anxiety may be influencing their kiddos’ disposition of mathematics, Or maybe they’re just in the midst of the battle <laugh>. What would you say to those folks, especially if it’s math that maybe they’re not comfortable with?

Marjorie Schaeffer (24:56):

One, I think we should like tone down the stress, right? Remind ourselves that it’s homework and homework feels really high-stakes, but these other outcomes are really high-stakes too, right? And so I’m really interested in the idea that can we help parents feel more comfortable about math by watching their own children teach it to them. So what’s a concept that the fourth grader actually feels really good about? And can they remind their parent how to do it? Can, together, they problem-solve the math homework? And so it’s not just on the parent to give the child the right answer. We know that’s a recipe for communicating some negative things about math. But instead, help the parent-child pair figure it out together. So what are some resources we can do? Can we look it up on the internet together? Can we write an email to the teacher together? Can we think about what are other problems that maybe we know how to do, and therefore we can use that same model here? So I want parents to feel like they are not solely responsible for it. That they can help figure it out with their child together. And so it’s a fun interaction.

Bethany Lockhart Johnson (26:02):

I love that. I love that.

Dan Meyer (26:03):

Yeah. Yeah. That’s wonderful. Yeah. A conviction that I have, and I think it’s true, is that any math that we’re learning at middle school, the attraction can be dialed down to a degree that a very small child, or a parent who has a very small child’s understanding of math, can appreciate. So instead of calculation, estimation. Instead of proof, just make a claim about something. And it makes me wonder about a companion to the work that’s happening in schools that parents feel inadequate to support, that students might not want to teach their parents. But which they could both, on a daily basis, say, “Here’s a way we can engage in this at a level that is comfortable to both of us.” Just dreaming out loud here. No question asked. No response needed. I just love your work. And made me wonder about that. Can you let me know your thoughts about technology? It is very rare that we have someone on the call who is an academic and very well-versed in research, but who also is published not just in in papers and textbooks, but also in digital media. It’s consumed by lots of people. So I am trusting that you have opinions about how math looks in technology. And I wonder if you’d offer some thoughts about how it goes, right? How it goes wrong from your own eyes.

Marjorie Schaeffer (27:14):

OK. That’s a great question. I think that we need more research. I first wanna say that I think that technology has really exploded in the last few years. How children have access to technology and screen times has really changed. And what we need is high-quality research happening. That said, I think that all of the things we know from child-development research still apply to technology. And so we know that children learn best when they are engaging in interactions with their parents. And so when families can use technology together, or at least can talk about what’s happening, it can be really effective. I also think technology, especially math apps, are best at teaching concrete skills with very clear answers. So I think practicing math facts is a great use of technology. So I love that Sushi math app where you solve multiplication problems and then get to quickly pull the sushi off the cart, right? But for higher-level questions, where we’re thinking about word problems or where what we’re helping to teach students is complex thinking, apps have a harder time doing that. Because students can often figure out the answer without engaging in the thinking that we are hoping that they’ll learn. And so I think technology absolutely has a piece. I think technology is helpful for parents. I think the logistics of helping parents live their lives is a good reason to use technology. But I think we need to be conscious of what it’s replacing. And so I think a world in which we think fourth graders can learn math only from apps is not realistic. But absolutely apps can be a great supplement to what’s already happening in the classroom.

Dan Meyer (28:56):

Yeah, that’s super-helpful. We have done a lot of work in digital curriculum here at Amplify, and often face the question on a daily basis, “Should this math be digital or on paper? Should we have the students stand up and talk or type something?” And those decisions are way too crucial and way more sensitive than a lot of the app-based education gives credit to. So appreciate your perspective there.

Marjorie Schaeffer (29:22):

OK. And I don’t think there’s one answer, or one answer for all classrooms. I think it’s like always a balancing act. I do think that one of the reasons our work is successful is because the parent-child interaction. And we want parents to learn from these experiences. And I think the same thing is true for for teachers.

Bethany Lockhart Johnson (29:41):

Dr. Schaeffer, thank you so much for being with us today and for sharing about your research, and again, for inviting us to reconsider ways that we can develop a more positive relationship with math. And that parent or caregiver or teacher relationship with a child, we’re seeing just how incredibly impactful that is. And I really appreciate your work and your voice on this. Thank you so much for your time.

Dan Meyer (30:07):

Thank you.

Marjorie Schaeffer (30:08):

Thank you for having me.

Bethany Lockhart Johnson (30:12):

Thank you again, Dr. Schaeffer, and thank you all for listening to our conversation. You can check out the show notes for more on Dr. Schaeffer’s work and to see a link to the app that we shared about Bedtime Math.

Dan Meyer (30:25):

Please keep in touch with us on Facebook at Math Teacher Lounge Community, and on Twitter at MTLShow.

Bethany Lockhart Johnson (30:32):

We would love to hear … you’ve been listening to this series; we’re dipping our toe into all these aspects of math anxiety. Is there something that you’re still wondering about? Something you wanna share about your own story with math anxiety?

Dan Meyer (30:43):

And if you haven’t already, if this is your first exposure to the Math Teacher Lounge podcast, please subscribe to Math Teacher Lounge, wherever you get your fine podcast products. And if you like what you’re hearing, please rate us! Leave us a review. You’ll help more listeners find the show.

Bethany Lockhart Johnson (31:01):

And let a friend know. But you know, it’s, it’s nice and cozy here in the Lounge, right? There’s no pressure. We’re hanging out. It’s all about learning. We’re learning together. We’re glad you’re here and we want others in your community to join us in the Lounge as well. You can find more information on all of Amplify’s shows at our podcast hub. Go to amplifycom.wpengine.com/hub. Next time on Math Teacher Lounge, we’re gonna be chatting about where we are today that we weren’t a few months ago in this topic.

Dan Meyer (31:31):

We’ll be chatting about this last series about math anxiety, and trading our favorite insights and observations from the run of the season.

Bethany Lockhart Johnson (31:41):

I just love this series, Dan. And thanks, all, for listening. We really appreciate having you in the Lounge.

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What Marjorie Schaeffer says about math

“We want it to be a fun, low-stakes environment, especially in high-stakes scenarios like testing. We want children to have fun math experiences.”

– Marjorie Schaeffer

Assistant Professor of Psychology at Saint Mary’s College

Meet the guest

Marjorie Schaeffer is an assistant professor of psychological sciences at Saint Mary’s College. She received her Ph.D in developmental psychology from the University of Chicago. Marjorie is interested in the role parents and teachers play in the development of children’s math attitudes and performance. She is specifically interested in the impact of expectations and anxiety and on children’s academic performance. Her work has been published in outlets including ScienceJournal of Experimental Psychology: General, and Developmental Science.

A laptop displaying a Facebook group page for "Math Teacher Lounge Community," featuring profile photos, a group banner, and geometric shapes in the image background.

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!

Defining math fluency with Jason Zimba

When we think of fluency, especially as a goal, we might think of speaking or reading a language. But fluency is also a goal in learning math! So what is math fluency? And what does it look like in the math classroom? In Season 6, Episode 1 of our Math Teacher Lounge podcast, Amplify’s own Jason Zimba helps us understand—using some analogies to baseball and chicken, of course.

Definitions of math fluency

We can develop fluency in many things, from coding to cooking. On the Math Teacher Lounge podcast, Amplify Chief Academic Officer of STEM Jason Zimba recounted becoming fluent in…roast chicken. 

Jason describes practicing one particular recipe until it was perfect. For Jason, that meant not just that the outcome was flawless or delicious, but that he was eventually able to make it from memory, without thinking—and to naturally adjust and calculate for variables like a smaller or larger chicken, or an unfamiliar oven. 

Math fluency works the same way. Practice brings effortlessness—freeing up time and mind space for new opportunities. 

The word “fluency” comes from the Latin fluentia, which means “flowing.” When applied to math, it means ”skill in carrying out procedures flexibly, accurately, efficiently, and appropriately,” says podcast host and math teacher and advocate Dan Meyer. As with someone fluent in a language (or a recipe), someone fluent in math is able to think and calculate mathematically without struggle or effort—that is, with fluidity. 

Podcast host and elementary educator Bethany Lockhart Johnson adds this informal description: “It’s that thing you don’t even think about anymore. ‘Cause it’s in there. You’re not still thinking about addition facts, because you’ve got it. And it fuels you. It’s the foundation that allows you to do all the other cool stuff.”

Fluency in the math classroom

What does fluency look like in practice? A young learner fluent in math will be able to smoothly recite the number word list in order (“one, two, three…”) and write the numerals from 0 to 9. As the student grows, so does their fluency with multi-digit calculation, rational-number arithmetic, and eventually even variable expressions. 

“It’s a wordless but still somehow almost verbal sort of fluency, with properties of operations as the grammar of the language,” says Jason.

But “it’s not fact recall,” he says. “Recall is remembering or just knowing. Fluency refers to calculation.”

Why and how to improve math fluency

There are different paths to fluency, but all can lead to “conceptual richness and mathematical joy,” says Dan.

If fluency provides that crucial foundation, what happens to students who are not math-fluent? 

“When kids don’t have access to [fluency], it keeps them from diving into the juicy parts of math,” says Bethany. “Math is so much bigger than addition facts, but when they don’t know those addition facts, that becomes all math is.” 

Without fluency, students miss opportunities to progress in (and enjoy) math, and may even develop math anxiety

So how can you support math students in developing fluency? 

For one thing, it’s important not to underestimate the value of practice and repetition. These approaches—especially when used in combination with other, more organic modes—can be highly productive, says Jason. “I worry about whether discomfort with repetitive practice is short-changing students of the power and confidence that fluency can bring.”

Dan compares it to achieving excellence in a sport—”like shooting from the same spot on the court over and over again,” he says. That kind of rote repetition is valuable in sports, and should also have its place in math instruction. 

It’s also important for students to understand why they’re learning and even drilling their numbers, arithmetic, or times tables, Jason notes. They need to be “invested in understanding and agreeing that this is going to do something for them.” 

One thing that helps: providing students a sense that they’ve accomplished something. “We need to have moments for them to reflect on what has been learned and what is now easy that was previously hard,” Dan says. He calls this process “humanizing fluency”—and Math Teacher Lounge will be here all season to help math educators do just that.

Save the date

Join us at NCTM in October for a live Math Teacher Lounge podcast recording with Dan Meyer and special guest Jennifer Bay-Williams! We’ll be investigating math fluency and finding fun ways to get all students engaged in math instruction. 

Math Teacher Lounge LIVE!
NCTM | Oct. 27 | 2:30 p.m. EST (doors at 2:15) | Room 158AB

More to explore

A closer look at grades K–2

Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage of four images: building a toothpick structure, a boy reading a book to a girl, two children conducting a water experiment, and a light projection setup.
Graphic showing a research process with four steps: spark intrigue with a real-world problem, explore evidence, explain and elaborate, and evaluate claims, connected in a cycle with arrows.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science California to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the California NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Educational curriculum chart showcasing a progression of amplify science lessons from kindergarten to grade 5, categorized by grade and subject areas like plants, animals, weather, and energy.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

An illustration from Needs of Plants and Animals unit
Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Download unit guide

Download lesson planner

An illustration from the Pushes and Pulls unit
Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Download unit guide

Download lesson planner

Silhouette of a playground structure against a blue sky with clouds and three yellow suns.
Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Download unit guide

Download lesson planner

Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.
Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Download unit guide

Download lesson planner

Two hands holding a paper with a drawing of a pyramid and a tree, illuminated by a flashlight, projecting another shadow of the image on the wall.
Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Download unit guide

Download lesson planner

An illustration from the Spinning Earth unit
Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Download unit guide

Download lesson planner

An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.
Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Download unit guide

Download lesson planner

A hand holds a red bean on a table, while a wooden stick spreads white glue and scattered beans. Also on the table are a white cup and a yellow pen.
Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Download unit guide

Download lesson planner

Illustration of a coastline with cliffs, a recreation center building with a red roof and a sign, evergreen trees, a blue flag, and a sandy beach below.
Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

Download unit guide

Download lesson planner

A closer look at grades K–2

Amplify Science is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage shows science activities: toothpick structure, two kids reading, two kids pouring liquid into cups, and a light experiment with shadows.
A four-step process diagram: Spark, Explore, Explain and elaborate, and Evaluate, connected by arrows, with a summary below about engaging through cohesive storylines.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Grid of nine educational subject cards for kindergarten, grade 1, and grade 2, each listing curriculum topics like "needs of plants and animals" and "engineering design" with lesson durations.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

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.

A closer look at grades K–2

Amplify Science California is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage of four images: building a toothpick structure, a boy reading a book to a girl, two children conducting a water experiment, and a light projection setup.
Graphic showing a research process with four steps: spark intrigue with a real-world problem, explore evidence, explain and elaborate, and evaluate claims, connected in a cycle with arrows.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science California to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the California NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Educational curriculum chart showcasing a progression of amplify science lessons from kindergarten to grade 5, categorized by grade and subject areas like plants, animals, weather, and energy.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

An illustration from Needs of Plants and Animals unit
Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Download unit guide

Download lesson planner

An illustration from the Pushes and Pulls unit
Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Download unit guide

Download lesson planner

Silhouette of a playground structure against a blue sky with clouds and three yellow suns.
Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Download unit guide

Download lesson planner

Illustration of sea turtles swimming among seaweed in the ocean, with a large shark in the background.
Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Download unit guide

Download lesson planner

Two hands holding a paper with a drawing of a pyramid and a tree, illuminated by a flashlight, projecting another shadow of the image on the wall.
Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Download unit guide

Download lesson planner

An illustration from the Spinning Earth unit
Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Download unit guide

Download lesson planner

An elephant standing next to a tree uses its trunk to pick a fruit from a branch while more fruit hangs above.
Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Download unit guide

Download lesson planner

A hand holds a red bean on a table, while a wooden stick spreads white glue and scattered beans. Also on the table are a white cup and a yellow pen.
Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Download unit guide

Download lesson planner

Illustration of a coastline with cliffs, a recreation center building with a red roof and a sign, evergreen trees, a blue flag, and a sandy beach below.
Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

Download unit guide

Download lesson planner

A closer look at grades K–2

Amplify Science is based on the latest research on teaching and learning and helps teachers deliver age-appropriate, high-quality, literacy-rich instruction that enables students to take on the roles of scientists and engineers to solve real-world phenomena every day.

In the K–2 classroom, this looks like students:

  • Collecting evidence from a variety of sources.
  • Making sense of evidence in a variety of ways.
  • Formulating convincing scientific arguments.
A collage shows science activities: toothpick structure, two kids reading, two kids pouring liquid into cups, and a light experiment with shadows.
A four-step process diagram: Spark, Explore, Explain and elaborate, and Evaluate, connected by arrows, with a summary below about engaging through cohesive storylines.

Program structure

Our cyclical lesson design ensures students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, their understanding gradually builds and deepens, ultimately leading to their ability to develop and refine increasingly complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science to teach less, but achieve more. Rather than asking teachers to wade through unnecessary content, we designed our K–2 program to address 100% of the NGSS in just 66 days.

Scope and sequence

Every year of our K–2 consists of 3 units and 66 total lessons. Said another way, each unit contains 20 lessons plus two dedicated assessment days (a Pre-Unit Assessment and End-of-Unit Assessment).

Lessons at grades K–1 are written for a minimum of 45-minutes, and grade 2 lessons are written for a minimum of 60-minutes—though teachers can expand or contract the timing to meet their needs.

Grid of nine educational subject cards for kindergarten, grade 1, and grade 2, each listing curriculum topics like "needs of plants and animals" and "engineering design" with lesson durations.

Unit types

While every unit delivers three-dimensional learning experiences and engages students in gathering evidence from a rich collection of sources, each unit also emphasizes a particular science and engineering practice.

In each grade K–2:

  • One unit emphasizes the practice of investigation.
  • One unit emphasizes the practice of modeling.
  • One unit emphasizes the practice of engineering design.
Investigation Units

Investigation units focus on the process of strategically developing investigations and gathering data to answer questions. Students are first asked to consider questions about what happens in the natural world and why, and are then involved in designing and conducting investigations that produce data to help answer those questions.

Modeling Units

Modeling units provide extra support to students engaging in the practice of modeling. Students use physical models, investigate with computer models, and create their own diagrams to help them visualize what might be happening on the nanoscale.

Engineering Design Units

Engineering design units provide opportunities for students to solve complex problems by applying science principles to the design of functional solutions, and iteratively testing those solutions to determine how well they meet preset criteria.

Units at a glance

Needs of Plants and Animals

Domains: Life Science, Earth and Space Science, Engineering Design

Unit type: Investigation

Student role: Scientists

Phenomenon: There are no monarch caterpillars in the Mariposa Grove community garden since vegetables were planted. 

Pushes and Pulls

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Pinball engineers

Phenomenon: Pinball machines allow people to control the direction and strength of forces on a ball.  

Sunlight and Weather

Domains: Earth and Space Science, Life Science, Engineering Design

Unit type: Modeling

Student role: Weather scientists

Phenomenon: Students at Carver Elementary School are too cold during morning recess, while students at Woodland Elementary School are too hot during afternoon recess.  

Animal and Plant Defenses

Domain: Life Science

Unit type: Modeling

Student role: Marine scientists

Phenomenon: Spruce the Sea Turtle lives in an aquarium and will soon be released back into the ocean, where she will survive despite ocean predators.  

Light and Sound

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Light and sound engineers

Phenomenon: A puppet show company uses light and sound to depict realistic scenes in puppet shows.  

Spinning Earth

Domain: Earth and Space Science

Unit type: Investigation

Student role: Sky scientists

Phenomenon: The sky looks different to Sai and his grandma when they talk on the phone.  

Plant and Animal Relationships

Domains: Life Science, Engineering Design

Unit type: Investigation

Student role: Plant scientists

Phenomenon: No new chalta trees are growing in the fictional Bengal Tiger Reserve in India.  

Properties of Materials

Domains: Physical Science, Engineering Design

Unit type: Engineering design

Student role: Glue engineers

Phenomenon: Different glue recipes result in glues that have different properties.  

Changing Landforms

Domain: Earth and Space Science

Unit type: Modeling

Student role: Geologists

Phenomenon: The cliff that Oceanside Recreation Center is situated on appears to be receding over time.  

Amplify Desmos Math
for New York

Welcome to Amplify Desmos Math, a powerful new core program from Amplify and Desmos Classroom built for NYC teachers and students.

Amplify Desmos Math is built on four core tenets:

  • Math can motivate students.
  • A structured approach to problem-based learning can best tend to all aspects of rigor.
  • Student thinking is valuable and visible.
  • Students can catch up while keeping up with grade-level math.
A teacher stands in front of a classroom, pointing toward a screen, while students with raised hands sit at desks with laptops, engaging with the core curriculum through Amplify Desmos Math.

What if your students asked to do more math?

Amplify Desmos Math lessons are powerful in their ability to elicit student thinking and spark interesting, productive discussions.

The lessons pose problems that invite a variety of approaches with their dynamic and interactive learning experiences on devices, as well as experiences on paper that are flexible, creative, and engaging.

As students work online, they interact with visuals and simulations that show their thinking and decisions. When appropriate, students see other students’ responses and engage in collaborative math discussions.

A Responsive Feedback feature responds to student thinking by showing the mathematical meaning behind it. This is more powerful than simply evaluating thinking as right or wrong, because it motivates and engages students in the learning process.

A grid-based puzzle showing a green ball at (-8, -8) and a yellow star at (5, 6); user is prompted to enter coordinates to reach the star.

In this Grade 6 activity, students internalize the coordinate plane by plotting points to navigate the marble through the maze to collect the star.

A blank coordinate grid is shown next to a list of coordinate pairs to plot, ranging from (–2, –9) to (3, –3). Instructions are to plot and connect each pair in order.

This prepares students to accurately and efficiently plot points with positive and negative coordinates on grids with different scales and explain the relationship between ordered pairs that differ only by the signs of the coordinates.

A yellow submarine with floats and anchors must be adjusted to reach and collect a star positioned at -3 units in the water. A table and "Check My Work" button appear to the right.

In this Grade 7 activity, students explore positive and negative integer operations using the up and down movement of a submarine.

Screenshot of a math problem asking for the new temperature in Beijing after it drops 5°C from –2°C, with a text box and a "Submit" button for the answer.

Students are then prepared apply this understanding in a variety of word problem contexts.

A math activity interface showing four lanes with turtles, labeled 1 to 4, on a track. A prompt asks to write an equation for the turtle in lane 4 to control its movement.

In this Grade 8 activity, students create rate, distance, and time equations based on turtle races.

A blank graph with cost in dollars on the y-axis and blueberries in pounds on the x-axis, labeled for a problem about blueberry pricing.

This prepares students to understand that a graph representing a proportional relationship is a line through (0, 0) and (1, k). They also begin to see connections between a context and features of a corresponding graph, equation, and table.

Data at your fingertips on the road to mastery

Digital assessment report with tabs for Reports, WAT, and Admin Reports. Displays classes, units, assessments, and scoring details for high and low-performing items, including raw scores.

1

Pre-Unit Checks show the range of student mastery for the entire class and identify strengths and needs by standard.

Two overlapping cards detail a math unit overview and learning goals, focusing on equivalent ratios and proportional relationships in tables, equations, and graphs.

2

In each unit, lessons are designed and sequenced to help students fully master critical standards and build computational fluency. Each lesson is part of a carefully constructed instructional sequence that scaffolds students’ cognitive mathematical development.

A math problem prompt is displayed above, with a table comparing orange and pineapple juice recipes below. Another box describes "7.2 Practice Day 1" learning goals.

3

Daily practice problems and frequent practice days reinforce concepts and build fluency.

Screenshot of an assessment report and instructions for Assessment Form A, highlighting score distribution, student performance, and requirements like blank paper and a calculator.

4

End-of-Unit Assessments and reporting analysis pinpoint students requiring remediation with specific standards and concepts.

Facilitate a collaborative, connected classroom community.

The powerful teacher facilitation tools in Amplify Desmos Math give teachers insight into student thinking in real time. Teachers can select student work to display and discuss quickly and easily, leading to better questions that guide more productive discussions.

Amplify Desmos Math helps guide the learning process by connecting students to each other and to an understanding that they can use math to make sense of the world. Students learn and collaborate in every lesson. Whether using print, digital, or a mix of both, students stay connected to each other’s ideas and thinking, fueling classroom conversations and a shared understanding of math.

Three students sit at a table in a classroom, smiling and looking at a laptop together, with notebooks and papers in front of them.
An illustrated Amplify Desmos Math textbook and a computer screen showing a digital math activity about making pizza ingredients.

Standards alignment

Amplify Desmos Math is customized specifically to meet the New York State Next Generation Math Learning Standards. Within each document below, you’ll find direct links to lessons and activities where each individual standard is addressed.

Grade 6 correlation
Grade 7 correlation
Grade 8 correlation

The program is also aligned with the expectations outlined in the New York City Department of Education Definition of Culturally Responsive-Sustaining Education and the New York State Culturally Responsive-Sustaining Education Framework. Download the CR-SE alignment.

Digital review

Ready to explore the program? To log in, click the orange “Review now” button below, select “Log in with Amplify” and use the following login credentials:

Username: t.nycadmsample-01@tryamplify.net

Password: AmplifyNumber1

To review Algebra 1 content from Desmos Math 6–A1, which serves as the foundation for Amplify Desmos Math, click this link after logging in using the credentials above.

Two illustrated math textbooks labeled Amplify Desmos Math for grades 7 and 8, shown above a laptop displaying a digital balance scale activity.
Two women in an office setting look at a computer monitor together, both appearing focused and engaged. One is seated while the other stands beside her.

Support

Throughout your review, you can reach our support team by email or phone. We are available any time over:

Live chat: Click the orange icon while logged in to get immediate help.

Phone: Call our toll-free number: (888)-960-0380.

Email: Send an email to help@amplify.com. In the message body, please include your name and question. Provide as much detail as possible, so we can help you find a solution.