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

Grade 6

Module 1: Ratios and Unit Rates

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

Module 2: Arithmetic Operations Including Division of Fractions

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

Module 3: Rational Numbers

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

Module 4: Expressions and Equations

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

Module 5: Area, Surface Area, and Volume Problems

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

Module 6: Statistics

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

Grade 7

Module 1: Ratios and Proportional Relationships

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

Module 2: Rational Numbers

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

Module 3: Expressions and Equations

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

Module 4: Percent and Proportional Relationships

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

Module 5: Statistics and Probability

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

Module 6: Geometry

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

Grade 8

Module 1: Integer Exponents and Scientific Notation

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

Module 2: The Concept of Congruence

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

Module 3: Similarity

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

Module 4: Linear Equations

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

Module 5: Examples of Functions from Geometry

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

Module 6: Linear Functions

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

Module 7: Introduction to Irrational Numbers Using Geometry

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

S1-05: How does coding fit in the science classroom? A conversation with Aryanna Trejo of Code.org

Podcast cover titled "Science Connections" featuring Aryanna Trejo, Season 1, Episode 5. It includes abstract illustrations of a globe and telescope, discussing coding in the science classroom.

In this episode, Eric sits down with Aryanna Trejo, a professional learning specialist of Code.org. Aryanna shares her journey from working as an elementary teacher in New York City and Los Angeles to teaching other educators at Code.org. Eric and Aryanna chat about computer literacy within the science classroom, problem-solving skills, and ways to model productive struggle for students. Aryanna also shares ways to teach coding and computer literacy in schools, no matter the classroom’s technology level. Explore more from Science Connections by visiting our main page.

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Aryanna Trejo (00:00):

I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.”

Eric Cross (00:19):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Aryanna Trejo. Aryanna is a member of the professional learning team at Code.org. Before joining Code.org, Aryanna led computer science professional development for elementary school teachers, and served as an instructional coach for new educators. She also taught fourth and fifth grade in both New York City and in Los Angeles. In this episode, we discuss Aryanna’s journey to Code.org, where she helps educators connect coding to real life, how to use a rubber duck to solve problems, and how coding and computer science principles can be taught to students in areas without access to the internet…or even a computer. I hope you enjoy my conversation with Aryanna Trejo. So I was born and raised here, and I saw that you went to UC San Diego.

Aryanna Trejo (01:11):

I did, I did. I actually just put a deposit down on an apartment in University Heights, ’cause I’m moving back.

Eric Cross (01:16):

You’re coming back?

Aryanna Trejo (01:17):

I’m coming back. Yeah.

Eric Cross (01:19):

So if you need a classroom to visit….

Aryanna Trejo (01:21):

I would love to do more classroom observations!

Eric Cross (01:24):

Are we doing this? Let’s do—we’re making this happen.

Aryanna Trejo (01:26):

We are. Yeah. So I’ll be there. I’m moving there in April. I actually grew up in Orange County too, so I’m like a very diehard SoCal person.

Eric Cross (01:35):

So I feel like I know the answer to, hopefully—Tupac or Biggie? ‘Cause you’re on the East Coast, and you’re on the West Coast.

Aryanna Trejo (01:40):

Yeah. I like Tupac, but I have more Biggie songs committed to memory. Which is not a lot. I have “Juicy” and “Hypnotized” memorized.

Eric Cross (01:53):

All right. So you’re just memorizing, and you have the Biggie songs memorized, but not the Tupac ones.

Aryanna Trejo (01:58):

No, but I do love Tupac songs. You know, it’s like, Biggie has the flow, but Tupac has the lyrics. Nobody’s—they both have something really amazing about them.

Eric Cross (02:06):

You know, I can respect that you broke it down into both of their strengths.

Aryanna Trejo (02:11):

Thanks for buttering me up before this interview. And not….

Eric Cross (02:15):

<laugh> Oh, we already started.

Aryanna Trejo (02:16):

Huh? We already started?

Eric Cross (02:17):

We’re already started. Yeah. We’re already into this.

Aryanna Trejo (02:19):

We’re into it.

Eric Cross (02:21):

You were in the classroom, fourth and fifth grade, and you were doing TFA.

Aryanna Trejo (02:26):

I did. I did Teach For America. I was 2012, New York City Corps. Right after graduation. ‘Cause I graduated UC San Diego in 2012. So graduation was on June 17th, and I touched down at JFK on June 19th.

Eric Cross (02:40):

Even though I wasn’t in TFA, I know a lot of the fellows that are in it. And there’s just some phenomenal teachers in there. How long were you doing elementary school when you were teaching?

Aryanna Trejo (02:49):

Yeah, I taught for—well, I did, three years of teaching fourth grade. Then there happened to be an instructional coach opening in my fourth year. I took that, did some instructional coaching within the same network, and then I moved back to LA and I taught fifth grade for a year.

Eric Cross (03:11):

  1. And what was it like now? Did you go to Code.org right after the classroom?

Aryanna Trejo (03:17):

No, I didn’t. No. I transitioned after teaching fifth grade for a year in downtown Los Angeles, in the Pico-Union neighborhood. I ended up getting this email out of the blue from someone who had actually found me through the Teach for America job site. ‘Cause I was hitting the pavement; I was really looking to transition out of the classroom. And she invited me to interview with this company called 9 Dots. And they taught computer science to kids K–6 throughout Los Angeles and Compton. And I was like, “Sure, no problem. Let’s do it.” So I interviewed, I got the job, and yeah, that’s how I transitioned to 9 Dots. And then after almost four years there, I transitioned to Code.org, with the same person. Actually, she moved over to Code.org first, and then she helped me get this job.

Eric Cross (04:07):

Oh, that’s happened a lot—like, that relationship kinda carries over.

Aryanna Trejo (04:11):

Yeah. We’re meant to be coworkers.

Eric Cross (04:13):

Yeah. Are you still? Is she still there? Are you both still together?

Aryanna Trejo (04:17):

Yeah, we’re on the same team and it’s nice. I saw her last night for Happy Hour, with another coworker who’s in LA. So we’re tight. And she’s a wonderful, wonderful mentor to me.

Eric Cross (04:28):

That’s great. Did you have computer-science background, when you were doing elementary school teaching? Did you have—

Aryanna Trejo (04:34):

No. <laugh> Not at all. When I was teaching in New York City, I had like four desktop computers in my classroom, and we rarely used them. Which was such a shame. And then when I moved to Los Angeles and taught fifth grade there, we were a one-to-one school, and the joys of that are just amazing. It was just really wonderful to, you know, get the students used to typing on the computer, using different software to submit their assignments. Getting creative—as creative as you can get—with Google Slides. You know, to show off what they know. And stuff like that. That’s all I had, though. And you know, when I transitioned to 9 Dots I was like, “Sure, why not? Let’s give a shot.” And I learned a lot. It was really interesting, yeah.

Eric Cross (05:26):

And so now at Code.org you are…well, so my journey with Code.org, I’ve been in the classroom for eight years. Still in the classroom as of…an hour ago, I was there. <Laugh> And I use Code.org, and I feel like I’ve checked it periodically, and I feel like it’s evolved over the gaps. And I’ve seen it. It’s become more robust in the things that they offer, over the years I’ve been an educator. Just to kind of…could you give a thumbnail sketch? Like, what is Code.org? Who’s it for? Who’s the target audience? What resources are there?

Aryanna Trejo (06:00):

Yeah. So it’s for everyone. It is a nonprofit that provides curriculum and training and a platform for teachers and students. We provide curriculum for K through 12. It’s completely free. And it comes with lesson plans, slideshows, all that. We focus specifically on underrepresented groups. So we have targeted measures for Black students, for Native American students, for students who identify as female. That’s a huge part of our mission. But we’re really working to expand access to computer science to as many students as we can.

Eric Cross (06:41):

One of the things I’m hearing in your story is you were teaching in Compton; you were in Bronx, New York. One of the reasons why I got into the classroom is because of educators, and the impact they made on me in exposing me to science and technologies I’d never had access to. And that intentionality, that you’re going about it…are there…not just the code, but how you bring that across to different groups…are there strategies, or are there ways to connect this idea of coding to diverse groups and diverse audiences? Or is it kind of, the curriculum applies for everyone? ‘Cause in science, when I’m teaching, I’m always trying to make what I’m doing relevant to the backgrounds of my students.

Aryanna Trejo (07:28):

Sure.

Eric Cross (07:28):

So I’m teaching biology, and I’m trying to make this kind of connection. Sometimes it’s more organic; sometimes it feels kind of forced. Because it’s just not always a nice fit. But it sounds like Code.org is really about inclusion. And in the numbers that I’ve seen for representation, in especially computer science software engineers, the groups that you’re focusing on are not necessarily represented in the professional workforce. At least disproportionately.

Aryanna Trejo (07:54):

Yeah, absolutely. Yeah, that’s correct.

Eric Cross (07:57):

And so how do you go about being intentional about reaching groups that we don’t see in, you know, the Silicon Valley software engineers? How do you start that? Like, at a young age, do you look for specific schools in specific areas to say, “We are going to bring this to the school. We’re going out to these populations of the cities”? Because we’re just not seeing…you know, on the map, we’re not seeing anybody really doing anything with coding here. Or we’re not seeing the numbers come out of these areas, out of these cities, of students who are going into STEM or going into computer science fields.

Aryanna Trejo (08:41):

Yeah. I don’t necessarily work on the recruitment side of it, is the issue, in my position. But I do work on the professional learning, that is brought out to teachers. And we have a huge focus on equity throughout the workshops that we create from K–12. It’s something we’re really passionate about. We definitely aim to prepare teachers to teach computer science. That’s a huge part of it. Knowing the content, but also thinking through, “What does recruitment look like at your school to make sure that the demographics of your classroom match the demographics of your entire school?” Also, thinking through, “How can we make sure that female students feel included in your classroom? How can we make sure that we are, giving students creativity to think about, or we are setting students up to be creative and think about the problems that are in their community, and how they can use computer science to solve them, or at least work towards them?”

Eric Cross (09:39):

So solving real-world problems and that inclusion aspect…are there things like…you were saying “female or students who identify as female”…are there things that teachers can do to ensure that they’re being more inclusive? Or to recruit, or encourage more female students to take part? One of the things I was thinking of, that I’ve seen, is I’ve seen coding kind of camps.

Aryanna Trejo (10:06):

Sure.

Eric Cross (10:08):

That were specifically for a female audience. And that seemed to help with recruitment. Is that something that you see on your side?

Aryanna Trejo (10:16):

That’s not something that we set up, no. But the curriculum that I work with is CS Principles. And it’s offered as an Advanced Placement course, as well as an AP class. So that’s a curriculum that’s designed for students who are in grades 10 through 12. And so at that point, we can really talk to teachers and ask them what the recruitment strategy is. But in terms of strategies that teachers can use to recruit those students…I mean, I’ve heard over and over from lots of different teachers who identify as female that they didn’t think that computer science was for them, until they saw a role model in that position. And so just being a role model for those students is really wonderful.

Eric Cross (11:00):

And I see it too, with—like, we do “Draw a Scientist” activity, which is like a popular science thing—

Aryanna Trejo (11:05):

Sure, yeah, I’m familiar.

Eric Cross (11:05):

But it’s the same thing, right? Like, it fleshes out. My students don’t draw themselves as scientists. They draw what they perceive, based on what television says. I imagine with computer science, it’s probably really similar, when you think about “What’s a software engineer look like?” Do students tend to draw themselves? Or is it even a mystery? Because I don’t even know what a software engineer looks like.

Aryanna Trejo (11:28):

Yeah, absolutely. Well, one of the things we love to do with our professional learning workshops is talk about understanding yourself, your identities, how they show up in the classroom as biases. And, you know, things like stereotype threat. We see that as really important to understand, and think through, and consider, before you step into the classroom. So that you’re not, you know, coddling certain groups of students because you don’t believe that they are able to be successful in computer science. Holding all the students to the same expectations and believing that they can succeed. And computer science, I think a lot of the times people have this conception of it being this utopian, bias-less, technocratic field. When in reality, everything has bias. And people talk about algorithmic bias and facial recognition, but also the people who created computers and computer languages have their own bias that comes through. And I think it’s really important to show students that. So that they can, one, know what they’re working with, and two, make sure that they can create products that reduce that bias.

Eric Cross (12:50):

It’s like…it’s not objective, just because we’re creating software. Like, once it gets to a point of being so sophisticated…I think, like, AI software, right? With facial recognition? And we’re seeing more and more articles come out about, you know, predicting trends based on historical data.

Aryanna Trejo (13:12):

Sure.

Eric Cross (13:13):

But then, the trends and things that they’re seeing tend to target things that have happened in the past. But it also doesn’t take into consideration a lot of other factors that can lead to certain groups or populations being identified. And I’ve seen some articles lately about how your code is really just representation of what you put into it. And like you just said, your bias—if you have that, conscious or unconscious—you’re gonna put that into your code. And the input is gonna be an impact, is gonna impact the output.

Aryanna Trejo (13:44):

Yeah, absolutely. Or even just—and I’m ashamed to say this, ’cause this is an idea that came to me just recently, through an article that I read—but computers themselves have bias. The hardware assumes that you have vision, that you can see the screen, that you are able-bodied, that you can use your hands to work the keyboard, the mouse, et cetera, and that you don’t have to use assistive technology. You know, there are small things like that, where we think that technology, like I said, is this utopian, futuristic science…but there are biases throughout.

Eric Cross (14:19):

You’re absolutely right. I’ve never even—I’ve never even considered that. Even though I do use assistive tech, and figure it out, I’ve never thought from the ground up, the process is built for an able-bodied, sighted, hearing person.

Aryanna Trejo (14:31):

Exactly.

Eric Cross (14:32):

To be able to engage with the hardware. And then these other things, these tertiary things that we kind of add on, so that you can do this, but it’s not designed from the ground up for people who are, you know, different audiences, physically. So I’m glad you brought that up, though. Now I’ve seen—and I haven’t done this—but I know Hour of Code is a big thing. And this is something that’s ongoing. Can you talk a little bit about what Hour of Code is? I know it’s, it’s a big thing for the classroom teachers.

Aryanna Trejo (15:08):

Yeah. So Hour of Code is really exciting, and it’s just blossomed from something small to something tremendous. This year is gonna be the 10th Hour of Code. So what it is, is it happens during CS Education Week in December, during Grace Hopper’s—or to honor Grace Hopper’s birthday. She was a computer scientist and Navy Admiral. And basically the aim of it is to get as many students on the computer doing an hour of code, and demystify what coding is. You know, to do seed-planting. To show teachers that this is something that you can facilitate for your students. And also to show students like, “Hey, computer science is something you can absolutely do. Not just for an hour, but more if you want.” So, yeah. Now it’s worldwide, and it’s really exciting.

Eric Cross (15:58):

That’s awesome. And I think about teachers and I still hear the apologetic—when I’m helping teachers in the classroom with education technology—the self-deprecating “I’m a dinosaur; I’m not good with tech,” which is never true. Like, they’re better than they even realize. And I feel like sometimes there’s still a stigma, too. It’s like <laugh> The Simpsons’ Comic Book Store Guy. The condescending tech support person—

Aryanna Trejo (16:27):

Sure.

Eric Cross (16:28):

—who has that tone. And so I feel like some people have been so negatively impacted by that person. So I know when I’m helping people, I actually try to go full-spectrum the other side. But I’m thinking about teachers’ barrier to entry. Sometimes code is like, “Whoa.” And I don’t teach computer science. Do you see those barriers to entry, or at least the perception of them? And then, what’s the reality for like someone listening, and going, “I’m a fourth grade teacher,” or “I’m a humanities teacher in ninth grade.” What’s the perception that you see, versus reality, with the teachers that you train? Is it much more accessible than we think? Or is there a level of sophistication that you have to have coming into it?

Aryanna Trejo (17:10):

No, not at all. I know computer science, and that says a lot! <Laugh> You know, I know my own corner of computer science. And you know, that’s me being self-deprecating, too. But I think learning computer science has helped me in so many different ways that I wasn’t expecting. I recently took the GRE in hopes of, you know, getting back into grad school. And I think just the way that computer science teaches you to search for bugs in your code, or errors, and kind of tirelessly look at a problem from multiple different angles, I was able to carry that into the math that I was doing. And I noticed just a huge difference in the way that I approached it, and the way that I was open to it. But you asked a great question, in regards to the barriers to technology. In my position at 9 Dots, I was working directly with teachers to lead professional development with them. Sometimes it would be a full day; sometimes it would be an hour after school. And the one thing that I always had in my back pocket that was really useful is that I would hear teachers saying things like, “Well, I just can’t do coding; this is too hard for me; the time has passed.” And I would ask them, “Would you say that to your student about math or English?” And they would always sheepishly go, “No.” And I’d say, “Well, be as kind to yourself as you would be to your student.” You know, it takes some patience and nobody’s gonna get it perfect 100 percent of the time. Have I banged my head against the wall trying to solve one tiny little syntax error in my code? Absolutely! But it feels absolutely phenomenal to fix that. And I was an English major in undergrad, and I had never done computer science before. So it’s something that becomes really satisfying.

Eric Cross (19:07):

Yeah, I imagine. I had someone—a trainer or a presenter—one time bring up the fact that our students rarely get to see us learn in real time.

Aryanna Trejo (19:19):

Yeah.

Eric Cross (19:19):

So we don’t get to ever really model failure. I mean, unless we’re in a classroom situation <laughs> in our failures, with classroom management. Then they see it, they see it! But they don’t get to see us model learning failure. And I don’t mean like failure—and yes, I know, “first attempt is learning,” and “no such thing as failure”—that’s not what I’m talking about. But just when we’re not successful with our code, and then we experience real-time frustration.

Aryanna Trejo (19:42):

Yep.

Eric Cross (19:42):

And they said that is actually a great learning experience for your students to watch you go through productive struggle. And that was really liberating for me. Because now I’m in the classroom, and I’m trying to go through it with my students, and the beautiful thing was, they started helping me. We were all trying to solve the problem. And then we had this authentic problem-solving experience. I think it was like a Scratch program, where we were trying to solve, trying to embed it somewhere, or something. And then, in the background of the class: “Mr. Cross! I got it! I figured it out!” And it was this really neat bonding experience. And I felt that—your ears get red, and you get hot, ’cause you’re not—

Aryanna Trejo (20:19):

Oh yeah.

Eric Cross (20:20):

You don’t know it! And you’re in front of 36 kids! And I said, “OK, I need to tell them how I feel.”

Aryanna Trejo (20:25):

Yeah.

Eric Cross (20:26):

So I said, “Now I feel really frustrated.” Like, “I want to go through this, and here’s my thoughts.” ‘Cause I knew that it would be helpful if they saw and would hear my thoughts. So I just did a quick think-aloud and I said, “In my head, <laugh> I want to just quit,” I said, “But I realize that this is the part where my learning’s happening. So I just want you all to hear what’s going on in my brain.” And now I feel like when I’m doing coding with my students, and it’s just basic coding, I feel much more comfortable, like, not knowing. But I needed someone to release me from that “I have to be the expert in everything” to do it.

Aryanna Trejo (21:06):

And teachers are used to being the experts. Right? And they should be. And coding is just such a different landscape. But I think once you kind of give over to the power of tinkering, I think it’s really gratifying. I love being able to…you can revise a sentence, and then read your paragraph back to yourself in English, and say, “OK, I get it.” But there’s something so gratifying about changing a line of code or a block and then being able to hit play and watch your program come to life, and say, “Hmm, that’s not quite what I wanted. Let’s try something different.”

Eric Cross (21:39):

I love your connection to tinkering. ‘Cause—I had never thought about it—’cause I love tinkering with my hands. But I always think about physical things. But coding is exactly that. It’s tinkering.

Aryanna Trejo (21:47):

It’s exactly that.

Eric Cross (21:47):

That’s exactly what it is.

Aryanna Trejo (21:49):

And a lot of it is, for me, especially when I’m trying something new, it’s guess-and-check. It’s like, “OK, that didn’t work. What if I add a semicolon here? Will it finally work? Or what if I add a ‘for’ loop? Will this get me what I want?” And it’s wonderful because you have that with students as well. Like, you have that record of their thinking, and you can ask them to go step-by-step and tell you, you know, “First, I added this, because I wanted the program to do this,” and so on and so forth. And so you have that record, but you can always get rid of it. Students often wanna get completely get rid of it. That’s something that I’ve noticed a lot as I’ve taught computer science. But, once you can get them to target the specific parts of the program, tinker with that, and continue, that’s a really wonderful learning space. There was also something you said about modeling failure. I love the fact that in computer science you can model failure for your students. You said to your students, “I’m getting frustrated.” I love that, because I never got that in math. Nobody ever showed me what it was like to be frustrated with graphing a parabola. Right? Like, my math teachers were always like, “Doot, doot, doot, here you go, you’re done!” <Laugh> And I would get so frustrated, because it didn’t come that easily to me. And I think there’s two parts to that. So there’s modeling the learning and the thinking and the productive struggle, but also there’s the identity of being a computer scientist and modeling what that looks like. So for me, when I get really frustrated with a program, I walk away. I take five minutes. I take a deep breath. I say, “I’m not gonna think about it in these five minutes.” And I come back to it. And I think once you start teaching computer science, you can facilitate that for students. And there’s so many different strategies that they can pick up. They can pick up rubber ducking, which is where they pick up a rubber duck or a similar object, and they talk to it as if they were a partner and talk through their code. And oftentimes, as you’re rubber ducking, you’re gonna find that error, because you’re explaining it to someone who’s a stand-in for a novice. And rubber ducking is a well-known strategy for computer scientists who make it their career. You know, there’s pair programming. Some students love pair programming; some students hate it. But the students start to build this identity about how they problem-solve. And how they approach failure. And I just love that.

Eric Cross (24:31):

I’m writing this down. Because the rubber-ducking strategy, I love. I just imagine my seventh graders, a bunch of 13-year-olds with, like, rubber on the desk. And not necessarily in coding, but I was thinking in my science class. And they’re working through a challenge, and they’re all looking at this duck, and they’re talking to it. But I just love the the idea of externalizing your thought process and talking through it yourself so that you can hopefully arrive at a conclusion. But it’s such a great practice, and this is something that’s been around for a long time, apparently. So.

Aryanna Trejo (24:59):

Yeah. Yeah. It’s a real thing. And you know, you can go low-fi. It doesn’t have to be a rubber duck. You can have students talk to their pencils or their imaginary friends. That’s not the issue; the issue is, you know, talking to somebody.

Eric Cross (25:10):

I know you support teachers. But I just wanted to…I was just curious about your typical day, what that’s like. And then what you do, how you support ’em.

Aryanna Trejo (25:15):

So, at my previous job at 9 Dots, I was in there with the teachers in the classrooms. I was coaching our internal staff who went out to co-teach with teachers. And I loved that. And I had such a great impact on a local scale. But now at Code.org, I have a much broader impact. But I don’t get to interface with—that’s such a tech-y word!—I don’t get to interact with—

Eric Cross (25:42):

You work at Code.org! You get to—

Aryanna Trejo (25:42):

I know! But I’m a teacher at heart, forever, right? That’s my identity that I forged when I was 22 years old. And a typical day looks like opening up my computer, taking a look at my calendar. I often have meetings to talk about, different things that we’re doing to support our facilitators who go out to our teachers and lead their workshops for them. I recently worked on a product that was designed for CS principles, teachers, to onboard to the course if they weren’t able to get into an in-person workshop. And it’s completely self-paced, so it gives teachers an on-ramp into the course. And now I’m working on some in-person workshop agendas. So I feel really wonderful that my work is going out to thousands of teachers. But at the same time, I really, really miss talking to teachers. Because that’s something that energizes me so much.

Eric Cross (26:46):

When should students start learning computer science? I feel like we see it in this kind of narrow lane. Like, this is computer science if you make an app. Can it be more than that? As far as like the benefit of computer science? And—I guess two-part question—when should students, one, start being exposed to it? And then two, what are some of the benefits beyond just, “I wanna just make an app”?

Aryanna Trejo (27:08):

I taught coding to kindergartners. It can start as early as you as you want it to. And it doesn’t necessarily need to be on the computer. A lot of students that I worked with didn’t have computers at home, were interacting with computers for the first time. And that’s a huge barrier, of course, to a lot of teachers. But there are so many unplugged lessons that you can do to start to start to have students think about algorithms, which is just a series of steps to complete to solve a problem. As long as a student can use a computer, I think they can do computer science. There are products out there like codeSpark, where students—and Code.org has these products too—where students are moving an avatar around a board, kind of like a quadrant to…you know, they feed the directions to a computer and then the computer enacts it for them. And with that, they can learn algorithms. You know, that is computer science. And a lot of people don’t see it that way, but it really is. And it starts to set students up for more complex thinking as they move on.

Eric Cross (28:13):

One of the biggest underserved communities, geographically, are students in rural areas.

Aryanna Trejo (28:20):

Yep.

Eric Cross (28:21):

They can be reservations; they can be places just not an urban area. Is there a way to serve our communities of students and bring these skills in an unplugged way?

Aryanna Trejo (28:32):

Yeah. Yeah. If you typed in “unplugged computer science lessons” to Google, you’ll have a ton of hits. And there are so many students out there—not just in rural areas. But there’s incarcerated students. It hurts my heart to even say those words, but in urban areas too. Like in my classroom, where I only had four desktop computers. Access is a real struggle. And there’s things, like I said, instead of moving an avatar around a grid on the computer, I used to have an actual mat that I would take out to my kindergarten classrooms, lay it out, and it would have a grid on it. And we’d have one of the students act as the avatar and the rest of the students would give them directions to get to a different point on the grid. And there, you’re building an algorithm or just a series of steps. Like I said, it’s not some fancy term to solve a problem. And there’s multiple ways to solve that problem, too. And I think investigating that can be a really good way to stretch those lessons.

Eric Cross (29:32):

It almost sounds like an oxymoron, but this low-tech computer science strategy. Develop these skills and then transfer that once you have access to the tools.

Aryanna Trejo (29:39):

Yeah. Yeah. Absolutely. And I think it’s a good way for students who need kinesthetic means to start to understand something, or just different learning styles, to start transferring that over.

Eric Cross (29:53):

I probably have students in the classroom where those kinesthetic moving things would help be a great way—or WILL be a great way—for them to learn the principles and the fundamentals of coding. Instead of only giving the option to just do the computer, actually giving them some choice. Or giving them a way to be able to manipulate things. We’re still in the system of education that’s still very siloed. It’s been the same way for a hundred years. We got math and then we got science and we got English. I’m wondering, how can a teacher fit this into their daily lessons? And then, do you have any experiences or stories or things that you’ve seen, just really creative ways that you’ve seen teachers incorporate this? Outside the norm of, “This is a computer science class; we’re just gonna code.” But have you seen it branch out? In the trainings that you’ve done?

Aryanna Trejo (30:40):

I’ve seen examples of that. I’ve seen a teacher use Scratch to demonstrate different climates of California, and show the different climates. This past year for Hour of Code, my friend Amy—the one who helped me move to 9 Dots and at Code.org—she created this incredible tutorial called Poetry Bot. And it was a way to get students to match the mood of the poem to some of the elements that were happening in the stage. So they would have different backgrounds show up at different parts of the poem. When the words would show up, they would have different sprites show up. They would have, sometimes, sounds. Or the text would show up with different animations. So there are cross-curricular opportunities everywhere, if you can be creative enough to find them, or if you beg, borrow, steal from other educators who are doing this incredible work out there.

Eric Cross (31:36):

Yeah. I say this all the time, but I’m an educational DJ, not an MC.

Aryanna Trejo (31:44):

Oh yeah.

Eric Cross (31:45):

So MCs write their lyrics and DJs remix with things that other people have done.

Aryanna Trejo (31:48):

Absolutely.

Eric Cross (31:48):

I was like, I’m a DJ. I was like, all day. Sometimes I’ll write a lyric, once or twice, but most of the time I’m remixing things. So teachers, if you’ve been out there and you got an awesome interdisciplinary thing, or you’ve incorporated coding and it’s something that’s traditionally not seen, please send it to us. Share it with us.

Aryanna Trejo (32:03):

Yeah. And there are so many different places where you can find that. We have a forum for Code.org, but there’s also CSTA, the Computer Science Teachers Association. You can join your local chapter and get to know other computer science teachers out there.

Eric Cross (32:19):

I guess…to wrap up, I’ve been using Scratch programming, the MIT website. My students do the basic animated name, CS First, stuff. But over the years, I’ve noticed that my students are coming in with a higher level of sophistication in Scratch to where now the differentiation…some of my students are just doing very basic…and then I have other students who’ve created full-on video games with complex…like, you look at their Scratch page and it’s just an amazing amount of blocks and integrations and things that they have. Is there anything on Code.org that could be a next step? That takes them beyond, maybe like the visuals? And if so, what would be a good next step, to take students to advance them to another platform? There’s so many coding languages out there, I feel like. Or I might not even be thinking about that the right way.

Aryanna Trejo (33:20):

No, I think you are. You know, we have three different curricula out on our website right now. We have CS Fundamentals, which is probably more in line with what you’re talking about. We have a free CS Discoveries curriculum, and that is designed for, grades, I believe, 6 through 10. And that would be a really good entry point, for both teachers and for students.

Eric Cross (33:44):

There’s a lot of new stuff that I hadn’t seen yet, a few years ago.

Aryanna Trejo (33:49):

Yeah.

Eric Cross (33:49):

So I was really excited.

Aryanna Trejo (33:50):

One thing that I do know is that CS Discovery has just added an artificial intelligence slash machine-learning unit, that you can just pick up and give to your students. You don’t have to go in order with CS Discoveries, like you do with CS Principles. And I’ve gone through some of those lessons. They are really rad. And I would’ve loved to have learned that when I was in middle school or high school. So yeah, we’re constantly thinking of how we can make things one, relevant to our students, and two relevant to what’s going on in the world.

Eric Cross (34:20):

So would I be overselling it if I said, “If you go through this, you’ll be able to create an AI or a neural net to do all your homework”?

Aryanna Trejo (34:26):

You would be overselling it.

Eric Cross (34:27):

I would be? OK. So what I’ll do is, I’ll wait until the end of the school year, and then introduce it, and then by the time they’ve realized it’s not true, they’ll be eighth graders.

Aryanna Trejo (34:35):

There you go. Good old bait-and-switch.

Eric Cross (34:37):

You’re amazing. Thank you for serving teachers, and for being part of such a great organization that puts out great stuff. So much free curricula for teachers to be able to use. Especially nowadays we hunt and scour the internet for those types of things. And to be able to bring computer literacy into the classroom, and with your focus of serving communities of underrepresented groups, it feels good to know that not only is it high-quality material, but it’s also trying to raise everyone up. Because ultimately when we have more people trying to solve a common problem, we come up with better solutions. And I was talking to somebody who was a materials engineer somewhere in Europe, and he said one of the things about the U.S., As he was critiquing me on this flight, critiquing the U.S., He said, “One of the things about your country is that you have a heterogeneous group of people who, in a group, when you have multiple perspectives attacking a problem, you come up with more novel solutions.” He says, “That’s one of the great things, is that there’s not necessarily just a hive mind.” And I think that that’s one of the great things. We uplift different communities, and we uplift women, people of color, people who, have backgrounds that parents didn’t go to college but have these amazing qualities and strengths. And we put everybody focusing on the same issue. We come up with novel solutions that we wouldn’t have come up with if only select groups were trying to look at it and solve it. And so—.

Aryanna Trejo (36:22):

Yeah.

Eric Cross (36:23):

And we couldn’t do that without organizations like yours, that help empower teachers. So.

Aryanna Trejo (36:27):

Yeah! You really said it.

Eric Cross (36:29):

You’re coming to my classroom when you’re back in San Diego?

Aryanna Trejo (36:31):

Yeah! I totally will. Yeah. Let’s make it happen.

Eric Cross (36:34):

Last question. If you think back in your schooling, your own schooling, K through college, is there a person or a teacher that had a big impact on you? Or a learning experience that had an impact on you? And it could be, you know, positive or negative. But something that impacted you, even to this day, that stands out to you, that you remember?

Aryanna Trejo (36:56):

This is a big diversion from the topics that we’re talking about. But in grades 10 through 12, my drama teacher, Mr. Byler, who I still talk with, was such a huge impression on me. Really wonderful. And I couldn’t tell you the teaching moves that he did that were wonderful. I don’t know much about his management. But I can tell you that he gave me space to be confident, and grow into myself, through drama productions. They were high school productions, so they weren’t amazing. But I just really came into myself in high school, because I had the confidence to get on stage. And he was just such a wonderful mentor to all of us. So, props to Mr. Byler.

Eric Cross (37:39):

Shout out to Mr. Byler for creating space for Aryanna to fly! Thanks for making time, after your workday, to talk with us and to share Code.org with teachers.

Aryanna Trejo (37:54):

Of course. Happy to.

Eric Cross (37:59):

Thanks so much for joining me and Aryanna today. We want to hear more about you. If you have any great lessons or ways to keep student engagement high, please email us at stem@amplify.com. Make sure to click subscribe wherever you listen to podcasts. And join our brand new Facebook group, Science Connections: The Community for some extra content.

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What Aryanna Trejo says about science

“I would hear teachers saying things like, ‘Well I just can’t do coding, it’s just too hard for me.’ And I would ask them…Would you say that to your student about math or English? Be as kind to yourself as you would be to your student.”

– Aryanna Trejo

Professional Learning Specialist, Code.org

Meet the guest

Aryanna is a member of the Code.org Professional Learning Team. Before joining Code.org, Aryanna led computer science professional development for K-6 teachers and served as an instructional coach for new educators. She also taught fourth and fifth grade in New York City and Los Angeles. In her spare time, Aryanna loves taking advantage of the California sunshine, creating wheel-thrown pottery, and hanging out with her dog Lola.

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About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

S4 – 03: LIVE from NCTM with Bethany and Dan

Hosts Bethany and Dan, both smiling, in a promotional image for the "Math Teacher Lounge" podcast, Season 4 Episode 3, titled "Live from NCTM!" with an

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer are LIVE with more than one hundred Math Teacher Lounge listeners at the recent National Council of Teachers of Mathematics conference. Listen in as they answer the pressing question: Who is the best teacher in film or television?

Explore more from Math Teacher Lounge by visiting our main page

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Presenter (00:00):
Ladies and gentlemen, from Math Teacher Lounge, we have Bethany Lockhart Johnson and Dan Meyer! <cheering>

Bethany Lockhart Johnson (00:08):
Doesn’t go well that the door was locked. Like, I could not get in! <Laugh>

Dan Meyer (00:12):
Yeah. Gotcha. All right. We’re gonna sit a little bit. Let’s see how that works—

Bethany Lockhart Johnson (00:16):
Hi!

Dan Meyer (00:16):
Yeah. I think we’ll stand up? Or whaddaya think, sit…?

Bethany Lockhart Johnson (00:19):
Should we stand? Hi.

Dan Meyer (00:22):
Hello. Great to see you folks. Yeah, I can hear you.

Bethany Lockhart Johnson (00:25):
Can you hear me? That’s—I know YOU can me. Can you hear me OK? OK! We’re here. Hello. Thank you for like, lining up and coming out and being here. Thank you!

Dan Meyer (00:35):
Means so much to me that you could be here for me, on my show, with Bethany Lockhart Johnson, my co-host. <Audience laughs>

Bethany Lockhart Johnson (00:40):
The hour has just started.

Dan Meyer (00:42):
We’re just getting going. Yeah. If you folks have heard the podcast, you don’t know how much gets cut out. And it’s like, mostly me just having, you know, anxious nerves and saying something silly and then we cut it out and we can’t do that here today. So it should be real fun for all of us, I think. Yeah.

Bethany Lockhart Johnson (00:55):
It’s not true. It’s mostly dancing. “Bethany, can you stop talking? Bethany?” Cause it’s mostly—

Dan Meyer (00:59):
“It’s my turn. It’s my turn! Bethany <laugh>! I haven’t been heard for a while.”

Bethany Lockhart Johnson (01:02):
Dan. We’re at an in-person conference.

Dan Meyer (01:05):
In-person BIG conference, I would say. I’d say a big conference. Yeah.

Bethany Lockhart Johnson (01:08):
And have you been to the Amplify booth?

Dan Meyer (01:11):
I have! Have these people? There’s a claw machine with free socks.

Bethany Lockhart Johnson (01:16):
Yeah. You’re saving me socks, right? That’s what you’re saying. <Laugh> I mean, it’s exciting. How has your conference been so far?

Dan Meyer (01:21):
So far it’s been a blast. I feel fed. I feel like the community’s been awesome. How are you feeling about it?

Bethany Lockhart Johnson (01:29):
OK. Let’s talk about me for just a second.

Dan Meyer (01:31):
Yeah. Talk about you.

Bethany Lockhart Johnson (01:31):
Last night, Dan, was the very first night that I was away from my toddler. <Audience: Aw!>

Dan Meyer (01:38):
Big commitment being here. Thank you.

Bethany Lockhart Johnson (01:40):
I got super-emotional walking back to the hotel after dinner, and then I got in my room, <laugh> I put on pajamas, and I turned on music. I slept so good!

Dan Meyer (01:50):
Yeah. <Audience laughs> Give it up for no kids! <Audience laughs> Hey!

Bethany Lockhart Johnson (01:55):
I love him so much. But I slept all the way through the night. Oh, by the way, I ordered room service in the morning.

Dan Meyer (02:01):
On Amplify.

Bethany Lockhart Johnson (02:01):
That bill’s coming. But it’s been a great conference and I’m so delighted to be here in person and to get to share energy…and hopefully that’s all we’re sharing today. Y’all got your tests, right? Yep. Sharing energy and community today. Because we know it’s been hard. Hardness. Hard.

Dan Meyer (02:25):
Yeah.

Bethany Lockhart Johnson (02:26):
Years. Hard. And to be in person, I know conferences reinvigorate me and I go back into my educational spaces feeling revitalized with new connections and new ideas to try. So yeah, I’ve been excited to be here. And thank you all for being here.

Dan Meyer (02:40):
Yep. I don’t care if I get six different strains of Covid here. I’m just thrilled to be here. <Audience laughs> I don’t know if you’ve had the same feeling, though, Bethany, you folks…I’m a little bit confused to some degree about what we’re doing. I just wanna be really transparent. This is my sarcastic voice but I’m being sincere here. It kind of feels like we’re in a little bit of a time capsule. Like we all got in a time capsule in 2019 and, you know, you open it back up and it’s like, OK, so we’re still, you know, talking about X, Y, or Z protocol for establishing classroom routines or whatever. And I’m like, OK! Like, I loved that in 2019! But I do admit, I’m still trying to figure out a little bit like, what are we doing now? What’s our relationship to the world out there? Things are very different. I have had some great sessions that I’ve enjoyed. I’m also like, still waiting for a session to draw a little blood. Do you know what I mean? Like there’s been sessions…no? OK. You’ve been in these sessions where it’s like, “Oh, ow.” Like, and you look down and there’s and there’s blood there. It’s like, I thought I knew what we were up to. Like, I thought I knew what teaching was and how we relate to the world. I dunno, like in any Danny Martin session in 2019, “Take a Knee” was one, where I was like, “Oh, OK. Like, I’m not as hot as I think I am here. Like, I’m part of a system.” That kind of thing for me draws blood. And I haven’t been in one of those yet. Been some great sessions. I’m a little hopeful that today we draw a little blood and think about what we’re doing here, is my hope here, if that’s OK. So Bethany’s gonna moderate that impulse and she’ll be the fun one and I’ll be the blood-drawing one.

Bethany Lockhart Johnson (04:05):
No, I don’t…that metaphor doesn’t speak to me personally. But what I will say is, I get what you’re saying about really wanting to be in that room where there’s like this synergy happening. No promises about that today other than—

Dan Meyer (04:18):
I promise. <Audience laughs> Go on.

Bethany Lockhart Johnson (04:20):
Other than I get what you’re saying. I’ll find my own metaphor that does not involve bloodshed, but.

Dan Meyer (04:25):
Sure. There’s a lot of ways we we could go about this today. And the one that I’m excited about is, you know, we could like, you know, analyze some results from students, and talk about what went into that. Look at classroom video. Lots of possibilities. But here’s what we’re up to today. Hope you’re into it. Which is, we are here in the heart of the entertainment industry. You know, Tinseltown! Um, the Big Apple! Uh…

Bethany Lockhart Johnson (04:47):
No!

Dan Meyer (04:47):
Come on. What do you got here? Um…

Bethany Lockhart Johnson (04:51):
It was daytime at night. Like the lights were so bright.

Dan Meyer (04:54):
The City of Lights.

Bethany Lockhart Johnson (04:55):
There was a movie premiere outside my hotel room, which I was not invited to, unfortunately. But so what are we doing today?

Dan Meyer (05:01):
So here’s what we’re doing. We are gonna settle, once and for all, a question you have not asked yourself yet, perhaps, but will want to know the answer to in a moment. Which is: Who is the best teacher in all of film or television? OK? We’re gonna do that. It’ll be fun. But I hope that in debating this a little bit with a special guest we’ll bring up in a moment, that we will start to uncover some truths about what makes good teaching. How that’s different from teaching as we see it in movies and tv. Why middle-class America wants teachers to look a certain way in movies and tv. What all that means. And it’ll be awesome. I think. I’m hopeful it’ll be awesome. So what we did here is we’ve invited eight people. Eight folks you people may have known. You’ve been in their sessions today, in this conference, perhaps. And asked them: Who’s your fave? Like, we might have our favorites, but we wanted to democratize it a bit. So asked some cool people who you folks like, who are very smart and thoughtful about teaching: Who’s your favorite teacher?

Bethany Lockhart Johnson (05:58):
A few of whom are in this room. Thank you for your submission.

Dan Meyer (06:00):
Thank so much. Yeah. We’ll see what happens here. <laugh>

Bethany Lockhart Johnson (06:03):
As they shrink down.

Dan Meyer (06:03):
Yeah. Might draw some blood that I don’t mean to right now. We’ll see. OK.

Bethany Lockhart Johnson (06:06):
That metaphor, what IS that??

Dan Meyer (06:07):
Yeah. Yeah. I love it. I’m still going with it. <laugh> And you folks will be a huge part of this. THE part of this, really. So what will happen is I’ll share with you our first nominees. A few of us will make a case for our favorites, or least favorites, as the case may be sometimes. And then by applause, by acclamation, you folks will decide who wins and advances to the next round. Start with eight, move to four. You folks know math.You know where this goes. OK.

Bethany Lockhart Johnson (06:34):
No, keep going. Keep going.

Dan Meyer (06:36):
Two, then one.

Bethany Lockhart Johnson (06:36):
Yeah. Got it.

Dan Meyer (06:37):
Then a half of it. No?

Bethany Lockhart Johnson (06:38):
He had to school me on the making of brackets. But we got it. Yeah.

Dan Meyer (06:41):
How brackets work.

Bethany Lockhart Johnson (06:41):
But we got it. March Madness, what?

Dan Meyer (06:44):
Yeah, in order to do this right, we had to bring up—all the folks that you’ll see are also former Math Teacher Lounge guests, or like, just fan favorites. And we’re also bringing up a former Math Teacher Lounge guest to help us decide this and debate this in a respectful manner.

Bethany Lockhart Johnson (06:59):
New dad.

Dan Meyer (07:00):
New dad.

Bethany Lockhart Johnson (07:01):
You see where my brain’s still at? I miss him. <Laughs>

Dan Meyer (07:03):
Friend from San Diego. Really cool teacher.

Bethany Lockhart Johnson (07:06):
Incredible teacher.

Dan Meyer (07:06):
Works at Desmos and Amplify. And I just want you to welcome up your friend and mine. Chris Nho!

Bethany Lockhart Johnson (07:11):
Chris Nho!

Dan Meyer (07:13):
Come up, Chris. Let’s go, buddy. We didn’t talk about it, but did you want to do the cornball stuff too?

Chris Nho (07:22):
Wow. Would I love to do—

Bethany Lockhart Johnson (07:23):
And then the door could be locked! And then you have to wait and like, just—

Chris Nho (07:27):
Yeah, I’ll skip that part.

Bethany Lockhart Johnson (07:28):
Hi. Welcome. You’re here. We’re here in person.

Chris Nho (07:30):
Very glad to be here. Thank you all for having me.

Dan Meyer (07:33):
Tell me who you are.

Chris Nho (07:34):
My name is Chris Nho. I live in San Diego. I’m a new dad. A three month old, just had. Yeah, she’s actually here at the conference with us in the hotel room. And I promise you she is not by herself. She is with…come on. I was like, “Hey, just gimme one hour. I’ll be right back. I have to do very important work.” But yeah, I think I got invited here because I have opinions and I’m willing to draw…some…blood.

Dan Meyer (08:02):
There we go! Two outta three! We’re good on the metaphor now.

Bethany Lockhart Johnson (08:06):
We’re so glad you’re here. If you haven’t listened to the episode where Chris and Molly and some other public math folks share their ideas and ideas of how to take math out into the world, please listen, because we had a blast.

Dan Meyer (08:19):
Inspiring work. Really inspiring work. Very cool. Cool. OK. Right on. OK.

Bethany Lockhart Johnson (08:23):
Let’s do this!

Dan Meyer (08:24):
Let’s get started here. Yeah! <Audience cheers> Yeah. And we might ask you who your favorite teacher is, who’s missing from our list of eight? We might have forgotten some people. Anyway. All right. So here’s our first two. Our first two are nominated by way of, let’s see, um, Mandy Jansen is a professor at the University of Delaware. Got some awesome talks here this week, a Shadow Con talk last night. She’ll be nominating one. And also, um, Lani Horn is a professor at Vanderbilt, also extremely cool, prolific author and speaker, just all-around great human and friend of teachers everywhere. And she’ll nominate another in this bracket, which is the Northeastern Comedy bracket, Northeastern comedy bracket.

Bethany Lockhart Johnson (09:06):
It just worked out that way.

Dan Meyer (09:07):
Yeah. Here it is. Here is Tina Fey in Mean Girls.

Tina Fey in Mean Girls (09:12):
“OK. Everybody close your eyes. All right. I want you to raise your hand if you have ever had a girl say something bad about you behind your back. Open your eyes. Now close your eyes again. And this time I want you to raise your hand if you have ever said anything about a friend behind her back. Open up. It’s been some girl-on-girl crime here.”

Lani Horn (09:52):
I am nominating Sharon Norbury from Mean Girls as the best movie math teacher. She is an awesome teacher who is always there for her kids. She always sees the best in them. She shows that she can forgive even some pretty bad behavior, if she sees that kids are trying. She’s a strong feminist who makes sure that smart girls don’t dumb themselves down just to impress boys.

Tina Fey in Mean Girls (10:22):
“Katie, I know that having a boyfriend may seem like the most important thing in the world right now, but you don’t have to dumb yourself down to get guys to like you.”

Lani Horn (10:30):
She’s also super hard-working. She works three jobs. She’s always there for the kids. She plays piano in the talent show and takes them to Mathlete competitions. And she’s also socially aware. And when things go really badly among the girls, she does some pretty creative things to try to get them to be kinder to each other.

Dan Meyer (10:54):
OK. That’s one.

Bethany Lockhart Johnson (10:55):
Helen Case.

Dan Meyer (10:57):
All right. Settle down. Settle down. Settle down. All right.

Bethany Lockhart Johnson (10:59):
Piano too!

Dan Meyer (11:00):
Bethany’s already trying to bias people here. All right. Chill out. Hold on. So next one is Mandy Jansen with Jack Black from School of Rock. Uh-oh. Uh-oh.

Jack Black in School of Rock (11:09):
“What was your name?”

Kid in School of Rock (11:10):
“Katie.”

Jack Black in School of Rock (11:11):
“Katie. What was that thing you were playing today? The big thing.”

Kid in School of Rock (11:14):
“Cello.”

Jack Black in School of Rock (11:15):
“OK. This is a bass guitar and it’s the exact same thing, but instead of playing like this, you tip it on the side. Chellooooo! You’ve got a bass! <Laugh> Try it on.”

Mandy Jansen (11:25):
And I’m nominating for best teacher in a film Jack Black as Dewey Finn playing Mr. Ned Schneebly in the film School of Rock. So why this portrayal? First of all, playing a longterm sub. Those are so hard to find right now. <Audience laughs> Really hard. And then he teaches using class projects. That’s brilliant. Integrated learning. And then love this. He gives students roles and tasks that are differentiated and align to the specific strengths that each student has.

Kid 2 in School of Rock (12:05):
“I can also play clarinet, you know!”

Jack Black in School of Rock (12:06):
“I’ll find something for you when we get back from lunch. I’ll assign the rest of you killer positions.”

Mandy Jansen (12:13):
And the film culminates in a performance of a collaborative song that they all wrote and performed together. And the students experience that collaboration and teamwork and creating something beautiful is much more important than winning first place. And finally, one of the songs that the character sings in the film is “Math is a Wonderful Thing.” Can’t beat that.

Dan Meyer (12:40):
All right. That’s tough. That’s tough. So here’s the deal. What we have right now is just a quick minute—so Bethany, you ranked, we all ranked our own faves here outta the list of eight. And Bethany put Jack Black in School of Rock a bit higher than Tina Fey in Mean Girls.

Bethany Lockhart Johnson (12:54):
Missed the piano part though.

Dan Meyer (12:55):
And Chris, vice versa here. So Bethany, would you start us off and just make a quick case here for Jack Black versus Tina Fey?

Bethany Lockhart Johnson (13:01):
OK. So here’s what I’m thinking. There’s been rumor that maybe they’re putting less than credentialed people into classrooms to fill teaching gaps. I mean, just rumor. And so here’s this guy who is a rocker. He is not a substitute. He has no teaching training. And yet he goes in there and it turns out that he has the ability to see students’ potential and to recognize their unique abilities. And like Mandy said, he really tapped into, like, he saw them and said, “No, more is possible for you than what you think is possible.” And there’s like real sub anxiety. When you walk in, you can either be like, happy there’s a sub, but I was usually really nervous. Right? And he goes in and he makes that classroom into a home.

Dan Meyer (13:53):
Wow.

Chris Nho (13:54):
Wow.

Dan Meyer (13:56):
Chris, speak on it. Tina Fey needs you. Chris.

Chris Nho (13:59):
Tina Fey. Here we go. I’m gonna argue here that—when was that movie made?

Dan Meyer (14:03):
T is for terrific. I is for Interesting.

Chris Nho (14:06):
Decades ago. And I’m gonna argue that Tina Fey was very progressive for her time. OK, let’s talk about social emotional learning. Hello. <Audience laughs> Love that. Right? Stand up if, I mean, she’s getting people to talk about their emotions. And there’s a curriculum. But let’s just pause, because that’s not what’s really happening in the classroom right now. So social emotional learning, I think she’s, she’s got that a lot. And then number two, you know, if you remember the plot of Mean Girls a little bit, she gets her name written in that Burn Book. Like she sees what they say about her. Restorative justice. Let’s go. <Audience laughs>.

Dan Meyer (14:38):
Whom amongst us. Yes.

Chris Nho (14:40):
You write Mr. Nho in the Burn Book?? Well, your grade book is gonna look like a Burn Book! OK? <Audience laughs> Tina Fey, Tina Fey, she was like, “No, you know, know what? I’m actually gonna spend more time with you. You’re gonna become a mathlete.” And Lindsay Lohan discovers—she drops the most iconic line in all of math education. “The limit does not exist.” Thank you, Tina Fey, for that. For that gift.

Dan Meyer (15:04):
Bless. Bless you. Tina Fey. Wow.

Bethany Lockhart Johnson (15:05):
Oh, man. Wow.

Dan Meyer (15:09):
Let’s see what the people say here. I do wanna just add one quick thing about—it’s interesting to me how often in these movies—just kind of go in a little bit, zoom out just a minute—how often it’s a teacher who has no training as a teacher. <Bethany laughs> I am kind of curious why it is. Like, those are the movies that get hot, that get made. Again, these are all kind of a mirror of the taste of the moviegoing public. You know what I’m saying? Like, these, these are not movies—I wanna believe they are made for me and for us as teachers. But they are not. There’s not enough of us to justify, you know, Jack Black’s, you know, M&M budget or whatever he’s got going on in his trailer or whatever. That needs to be for everybody in middle-class America. So what is it about middle-class America that wants to see teaching as something that anybody can do? Just like, you know, just, just run up there in your van and make it happen.

Bethany Lockhart Johnson (15:54):
Magic magically manifests.

Dan Meyer (15:56):
Yeah. Manifest. Yeah. That’s just interesting to me. I just toss that out there as some red meat. Let’s see what the people say here. All right, OK, so you’re ready. Let’s get the bracket going here. The question is Tina Fey versus Jack Black. You had a moment here. Just whisper to someone real fast who you’re going for here real quick. What are you thinking here? <Crowd murmuring> All right. Crowd’s buzzing. Crowd’s buzzing. Would you folks…? All right. Bring it back. Go ahead and make some noise for Tina Fey. <Crowd cheers> OK. OK. Make some noise for Jack Black! <Crowd cheers> Judges say Tina Fey. Tina Fey moves on. All right. All right.

Chris Nho (16:44):
Stunned. I’m stunned. I’m speechless.

Bethany Lockhart Johnson (16:46):
Tina Fey moves on. Wow.

Dan Meyer (16:48):
This has exceeded my expectations in terms of having some fun, but also getting deep, getting deep and real about teaching. I’m into this right here. Yeah. What’s up?

Bethany Lockhart Johnson (16:54):
That’s the goal. That’s the goal. OK. You wanted blood? Oooh, this next matchup might just be where that blood comes forth! OK. Stretch. Warm up. Dan Meyer, who’s up next?

Dan Meyer (17:11):
We’ve got the animated/animatronic round here in the Southeast. And repping the two contestants here, who do we have? We have Allison Hintz, professor, author outta Washington, as one of the two nominators. And the other nominator is one of my heroes, though we’ll find out very wrong about this nomination, Jenna Laib, who’s in the crowd, and I’m trying not to make eye contact here. <Laugh> And here are the two nominations. A couple minutes each. And then we’ll chat about it. And one of us will probably die. But we’ll see how it goes.

Allison Hintz (17:50):
A long, long time ago, in a galaxy far, far away, MTL, we began learning from the Jedi Master of Teaching. With the Socratic and experiential approach. With unparalleled mindfulness, compassion, and humility. The best teacher in TV and film, Yoda is. <Audience laughs> Yoda lives the values we share as teachers and learners. He humbly comes alongside us as we construct new knowledge.

Yoda (18:29):
“You must unlearn what you have learned.”

Allison Hintz (18:32):
Yoda allows us to struggle and sees mistakes as critical to learning.

Yoda (18:39):
“The greatest teacher, failure is.”

Allison Hintz (18:43):
Yoda values curiosity and reminds us of the beauty and joy of teachers learning from children.

Yoda (18:52):
“Truly wonderful, the mind of a child is.”

Allison Hintz (18:59):
MTL! Join the Resistance! Let the force flow through you in declaring, the best teacher in TV and film, Yoda is.

Dan Meyer (19:18):
Give it up for Allison Hintz! All right! <Audience applauds>

Bethany Lockhart Johnson (19:20):
Alison! And to have that on hand too, which Is kind of perfect.

Bethany Lockhart Johnson (19:26):
Just to be clear, the helmet is not a part of a Zoom background.

Dan Meyer (19:29):
You may evaluate the quality of the nomination based on the costumes of the nominator. That is acceptable. That’s acceptable.

Bethany Lockhart Johnson (19:35):
That is a REAL HELMET.

Dan Meyer (19:35):
All right. The next nominator here, this one is from Jenna Laib, math coach, all-around stellar human. Here we go. This is Ms. Frizzle.

Ms. Frizzle (19:42):
“Single file, class. Our rotten field trip has only just begun.”

Jenna Laib (19:47):
And I think that the best teacher from TV or movies is Ms .Valerie Frizzle from The Magic School Bus. First and foremost, Ms. Frizzle believes in her students. She encourages them to take an active role in their learning, and also to advocate for change in their local community. For example, there’s an episode where there is a logger who’s gonna cut down a rotting log that would benefit the local ecosystem. And the students figure out a way to convince him to leave the log so that all of the animals and the plant life can benefit. She orchestrates really challenging situations for these students, and she allows them the space to ask questions and engage in problem-solving and puzzle their way out of these really, really difficult scenarios. Ms. Frizzle has unmatched pedagogy. She’s bold, she’s innovative, and she’s a major proponent of experiential learning. So these students are heading straight into a storm to learn about weather systems. <Audience laughs> These students are heading into the human body to learn about digestion and disease. They literally get baked into a cake to learn about some chemistry and reactions.

Children in The Magic School Bus (20:54):
“What’s happening?” <Audience laughs> “Why is it suddenly getting so hot?” “Maybe it’s because the floor is on fire!” <Audience laughs>

Jenna Laib (21:02):
This pedagogy is all led by her outstanding catchphrase, which is:

Ms. Frizzle (21:06):
“Take chances; make mistakes; get messy!”

Jenna Laib (21:14):
From her pedagogy to the classroom community that she creates, Ms. Frizzle is an inspiration, and that is why I think that she is the best teacher from TV or film. <Audience applauds>

Dan Meyer (21:25):
Right on! Give it up for Jenna. Give it up for Jenna. All right. I’m gonna take first pass at this. Chris knows my argument already, so I’m gonna take this here. I see some of you are feeling how I’m feeling on this one. OK, so I don’t have tons to say in favor of Yoda. I think it was all true what Allison said. I think the costume was banging. It was awesome. So there’s all that, but I have more to say against Ms. Frizzle than for Yoda.

Bethany Lockhart Johnson (21:48):
No, no, no. Wait a second!

Bethany Lockhart Johnson (21:49):
Let’s let it happen. Bethany, I’ve come prepared.

Dan Meyer (21:54):
I may have made a misstep here, I realize.

Bethany Lockhart Johnson (21:56):
I’ve come prepared.

Dan Meyer (21:56):
So I think Jenna is all correct. I think those clips spoke for themselves. I think that what they add up to, to me, is not “great teacher,” but more “someone who should be locked up.” <Audience laughs> Or at the very minimum, “someone who should be kept away from children.” <Audience laughs> Do not let that woman around children. I mean, check it out. Look, I don’t wanna throw down credentials. I’ve been to grad school, though. I know how this works. When your brain is stressed, you get these—all the cortisol happens. Your working memory shrinks up. You cannot learn when you’re stressed. And those kids, like whatever lesson Ms. Frizzle is teaching by sending them into an oven, I repeat, an oven <audience laughs>, like, they’re not gonna learn anything ’cause their brains are freaking out with stress and fear. OK?

Bethany Lockhart Johnson (22:41):
“What’s happening??”

Dan Meyer (22:43):
“What’s happening? Am I on fire? Well…I’m learning lots, though! Sure is magical!” <Audience laughs> It’s like, “No. Get that woman out of a classroom.” That’s my opening and closing argument. Right? There’s all it is.

Chris Nho (23:01):
All right. All right. All right.

Bethany Lockhart Johnson (23:02):
Chris knows.

Chris Nho (23:03):
I’ve got, I’ve got lots to say. First off, I think Dan was in charge of the editing of those video clips. So let’s let that be—you know, let the record stand. <Audience laughs>

Dan Meyer (23:11):
Where’s the lie though? Where’s the lie?

Chris Nho (23:14):
And, you know, second, I think, um—this is the guy up here saying, “I wanna see blood.” You know? And then he has a teacher who literally takes the students into a blood cell and, and you get a little scared! You get a little worried for the students, you know? So I just don’t get it, Dan. This or that. OK? I think Ms. Frizzle—so I actually went to a project-based learning school. I taught at a project-based learning school. And the best thing about it is like, your learning, it doesn’t just stay in this box of math lesson or writing lesson, history lesson. And I think with Ms. Frizzle, like you can’t help but learn things because you are getting baked in a cake. <Audience laughs> Yeah, it is a little scary. And I imagine there’s cortisol and things happening, but guess what? Probably the next episode, they go into their own brains and explore what’s happening. That kind of thing. You know?

Dan Meyer (24:07):
The kids that survived, just be clear. <Audience laughs>

Chris Nho (24:10):
Yeah. OK. Would I want Nora, my three-month-old, to be babysat by Ms. Frizzle? Maybe not. <Audience laughs> But what I have to say about Yoda is Yoda maybe wins the best tutor award. Give it up for Yoda’s Best Tutor Award.

Bethany Lockhart Johnson (24:24):
Oh, yeah…

Chris Nho (24:25):
That ratio’s looking really nice. I could teach the heck outta Luke Skywalker. OK? But 20 little Luke Skywalkers running around. I’m not sure. OK?

Dan Meyer (24:34):
Luke did survive the training, though. <Audience laughs> So that’s awfully nice to say about it. All right, Great words from Chris here. I’m still not convinced. We’ll see how you’re convinced here. Would you whisper to someone where you’re leaning here? Frizzle or Yoda? <Audience buzzing>

Chris Nho (24:47):
I tried. I tried.

Dan Meyer (24:53):
All right. That’s enough of that. Let’s hear it folks. Give it up for Yoda. <Audience cheers> Give it up. Give it up. You. Give. It. Up.

Chris Nho (25:05):
Hey, next. Next.

Dan Meyer (25:06):
All right. All right, all right. <Mutters> Give it up for Ms. Frizzle. <Audience cheers louder> I dunno, it’s pretty close. Call a tie. Maybe Yoda? Yoda by nose? <Audience laughs> All right. All right. Let’s…let me see who’s it. Let’s get the people advancing here. I’ll keep on moving here.

Chris Nho (25:26):
As you’re doing that. Um, Dan ranked Ms. Frizzle last in his personal ranking. And I ranked Ms. Frizzle very high, so we knew this one would be spicy,

Bethany Lockhart Johnson (25:36):
<laugh> Spicy it was. Are you having a good time so far? <Audience cheers> So while we love seeing these images and we love seeing these video clips, at the core, what are these things about how teachers are portrayed? And how accurate is that to our real lives? I mean, besides the cake part, right? That my chemistry class did often feel like I was on fire. I was so stressed in it. Um, we’re ready?

Dan Meyer (26:05):
Yep. Great. We’re ready, we’re up here. So the next two nominees are coming to you folks from Tracy Zager, who is the editor of my book, forthcoming in 2027 at the earliest and 2032 at the latest. And also your very own Zak Champagne from Florida, here in the room. Hey, Zak. Zak, let’s see who the nominations are. I’m gonna skip past that, didn’t work out so well for me. Here it is. This is Marshall Kane from the TV show Community.

Michael K. Williams in Community (26:32):
“You two complete your case to the class and let them decide your grades.”

Joel McHale in Community (26:37):
“Professor, thank you.”

Michael K. Williams in Community (26:40):
“It’s not a favor, Mr. Winger. Man’s gotta have a code.”

Joel McHale in Community (26:44):
“Awesome.”

Zak Champagne (26:46):
This is a pitch for an underdog. This teacher didn’t stand on desks or encourage his students to follow their musical passions. In fact, this teacher was seen only in a few episodes of my favorite TV show of all time, Community, Community has set at Greendale Community College in Colorado. And in season three, we get to meet Dr. Marshall Kane, a biology professor whose story is an inspiration to anyone who just takes the time to look and listen. Dr. Marshall Kane slowly earned his PhD while in prison, serving a sentence of 25 to life. In his classroom, he inspires students to love biology, question why LEGO has become so complicated, and randomly pairs his students for group projects to ensure no one feels left out. His greatest performance comes when a group of students believe their yam project was intentionally sabotaged. Dr. Kane took this as an opportunity for some trans-disciplinary real-world learning. So yes, at community college, he felt that a middle-school mock trial was the best way to determine who killed the yam. So let’s all pick the underdog and vote for Dr. Marshall Kane. After all, man’s gotta have a code. <Audience goes “oh!” and applauds>

Dan Meyer (27:53):
Thank you, Zak.

Bethany Lockhart Johnson (27:54):
I have a code.

Dan Meyer (27:56):
Next up is Tracy Zager, nominating an unusual nomination, not a single person, but an ensemble performance. A bunch of people from a movie called Searching for Bobby Fisher. Here we go.

Rapid-fire movie dialogue (28:11):
“What’s that?” “Schleimann attack.” “Schleimann attack? Where’d you learn that from, a book?” “No, my teacher taught me.” “Aw, your teacher. Well, forget it. Play like you used to, from the gut. Get your pawns rolling on the queen’s side.”

Tracy Zager (28:26):
Hey, Math Teacher Lounge. This is Tracy Zager. I’m excited to share my nominee for the best movie teacher. But I have to admit that when I first got the email, I thought, oh, who am I gonna nominate? Because most movies about teachers are highly problematic. They usually have like a saviorism thing, usually white saviors. And I just felt like I couldn’t suggest any of those. So rather than nominate a movie about a single teacher, I wanted to nominate a movie that taught me something about teaching. And that movie is a deep cut. It’s Searching for Bobby Fischer. It’s a movie about a chess prodigy. And what I love about it is that all of the different adults in the movie are in teacher roles in some way. And the student, Josh, the chess player, is a fully realized character, not an empty pail, who pulls from the strengths of each one of those adults while also dealing with their flaws and humanity. And there’s just beautiful synergy in the way he gets the best out of everybody, but also has to overcome some of the barriers that they put in front of him. So I feel like it’s a much more authentic and humbling, but also inspiring, movie about the power of teaching. So if you haven’t ever seen it, check it out. And I can’t wait to see who the other nominees are. Thanks so much.

Dan Meyer (29:53):
Right on. Thank you, Tracy. Wherever you are. <Applause> We’ll move a little quicker here. I’m curious, Bethany, you put Marshall Kane pretty high. I put Bobby Fischer pretty high. What do you have to say about Marshall Kane for us here?

Bethany Lockhart Johnson (30:04):
Well, I just wanna say two things. One is that, like Zak said, he has this code of conduct that he brings in. And he stays true to it no matter what happens. If you saw him in in Community, you know that he held himself up to such high esteem, but not just himself, his students as well. And he took accountability when he felt he had done wrong, even though, well, that’s controversy. But first—oh, the other thing, rest in peace, Michael K. Williams. Oh my gosh. The actor who plays Marshall K. And the thing that I wanna say most of all about it is that he brings his whole self to the classroom. He was in prison for decades. He brings his whole self and says, “This is who I was. This is who I am today. And this is how we can work together as a community.”

Dan Meyer (30:58):
That’s big. I love your comments about code of conduct too. It makes me wish that Ms. Frizzle had a code of conduct also.

Bethany Lockhart Johnson (31:05):
I knew that was coming back!

Chris Nho (31:06):
Two slides ago, Dan. That was two slides ago.

Dan Meyer (31:08):
Can’t let it go. So yeah, I love what you said there. I have no strong beef here either way. Bobby Fischer’s a movie I have loved dearly and can’t be objective about it. I love that the kid in that movie, more than any other movie here, the kid teaches the adults so much through his innocence and how he challenges them and how they’re treating him. Dig all that so much. Will not, will not begrudge anyone any vote either way here. I do begrudge many of you your vote in previous rounds. <Audience laughs> So let’s just, let’s hear. We’re not gonna ask you folks at all to chitchat. We’re gonna move on this one. So would you folks make some noise here for Marshall Kane in Community? OK. OK. And would you make some noise here for Bobby Fischer, the kid in Bobby Fischer, the ensemble? <Audience cheers, applauds>

Bethany Lockhart Johnson (31:56):
Marshall Kane.

Dan Meyer (31:57):
Marshall Kane takes it. All right. Good job, Marshall Kane! All right. Zak’s feeling good. Moving on to the final four here, Zak, right on. OK. Our last—the Northwest Division here is also the large urban district division here. We have a couple different teachers in sets of large urban schools. They’re nominated, they’re advanced by a couple people here. One is past president of NCTM, Robert Berry. And another is Fawn Nguyen, Southern California phenom. Great teacher and friend of lots of us. Um, let’s see who they nominated here. First from Robert Berry, let’s see, who is it here? Janine Teagues from Abbott Elementary.

Abbott Elementary dialogue (32:37):
“Hey, you know what? I’m probably probably gonna be Kenny’s second-grade teacher. Why don’t you just let him get a head start with me today?” “That’d be great.” “Yeah? OK. Hey, Kenny, would you like to be in my group today?” “Not really.” “That’s the spirit.”

Robert Berry (32:54):
My nomination is gonna be Quinta Brunson, the Emmy Award-winning Quinta Brunson from Abbott Elementary. Janine Teagues is the character. She exemplifies care not only from an affect way, but she also exemplifies care in the things that she does for her students. While the scenes in the show are entertaining, they do represent the challenges that teachers experience when they’re trying to meet the needs of her students. So she goes, goes all out for her students and finding resources. She accesses other people to get resources for her students. But the care shows up in the way that she is mindful of their needs. And so, for me, when I think about teachers and teaching, sometimes we can talk about pedagogy, but sometimes we also can talk about those kind of intangibles that makes a teacher a great teacher. It is apparent from her students that she cares about them, she supports them, and she goes all out 100% for her students. Janine Teagues, Quinta Brunson is, I think, is my choice of the best teacher on television because of the realism and the representation that she brings to this character of what teaching is about. <Applause>

Dan Meyer (34:28):
Right on. Right on. OK. OK. Next up, we’ve got, Fawn Nguyen is nominating Erin Gruwell from Freedom Writers. Here we go.

Hilary Swank in Freedom Writers movie (34:39):
“Look, you can either sit in your seats reading those workbooks or you can play a game. Either way, you’re in here till the bell rings. OK? This is called the Line Game. I’m gonna ask you a question. If that question applies to you, you step onto the line and then step back away for the next question. Easy, right? The first question. How many of you have the new Snoop Dog album? <kids move around> OK, back away. Next question. How many of you have seen Boys in the Hood?”

Fawn Nguyen (35:26):
We all learn about Miss G and her 150 students in the movie Freedom Writers starring Hilary Swank. All great teachers share a common set of traits. They care deeply about their students, have high expectations of them, and always believing wholeheartedly that they will succeed. Great teachers go above and beyond, not because they extraordinary—as Anne Gruwell would always refer to herself as an ordinary teacher—but because extraordinary things happen to people when we believe in them, give them hope, help them write their own story with a different ending. So what stood out for me with Miss G is the scope of her reach, the ever-expanding sphere of her humanity. The red tape she had placed on the classroom floor for the line game shows just how much we all have in common despite our differences. Her students didn’t just learn from her; they learned from one another. If you’d like to be part of this expanding sphere to give voice and hope, please check out Freedom Writers Foundation dot org.

Dan Meyer (36:38):
OK. This right here is a tough one for us. Thank you, Fawn. We collectively ranked—that’s our number one seed and number eight seed, which I hasten to say does not have to do with Erin Gruwell, a person, but the portrayal and the movie. So we don’t have like a whole lot of…there’s not a lot of defense we have to offer here of our eighth seed. And I heard like a kind of a little bit of a murmur over the crowd on Erin Gruwell. So I’m more interested than having a defense back and forth. I’d be curious what you, Bethany, think about what, like, what both movies have to say about like, what teaching is, especially teaching urban schools with black and brown kids and lower-class kids, for instance. They both have, I think, very different things to say about them. Do you have thoughts about that?

Bethany Lockhart Johnson (37:19):
Well, it’s interesting because there is some overlap in the sense that the arguments that both Fawn and Robert Berry put out, they both care deeply about their students, right? We’re not gonna argue that. They care deeply. And something that I would say about Miss Teagues is there’s something about the way that she sees not only her classroom, her students, but she sees all of the students in the school as her students. And her idea of resource generation is really helping the teachers to generate resources from their community themselves, and to also realize that the students see themselves reflected in the teachers. And I think that—you know, again, this is not about the real person—but the movie portrayal, and we often see kind of this, for Freedom Writers, we often see this like, Great Last Hope whisked in and her personal sacrifices are what makes these students, these brown and black students’ transformation possible. Because of her sacrifices. Including her marriage. Including, you know, three jobs. And it’s just portrayed in a way that I think really celebrates her sacrifices rather than what the students have already brought—they already come into the room bringing so much as they are, already, without her intervention.

Dan Meyer (38:38):
I love the portrayal of the teacher as part of a community of teachers. Versus in so many of these movies, it’s the teacher as the only person who gets it, you know, oftentimes coming from outside of the world of teaching and everyone’s against them and wants ’em just to fall in line and do the thing we always do, and they’re the outlier. But in Abbott Elementary, it’s like we all rise and we fall together. And teachers are investing in each other’s success, especially with Gregory the longterm sub. We’re all rooting for his, you know, his flourishing. I love that. And yeah. That’s bigtime.

Chris Nho (39:09):
Yeah, I think one interesting thing is that Freedom Writers, when it came out, I think it was like a commercial success.

Bethany Lockhart Johnson (39:17):
Oh, big time. Yeah. It was.

Chris Nho (39:18):
It probably influenced a lot of people to try teaching out. So I do wonder what it says about us, right? Like that we want teaching to fit this narrative, and we wanna be those people who could go into a classroom and <puts on “cool voice”> “Y’all listen to Snoop Dog?” and just have that question HIT. <laughter> And you know, I’ve taught in a large urban school district, and I’ve been that person and I’ve seen other people try and be that person. And I think stepping away from it a little bit, just—it’s a reflection of what people want out of teaching and what they think better education looks like.

Dan Meyer (39:57):
Yeah, yeah. This idea that, so I’m a middle-class person, let’s say, and like, there’s this idea, like, “I know what I would do if I was going into circumstances of impoverishment.” Like I have—

Bethany Lockhart Johnson (40:06):
“All they really need is…”

Dan Meyer (40:07):
…for me to give ’em some real talk and tell ’em, you know, pull their pants up or whatever, listen to Snoop Dog, that kind of thing. And that will be the key. And that’s not how it is in, you know, in Jack Black in School of Rock or Tina Fey school, which are, you know, coded as largely like upper-class or largely white schools. And in those movies, it’s interesting, like how it’s about students discovering themselves, oftentimes. And the central figures are often students. And the students need to reject an oppressive parent figure or something and find themselves. But no, in Freedom Writers, it’s like, “You need to become more like the middle-class teachers who are coming in here to give you this wisdom.” It’s just interesting. I do find it—a pet peeve of mine is when movies portray teachers as only successful if you endure, for instance, the failure of your marriage, or even in Stand and Deliver, for instance, like Jaime Escalante, they depict him having a heart attack. And, like, the job oughta be…easier. <Audience laughs>

Chris Nho (41:04):
Truth.

Bethany Lockhart Johnson (41:05):
That’s the barometer for how much….

Dan Meyer (41:09):
Like, no heart attacks and no divorces related to the job, that kind of thing. I do love how in Abbott—one last thing and we’ll vote and Abbott will win <audience laughs>—is like how, like there, there is a lot of degradation in Abbott, but it’s not a divorce or a heart attack—it’s the petty indignities of asking a student, “Do you wanna hang with me?” And a student says, “Nah, not really.” And that just spoke to me like how it’s not cinematic, but teaching, successful teaching, is like a collection of developing an immunity to students saying, “You’re not hot.” <Laugh> You know? And so I love that. I do wish that there was more depiction of students in Abbott Elementary. It’s a lot of adult stuff. Whatever. Give it up for Abbott, if you would, please. Let’s just get this done here. All right. That’s plenty. That’s plenty. Not gonna ask folks about Freedom Writers. OK, let’s move on to— all right, let’s hear it for Freedom Writers! Yeah. OK, cool. We go, yep.

Chris Nho (42:05):
Plot twist!

Bethany Lockhart Johnson (42:07):
OK, let’s see our final four. Cut and paste. Real time. Real time.

Audience member (42:12):
Where’s Dolores Umbridge?

Dan Meyer (42:14):
Oh….

Bethany Lockhart Johnson (42:16):
Hey, did you hear that? He said, “Where’s Dolores Umbridge?”

Dan Meyer (42:20):
All right. OK.

Bethany Lockhart Johnson (42:20):
See, we missed so many. We could…

Dan Meyer (42:21):
So coming up here, we’ve got in the Eastern Conference, Tina Fey and Ms. Frizzle. Y’all know how I feel about that one. Let’s just get this one done. OK, let’s give it up for Tina Fey. Let’s hear it. <Audience cheers> OK. All right. Yes! Let’s give it up for menace to children everywhere, the terror, the Ms. Frizzle. <Audience cheers> One more time for Tina Fey. Let’s hear it. <Audience cheers> One more time for Ms. Frizzle. Let’s hear it. <Audience cheers>

Bethany Lockhart Johnson (42:59):
Yeah. OK.

Dan Meyer (43:00):
It took ’em one round, but they made the right call in the end. <Laugh>

Chris Nho (43:04):
All it took was 10 minutes of constant Ms. Frizzle-bashing. <Laugh>

Dan Meyer (43:09):
Persevering and problem-solving, that’s my game. Yes. All right. So, do either of you want to influence the audience one way or the other?

Bethany Lockhart Johnson (43:16):
That’s not how I play, Dan.

Dan Meyer (43:18):
Oh, OK. Yeah, that’s true. That’s true. You’re good. On Abbott versus Marshall Kane, should we just let ’em have it? All right. All right. Give it up For Abbott Elementary. Not bad. And for Marshall Kane. OK. OK. I hear Zak and five other people. All right, cool. <laugh> Right on. All right. We got our, we got our finals,

Bethany Lockhart Johnson (43:45):
We did it. We made it to two. And we know: We left out a lot of people. Right? And honestly, I kind of wish we could poll like everyone. I mean, think you put it on Twitter, right? Like, who would you pick? But I would say we had a pretty solid eight there. I’m excited to see who… Look at the little crown he put, you guys. Come on.

Dan Meyer (44:05):
I worked hard for you. For you. <Laugh> Yeah. I liked that it was a good bunch that had a lot of different kinds of qualities…and lack of qualities in some cases. And it allowed us that—I shouldn’t knock her while she’s down, and she IS down, it’s true. <Laugh> And I appreciate the conversation we’ve had, what they have revealed overall about teaching and what the world wants teaching to be versus what it actually is or actually should be. I appreciate that. So let’s settle this here. Give it up, if you would, for Abbott Elementary. <Audience cheers> And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (44:49):
Wow.

Dan Meyer (44:51):
That was close. I almost give that to Tina Fey.

Audience member (44:55):
Yeah, we do!

Dan Meyer (44:55):
I don’t know. That was a bracket-buster for me right there. Yeah. I lost money in the office pool off that right there. Maybe let’s just find out one more time here. One more time.

Bethany Lockhart Johnson (45:03):
Last time.

Dan Meyer (45:03):
Time to summon up all your conviction on one or the other here. No half-measures right now. All right.

Bethany Lockhart Johnson (45:07):
Emmy Award-winning Quinta Brunson.

Dan Meyer (45:09):
Yeah, you saw Robert Berry on that, right? He was like, “Oh, I got one more card to play. Emmy Award-winning.” That’s admissible. That’s admissible. We’ll take that. All right. So…give it up for Abbott Elementary, one last time. <Audience cheers> OK. All right. All right. And give it up for Tina Fey in Mean Girls. <Audience cheers>

Bethany Lockhart Johnson (45:30):
Drumroll, please!

Chris Nho (45:33):
Best teacher is….

Dan Meyer (45:34):
Tina Fey in Mean Girls! Yeah. Not a bad pick.

Bethany Lockhart Johnson (45:39):
I love it. And I think, too, I think we’re gonna have a little bit of a more reflective lens than we thought we did when we see depictions of teachers in film and television. And, you know, hopefully we’ll see some new tropes come in, right?

Dan Meyer (45:55):
Yep. Yeah. Every dollar we spend on movies with lousy teachers is just encouraging these people to make more lousy teacher movies, you know? Awesome. Thank you for being here for a live taping—

Bethany Lockhart Johnson (46:06):
Thank you for being here.

Dan Meyer (46:06):
—of our podcast, Math Teacher Lounge, in a hot room. Appreciate that. Yeah, it’s been fun for us to have you here. Um, super-important, super-important final remark: Bethany loves Oprah and Oprah occasionally, in the show—

Bethany Lockhart Johnson (46:18):
Is she coming?! Is she here?!

Dan Meyer (46:19):
Not here! Not here! Calm down. Calm down. Um, but we do have in Oprah fashion, not something—

Bethany Lockhart Johnson (46:24):
Oh. Oh, OK. Oh, that’s, that’s OK. Sorry. I got, had really excited for a second. As if the Amplify playing cards, The Amplify t-shirts being chucked at you at high speed—I did try to get a t-shirt cannon, and that was quickly ruled out <laugh>. They didn’t know about my rocket arm, right?

Dan Meyer (46:46):
Yeah, you got a cannon. <Laugh>

Bethany Lockhart Johnson (46:47):
Yeah. Oh, that’s a compliment. Oh, is that a compliment? Thank you, Dan. Thank you. Look under your seat because we have five winners. We wanna thank you for being here in person. We wanna thank the folks who are listening. We wanna thank Amplify. Oh my God. Somebody just pulled off the chair tag. You get to take that chair home with you.

Dan Meyer (47:08):
Does anybody have a prize?

Bethany Lockhart Johnson (47:10):
OK, stand up if you…stand up if you…Yes! Stand up if you have one!

Dan Meyer (47:16):
Free set of classroom dry-erase boards, right here. Congratulations.

Bethany Lockhart Johnson (47:22):
And for you who pulled off the chair tag, I don’t know. We gotta we gotta find something for you.

Dan Meyer (47:27):
Put that in your backpack.

Bethany Lockhart Johnson (47:30):
Thank you again for being here. Thank you. Amplify. Thank you, Desmos. Thank you. Dan Meyer.

Dan Meyer (47:36):
Thank you folks. Chris, thank you buddy.

Bethany Lockhart Johnson (47:38):
Chris! Chris Nho, everybody!

Dan Meyer (47:40):
We will be, we will be at—Bethany and I will be at the booth, if you wanna chit-chat and hang out, sign some stuff. Whatever. You wanna have Bethany sign you, she’ll do that. Um, come on down to the Amplify booth and we’ll—

Bethany Lockhart Johnson (47:50):
We’ll talk to you more about Ms. Frizzle.

Dan Meyer (47:52):
Fun and prizes. I will share with my real thoughts about Ms. Frizzle down there. I’d love to see you. Thanks for being here, folks.

Bethany Lockhart Johnson (47:57):
Thanks for listening. Bye.

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What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer—or don’t offer—now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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About Math Teacher Lounge: The podcast

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

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

S3-03: Instructional strategies for integrating science and literacy

A graphic with the text "Science Connections" and "Amplify" features colorful circles and curved lines on a dark gray background.

We’re continuing our investigations around science and literacy with Doug Fisher, Ph.D., professor and chair of educational leadership at San Diego State University. We talk about the importance of integrating science and literacy, as well as practical guidance for teachers who want to unite the two disciplines in their own classrooms.

Listen as we discuss how science and literacy can be powerful allies and specific strategy areas to focus on when integrating the two disciplines. And don’t forget to grab your Science Connections study guide to track your learning and find additional resources!

We hope you enjoy this episode and explore more from Science Connections by visiting our main page!

DOWNLOAD TRANSCRIPT

Douglas Fisher (00:00):

It’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work.

Eric Cross (00:10):

Welcome to Science Connections. I’m your host, Eric Cross. This season, we’re making the case for our favorite underdog, which of course is science. Each episode we’re showing how science can be better utilized in the classroom, and making the case for why it’s so important to do so. In our last episode, we examined the evidence showing that science and English instruction can support each other. And now on this episode, we want to give you some more strategies for really making that a reality in your own home or classroom or community. So to help me, I’m joined on this episode by Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Dr. Fisher is actually someone who has conducted literacy training at my own school, so I’m excited to be able to share some of his wisdom with all of you. Oh, and just a heads up, Dr. Fisher dropped some gems about the ways teachers can integrate literacy and science in their classrooms. So you may want to have a notepad. Ready. And now here’s my conversation with Dr. Douglas Fisher.

Eric Cross (01:12):

Well, Doug, thank you for your time and for being willing to come and talk about literacy and science. I know you’re busy, all over the place, and so I was super-excited that we were able to lock you in and talk about this. And, on this episode, we’re gonna talk about the ways that science and literacy can support each other. And one of the reasons why I’m really excited for you is because you said some really key things for me as a science teacher, when you talked about literacy and supporting students. That just resonated so deeply in me. And I was like, “I need more Doug!” Because we’re on that same frequency. And I know it’s a subject that you’ve spent a lot of time writing about. So can you tell us a little bit about how this became an area of interest or a passion for you? Just literacy, and all of the work that you’ve put into it?

Douglas Fisher (01:54):

Yeah. So I’ve wanted to be a teacher for a really long time. And I went to San Diego State as an undergraduate, and I was taking English class and we were assigned topics. You know, like, you’ll do an assignment, you’ll write a paper for this English class. And I got the topic “illiteracy,” and I was a freshman at San Diego State reading all of these things about adults who don’t read very well or not at all. And I ended up writing my very first college essay on illiteracy — at the time, you know, called illiteracy, at the time. And so I got super interested in this. And so as I moved through college and into my teaching career, literacy became a really important thing for me to think about, because it’s the gatekeeper. You know, you can be taken advantage of, if you’re not very literate. People can use vocabulary against you, if you’re not very literate. We know that people who have higher levels of literacy have better health outcomes. They have better lifespans, longer lifespans. I mean, there’s just — literacy impacts so much more than “Are you reading your fourth-grade textbook?” It really has lifelong implications.

Eric Cross (03:01):

That part that you said about being taken advantage of … I just got a flyer in the mail yesterday. It was one of these mailers that looked like it was an authentic debt-reduction type of thing, but it was really just like a marketing email. If you read the fine print at the very bottom, it had all of this jargon about “This is a paid, you know, for-profit company.” But when you look at it, it had official stamps all over it. And I could imagine if someone’s receiving that, that probably fools a lot of people. Is that kinda like what you’re talking about, like being taken advantage of?

Douglas Fisher (03:28):

Yes. I had a student turn 18, got a letter from a “credit card company” that was offering her daily compounding interest. And if you don’t know what that means — at 23 percent! — if you dunno what that means, you are gonna be a victim. Literacy really influences a lot of our life. It’s also how our brain works. We have a language-based system in our brain. We read, write, speak, listen, and view. And the things we learn, we learn through speaking, reading, writing, listening, and viewing. From what we know, we are the only species that has an external storage mechanism. Like, we have the ability to store complex information outside of our body, in the form of notes. We can type them. We can write them. And we can then go back and retrieve that information, that complex orthographic information later. And it means the same thing. We can say we have a storage system and we’ve been doing this for a really long time. Way back to, you know, hieroglyphics and messages on cave walls. And throughout the ages of humans learning, how to store information that they can re-access again later. That’s become a super-complicated system. It’s how computers operate. And we send messages to each other and we text each other and we write things down, and we’re really good at putting ideas, information out there. Now, if it’s just speaking and listening, then we can forget it. We can say, “No, you said this,” or “I said that.” But when it’s written, and it’s print literacy, you know, it’s the orthographics there, you can go back to the same message and over and over again. Now, you might change the interpretation of it, but the message is still there.

Eric Cross (05:16):

Right. And that is such a key element, at least of modern education, is this written element of it. It’s what many schools live and die by. They’re quantitatively and qualitatively analyzed by it. It’s public. They can see it. And so there’s this heavy emphasis. And why do you think science and literacy can be powerful allies together?

Douglas Fisher (05:38):

Awesome. Well, it’s hard to learn science if you’re not literate.

Eric Cross (05:42):

This is true.

Douglas Fisher (05:42):

But that’s a one-way direction. And yes, science teachers and scientists do a lot of reading, writing, speaking, and listening and viewing. They use the five literacy processes all the time. When we interview scientists, they spend a lot of their time reading the work of other scientists and writing their findings, writing grant proposals, presenting at conferences, you know. So a huge part of the work of a scientist is not just at a bench conducting experiments. But even if you’re conducting experiments, you’re using your literacy processes to think about what you’re seeing in your experiment. So that’s a one-way direction. And I do think literacy has an influence on science. But since science goes the other way, it influences literacy. As you learn more and you understand more about the world, your background knowledge grows, your vocabulary grows, you become more literate in those different areas. And how you think. So if I’m learning about life science; I’m learning how the world works in a more, biologic physical world. And that knowledge helps me think about when I’m reading a novel, and there’s an appeal to some science knowledge or a concept that gets played with, you know, perhaps time-space continuums … well, if I don’t have the science knowledge of how I think the world works, it’s hard for me to understand what this author is doing. So it does go both ways. They feed each other. And the more literate we become, the more complex science information we can understand. ‘Cause our background knowledge and our vocabulary influence how much we understand about what we read. And as we access more complex science information, it starts to change the way we think about other things in our world.

Eric Cross (07:23):

There was a couple of things that you said in that, but one of the first things that kind of perked my ears is when you said grant proposals. Because I have friends that are scientists — and this is one of the things that when I was in school, they don’t talk about — but how much of their research is reliant upon getting funding —

Douglas Fisher (07:37):

Mm-hmm. <affirmative>,

Eric Cross (07:38):

— which you don’t think about if you’re becoming a chemist or a physicist or a biologist or working in the field, is that that funding, coming from the NSF or anywhere else. And sometimes students ask in class like, “Why am I writing so much? Like, I want to go into science!” Or “I wanna do this!” And this is a real-life example of how the writing could actually apply, in addition to all of the things of collecting data and conclusions and results. But that grant proposal thing just really perked my ears, yeah.

Douglas Fisher (08:01):

And if you can’t write a grant proposal, your ideas and experiments are not gonna get funded. And if you can’t write a strong proposal, that compellingly convinces your readers to fund you, you’re not gonna get funded. But then once you get the grant, you have to write publications. You have to share your work with other people. Make PowerPoint presentations and write journal articles or books or whatever. So it’s a cycle that literacy influences the things we do, including the things we do in science.

Eric Cross (08:31):

Now to get in maybe some data, if you were trying to convince someone that like this happy marriage can exist, what would be like your number one piece of evidence to support this, this back and forth of supporting each other?

Douglas Fisher (08:44):

Awesome. So the quote I’ll often say — and this is from studies from more than two decades ago now — but in general, in high school science, students are introduced to 3000 unfamiliar words, 3000. Each year! Because there are words that are used in a scientific way that are used commonly in other places. And there are discipline-specific words. So 3000 words a year in high school science. The Spanish 1 textbook only has 1500 words in it. So science teachers have double the academic-language vocabulary demand that a typical introductory world-language class has. So just the vocabulary alone should say to us, literacy is gonna be important if you’re gonna learn science. And if you don’t understand these technical words, and you don’t understand the way science uses this particular word in this particular way… . When you say the word “process,” it means something very specific In science. “Division” — cellular division is not the way we think about it in mathematics; there’s a similar concept, but cellular division is different than dividing numbers. And those are words that get used in multiple areas. Then you have all these technical terms that you have to be able to use, to understand the concepts. To share the concepts. To talk to other people. Whether you’re in, you know, fifth grade and talking science, or you’re a university professor, there’s a shared language, appropriate for our grade level, that we have shared meanings of.

Eric Cross (10:22):

And we’re essentially … what I’m hearing you say is … most of the people that are listening to this are science teachers. We’re we’re also language teachers. In a sense.

Douglas Fisher (10:29):

So my frustration is when people say, “Every teacher’s a teacher of reading.” And I don’t like that. I’ve written against that phrase. I don’t think all teachers are teachers of reading, any more than all teachers are teachers of chemistry. Or all teachers are teachers of algebra. But what I will say is the human brain learns through language. And all of us — every teacher that I’ve ever met understands that language is important in my class. If my students don’t have strong listening skills and speaking skills; reading, writing, and viewing skills; I’m gonna have a hard time getting them to learn things. If I can help them grow their speaking, listening, reading, writing, and viewing in my content area, I’m gonna do a service for my learning of my subject and also their more broad literacy development.

Eric Cross (11:16):

  1. So, at a high level, what does it look like to integrate science and literacy? We’ve done education for the last, what, hundred years?

Douglas Fisher (11:24):

Mm-hmm. <affirmative>

Eric Cross (11:25):

—kind of pretty similarly, right? Kind of siloed way. What does this look like at the 30,000-foot level? You’re a professor, department chair. Run schools. Speak everywhere. Like, when you think about this from that high level, what does it look like?

Douglas Fisher (11:39):

A high level? Every time I meet with students in a science class, you know, biology or fifth grade or whatever? They should be reading, they should be writing, they should be speaking and listening. Every class. So what print do you want them to access? And it can be a primary source document, it can be an article, it can be from a textbook. Are they reading something? Are they writing to you? Because writing is thinking. If they are writing, they are thinking. As soon as their brain goes somewhere else, they stop writing. The pen won’t move or the fingers don’t type. And then speaking and listening, of course, is the dynamic of our classes. So every day we should see some amount of reading, writing, speaking, and listening, viewing in our classes. That’s at a high level. There are some generic things that seem to work across the literacy. So, learning how to take notes. Focusing on vocabulary. Using graphic organizers. These are generic things that as educators we can use in our classes. Then there’s more specialized things. So, scientists and science teachers think differently than historians and literary critics and art critics. So scientists, if you look at the disciplinary literacy work, there’s a whole body of research where they interview and study high-end experts in their field: chemistry, physics, biology, et cetera. And there are some characteristics that were more disciplined, specific. Scientists like cause and effect relationships. They look for them when they’re reading. They like sourcing information. “Where this come from?” “What’s the history of this idea?” Scientists have a long view in terms of time. Historians have a shorter view of time. English teachers have even shorter view of time. Scientists tend to think in long periods of time. And so all of that influences how a scientist reads and how we should apprentice young people after they get past the generic “I know how to take notes. I know how to study my vocabulary. I know how to do summary writing for my teacher in my notebooks and things,” there’s some generic tools. Once we get past those, we need to be looking at specifically how do people in science use literacy.

Eric Cross (13:52):

I’ve never had my thought process of reading deconstructed just now, but we just described how scientists read. I was like, “Yeah, that’s pretty much how I read, right there.” I also like how you said how we should apprentice young people. And I feel like you as the literacy guy, you chose that word very specifically, as far as apprenticing young people. That is a view, I think, that’s really important to hold. ‘Cause that’s what we’re doing essentially … is, if we’re doing what we should be doing, we are apprenticing these young people.

Douglas Fisher (14:18):

Yes.

Eric Cross (14:18):

And helping them develop. Now, let’s imagine there’s a listener out there and they’re interested in getting better at integrating science and literacy instruction. They want to start somewhere. Before we dive in, do you have any initial words of encouragement for the person who’s like, “Everything is like a priority right now,” in their classroom or in their world?

Douglas Fisher (14:37):

Yeah. So I’ll talk about elementary for just a moment. When we’re reading informational texts in our literacy block, we should be reading information that is aligned to what kids need to learn in science and history in, in that grade level. Why are we reading things that are gonna be in conflict with what they’re gonna learn in science later that day in fourth grade, for example? So when we look at our standards, our expectations, what is it that third graders need to know in history, science, mathematics, language arts? And when we’re reading text and we’re learning to apply our reading strategies during our literacy block, why aren’t we reading topics that build our background knowledge for our science time? So we’re seeing some synergy there. We should be looking at life cycles in grades that are appropriate for life cycles and knowing there’s more to life cycles than the frog and the plant or the seed. There are all kinds of life cycles. And we call ’em life cycles for a reason. That’s a general concept. Now in science, we’re looking at this particular lifecycle right now. And so that’s a high level. If we could get more connection to the content standards during our literacy blocks, it would be very good. When we talk about the time at which we call “science” in the day, in more of the K–8 continuum, the science needs to include some primary source documents. Some real things that students are reading. Read about a scientist; read about a scientist’s discovery; read about what they discovered. So that we’re building our background knowledge. So when we go to do things, activities, labs, simulations, we have background knowledge and we understand what we’re experiencing. It can’t be like—I watched this awesome lesson on lenses and the teacher had all these different lenses in the room and the students came in and they were brand new. They don’t know anything. They were picking ’em up. They’re exploring them. They’re trying to figure out, and they’re trying to come up with theories about what this is and how it works. And then the teacher gave them a reading, a short reading, on refraction of light. And they read this thing. And the clarity that they had about what these lenses must do, well! All of a sudden they’re putting them up to the lights! They’re asking if they can go get the lights out of the storage unit! ‘Cause there’s — and they’re shining different lights through the lenses to see what happens to the light. Because that little bit of reading turned some focus on for the students. And it allowed them to take what I’m thinking about, what I’m trying to figure out, how this thing works in another direction. That’s the power of using literacy in our classes.

Eric Cross (17:20):

And what I’m hearing essentially is transfer across disciplines, across content areas, ultimately. And in an elementary school classroom, would it be fair to say, probably the teacher has more autonomy to be able to do that, since they’re teaching all the subjects? But secondary, logistically, planning and those types of things … from what you’ve seen, is it fair to say this kind of needs to be like a top-down, full vertical alignment, to teach like this?

Douglas Fisher (17:45):

I think that would be awesome to do that. But if I’m a sixth grade English Language Arts teacher and I’m working with my sixth grade science teacher, the conversation should be, “What units are you teaching?” Because I’m choosing informational text. My job is to teach them how to find central ideas. My job is to teach them how to find the details in the text. My job is to have them make a claim and support that claim with evidence. The stuff I use is generic. Yes, we do read some literature and some narratives, but we also read about 50% of the text in English around informational text. So if I can help you and accomplish my standards as well, fantastic. So let’s have this conversation and say, “Oh, this is what you’re teaching in science in the next three weeks? I’m gonna choose some texts and we’re gonna analyze ’em for central idea. We’re gonna analyze ’em for details. We’re gonna, for mood or tone or whatever that we’re teaching. And by the way, I’m building background knowledge. So when they come to you, they know some stuff about what you’re going to be teaching next.” So I don’t think it’s impossible to say teams of teachers could come together and say, “What do we believe that our students need to know and learn and be able to do? And then how do we choose things that are gonna help them accomplish exactly that?”

Eric Cross (19:01):

And that’s empowering. Because that’s one thing that we can control maybe is this East-West, peer-to-peer, different content areas. A system may not be able to change as quickly, but I can definitely go talk to my English team or math team and check in and kind of see, “Hey, where do we have overlap in that?” And I know the times that I’ve accidentally had overlap with the teams, it’s super-exciting. And the students have been more bought in! Because it’s like, we’ve done something on the human microbiome and we’ve talked about genetics and all these different things, and then when they read The Giver, or they read some book about genetics, they have all this knowledge. And they’re excited. And they talk about colorblindness or they come to my class and they’re like, “Hey, we read about this!” It’s almost like they saw a magic trick, the fact that these things linked up. And the engagement has been so much higher when it’s the same content in different classes, but through different lenses. At least, that’s what I’ve seen in my years of teaching.

Douglas Fisher (19:54):

I saw a lesson on space junk that was so cool. Middle-school students learning space junk. And the history teacher had a part of it, science teacher had a part of it, English Language Arts teacher had a part of it. And these students, I mean, you watch them look up all the time, ’cause there’s space junk up there. Where’d it come from? Why is it there? What are the politics of this? How do we clean it up? I mean, it was just so interesting to watch them when the teachers came together. And the teachers met their standards in this couple-week-long space-junk exploration. Investigation was met. Politics was met. All these different things. Economy. You know, how much does it cost to clean up this problem? So there’s really cool opportunities when teachers come together and realize we can work together and improve the literacy and learning of our students.

Eric Cross (20:50):

Absolutely. So before this recording, we picked your brain a bit. And I know that there were three specific strategy areas that you wanted to touch on. And one of those — which is kind of coming back to the 3000-words language teachers — was vocabulary. So what are the opportunities that you see, as far as the way of educators to approach vocabulary? Because, you know, there’s a lot. We got a lot of it. The 3000 words.

Douglas Fisher (21:14):

Yeah. There’s a lot of it. So the worry is, we make a vocabulary list and have students look up the words in definitional kinds of things. That’s not really gonna help. Students need to be using the words. They need to be using the words in their conversations, in their writing, in how they think about your content in science. So vocabulary is a huge predictor of whether or not you understand things. Vocabulary is also a pretty good predictor if you can read on grade level. So when we think about vocabulary, there’s something called word solving. You show students a piece of text and you’re reading it, you’re sharing your thinking, and you say, “Oh, here’s a context clue!” Or “I know this prefix or suffix or root!” And in science, a lot of the words are prefixed, suffixed, or root words. We tend to add things together with a lot of prefixes and suffixes and have roots and bases in science. So we can help students think about, “Oh, what does geo- mean? We already know what geo- means here. It means the same thing in this word. Let’s apply that knowledge.” So word solving is part of it, showing students how we think about words that we might not know. The second is more direct instruction of vocabulary. As students encounter the words, we work on what it means, how we say it. We practice it a few times. The process is called orthographic mapping. It’s kind of a scientific idea here. But you have the sound and the recognition of by-the-word, by sight, and what it means. And your brain starts to automatically recognize that word in the future. So I don’t have to slow down, disrupt my fluency, and try to figure out what the word is saying. ‘Cause I’ve seen it enough. I’ve heard it pronounced enough, I’ve pronounced it enough, and I know what it means. So teachers should be saying, “What words in sixth grade science, what words in third grade science, do my students really need to know?” And I’m gonna have them encounter those words over and over. I’m gonna have them use the words. I’m gonna have them see the words. I’m gonna have them say the words. I’m gonna say the word and we’re gonna be over and over with these terms, so that students incorporate them into their normal view of, “These are the things I know about the world.” By the way, when they go to read that next thing, and they understand “geology,” you know, for sixth graders, for example, they know how to say it. They don’t stumble on it. And it activates a whole bunch of memories in their brains. “This is what geology is.” There are branches of geology, there’s physical geology, there’s all this thinking that activates as they read.

Eric Cross (23:35):

There was a practice that I participated in and am trying to incorporate — I don’t know what the name of it is. But essentially what happened was we were dissecting a flower. And the instructor had us name parts of the flower. But we got to come up with our own names for it.

Douglas Fisher (23:49):

Ah.

Eric Cross (23:50):

So, for instance, the stamen we call “the fuzzy Cheeto.” And we all used our own words and then everything was legitimized. And so we went through and learned the whole activity using our own vocab words. But then, in the end, after we presented and talked about it, then the words, the actual academic language was attached to our word. And we were able to say, “OK, the fuzzy Cheeto is the stamen,” and this, this, this, and this. But it was such an interesting practice, because it kind of legitimized all of our definitions. But we weren’t stumbling on these long Latin terms and things like that. Is there a name for that? Or. … ?

Douglas Fisher (24:29):

Yes. I don’t know the name for that. I think it’s really smart. So here’s what I would say about that, is: we don’t learn words, we learn concepts. Words are labels for our concepts. So what that teacher did for you was allow you to develop concept, a concept knowledge. “There’s a part of this plant, it goes like this, we’re gonna call it fuzzy Cheeto. Now I have this concept. And look, it occurred in all these plants. And those people called it that and that other group called it that. We called it a fuzzy Cheeto. Here’s the part of it.” And then the concept is in your brains. And the teacher said, “It’s really called stamen.” And it’s an instant transfer, because you already had the concept. What we often see is students are trying to learn a really hard academic word and the concept for the word at the same time. And so it slows down the whole process. And there’s higher levels of forgetting. Because human beings, we don’t learn words; we learn concepts. If you don’t have the concept, if I gave you a word out of the blue that you’ve never seen, never heard, and a week from now I asked you to remember it, you probably would not, because it didn’t register. It wasn’t part of your schema. You didn’t have a way to organize the information. You don’t have a concept. So that teacher? It’s a great idea. Got you to develop concept knowledge. And then said, “Here’s a real label for it: What some other people called it when they had the chance to come up with their own names.”

Eric Cross (25:50):

Shout out to my teacher, who was—

Douglas Fisher (25:51):

Right.

Eric Cross (25:52):

It was learned then. It was a great practice. And the fact that you’re right, like, I just mean from my own personal experience, I agree that learning concepts versus complicated words. And it’s interesting that you said higher levels of forgetfulness, you know. And you often hear that complaint about it: “Students forget! Students forget!” But this complex topic and this complex word that’s new to me, and I have to remember both of those things.

Douglas Fisher (26:12):

That’s right.

Eric Cross (26:13):

And the other neat thing that it did, is it actually honored the background and like the founts of knowledge of all the different groups in the classroom. You just said something about “this group called it this and this group called it this,” and so by letting different groups share all of those names, now we’re starting to build these kind of interesting connections. That’s at least what I remember experiencing. And so this, even this practice of this approach is very layered, beyond just kind of generating new knowledge of things. So I appreciate that aspect of it. Now another area that you mentioned was complex text.

Douglas Fisher (26:41):

Yeah.

Eric Cross (26:42):

And how we can get students into complex text. So what can we do there?

Douglas Fisher (26:46):

I think science is an ideal place to get students reading things that are hard for them. And I do believe that some parts of school should be a struggle. Not all day, every day. But there should be doses of struggle, which are good for our brains. And these complex pieces of texts that don’t give up their meanings easily allow students to go back and reread the text and maybe mark the text and talk to peers about the text and answer questions with their groups. And the whole point of complex text is to say, “We persevere through it. We may not understand it fully on our first read. But we go back and we might underline, we might highlight. We might write some margin notes. Our teacher might say, ‘What did this author mean here?’ And we go back and look at that part and we take it apart. What do we think about that? And we talk to each other. It’s showing that when we read things, we work to understand. We work through our thinking, often in the presence of other people. And our understanding grows as we go into the text over and over and over again.” So I said geology earlier. There’s about a two-page article on “what is geology” that sixth graders often read. And some kids find it super boring. It’s a once-read, “OK, geology, I don’t really understand it. There’s a bunch of words in here that I don’t understand.” But if you go back to it a few times and you start taking apart, “What are the branches of geology? Oh, I’m gonna go reread that.” How are these two branches related to each other?” “What are the subtypes of each branch of geology?” “How do geologists do their work?” You start asking questions where students are going back into the text. You spend a little bit of time. Now, the introduction to geology, the students know so much more. So whatever you do next— video experiments, whatever—they have a frame of reference, because of that deep, complex read. It’s probably better than simply telling them, “Here’s the information.”

Eric Cross (28:45):

Right. And I even feel like as an educator, when I reflect on my own learning in the classroom, and then looking at it through the perspective of an educator <laugh>, you find this difference between how you were taught and then what the data says good teaching is.

Douglas Fisher (28:59):

Mm-hmm. <affirmative> mm-hmm. <affirmative>.

Eric Cross (29:00):

It’s so easy to slide back into how you were taught!

Douglas Fisher (29:02):

Yeah.

Eric Cross (29:02):

Even though, you know, you mentally assent to, “This is the best way. This is the data shows.” And you find yourself kind of sliding back at times.

Douglas Fisher (29:10):

Yep. And there’s good evidence to support what you just said, that most people teach the way they experienced school. And it is very hard to change that. And people have studied this. And it’s very hard to change that. Because it worked for us. And we have an n of 1, and it worked for us. Now, remember, there were a whole bunch of other kids in the class that it may not have worked for. And we chose to be in school the rest of our lives, and some of your peers did not choose to be in school the rest of their lives. In fact, some of them hated school and found no redeeming qualities of their experience. So just because it worked for us in a case of one, n of 1, doesn’t mean it worked for all of the kids, or even the majority of them.

Eric Cross (29:57):

Very well said. It’s that, what is that, the survivor bias? Survivorship bias? Where you were the one that made it. But you don’t think about all the other folks. ‘Cause we’re thinking about ourselves.

Douglas Fisher (30:05):

That’s right.

Eric Cross (30:06):

Great case for empathy too, is thinking about the people left and right. Because my friends are like, “I hated science.” And I say, “Who hurt you? Like, what did they do? It’s so amazing, so much fun!”

Douglas Fisher (30:16):

“What happened to you? Science is the coolest. Right? It’s so amazing!”

Eric Cross (30:21):

But I also had a unique experience in seventh grade with my teacher who did some of these things, and made it accessible for so many of us, in opening opportunities that I wouldn’t have had otherwise. But you’re absolutely right. That was my story. That wasn’t the story of everybody that was around me. And I think that’s really important. Now, I know this is also a big one for you, but I wanna talk about writing. What are the opportunities that you see in terms of writing specifically?

Douglas Fisher (30:51):

So would love it if science teachers had short and longer writing tasks in the science time. Of course, you can integrate some of the science writing, the longer ones, in the English language arts time, especially if you’re the elementary teacher and you can have control of the whole day. But I said this earlier; I’ll say it again. Writing is thinking. While you are writing, there’s nothing else you can do but think about what you are writing. Your brain cannot do something else. So if a science teacher wants to know, do their students really understand the concepts? Have them write. Now some of the shorter ones, I like something called “given word” or “generative sentences”: “I’m gonna give you a word: CELL. C-e-l-l. We’re in science. I want you to write the word ‘cell,’ c-e-l-l, in the third position of a sentence. So it’s gonna go word, word, cell, and then more words.” You could also say, “I want the sentence longer than seven words,” or whatever. But the key is, I’m telling you where I want the word. You will know instantly if your students have a sense of what the word “cell” means in the context of science. If they write “my cell phone,” they don’t get it. If they write about spreadsheet cells or jail cells or whatever, they didn’t get it. But if they talk to you about plant cells and animal cells and the components of those cells, and then once they have that sentence down, you can say to them, “Now write three or four more sentences that connect to that sentence.” It’s super simple. So whatever concepts you’re teaching, put ’em in a specific position. Now you don’t have to only put it in the third position. You can say the first position, the fifth position, the fourth position. But it forces them to think about what they know about the word and then how to construct a sentence for you. That’s a very simple way to get some writing from your students that helps you think about what they understand. Other kinds of writing, you can have quick writes, you can have exit-slip writes. There’s something in the research space called the muddiest part, where halfway through the lesson you have them write so far what has been the least understood or the most confusing part of this lesson. And they do a quick write, right there, at the muddiest part. And as a teacher, you flip through these and you start to say, “Oh, these are the points that are confusing to my students.” So if 80% of them all have the same thing, I gotta reteach that. If these five got, “This is the muddiest part,” If these five thought, “This is the muddiest part,” these seven, “I thought this was the muddiest part,” what do I need to do? Because it’s gonna be hard to move forward if this is their area of confusion. There are also all kinds of writing prompts that have a little bit longer. My favorite one is RAFT. What’s your Role? Who’s your Audience? What’s the Format? And what’s the Topic we’re writing about? Super flexible writing prompt. When you teach something, we don’t want students to only think they write to their teacher. So your role is an atom. You are writing to the other atoms. What do you wanna write about? What’s the topic? What’s the format of it? Is it a love letter? Is it a text message? Is it … so we, we mix it up with students in saying, how do they show some knowledge through a prompt that we give them? And then of course, longer pieces as they get older. More opinion pieces through fifth grade. More claims and arguments starting in sixth grade. So that they’re starting to see, “I have to use the evidence from things I’ve learned, read, listened to, watched, and construct something: an opinion, an argument where I back it up with reasons or evidence.” And those longer pieces, you know, less frequently. The shorter pieces, pretty regularly. So the teacher sees the thinking of the students.

Eric Cross (34:29):

When you were speaking about these really creative writing prompts, there were specific students coming into mind, that were coming into mind … they’re, they’re great science students, but they also have this really strong artsy side drawing, creative writing, and things like that. And when you said something about atoms talking to each other, it elicited, in my brain, certain students that would really love this aspect of creativity in the sciences. And it’s not how we’re typically trained as science teachers, to kind of incorporate this, like you said. A book of props. But I’m imagining, like, as a science teacher, if I took this, this would be a great way to reach more students to be able to show what they know, in a way that might resonate with their own intrinsic “Oh, I get to write creatively!” So I was kind of writing furiously as you were sharing all that information there.

Douglas Fisher (35:12):

So here, I’ll give you another example for elementary people. Again, with RAFT. There’s a book called Water Dance. It’s a pretty popular book for elementary teachers. It’s really about the life cycle of water. For example, you are a single drop of water. You are writing to the land. The format is a letter. And you’re explaining your journey. Now, if they can do this, they’re essentially explaining to you the cycle of water. But you got it in a way that people are now, “Oh, I’m a drop of water. So it’s me. My perspective. Where do I go from? Where do I start?” Because you can start anywhere in the cycle, right? My drop could have started in the clouds. My drop could have started in the ground. My drop could have started in the lake. But it has to show you the journey. So there are many ways of showing you the right answers.

Eric Cross (36:02):

And that’s using the RAFT protocol.

Douglas Fisher (36:04):

That’s RAFT: Role, Audience, Format, Topic. It’s been around 20 or 30 years.

Eric Cross (36:09):

You just gave the name to something a teacher shared in our podcast community, Science Connections: The Community, on Facebook. Teacher shared a Google slide deck and on it were just three slides. And the role that the student had to have is they had to show, then tell, the story of a journey of a piece of salmon being eaten, a piece of starch from pasta being eaten, and then an air molecule in a child’s bedroom. And they had to give the path of travel and the experience from the mouth and then breaking down into protein and all those kinds of things. And this teacher shared it and I wish I knew the teacher’s name because I wanna give ’em credit, but they shared it. And so I used it with my students and then had ’em read aloud their stories and dramatize it. And they were so into it!

Douglas Fisher (36:49):

So cool.

Eric Cross (36:50):

But through it, I was able to see that they understood different parts of the body. They understood cell respiration. The whole thing. And it was fun! To watch them get so into this creative writing. And now I know the name of it. That’s been 30 years they were using RAFT. So you just talked a bit about complex texts and writing. And before we go, I wanted to circle back to something that you said, because I think it’s important, and if you could elaborate on it a little bit, about the value of struggle. Can you talk more about that?

Douglas Fisher (37:21):

Sure. I do believe in a lot of the U.S. we’re in an anti-struggle era of education. And it predates Covid. I think it made it worse during Covid. We front load too much. We pre-teach too much. We reduce struggle. We quote, “over-differentiate” for students. And there’s value in struggle. The phrase, “productive struggle” — if you haven’t heard it, Google productive struggle — it’s an interesting concept, that we actually learn more when we engage in this productive struggle. Now, productive struggle originally came from the math world, and it was this idea that it’s worth struggling through things to learn from it, that you’re likely to get it wrong, and then there was productive success. And there are times when we want students to experience success and we make sure we put things in place for productive success. But there are times where we want them to struggle through a concept. ‘Cause it feels pretty amazing when you get on the other side, when you know you struggled and you get to the other side. If you think about the things, listeners, think about the things in your life where you struggled through it and you are most proud of what you accomplished. I want students to have that. I don’t wanna eliminate scaffolding, eliminate differentiation. But I do want some regular doses of struggle. So if you look at the scaffolding, we have a couple choices. We have front-end scaffolds, distributed scaffolds, and back-end scaffolds. Right now we mostly use front-end scaffolds: We pre-teach, we tell students words in advance, that kind of stuff. But what if we refrained from only using front-end scaffolds, and we use more distributed scaffolds, when they encounter. So there’s a difference between “just in case” and “just in time” support for students. So we tend to plan on the “in advance, here are all the things we’re gonna do to remove the struggle before students encounter the struggle.” What if instead we said, “Let them encounter some struggle. Here’s the supports we’re gonna provide. We’re gonna watch; we’re gonna remove those scaffolds, and allow them to have an experience of success, where they realize, ‘I did it. I got it.’” Every science teacher I’ve ever worked with, when they do an experiment or a lab or simulation, they are looking for productive struggle. They don’t tell the answers in advance. They don’t tell if the answers are right. That’s your data. What does your data tell you? I mean, this is what you do. But then the other part of your day when you move into, like, reading, you don’t do that. You fall into the trap of removing struggle. And so allow them to grapple with ideas. Allow them to wonder what words mean. Allow them to say, “I’m not getting this, teacher! It’s really frustrating!” And you say, “Yeah, this is really hard. This is why we’re doing it at school. ‘Cause it’s really hard. If it was easy, I’d have you do it at home. But we’re doing it here, ’cause it’s really hard and it’s OK not to get it at first.” And create a place where errors are seen as opportunities to learn, and struggling through ideas and clarifying your own thinking and arguing with other people to reach an agreement or reach a place where we agree to disagree is part of the power of learning.

Eric Cross (40:38):

There’s a teacher, who I took this from. My master teacher when I was student teaching. And she said that there’s no such thing as failure in science, just data. And I took that same mantra. And I resonate with what you said about how science teachers, all of us, hold onto that productive struggle, because it’s part of being a scientist. It’s part of the experiments. That genuine “aha” moment. Or it didn’t work out? That’s great! That’s totally fine! Let’s write about it and let’s take photos and let’s publish it and let’s be scientists. That’s totally true. As we wrap up, Dr. Fisher, is there any final message that you have to listeners about bringing science and literacy together? I know you speak everywhere, but for everyone that’s listening, if you can put out your encouragement or message or suggestion … you’ve given so many great tips and practical applications. But, any final thoughts on the subject?

Douglas Fisher (41:32):

I think many science teachers are intimidated because they think they have to be reading teachers. And there’s a knowledge base to reading. And some teachers are reading teachers and science teachers, and I don’t wanna dismiss that. But it’s not that you have to become a reading specialist to integrate literacy into science. It’s how our brains work. And so as you think about the way in which you are learning and the ways in which you want your students to learn, what role does language play? What role does speaking, listening, reading, writing, viewing, play in your class? And then provide opportunities for students to do those five things each time you meet with them.

Eric Cross (42:12):

Dr. Fisher, thank you so much for being here and for your encouragement, and sharing your wisdom and experience. And then personally serving my city, here in San Diego, and my students, when they make it to your high school and ultimately the alma mater of San Diego State University.

Douglas Fisher (42:30):

That’s right.

Eric Cross (42:31):

Yeah. We really, really appreciate you in serving all kids and lifting the bar and making things more equitable for all students. And encouraging teachers. So thank you.

Douglas Fisher (42:39):

Thank you very much.

Eric Cross (42:42):

Thanks so much for listening to my conversation with Dr. Douglas Fisher, Professor and Chair of Educational Leadership at San Diego State University. Check out the show notes for links to some of Doug’s work, including the book he co-authored titled Reading and Writing in Science: Tools to Develop Disciplinary Literacy. Please remember to subscribe to Science Connections so that you can catch every episode in this exciting third season. And while you’re there, we’d really appreciate it if you can leave us a review. It’ll help more listeners to find the show. Also, if you haven’t already, please be sure to join our Facebook group, Science Connections: The Community. Next time on the show, we’re going to continue exploring the happy marriage between science and literacy instruction.

Speaker  (43:26):

I had this moment of realization I felt a few months ago: I’m like, if I don’t teach them how to use the AI as a tool, as a collaborator, then they’re gonna graduate into a world where they lose out to people who do know how to do that.

Eric Cross (43:39):

That’s next time on Science Connections. Thanks so much for listening.

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What Dr. Douglas Fisher says about science

“There are really cool opportunities when teachers come together and realize we can work together to improve the literacy and learning of all our students.”

– Dr. Doug Fisher

Professor and Chair of Educational Leadership, San Diego State University

Meet the guest

Douglas Fisher, Ph.D., is professor and chair of Educational Leadership at San Diego State University and a leader at Health Sciences High & Middle College having been an early intervention teacher and elementary school educator. He is the recipient of an International Reading Association William S. Grey citation of merit, an Exemplary Leader award from the Conference on English Leadership of NCTE, as well as a Christa McAuliffe award for excellence in teacher education. He has published numerous articles on reading and literacy, differentiated instruction, and curriculum design as well as books, such as The Restorative Practices PlaybookPLC+: Better Decisions and Greater Impact by DesignBuilding Equity, and Better Learning Through Structured Teaching.

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About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. 

S5.E6. Why skepticism is essential to the Science of Reading, with Dr. Claude Goldenberg

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Winter Wrap-Up 03: Ideas to build math fluency

Promotional graphic for "Math Teacher Lounge" episode featuring Valerie Henry, Ed.D., on ideas to build math fluency, with a photo of Valerie Henry in the bottom right corner.

Join us for the third episode in our Winter Wrap-Up! In this episode from season 3 of Math Teacher Lounge: The Podcast, we sit down with Dr. Valerie Henry to talk about math fluency and what that means for students. Listen as we dig into the research, hear Val’s three-part definition of fluency, and explore her five principles for developing it.

Explore more from Math Teacher Lounge by visiting our main page

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Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

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What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guest

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

An older person with short gray hair and glasses, wearing a blue sweater, is outdoors with greenery and a fence in the background.
Podcast cover for "Math Teacher Lounge" with Bethany Lockhart Johnson and Dan Meyer; bold text on orange and teal semicircle background.

About Math Teacher Lounge: The podcast

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

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

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

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

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

Explore more from Science Connections by visiting our main page.

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Juan Vivas (00:00):

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

Eric Cross (00:28):

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

Juan Vivas (01:14):

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

Eric Cross (01:19):

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

Juan Vivas (01:45):

Yeah.

Eric Cross (01:46):

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

Juan Vivas (01:51):

<Laugh>

Eric Cross (01:51):

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

Juan Vivas (01:59):

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

Eric Cross (05:36):

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

Juan Vivas (05:53):

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

Eric Cross (05:56):

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

Juan Vivas (06:11):

Yep. Yep.

Eric Cross (06:11):

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

Juan Vivas (06:20):

Buoyancy tanks, yep.

Eric Cross (06:21):

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

Juan Vivas (07:39):

Yeah.

Eric Cross (07:39):

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

Juan Vivas (07:51):

<Laugh>

Eric Cross (07:51):

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

Juan Vivas (07:55):

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

Eric Cross (08:54):

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

Juan Vivas (09:03):

Yeah. Yeah.

Eric Cross (09:04):

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

Juan Vivas (09:28):

Yeah.

Eric Cross (09:28):

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

Juan Vivas (10:03):

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

Eric Cross (11:10):

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

Juan Vivas (11:33):

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

Eric Cross (12:17):

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

Juan Vivas (12:23):

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

Eric Cross (13:50):

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

Juan Vivas (15:28):

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

Eric Cross (17:51):

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

Juan Vivas (17:59):

Ad Astra? Yep.

Eric Cross (18:01):

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

Juan Vivas (19:49):

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

Eric Cross (20:11):

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

Juan Vivas (20:56):

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

Eric Cross (22:19):

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

Juan Vivas (23:04):

Yep.

Eric Cross (23:04):

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

Juan Vivas (23:16):

Exactly.

Eric Cross (23:17):

And so that created a lot of value for you.

Juan Vivas (23:19):

Yep.

Eric Cross (23:20):

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

Juan Vivas (23:47):

Yeah. Yeah.

Eric Cross (23:49):

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

Juan Vivas (24:16):

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

Eric Cross (27:38):

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

Juan Vivas (27:46):

Yeah.

Eric Cross (27:46):

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

Juan Vivas (28:03):

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

Eric Cross (28:37):

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

Juan Vivas (29:11):

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

Eric Cross (31:11):

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

Juan Vivas (31:33):

Right. Right.

Eric Cross (31:34):

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

Juan Vivas (31:38):

Yep.

Eric Cross (31:39):

Low orbit?

Juan Vivas (31:39):

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

Eric Cross (31:46):

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

Juan Vivas (32:26):

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

Eric Cross (33:26):

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

Juan Vivas (34:28):

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

Eric Cross (35:28):

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

Juan Vivas (36:13):

Yep.

Eric Cross (36:14):

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

Juan Vivas (36:19):

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

Eric Cross (37:00):

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

Juan Vivas (37:06):

Yep.

Eric Cross (37:07):

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

Juan Vivas (37:49):

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

Eric Cross (38:25):

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

Juan Vivas (39:33):

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

Eric Cross (40:09):

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

Juan Vivas (40:20):

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

Eric Cross (40:23):

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

Juan Vivas (40:34):

Yeah. Yep.

Eric Cross (40:37):

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

Juan Vivas (40:46):

Yeah.

Eric Cross (40:47):

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

Juan Vivas (41:22):

Yeah. No promises.

Eric Cross (41:24):

<laugh>

Juan Vivas (41:25):

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

Eric Cross (41:42):

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

Juan Vivas (42:30):

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

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What Juan Vivas says about engineering

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

– Juan Vivas

Supplier development engineer, SpaceX

Meet the guest

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

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

About Science Connections: The podcast

Welcome to Science Connections: The Podcast! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher.

S3 – 04. Ideas to build math fluency with Valerie Henry, Graham Fletcher, and Tracy Zager

Promotional image for "Math Teacher Lounge" Season 3, Episode 4 titled "Ideas to Build Math Fluency," featuring Valerie Henry, Tracy J. Zager, and Graham Fletcher.

Fluency in math can oftentimes be associated with negative experiences with its development— timed worksheets, for example. Bethany and Dan are joined by three guests to better understand fluency and how to make its approach fun. Dr. Val Henry shares her three-part definition of fluency and her five principles for developing it. Additionally, Tracy Zager and Graham Fletcher join Bethany and Dan to better understand fluency through a lens of equity and using multimedia as a tool.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:03)

Hey folks. Welcome back. This is Math Teacher Lounge, and I am one of your hosts, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I’m your other host, Bethany Lockhart Johnson. Hi, Dan.

Dan Meyer (00:11):

Hey, great to see you. We have a big one this week to chat about and some fantastic guests. We are chatting about fluency, which is the sort of word and concept that I feel like people have very, very non-neutral associations with it. A lot of them are very negative, for a lot of people.

Bethany Lockhart Johnson (00:26):

I saw you frown a little. What’s up with that, Dan? You kind of, like, shrank.

Dan Meyer (00:30):

I have strong feelings about it. You know, there’s lots of ways that people go about helping people become fluent in mathematics. And a lot of them are harmful for students, and ineffective. And it got me thinking about fluency as it exists outside of the world of mathematics, where we have a lot of very clear images of it. We’re getting fluent in things all the time. Like, as humans. Human development is the story of fluency. And I just was wondering….Bethany, would you describe yourself as fluent at something outside of the world of mathematics? What is that? How’d you get fluent at it? What was the process?

Bethany Lockhart Johnson (01:05):

Hmm, I think I’m a pretty fluent reader. I read all the time. I’m a happier person if I’ve read that day. I once saw this poster in a classroom; it said “10 Ways to Become a Better Reader: Read, Read, Read, Read, Read…you know, 10 times. Get it? Reading? You get better at reading by reading! So I would say reading. And it’s been kind of cool—I have a one-year-old who, it’s been really exciting slash overwhelmingly anxiety-producing to see him get very fluent with walking slash running, ’cause he’s getting faster every day. And it’s kind of fun. When I think of what’s something somebody’s trying to get fluent with…walking! He’s trying to be more fluid. He’s practicing transitions. He doesn’t wanna hold my hand while he traverses rocky terrain. He’s getting better at it. He’s practicing. What about you? What’s something…?

Dan Meyer (02:08):

I think about driving a lot. I’m a very fluent driver and I think a lot about when I was first a driver, you know? And how l have my hands on 10 and 2, vice grip, and do not talk to me; do not ask me anything; don’t ask me my NAME. I need to focus so hard. And then a year later, you know, I’m driving with one hand, smash the turn signal, take a sip off of whatever, change the CD. And then it’s no big deal.

Bethany Lockhart Johnson (02:38):

Wait, did you pass the first time? Your test?

Dan Meyer (02:40):

Yeah, I don’t like to brag about it. <laugh> But I do all the time. <laugh> But I got a hundred on my driving test. I don’t care who knows it. And I hope it’s everybody. But I guess all of this is just to say there are areas of life where fluency feels natural, with the case of walking. There’s areas of life where fluency feels motivating, with like driving—I wanna be able to switch the CD out or whatever. And there’s areas where fluency feels terrifying and hard to come by, like mathematics, sometimes. So we have a set of guests here. Our first guest will help us figure out what do we mean by fluency? And what’s the research say about what fluency is and how students develop it in mathematics? And then our other guests will help us think about what it looks like in practice in the classroom. What are some novel, new ways to work on fluency? So first up we have Val Henry, Dr. Val Henry.

Bethany Lockhart Johnson (03:32):

So we knew we needed help with the fluency definition, because when we think about it, it’s kind of big, right? And we wanted to look at what research about fluency really says. So we called on Valerie Henry. Val is a nationally board-certified teacher, taught middle school for 17 years, and since 2002 has worked with undergraduates graduates, credential candidates as a lecturer at the University of California, Irvine, one of my alma maters. So after doing her dissertation on addition and subtraction fluency in first grade, Val created a project to study ways to build addition and subtraction and multiplication and division fluency while also developing number sense in algebraic thinking. And the pilot grew and grew over the last 18 years into a powerful daily mini-lesson approach to facts fluency called FactsWise. And when we thought of fluency, the first person I thought of was Val. Welcome, Val Henry, to the Lounge! I’m so excited to have you here. Welcome.

Valerie Henry (04:36):

Thanks, Bethany. And thanks to you, Dan. It’s great to be here today.

Dan Meyer (04:41):

Great to have you; help yourself to whatever you find in the fridge. The names that people write down on those things in the bags are just recommendations. It’s potluck-style here. I’m curious, Val, if you’re, like, on an airplane, someone asks you what you do, and you say you study fluency…what is the layperson’s definition of what does it mean to be fluent in mathematics? And if you can give a brief tour through what the research says about what works and what doesn’t that would really help us orient our conversation here.

Valerie Henry (05:12):

The first thing I have to do when I talk to somebody on a plane is define the idea of fluency. And I often use an example of tying your shoelaces. Because that works with first graders as well as adults. This idea that when we first start trying to put our shoes on and get those shoelaces tied, somebody tries to, first of all, just do it for us. But then of course maybe tries to teach us the bunny-ears approach. And we struggle and struggle as little kids and eventually either the bunny-ears approach or something else starts to work for us. But we still have to pay attention to it. We have to think hard and it’s not easy. And then over time we get to the point where we basically don’t even think about it. When I tie my shoes in the morning. I’m not thinking about right-over-left and left-over-right and all of those things. I just do it. And so that’s a good, easy example of becoming fluent with something. I think what we’re talking about today though, is the basics, the adding and subtracting that we hope kids are going to have mastered maybe by second grade, and the multiplication and division facts that we wanna maybe have mastered by third, maybe fourth grade. So now what does that mean to become fluent with those basics? I have a three-part definition that seems to match up really nicely with the common core approach to fluency. Which is, first of all, we want the answers to be correct. And then second, we want the answers to be easy to know. And so what does that mean? Well, to me, it means without needing to count,

Bethany Lockhart Johnson (07:12):

You mean without having to kind of muscle through it? Or say more about you mean.

Valerie Henry (07:16):

Well, I guess what I mean is that when you watch a young child try and solve something even as simple as two plus three, they might put up two fingers and then go 3, 4, 5 with three more fingers winding up on their hand, one or the other of their hands. While they’re doing that, they don’t really have a sense of whether even their answer is right or not, quite often. Especially when you get to the larger adding and subtracting problems, you can see a lot of errors happening as they’re trying to count. And it’s taking up cognitive energy to do that counting process, especially as you get to the larger quantities. So my definition of fluency now is “getting it right without needing to do that hard work like counting.” Now, some people might say, well, we just want them to have ’em memorized. But in my research, I’ve learned that a lot of very fluid adults don’t always have every fact memorized. In fact, if you ask a room full of adults, what’s seven plus nine, you might learn that they can all get it correct quickly, quickly…but they don’t all have it memorized. And so when you ask them, “How did you get that?” Many of them will say, “Well, I just gave one from the 7 to the 9 and I know that 10 plus 6 is 16.”

Bethany Lockhart Johnson (08:53):

That’s such an important distinction. My brain literally just did that actually!

Valerie Henry (08:58):

<laugh> Right? <laugh> But you’re fluid with it, because it doesn’t take you much cognitive energy at all.

Bethany Lockhart Johnson (09:05):

Right.

Valerie Henry (09:07):

So now we have “correct without needing to put that cognitive energy,” which usually means that you’re counting. And then the third thing is “relatively quickly,” so that you’re not spending 15 seconds trying to figure it out. Even that part-whole strategy approach can be done really quickly, almost instantaneously. Or it can take a long time. So if a student can get the answer correct within, you know, three or four seconds— is I’m pretty generous—I figure that they’re pretty darn fluent with that fact. So that’s my three-part definition of these basics, fluency.

Dan Meyer (09:55):

I love the distinction between getting it correct and getting it quick. It’s possible to be quick with wrong answers. It’s possible to be like, “Those are separate components there.” And I echo Bethany’s appreciation for this third option in between knowing it instantaneously through memorization and muscling through it. But there’s like a continuum there of how much energy it took you to come up with it that all feels extremely helpful.

Valerie Henry (10:21):

And you know, one of the things that I’ve noticed is that when kids are pressured to come up with those instantaneous answers, they often default to guessing and get it wrong.

Bethany Lockhart Johnson (10:30):

Mm, yeah.

Valerie Henry (10:30):

So that’s one of the things that I’ve learned is that as we’re trying to help students develop fluency, it’s important to start with building their conceptual understanding of what it means to do, you know, 3 times 9 and what the correct answer is, maybe using manipulatives or representations of some sort. Not skip-counting! I really have found that skip-counting just perpetuates itself in many students’ minds and that they never stop skip-counting, which means they’re putting in not very much mental energy if it’s 2 times 3 but a ton of mental energy if it’s 7 times 8. Because frankly, it’s really hard to skip count by sevens. And by eights.

Bethany Lockhart Johnson (11:18):

I can get to 14 and then I’m like, wait, wait, what was next? Right? No, no, no…21! What do you feel are some misconceptions that maybe teachers, maybe parents have about fluency in math?

Valerie Henry (11:30):

I think maybe one of the first ones is that if students count or skip-count, their answers repetitively over and over and over and over, that they’re bound to memorize them. And the study that I did back in 2004, I actually had a school that had decided that they were going to do time tests with their students every day, all year. And that undoubtedly by the end of the year, those students would be fluent.

Bethany Lockhart Johnson (12:06):

And to clarify by time test, you mean like, sit down, pencil, paper, ready, go, worksheet kind of thing.

Valerie Henry (12:15):

Yes.

Bethany Lockhart Johnson (12:16):

Some of us might remember quite vividly.

Valerie Henry (12:18):

<laugh> Very vividly. And you know, you have to get it done within a certain amount of time. So they made it fun for the students. Apparently the students enjoyed it. I was a little leery about that, but in the end, when I went and checked on the students and I did one-on-one assessments with half of the students in every class that were randomly selected so that I could get a sense of where they were with their fluency—and these were first graders—they basically had nothing memorized. They were simply counting as fast as they possibly could. And, you know, mostly getting the right answers. But they had not memorized. So that’s one of the myths, I think, is that repetitive practice of counting gets you to memorization.

Bethany Lockhart Johnson (13:10):

If I put it in front of you enough times, you’ll become fluent.

Valerie Henry (13:14):

Right, right. Now these students didn’t really get any instruction, any help learning these. They just simply tested over and over and over. So that’s another thing that I think is a misconception. It’s that if we test students, but don’t really teach them fluency, then they’re going to become fluent. If we just test them every Friday or that kind of thing. And that they’ll learn them at home. But really what that means is a few lucky kids who have parents who have the time and the energy and the background to know how to help will take that job on at home. Not that many students are really that fortunate.

Dan Meyer (14:01):

It’s almost like the traditional approach, or the approach you’re describing, confuses process and product. It says, “Well, the product is that eventually fluent students will be able to do something like this, see these problems and answer them, answer them quickly,” and says, “Well, that must be the process then as well; let’s give them that products a whole lot.” But as I hear you describe fluency with bunny ears on shoelaces, there’s these images and approaches and techniques that require a very active teacher presence to support the development of it. That’s just kind of interesting to me.

Valerie Henry (14:35):

My initial project, the pilot project that I tried, was to simply ask teachers to follow five key principles. And the first one was to do something in the classroom every day for—I told them, even if you’ve only got five or 10 minutes, work on fluency for five or 10 minutes a day, and let’s see what happens. So that was one key element was just to teach it and to give students opportunities to get what the research calls for when you’re trying to memorize, which is actually immediate feedback. When I talk about immediate feedback with my student teachers, I say, “I’m talking about within one or two seconds of trying a problem, and then sort of immediately knowing, getting feedback of whether you got the answer right or not so that your brain can kind of gain that confidence. ‘Oh, not only did I come up with an answer, but somebody’s telling me it’s the correct answer.’”

Dan Meyer (15:38):

There’s a lot of apps now in the digital world that offer students questions about arithmetic or other kinds of mathematical concepts and give immediate feedback of a sort: the feedback of “You’re right; you’re wrong” sort. Is that effective fluency development, in your view?

Valerie Henry (15:57):

I haven’t heard and I haven’t seen them being super-effective. The ways I think about this are “Immediate feedback isn’t the only thing we need.” Probably one of the biggest things that we need is for students to develop strategies. And this is one of the other things I’ve learned from international research, from countries that do have students who become very fluent very early, is that they don’t shoot straight for memorization, but they go through this process of taking students from doing some counting and then quickly moving them to trying to use logic. So, “Hey, you really are confident that 2 + 2 is 4; so now let’s use that to think about 2 + 3.” Actually, as an algebra teacher, I would much rather have students that have a combination of memorization and these strategies, than students who’ve only memorized. Isn’t that interesting that my most successful algebra students were good strategy thinkers. Not just good memorizers.

Bethany Lockhart Johnson (17:09):

So you mentioned there were five that kind of helped root this idea in like, “What can teachers do? What is the best thing that teachers can do to support with fact fluency?” So, everyday was key.

Valerie Henry (17:22):

Then the next principle that I really focus on is switching immediately to the connected subtractions so that students—

Bethany Lockhart Johnson (17:33):

Not waiting until you’ve gotten all the way through addition. But making “Ooh!”

Valerie Henry (17:38):

Totally. And I didn’t do that the first year. And when we looked at the results of the assessments at the end of the year, we realized that our students were so much weaker in subtraction than addition. So the following pilot year, we tried this other approach of doing subtraction right after the students had developed some fluency with that small chunk of addition. And we got such better subtraction results.

Bethany Lockhart Johnson (18:11):

What are the other principles?

Valerie Henry (18:13):

The biggest one is to use these strategies. So the strategies makes the third. And then the fourth I would say is to go from concrete to representational to abstract.

Bethany Lockhart Johnson (18:27):

Don’t put away those manipulatives. Don’t put away those tools.

Valerie Henry (18:31):

Oh, so important to come back to them for multiplication and division. And my fifth principle is to wait on assessment. To use it as true assessment, but not race to start testing before students have had a chance to go through this three-phase process. Which is conceptual understanding with manipulatives; building strategies, usually with representations; and then working on building some speed until it’s just that natural fluency.

Bethany Lockhart Johnson (19:07):

I wanna say thank you so much for offering your really learned perspective, because you have not only done the research, but seen it in action and seen how shifting our notions of fluency and what fluency can be and what a powerful foundation it can be for all mathematicians. Really, that shift is so powerful. And I appreciate you sharing it with our listeners and with us. So we’re so excited that we got to talk with you today, Val—

Dan Meyer (19:35):

Thank you, Dr. Henry.

Valerie Henry (19:37):

You’re welcome!

Dan Meyer (19:41):

With us now we have Graham Fletcher and Tracy Zager, a couple of people who understand fluency at a very deep and classroom level. I wanna introduce them and get their perspective on what we’re trying to solve here with fluency. So Graham Fletcher has served in education in a lot of different roles: as a classroom teacher, math coach, math specialist, and he’s continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary math. He’s the author, along with Tracy, of Building Fact Fluency, a fluency kit we’ll talk about, and openly shares so much of his wisdom and resources at gfletchy.com. Tracy Johnson Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of this toolkit, Building Fact Fluency, and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books for teachers at Stenhouse Publishers, including, yours truly. Thank you for all that insight, Tracy, and support on the book.

Bethany Lockhart Johnson (20:49):

Dan and I were talking at the beginning of the episode about things we feel like, “Hey, I’m fluent in that. I’m fluent in that.”

Dan Meyer (20:55):

Just very curious: What’s something you would like to get fluent in outside of the world of mathematics, let’s say?

Tracy Zager (21:00):

I’ll say understanding the teenage brain, as the parent of a 13-year-old and 15-year-old. That’s the main thing I’m working on becoming fluent in!

Bethany Lockhart Johnson (21:10):

Ooh!

Dan Meyer (21:13):

A language fluency, perhaps. All right, Graham. How about you?

Graham Fletcher (21:16):

For me typing, it’s always been an Achilles heel of mine. So voice-to-text has been my friend. But it’s also been my nemesis in much of my texting here and working virtually over the last couple years. So yeah, typing.

Dan Meyer (21:33):

Do you folks have some way of helping us understand the difference in how fluency is handled by instructors and by learners?

Tracy Zager (21:40):

I would say that the lay meaning of fluency is definitely a little different than what we mean in the math education realm. When we’re talking about math fact fluency, which is just one type of fluency. So you gotta think about procedural fluency and computational fluency; there are lots of types of fluency in math. And Graham and I had the luxury of really focusing in specifically on math fact fluency. We’re looking at kind of a subset of the procedural fluency. So the words you hear in all the citations are accurate, efficient, and flexible. There’s this combination of kids get the right answer in a reasonable amount of time and with a reasonable amount of work and they can match their strategy or their approach to the situation. That’s where that flexibility comes in. And there’s like lots more I wanna say about that about sort of…I think one issue that comes up around fluency is that people are in a little bit of a rush. So they tend to think of the fluency as this automaticity or recall of known facts without having to think about it. And that is part of the end goal, but that’s not the journey to fluency. So this is one of the things that Graham and I thought about a lot was the path to fluency. The goal here it’s that student in middle school who’s learning something new doesn’t have to expend any effort to gather that fact. And they might do it because they’ve done it so many different ways that they’ve got it, and now they just know it, or they might be like my friend who’s a mathematician who still, if you say, “Six times 8,” she thinks in her head, “Twelve, 24, 48…” and she does this double-double-double associative property strategy. And it’s so efficient, you would never know. And that’s totally great. That’s fine. That’s not slowing her down. That’s not providing a drag in the middle of a more complex problem or new learning. So we’re really focused on having elementary school students be able to enter the middle and high school standards without having that pull out of the new thinking.

Graham Fletcher (23:53):

And as I think about that, I think about how so many students will memorize their facts, but then they haven’t memorized them with understanding. So that when they move into middle school and they move into high school, it’s almost like new knowledge and new understanding that’s applied from a stand-alone skill.

Bethany Lockhart Johnson (24:10):

So something that felt really unique to me, Graham, as I was diving into the toolkit, is your use of images, Tracy, Graham, is the way that you use images to help students notice and wonder to start making sense of these quantities and the decomposition of numbers using images. Can you talk a little bit about how images played a part in the way that you think about this building a fact fluency?

Graham Fletcher (24:41):

What I realized is so many times when we approach math with just naked numbers with so many of our elementary students, the numbers aren’t visible. The quantities. They can’t see them; they can’t move them. They’re just those squiggly figures that we were talking about earlier on. So how is it that we make the quantities visible, to where students feel as if they can grab an apple and move it around? Because a lot of times we start with the naked numbers and then if kids don’t get the naked numbers, then we kind of backfill it. But what would happen if we start with the images? And then from there, these rich, flourishing mathematical conversations develop from the images. And I think that was the premise and the goal of the toolkit.

Tracy Zager (25:22):

When you look at how fact fluency has traditionally been taught, it’s all naked numbers. And sometimes we wrote ’em sideways. Like, that’s it. That was our variety of task type. Right? Sometimes it’s vertical; sometimes it’s horizontal. And that was it. And I’ve just known way too many kids who couldn’t find a hook to hang their hat on with that. It didn’t connect to anything. And so part of why I knew Graham was the perfect person for this project was his strength in multimedia photography, art, video. And so we started from this idea of contexts that for each lesson string in the toolkit, there’s some kind of context. An everyday object, arranged in some kind of a way that reveals mathematical structure and invites students to notice the properties. So we start with images of everyday objects: tennis balls, paint pots…um, help me out; here are a million of them. Crayons—

Bethany Lockhart Johnson (26:18):

Crayons, markers.

Tracy Zager (26:18):

Shoes, right? Sushi, origami paper, all kinds of things in the different toolkits. So there’s a series of images or a three-act task or both around those everyday objects, and then story problems grounded in that context. And then there are images with mathematical tools that bring out different ideas, but relate in some way to the image talks. And we do all of that before we get to the naked number talk. Which we do, and by the time you get to the number talk, it’s pretty quick, ’cause they’ve been reasoning about cups of lemonade. And now when you give them the actual numerals, they’re all over it.

Bethany Lockhart Johnson (27:03):

I have to say too, as somebody who—particularly in middle school—navigated math anxiety, we recently talked with Allison Hintz and Anthony Smith about their amazing book Mathematizing Children’s Literature.

Tracy Zager (27:14):

Yay!

Bethany Lockhart Johnson (27:14):

And I was explaining, like, if I sat down at the beginning of a math class and my teacher opened a picture book and said, “We’re gonna start here,” I felt my whole body relax. And if we start with this image, if we start with just looking at an image and making sense of an image, I feel like that could be such a powerful touchstone for all the work you do from there.

Tracy Zager (27:41):

That’s core. That’s a core design principle, is that invitational access. There are no barriers to entry. There’s nothing to decode. There’s nothing formal. We’ve been learning from Dan for years about this, right? Of starting with the informal and then eventually layering in the formal. I was in a class in Maine where they were doing an image talk and it’s these boxes of pencils. It’s a stack of boxes of pencils and they’re open and you can see there are 10 pencils in each box. And so there are five boxes of pencils each with 10 pencils in it. And then the next image is 10 boxes of pencils and each box is half full. So now it’s 10 boxes each with five. And the kids are talking and talking and then the third image, I think there are seven boxes each with 10 pencils in it. And she said, “What do you think the next picture’s gonna be?” And this girl said, “You just never know with these people!” <laugh> I dunno!”

Bethany Lockhart Johnson (28:37):

That’s kinda true. Knowing you both, it’s kinda true.

Tracy Zager (28:42):

Like if it’s seven boxes with 10 in it, one kid said, I think it’s gonna be 14 boxes of five. And other kids are like, I think it’s gonna be 10 boxes with seven. And they start talking about which of those there are and the relationships between—

Bethany Lockhart Johnson (28:58):

But they’re making sense of numbers!

Tracy Zager (28:59):

Totally. So all the kids felt invited. They can offer something up. They’re noticing and wondering about that image. They’re talking about it in whatever informal language or home language that they speak. And that was core to us. That was a huge priority, because honestly, one of the motivations to talk about fluency is that it’s always been this gatekeeper. It has served to keep kids out of meaningful math. Particularly kids from marginalized or historically excluded communities. So they’re back at the round table, doing Mad Minutes, while the more advantaged kids are getting to do rich problem solving. And so, we thought, what if we could teach fact fluency through rich problem solving that everybody could access? That was like square one for us.

Bethany Lockhart Johnson (29:45):

That’s huge.

Dan Meyer (29:46):

That’s great to hear. What’s been helpful for me is to understand that students who are automatic, that’s just kind of what’s on the surface of things. And that below that might be some really robust kind of foundation or scaffolding that bleeds to a larger building being built, or it might be just really rickety and not offer a sturdy place to build farther up. It’s been really exciting to hear that. I wonder if you’d comment for a moment about, in the digital age and—I’m at Desmos and our sponsors are Amplify and we all work in the digital world quite a bit. There are a lot of what report to be solutions to the fluency issue, to developing fluency in the digital world. Just lots and lots of them. Some that are quite well used, others that are just like X, Y, or Z app on the market. You can find something. Do you have perspectives on these kinds of digital fluency building apps? Like, what about them works or doesn’t work? Let us know. Graham, how about you? And then Tracy, I’d love to hear your thoughts too.

Graham Fletcher (30:47):

Yeah, I think that’s a great question, ’cause there’s a lot of shiny bells and whistles out there right now that can really excite a lot of teachers. But I always come back to what works for me as a classroom teacher is probably gonna work in a digital world as well. So what are the things that I love and honor most about being in front of students, and how can I capture that in that virtual world? I think one of the things that really helps students make connections is coherence. I think coherence, especially when you leave students for—you don’t get to talk with them after the lesson is done—so I think about how we can purposefully sequence things through a day-to-day basis. I think coherence is something that gets really lost when we talk about fluency, especially with whether it be digital or whether it be print, because what ends up happening is we say, “OK, we have all these strategies we need to teach,” and it becomes a checklist. So how is it that we can just provide students the opportunity to play around in a space, whether it be digital or in person, but in a meaningful way that allows them the time and the space and that area to breathe and think, but be coherent. And connecting those lessons along the way. And I think coherence is one thing that a lot of the times it’s harder to—when we’re in the weeds, it’s so hard and difficult to zoom back out and say, “Do all these lessons connect? How do they intentionally connect? And how do they purposefully connect?” And without coherence, everything’s kind of broken down into that granular level. So when looking at—I think about Desmos and I think about the Toolkit and I think about how Tracy and I talked a lot about, “Well, this, does it connect with the context problem, does it connect with the image talk, or the lessons? Like, how does it all connect and how are we providing students an opportunity to make connections between the day-to-day instruction and lessons that we tackle?”

Tracy Zager (32:44):

I’m reminded of a conversation that Dan, you and I had a long time ago, in Portland, Maine, in a bar. I’ll just be honest. <laugh> And we were talking about how, in the earlier days of Desmos, you were stressed out by what you saw, which was kids one-on-one, on a device, in a silent room. And you were like, no, this is not it. This is not what technology is here to serve. We can do so many things better using technology appropriately, but we can’t lose talk and we can’t lose relationships and we can’t lose formative assessment and teachers listening to kids and kids listening to each other and helping each other understand their thinking. Right? So when I think about the tech that’s out there for fact fluency, most of it is gonna violate all rules I have around time testing. So that a whole bunch of it, I would just toss on that premise. They’re really no different than flashcards. It’s just flashcards set in junkyard heaps. Or, you know, underground caverns. Or with a volcano or whatever. It’s the same thing. There are some lovely visuals—I’m thinking of Berkeley Everett’s Math Flips. Those are really pretty. Mathigon has some really nice stuff that’s digital. And I think that those resources invite you to kind of ponder and notice things and talk about them. All the tools that we design in the toolkit are designed to get people talking to each other, and give teachers opportunities to pull alongside kids and listen in and understand where they are. For example, our games, we didn’t design the games to be played digitally, even though you could, and people did during COVID, because we want kids on the rug, next to each other, on their knees; I’ve seen kids like across tables. I was in a school recently where a kid was like, “I hope you believe in God, ’cause you’re going…!” You know what I mean? <laugh>. Like they’re all pumped up.

Bethany Lockhart Johnson (34:41):

They’re invested!

Tracy Zager (34:45):

They’re psyching each other up and down and they’re interacting and it’s social and the teacher’s walking around and she’s listening to the games. And they don’t actually need any bells and whistles. They need dice and they need counters and they need this game that is actually a game. In all of our conversations, games have to actually be games. Games cannot be “roll and record.” Games have to involve strategy. They have to be fun. So in designing those games, we didn’t feel like it brought any advantage to make that a digital platform. But things that did bring advantages digitally, like the ability to project these beautiful images or to use short video in the classroom, that really was a value-add that enabled us to do something different in math class than we had done before, and to get kids talking in a different way than they ever had before. When I think about fluency, historically, if you say like, “OK, it’s time to practice our math facts,” you hear a lot of groans. And when I see a Building Fact Fluency classroom and I say, “OK, it’s BFF time!” There’s like a “YEAAAAHHH!” You know? And so that’s what we’re after.

Graham Fletcher (35:47):

It’s all about kids, really, for us. And I think at the heart of it, we made all the decisions with teachers and kids at the forefront of it.

Tracy Zager (35:55):

I know of high schoolers who are newcomers, who have experienced very little formal education, and speak in other languages, are using it as high schoolers, because it involves language and math and all the deep work in the properties and it’s accessible, but it’s also not at all condescending or patronizing. Like we designed it to be appropriate for older kids. So that’s just something that I think we’re both really proud of. One thing we thought a lot about, especially in the multiplication-division kit is how a classroom teacher could use it and a coordinating educator in EL, Title, special education, intervention could also use it because there’s so much in it, that students could get to be experts, if they got extra time in it, using something that’s related and would give them additional practice. So they could play a game a little bit earlier than the rest of the classes. And they could come in already knowing about that game, or they could do a related task. We have all these optional tasks that no classroom teacher would ever have time to teach it all. So the special educator could use it and have kids doing a Same and Different or a True/False, or some of the optional games. And then the work in both special education and general education could connect.

Dan Meyer (37:20):

I just wanna say that this is an area that for so many students, as you’ve said, Tracy, it presents a barrier for their inclusion in mathematics. It’s a very emotionally fraught area of mathematics. And we really appreciate the wisdom you brought here. And just the care you’ve brought to the product itself. Your knowledge of teaching, knowledge of math, and yeah, especially a love for students feels like it’s really infused throughout Building Fact Fluency. If our listeners want to know more outside of this podcast, outside of the product itself, where can they find your words, your voice? Where you folks at these days? Tell ’em, Graham would you?

Graham Fletcher (37:57):

You can find us at Stenhouse, Building Fact Fluency. And then Tracy and I, currently playing around, sharing ideas a lot on Twitter, under the hashtag #BuildingFactFluency. That’s kind of where we can all come together and share ideas. And then also on the Facebook community, where there’s lots of teachers sharing ideas.

Bethany Lockhart Johnson (38:19):

If you were to ask our listeners like, “Hey, if you wanna keep thinking about this, here’s something you could try or here’s something you could go do,” what could be a challenge that we could share that could help us continue this conversation?

Graham Fletcher (38:35):

Online you can actually download a full lesson string. And a lesson string is a series of activities and resources that are purposefully connected. You can pick one or two of those from the Stenhouse web site, Building Fact Fluency. You can try the game. You can try one of those strategy-based games. You can try an image talk and just see how it goes. And just share and reflect back, whether on Twitter or on Facebook. But it’s kind of there, if you wanna give it a whirl. And as Tracy was sharing, even if you’re a middle-school teacher or a high-school teacher, we really tried to think about those middle-school and high-school students keeping it grade level-agnostic. Just so every student has those opportunities for those mathematical conversations. So download a lesson string and give it a whirl, and we’d love to hear how it goes.

Dan Meyer (39:25):

Bethany and I will be working the same challenge with people in our life.

Bethany Lockhart Johnson (39:29):

Yes.

Dan Meyer (39:29):

Enjoying some fact fluency with people in our homes, perhaps. We’ll see. And we’ll be sharing the results in the Math Teacher Lounge Facebook group. Graham and Tracy, thanks so much for being here. It was such a treat to chat with you both.

Bethany Lockhart Johnson (39:42):

I love learning with you and just helping to shift this idea of fluency into something that can be accessible and powerful and positive.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Valerie Henry says about math

“A lot of very fluent adults don’t always have every fact memorized. ”

– Val Henry

Meet the guests

Valerie Henry has been a math educator since 1986. She taught middle school math for 17 years and has worked as a lecturer at University of California Irvine since 2002. After doing her 2004 dissertation research on addition/subtraction fluency in first grade, Valerie created FactsWise, a daily mini-lesson approach that simultaneously develops  fluency,  number sense, and algebraic thinking. Additionally, she has provided curriculum and math professional development for K-12 teachers throughout her career, working with individual schools, districts, county offices of education, Illustrative Mathematics, the SBAC Digital Library, and the UCI Math Project.

Graham Fletcher has served in education as a classroom teacher, a math coach, and currently as a math specialist. He is continually seeking new and innovative ways to support students and teachers in their development of conceptual understanding in elementary mathematics. He is the author of Building Fact Fluency and openly shares many of his resources at gfletchy.com. Follow him on Twitter.

Tracy Johnston Zager is a district math coach who loves to get teachers hooked on listening to kids’ mathematical ideas. She is a co-author of the Building Fact Fluency toolkits and the author of Becoming the Math Teacher You Wish You’d Had: Ideas and Strategies from Vibrant Classrooms. Tracy also edits professional books by teachers, for teachers at Stenhouse Publishers. Follow her on Facebook.

A collage of three headshots: an older woman with glasses, a man with a beard in a blue shirt, and a woman with dark hair smiling in front of greenery.
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About Math Teacher Lounge: The podcast

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

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

Desmos Math 6–A1 correlations with Carnegie Math Texas

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Eureka Math® crosswalk to Amplify Desmos Math free lessons

Grade 6

Module 1: Ratios and Unit Rates

Eureka MathAmplify Classroom
Topic A Representing and Reasoning About Ratios 
Lesson 3: Equivalent Ratios
Lesson 4: Equivalent Ratios
Unit 2
Lesson 4: Fruit Lab
Topic C Unit Rates 
Lesson 16: From Ratio to RatesUnit 3
Lesson 6: Soft Serve
Lesson 18: Finding a Rate by Dividing Two QuantitiesUnit 3
Lesson 6: Soft Serve
Lesson 24: Percent and Rates per 100Unit 3
Lesson 9: Lucky Duckies

Module 2: Arithmetic Operations Including Division of Fractions

Topic A Dividing Fractions by Fractions
Lesson 2: Interpreting Division of a Whole Number by a Fraction —Visual Models.Unit 4
Lesson 3: Flour Planner
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Unit 4
Lesson 6: Fill the Gap
Lesson 8: Dividing Fractions and Mixed NumbersUnit 4
Lesson 6: Fill the Gap
Topic B Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
Lesson 9: Sums and Differences of DecimalsUnit 5
Lesson 2: Decimal Diagrams and Algorithms

Module 3: Rational Numbers

Topic B Order and Absolute Value
Lesson 7: Ordering Integers and Other Rational Numbers
Lesson 8: Ordering Integers and Other Rational Numbers
Lesson 9: Comparing Integers and Other Rational Numbers
Unit 7Lesson 4: Order in the Class

Module 4: Expressions and Equations

Topic D Expanding, Factoring, and Distributing Expressions 
Lesson 9: The Relationship of Addition and SubtractionUnit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Lesson 10: Writing and Expanding Multiplication Expressions
Lesson 11: Factoring Expressions
Lesson 12: Distributing Expressions
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic F Writing and Evaluating Expressions and Formulas 
Lesson 18: Writing and Evaluating Expressions—Addition and Subtraction
Lesson 19: Substituting to Evaluate Addition and Subtraction Expressions
Lesson 20: Writing and Evaluating Expressions—Multiplication and Division
Lesson 21: Writing and Evaluating Expressions—Multiplication and Addition
Unit 6
Lesson 8: Products and Sums
Take Away (coming soon!)
Topic G Solving Equations 
Lesson 23: True and False Number Sentences
Lesson 24: True and False Number Sentences
Unit 6
Lesson 1: Weight for It
Lesson 25: Finding Solutions to Make Equations TrueUnit 6
Lesson 1: Weight for It
Lesson 26: One-Step Equations—Addition and SubtractionUnit 6
Lesson 1: Weight for It
Topic H Applications of Equations 
Lesson 33: From Equations to Inequalities
Lesson 34: Writing and Graphing Inequalities in Real-World Problems
Unit 7
Lesson 7: Tunnel Travels

Module 5: Area, Surface Area, and Volume Problems

Topic A: Area of Triangles, Quadrilaterals, and Polygons
Lesson 1: The Area of Parallelograms Through Rectangle FactsUnit 1
Lesson 3: Exploring Parallelograms
Exploring Parallelograms, Part 2
Topic D Nets and Surface Area 
Lesson 18: Determining Surface Area of Three-Dimensional FiguresUnit 1
Lesson 10: Renata’s Stickers

Module 6: Statistics

Topic A Understanding Distributions 
Lesson 2: Displaying a Data Distribution
Lesson 3: Creating a Dot Plot
Unit 8
Lesson 3: Minimum Wage
Lesson 4: Creating a Histogram
Lesson 5: Describing a Distribution Displayed in a Histogram
Unit 8
Lesson 5: The Plot Thickens
Topic C Summarizing a Distribution That Is Skewed Using the Median and the Interquartile Range 
Lesson 12: Describing the Center of a Distribution Using the MedianUnit 8
Lesson 11: Toy Cars
Topic D Summarizing and Describing Distributions 
Lesson 18: Connecting Graphical Representations and Numerical SummariesUnit 8
Lesson 5: The Plot Thickens
Lesson 3: Creating a Dot PlotUnit 8
Lesson 3: Minimum Wage

Grade 7

Module 1: Ratios and Proportional Relationships

Eureka MathAmplify Classroom
Topic A Proportional Relationships 
Lesson 1: An Experience in Relationships as Measuring RateUnit 2
Lesson 1: Paint
 
Unit 4
Lesson 1: Mosaics
Lesson 5: Identifying Proportional and Non-Proportional Relationships in Graphs
Lesson 6: Identifying Proportional and Non-Proportional Relationships in Graphs
Unit 2
Lesson 8: Dino Pops
Topic B Unit Rate and the Constant of Proportionality 
Lesson 8: Representing Proportional Relationships with Equations
Lesson 9: Representing Proportional Relationships with Equations
Unit 2
Lesson 6: Two and Two
Lesson 10: Interpreting Graphs of Proportional RelationshipsUnit 2
Lesson 8: Dino Pops
Topic C Ratios and Rates Involving Fractions 
Lesson 11: Ratios of Fractions and Their Unit Rates
Lesson 12: Ratios of Fractions and Their Unit Rates
Unit 2
Lesson 6: Two and Two
Lesson 15: Equations of Graphs of Proportional Relationships Involving FractionsUnit 2
Lesson 8: Dino Pops
Topic D Ratios of Scale Drawings 
Lesson 16: Relating Scale Drawings to Ratios and RatesUnit 1
Lesson 1: Scaling Machines
Lesson 18: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Lesson 19: Computing Actual Areas from a Scale DrawingUnit 1
Lesson 7: Will It Fit?

Module 2: Rational Numbers

Topic A Addition and Subtraction of Integers and Rational Numbers 
Lesson 1: Opposite Quantities Combine to Make ZeroUnit 5
Lesson 1: Floats and Anchors
Lesson 2: Using the Number Line to Model the Addition of Integers
Lesson 3: Understanding Addition of Integers
Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Unit 5
Lesson 4: Draw Your Own
Lesson 10: Integer Puzzles
Lesson 7: Addition and Subtraction of Rational NumbersUnit 5
Lesson 4: Draw Your Own
Lesson 10; Integer Puzzles
Topic B Multiplication and Division of Integers and Rational Numbers 
Lesson 10: Understanding Multiplication of Integers
Lesson 11: Develop Rules for Multiplying Signed Numbers
Unit 5
Lesson 10: Integer Puzzles
Lesson 15: Multiplication and Division of Rational NumbersUnit 5
Lesson 10: Integer Puzzles

Module 3: Expressions and Equations

Topic A Use Properties of Operations to Generate Equivalent Expressions 
Lesson 3: Writing Products as Sums and Sums as Products
Lesson 4: Writing Products as Sums and Sums as Products
Unit 6
Lesson 10: Collect the Squares
Topic B Solve Problems Using Expressions, Equations, and Inequalities 
Lesson 8: Using If-Then Moves in Solving Equations
Lesson 9: Using If-Then Moves in Solving Equations
Unit 6Lesson 10: Collect the Squares
Lesson 10: Angle Problems and Solving EquationsUnit 7
Lesson 2: Friendly Angles
Lesson 4: Missing Measures
Lesson 12: Properties of Inequalities
Lesson 13: Inequalities
Lesson 14: Solving Inequalities
Unit 6
Lesson 16: Shira the Sheep
Topic C Use Equations and Inequalities to Solve Geometry Problems 
Lesson 16: The Most Famous Ratio of AllUnit 3
Lesson 3: Measuring Around
Lesson 17: The Area of a CircleUnit 3
Lesson 9: Area Challenges
Lesson 18: More Problems on Area and CircumferenceUnit 3
Lesson 9: Area Challenges

Module 4: Percent and Proportional Relationships

Topic A Finding the Whole 
Lesson 1: PercentUnit 4
Lesson 1: Mosaics
Lesson 2: Part of a Whole as a PercentUnit 4
Lesson 1: Mosaics
Lesson 3: Comparing Quantities with PercentUnit 4
Lesson 1: Mosaics
Lesson 4: Percent Increase and DecreaseUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 5: Finding One Hundred Percent Given Another Percent 
Lesson 6: Fluency with PercentsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Topic B Percent Problems Including More Than One Whole 
Lesson 7: Markup and Markdown ProblemsUnit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 8: Percent Error Problems
Lesson 9: Problem Solving When the Percent Changes
Unit 4
Lesson 5: Percent MachinesLesson 12: Posing Percent Problems(coming soon!)
Lesson 10: Simple Interest 
Lesson 11: Tax, Commissions, Fees, and Other Real-World Percent ApplicationsUnit 4
Lesson 12: Posing Percent Problems
(coming soon!)
Topic C Scale Drawings 
Lesson 13: Changing ScalesUnit 1
Lesson 1: Scaling Machines
Lesson 7: Will It Fit?
Lesson 14: Computing Actual Lengths from a Scale DrawingUnit 1
Lesson 7: Will It Fit?
Topic D Population, Mixture, and Counting Problems Involving Percents 
Lesson 16: Population ProblemsUnit 8
Lesson 10: Crab Island

Module 5: Statistics and Probability

Topic A Calculating and Interpreting Probabilities 
Lesson 1: Chance ExperimentsUnit 8
Lesson 1: How Likely?
Lesson 2: Prob-bear-bilities
Topic C Random Sampling and Estimating Population Characteristics 
Lesson 13: Populations, Samples, and Generalizing from a Sample to a PopulationUnit 8
Lesson 10: Crab Island
Lesson 14: Selecting a Sample
Lesson 15: Random Sampling
Lesson 16: Methods for Selecting a Random Sample
Unit 8
Lesson 10: Crab Island
Topic D Comparing Populations 
Lesson 22: Using Sample Data to Compare the Means of Two or More Populations
Lesson 23: Using Sample Data to Compare the Means of Two or More Populations
Unit 8
Lesson 10: Crab Island

Module 6: Geometry

Topic A Unknown Angles 
Lesson 1: Complementary and Supplementary AnglesUnit 7
Lesson 2: Friendly Angles
Lesson 2: Solving for Unknown Angles Using Equations
Lesson 3: Solving for Unknown Angles Using Equations
Lesson 4: Solving for Unknown Angles Using Equations
Unit 7
Lesson 4: Missing Measures
Topic B Constructing Triangles 
Lesson 8: Drawing TrianglesUnit 7
Lesson 5: Can You Build It?
Lesson 11: Conditions on Measurements That Determine a TriangleUnit 7
Lesson 5: Can You Build It?
Topic D Problems Involving Area and Surface Area 
Lesson 22: Area Problems with Circular RegionsUnit 3
Lesson 9: Area Challenges

Grade 8

Module 1: Integer Exponents and Scientific Notation

Eureka MathAmplify Classroom
Topic A Exponential Notation and Properties of Integer Exponents 
Lesson 1: Exponential NotationUnit 7 
Lesson 1: Circles
Lesson 2: Multiplication of Numbers in Exponential Form
Lesson 3: Numbers in Exponential Form Raised to a Power
Unit 7 
Lesson 3: Power Pairs
Topic B Magnitude and Scientific Notation 
Lesson 9: Scientific Notation
Lesson 10: Operations with Numbers in Scientific Notation
Unit 7 
Lesson 9: Specific and Scientific
Lesson 11: Balance the Scale

Module 2: The Concept of Congruence

Topic A Definitions and Properties of the Basic Rigid Motions 
Lesson 1: Why Move Things Around?
Lesson 2: Definition of Translation and Three Basic Properties
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 3: Translating LinesUnit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Definition of Reflection and Basic Properties
Lesson 5: Definition of Rotation and Basic Properties
Lesson 6: Rotations of 180 Degrees
Unit 1
Lesson 1: Transformers
Lesson 2: Spinning, Flipping, Sliding
Lesson 4: Moving Day
Topic B Sequencing the Basic Rigid Motions 
Lesson 9: Sequencing Rotations
Lesson 10: Sequences of Rigid Motions
Unit 1
Lesson 13: Tessellate
Lesson 14: More on the Angles of a TriangleUnit 1 
Lesson 12: Puzzling It Out

Module 3: Similarity

Topic A Dilation 
Lesson 1: What Lies Behind “Same Shape”?Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 2: Properties of Dilations
Lesson 3: Examples of Dilations
Unit 2
Lesson 1: Sketchy Dilations
Lesson 2: Dilation Mini Golf
Lesson 4: Fundamental Theorem of Similarity
Lesson 5: First Consequences of FTS
Unit 2
Lesson 6: Social Scavenger Hunt
Topic B Similar Figures 
Lesson 8: Similarity
Lesson 9: Basic Properties of Similarity
Unit 2
Lesson 6: Social Scavenger Hunt
Topic C The Pythagorean Theorem 
Lesson 13: Proof of the Pythagorean TheoremUnit 8
Lesson 8: Triangle-Tracing Turtle

Module 4: Linear Equations

Topic A Writing and Solving Linear Equations 
Lesson 4: Solving a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Lesson 5: Writing and Solving Linear EquationsUnit 4
Lesson 5: Equation Roundtable
Lesson 6: Solutions of a Linear EquationUnit 4
Lesson 5: Equation Roundtable
Topic B Linear Equations in Two Variables and Their GraphsUnit 3
Lesson 4: Flags
Lesson 10: A Critical Look at Proportional RelationshipsUnit 3
Lesson 1: Turtle Time TrialsLesson 4: Flags
Lesson 11: Constant RateUnit 3
Lesson 4: Flags
Lesson 13: The Graph of a Linear Equation in Two VariablesUnit 3 
Lesson 4: Flags
Topic C Slope and Equations of Lines 
Lesson 15: The Slope of a Non-Vertical LineUnit 3
Lesson 4: Flags
Lesson 18: There Is Only One Line Passing Through a Given Point with a Given SlopeUnit 3
Lesson 4: Flags
Lesson 19: The Graph of a Linear Equation in Two Variables Is a LineUnit 3
Lesson 4: Flags
Lesson 20: Every Line Is a Graph of a Linear EquationUnit 3
Lesson 4: Flags
Lesson 22: Constant Rates RevisitedUnit 3
Lesson 1: Turtle Time Trials
Topic D Systems of Linear Equations and Their Solutions 
Lesson 25: Geometric Interpretation of the Solutions of a Linear SystemUnit 4  
Lesson 11: Make Them Balance
Lesson 12: Line Zapper

Module 5: Examples of Functions from Geometry

Topic A Functions 
Lesson 1: The Concept of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 2: Formal Definition of a FunctionUnit 5
Lesson 1: Turtle Crossing
Lesson 2: Guess My Rule
Lesson 3: Linear Functions and ProportionalityUnit 3
Lesson 1: Turtle Time Trials
Lesson 5: Graphs of Functions and EquationsUnit 5
Lesson 5: The Tortoise and the Hare
Lesson 6: Graphs of Linear Functions and Rate of ChangeUnit 3
Lesson 4: Flags
Lesson 7: Comparing Linear Functions and GraphsUnit 5
Lesson 5: The Tortoise and the Hare
Topic B Volume 
Lesson 10: Volumes of Familiar Solids—Cones and CylindersUnit 5
Lesson 11: Cylinders

Module 6: Linear Functions

Topic A Linear Functions 
Lesson 2: Interpreting Rate of Change and Initial ValueUnit 3
Lesson 1: Turtle Time Trials
Lesson 4: Increasing and Decreasing Functions
Lesson 5: Increasing and Decreasing Functions
Unit 5
Lesson 1: Turtle CrossingLesson 5: The Tortoise and the Hare
Topic B Bivariate Numerical Data 
Lesson 6: Scatter Plots
Lesson 7: Patterns in Scatter Plots
Unit 6 
Lesson 3: Robots
Lesson 8: Informally Fitting a LineUnit 6
Lesson 4: Dapper Cats
Lesson 6: Find the Fit
Lesson 10: Linear Models
Lesson 11: Using Linear Models in a Data Context
Unit 5
Lesson 5: The Tortoise and the Hare
Topic D Bivariate Categorical Data 
Lesson 14: Association Between Categorical VariablesUnit 6
Lesson 11: Finding Associations

Module 7: Introduction to Irrational Numbers Using Geometry

Topic A Square and Cube Roots 
Lesson 2: Square RootsUnit 8
Lesson 4: Root Down
Lesson 4: Simplifying Square RootsUnit 8
Lesson 4: Root Down
Topic C The Pythagorean Theorem 
Lesson 18: Applications of the Pythagorean TheoremUnit 8
Lesson 10: Taco Truck

Algebra 1

Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs

Topic A: Introduction to Functions Studied this Year—Graphing Stories

Lesson 1: Graphs of Piecewise FunctionsPumpkin Prices
Lesson 2: Graphs of Quadratic FunctionsRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns

Topic C: Solving Equations and Inequalities

Lesson 10: True and False EquationsSame Position
Lesson 11: Solution Sets for Equations and InequalitiesWorking Backwards
Solving Strategies
Shelley the Snail
Lesson 19: Rearranging FormulasSubway Seats
Various Variables
Lesson 21: Solution Sets to Inequalities with Two VariablesPizza Delivery
Lesson 22 & Lesson 23: Solution Sets to Simultaneous Equations (and Inequalities)Shape It Up
Lizard Lines
Quilts
Seeking Solutions

Module 2: Descriptive Statistics

Topic D: Numerical Data on Two Variables

Lesson 14: Modeling Relationships with a LineCity Slopes
Residual Fruit
Penguin Populations
Lesson 19: Interpreting CorrelationCorrelation Coefficient
How Hot Is It?
Behind the Headlines
City Data

Module 3: Linear and Exponential Functions

Topic A: Linear and Exponential Sequences

Lesson 3: Arithmetic and Geometric SequencesSequence Carnival
More Visual Patterns
Lesson 5: The Power of Exponential GrowthCarlos’s Fish

Topic B: Describing Variability and Comparing Distributions

Lesson 4: Summarizing Deviations from the MeanFinding Desmo
Lesson 13: Interpreting the Graph of a FunctionCraft-a-Graph
Lesson 14: Linear and Exponential Models – Comparing Growth RatesDetroit’s Population, Part 1
Detroit’s Population, Part 2

Topic D: Using Functions and Graphs to Solve Problems

Lesson 21: Comparing Linear and Exponential Models AgainPlane, Train, and Automobile
Lesson 21: Comparing Linear and Exponential Models AgainCarlos’s Fish

Module 4: Polynomial and Quadratic Expressions, Equations, and Functions

Topic A: Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles

Lesson 8: Exploring the Symmetry in Graphs of Quadratic FunctionsOn the Fence
Plenty of Parabolas
Robot Launch
Lesson 9: Graphing Quadratic Functions from Factored Form, 𝑓(𝑥)=𝑎(𝑥−𝑚)(𝑥−𝑛)Two for One
Parabola Zapper
Shooting Stars
Lesson 10: Interpreting Quadratic Functions from Graphs and TablesStomp Rockets

Topic B: Using Different Forms for Quadratic Functions

Lessons 11–12: Completing the SquareSquare Tactic
Lesson 15: Using the Quadratic FormulaStomp Rockets in Space

Topic C: Function Transformations and Modeling

Lesson 18: Graphing Cubic, Square Root, and Cube Root FunctionsSorting Relationships
Lesson 22: Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different WaysSorting Relationships

Disclaimer

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

Grade 6

Chapter 1: Use Positive Rational Numbers

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

Chapter 2: Integers and Rational Numbers

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

Chapter 3: Numeric and Algebraic Expressions

Chapter 4: Represent and Solve Equations and Inequalities

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

Chapter 5: Understand and Use Ratio and Rate

Chapter 6: Understand and Use Percent

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

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

Chapter 8: Display, Describe, and Summarize data

Grade 7

Chapter 1: Rational Number Operations

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

Chapter 2: Analyze and Use Proportional Relationships

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

Chapter 3: Analyze and Solve Percent Problems

Chapter 4: Generate Equivalent Expressions

Chapter 5: Solve Problems Using Equations and Inequalities

Chapter 6: Use Sampling to Draw Inferences About Populations

Chapter 7: Probability

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

Chapter 8: Solve Problems Involving Geometry

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

Grade 8

Chapter 1: Real Numbers

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

Chapter 2: Analyze and Solve Linear Equations

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

Chapter 3: Use Functions to Model Relationships

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

Chapter 4: Investigate Bivariate Data

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

Chapter 5: Analyze and Solve Systems of Linear Equations

Chapter 6: Congruence and Similarity

Chapter 7: Understand and Apply the Pythagorean Theorem

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

Chapter 8: Solve Problems Involving Surface Area and Volume

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

S2-04: Gamification in the K–8 classroom

Podcast episode graphic featuring guest Fabian Hofmann, titled "Gamification in the K–8 classroom," from Science Connections Season 2, Episode 4, with an illustration of a planet.

In this episode, Eric Cross sits down with his colleague and friend Fabian Hofmann to talk through gamification in the K–8 classroom. They discuss Fabian’s experience teaching outside of the United States, and the differences in classrooms outside of the country. Fabian explains the integration of game mechanisms in the classroom, standard-based grading, and shifting student thinking about learning by forming strong relationships. Fabian also shares how he created a new STEM course at his school revolving around his own passion for Star Wars. Explore more from Science Connections by visiting our main page.

DOWNLOAD TRANSCRIPT >

Fabian Hofmann (00:00):

In Mr. Hofmann’s class, I get to earn points and I get to be a Jedi. I can suspend my disbelief and I’m learning history, but at the same time, I’m traveling through the galaxy.

Eric Cross (00:13):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Fabian Hofmann. Fabian is a middle school IB educator, currently teaching seventh grade multimedia design and history at Albert Einstein Academy’s middle school here in San Diego, California. He also hosts the podcast Rebel Teacher Alliance, a podcast dedicated to encouraging and supporting teachers to rethink student engagement. Fabian’s one of the most innovative teachers that I’ve ever met. His use of technology and gamification makes learning fun and accessible for our students. And I have firsthand experience with these students because we teach on the same team and have worked alongside each other during my entire career as a teacher. In this episode, we discuss gamification of the classroom, how he approaches grading from an innovator’s mindset, and his newest STEM class, Immersive Design, where his students are working with former Disney Imagineers to completely renovate their classroom into an interactive Star Wars-themed learning environment. And now, please enjoy my conversation with my good friend and colleague, Fabian Hofmann. We’ve worked together for how many years now? How many years have you been at Einstein?

Fabian Hofmann (01:23):

Well, I started when you started, like after you were student teaching, so 2014.

Eric Cross (01:28):

OK, so it’s been a while.

Fabian Hofmann (01:30):

Yeah. And then I took two years off and I went to Hawaii. I couldn’t handle the pressure. And then I came back. So we’ve worked together for six years but known each other for eight.

Eric Cross (01:39):

What’s your origin story? We’re gonna talk about your origin story. I told you.

Fabian Hofmann (01:42):

All right, cool. Right. So when I was a little boy…no. <Laugh>

Eric Cross (01:46):

This podcast is not that long!

Fabian Hofmann (01:49):

So no, I started out, teaching in 2009. I started student teaching in Germany and was teaching history and English. Did this two-year student-teaching program there. And then, when I was done, my wife and I, she’s American, we got married and we decided to move to the States. And then I started teaching at a German cultural center called the Goethe-Institut in San Francisco. We lived in the Bay Area. And from there, after a year we moved down to San Diego; I started subbing; I worked for a year at High Tech High. I taught humanities there. And then, after that year, I ended up at Einstein teaching German because that was what was available. I didn’t want to teach German. That wasn’t like, on the top of my list. But it made sense because I had taught German in San Francisco and it kind of was like, “Well, I can do that, I guess.” And then, yeah, and then I went back to—we went to Hawaii for a couple of years and then I came back here to start teaching history. So I’ve taught like a million things essentially.

Eric Cross (02:52):

And then during that time, what’s your evolution been like in the classroom? Kind of like your view of education? And how does that play out in your day-to-day with kids?

Fabian Hofmann (02:59):

So when I started teaching here in the States, I noticed that it’s very different. Technology was much further along here than it was in Germany. So when I got here and we had like an iPad cart; I helped setting up the iPad carts. And I worked with the Chromebooks and I was like, holy, holy crap, this is so cool. Like, kids can like actually do things with this technology. And then, I mean, I love technology. I’ve had an iPad when it came out and stuff like that. And so I was like, “Oh, so how about we use this in our classroom?” And so I always moved—I moved very quickly to having students create on the iPad. And at first it was like, “Oh, we use the Apple apps and stuff.” And then I went to an ed-tech teacher summit here in San Diego and my eyes were like opened to, “Oh my God, there’s so much more than just the Apple apps.” And ever since then I was like, “OK, we’re gonna use this; we’re gonna do that.” It’s just crazy stuff that I thought was cool and that students really seemed to enjoy, because it wasn’t like a typical language class; it was more like, “Well, what can we do to create, and how can we somehow still use the language but we are learning coding at the same time, or we are creating something in 3D at the same time?” Like, I was always trying to make it have two angles: the language angle, obviously, and then also the technology angle.

Eric Cross (04:25):

What was it that kept you kind of pushing? ‘Cause I remember the beginning in the Classcraft days to where you are now, I feel like you’re like light-years ahead of where you started.

Fabian Hofmann (04:37):

So you were actually the one who showed me Classcraft, which is like a gamification portal, kind of off-the-shelf thing that you can subscribe to. It has some free features and it’s like a gamification platform where students can create characters. And then these characters go on adventures. That’s like their avatar, and they get experience points in the classroom game and stuff happens. You can create, like, adventure paths for them. So if you have an assignment that you want students to do that has different steps, so, that could be an adventure path. That’s what I liked about Classcraft, is like this idea of like, “OK, we’re taking a game and applying it.” But it wasn’t enough for me. And so I started developing my own classroom game. I did some reading. I met online with John Meehan, worked with him. I read the book by Michael Matera, Explore Like a Pirate. And so it just broadened my whole world to, or just opened the world of gamification to me.

Eric Cross (05:38):

You present on gamification; you mentor other teachers on gamification. You host a podcast where you talk about it. But for those people who haven’t done it or gotten into it or maybe have a perception of it maybe that’s not quite accurate, can you talk a little bit about like what gamification is and what it’s not?

Fabian Hofmann (05:54):

  1. So the biggest difference…we all know game-based learning, because we all do it. We use Quizlet; we use quizzes; we use Gimkit, Blookit, Jeopardy, anything like that. Those are game based. That’s game-based learning. So using a game to facilitate learning. Which is great. I love game-based learning too. But the difference is with gamification, in the pure definition of gamification, is that you’re using game mechanics and elements and apply them to a non-game setting. A couple of smart educators were like, “Why don’t we just do that in our classroom?” And so we borrow these elements, these mechanics, these game mechanics, like getting experience points, and applying them to the classroom. So anything that students do, they earn points. So they turn in an assignment, that gets you a hundred points. They go and do something extra for the class, they get 50 points. Whatever it is, whatever your value is. That’s one aspect, like a leaderboard, virtual money, stuff like that that just in reality is not necessary, but you’re putting it somewhere where it doesn’t exist. And all of a sudden students have this weird shift in their view where it’s like, “Well, school is school, but in Mr. Hofmann’s class, I get to earn points and I get to be a Jedi and I can suspend my disbelief and I’m learning history, but at the same time I’m like traveling through the galaxy.” And it’s just amazing how that shift happens just because we’re changing the language a little bit.

Eric Cross (07:29):

Yeah. You seem to have like tapped into something that is already kind of in that zeitgeist culture thing. We’re gaming and it appeals to—I know it appeals to our students regardless of how they feel about even the subject that’s being taught, the fact that they’re immersed into this environment where they’re taking on this character role and they’re part of this bigger narrative. And you’ve so dynamically constructed this whole storyline and these experiences, and they’re learning experiences, like, they’re learning, but they’re enjoying it in a different way. But I wanted to ask you about something that I really admire that you do, and it’s how you grade. And I remember the first time you said this, we were in a parent-teacher conference and we’re all talking on Zoom with these parents and we’re all sharing our spiel. And you go, I don’t grade kids. They grade themselves. Can you talk a little bit about your conferencing with students? The rubric you use like that that, I’ve really been paying close attention to lately.

Fabian Hofmann (08:24):

Yeah. So, when I was working in Hawaii, I noticed I was teaching English, and grading papers in English is really not fun. Like, that is like my least favorite thing. Some teachers are like, “Yeah, it’s grading! Awesome! I can read stuff!” For me, it’s like, yes, I like to read stuff, but I—and it was the same in German class. I gave them feedback. Sometimes I would use oral feedback, I would, like, record stuff for them, and they would listen to it, and then they would work on it. And so I noticed when I’m giving them feedback and its oral feedback, they’re more inclined to actually work on the stuff that I was critiquing, versus when I sat down and I wrote something. They would never read it. Or some would, and most of them would not. And so I was like, this sucks. <Laughs> And I encountered this book called Hacking Assessment, because it’s such a waste of time, right? You spend so much time, because you wanna do the due diligence. And for those few kids who actually do care, that benefits them. But I want this to benefit everybody. And so I read this book called Hacking Assessment, by Starr Sackstein. And she talks about how she put the onus of grading into the student hands, essentially. And so she did standard-based grading and essentially said, “You know what? Here’s the thing. I am not going to grade you anymore. You are going to get a rubric that we are going to dissect and explain and make sure that you understand. And then you sit down and you give yourself a grade based on this rubric.” And I was like, “Wow, what? That is….I can do that? And the cool thing about this book is that she covers all the roadblocks that we as teachers have. And she explains, like, she gives examples on what we can do to convince parents, to convince admin, to convince the community, convince other teachers why what we’re doing is much, much better for a student than the previous system is. If you think about it, when a student comes into school, they start at a hundred, they start the year at a hundred, and all they’re doing is just lose points. And they’re just trying to keep up. Right? And it kind of flips this on its head, because not only with the gamification, I’m changing the name of the game, literally, but I’m also now with ungrading, I’m giving them the responsibility and the accountability to really look at their stuff and really be critical about how they’re doing. And I taught like normal in my first year in Hawaii when I was teaching English, by me grading everything and turning it and giving it to them. And I used peer grade and I did all that kind of stuff. But in the end, I was always the one responsible for the grade. But then I started to do the ungrading move and I just started to conference with kids and started giving them feedback, with the help of gamification, because there’s like a bunch of rubrics you can use to make it more fun. But all of a sudden, kids that in the year before would’ve failed my class in English, because they were English learners; they were just not into it; they didn’t care as much…all of a sudden that flipped completely. I did the exact same content again. We had to write an essay and all of a sudden, the essays were all like, up there, because we sat down, we talked about it, we went through this review process, gave them feedback. In the end, they could say, “Hey, I want this grade. And then I still have the last say. I would say, say, “Yep, sounds good.” Or “If you wanna get an A on this, or whatever it was, a 4, then here are the things you still need to do.” And because I did that, all of a sudden, the students are like, “Oh, that’s all I need to do?” And then they did it and turned it in, and all of a sudden, they got a 4. It’s, it’s amazing how that the conferencing with students, how that shifted their attitude. And I got to know my students way better than I ever had.

Eric Cross (12:20):

Yeah. That’s, that’s one of the things that I’ve noticed. And I watch you get so much more facetime with students having conferences than I do. I find myself grading…and, you know, at our school, it’s mastery-based instruction, so students can retake assessments, but you’re absolutely right: I give a grade; they get a score; and some of ’em score lower, but in their minds it’s like, OK, I’m done with that. And even though they can retake it, such a small percentage actually do. But the information that I give them in the feedback is often not read. But you’re sitting down and having a conversation and really listening and there’s so much more of a connection that you have. I just think it’s so rich. But the question I have now is how do you make the time for those conversations with those kids in your class?

Fabian Hofmann (13:01):

Yeah, it’s definitely a learning curve. Like the first year I did it, it was horrible. Like <laugh>, it cost so much time. Because kids came, because when it was time to grading, because I had not figured it out yet, I had not streamlined it. And I’m still learning. I’m still trying to figure this out and do it even better. But the idea is that you do something, you check in with me really quick. That doesn’t have to be like a full-on conference. It’s—I walk around or I call them up and say, “Hey, I saw you working on this. How did, how are you doing there? How many—” Like, let’s say I use a rubric that gives them crystals for different parts. They write the introduction; they write a bibliography; whatever, so I can bring them up and say, “Hey, how is the bibliography looking?” And they’re like, “Oh yeah, I’m missing…like, I only have like one or two sources.” And then we say, “OK, so right now you would get two crystals out of three because you have something. When you come back, you get all the crystals.” And so that’s a gamified aspect again, right? They’re coming back to get more crystals, not because they wanna do better necessarily. But because they’re like, “Hey, I wanna get those crystals because it gives me points in the game.” They are very good about like grading themselves and kind of like, they’re really hard on themselves sometimes too. And I have students who are like—

Eric Cross (14:08):

Yeah, they are.

Fabian Hofmann (14:09):

“Well, how can you make sure that people don’t just give themselves an eight?” And I’m like, “Because there’s a system in place that that does not happen. Like, there is a rubric, and if they cannot back up what they want, then it’s not gonna happen. They can write an eight all day long. I’m still the person entering it into the grade book!” <Laugh>

Eric Cross (14:27):

And let me premise this for listeners who don’t teach at IB schools, which is probably like most people.

Fabian Hofmann (14:31):

Yeah.

Eric Cross (14:32):

So IB, we teach zero through eight on a rubric system. And seven-eight is kind of like the A, kind of, quote-unquote. I know IB people are probably cringing when I say that, but <laugh>, you know, when you transfer it to like a high school? Seven, eight would be the highest score, you know. Four, five, six. So when we say eight, we’re talking about the highest score.

Fabian Hofmann (14:49):

Yeah. And so it’s really interesting because I can call them out on stuff, and it’s a one-on-one conversation, right? And if, especially if they turn something in that is not great, and they give themselves like a—I don’t know, like a C, let’s say, or a four, or whatever it is—and they’re like, “And you’re happy with that?” And then they’re standing there and they’re like, like, “No…?” <Laugh> And all of a sudden there’s a conversation. Where it’s like, and then I can be very intentionally like, “Hey man, I know you can do better. I would not—I’m not gonna accept this. I’m gonna push you to turn this in again.” And most of them actually sit down and do more. It’s a process. It takes a while. It’s not pretty in the beginning. But the payout is, so it’s incredible. Just like the amount of time that I get to spend with students, like specifically talking to them about things that they still need to work on, celebrating stuff they do, it’s incredible. Like the relationships are just so different than what I had years ago.

Eric Cross (15:50):

And you’ve also created a system where we preach—and schools always talk about this Dweck growth mindset and not having a fixed mindset, but I wonder how many opportunities or how systems are set up that are actually fixed, where it’s like one and done, OK, you did this exam and then that’s it, but there’s no opportunities to grow until the next exam! Which is gonna be….or whatever the assessment is, which is a whole different area of content or different topic or whatever. But here, you’re actually able to facilitate this growth mindset and push back if a student says, like, “Well that’s—I just got a four,” and you can actually pour into them and talk to them. And do you ever hear more about a student’s story as to why they were where they’re at, as you’re having these conferences?

Fabian Hofmann (16:29):

Oh, absolutely. Like for some kids who, who are just like not getting the work done or whatever, there’s always something where it’s not because they’re not smart or because they’re lazy. It’s like, sometimes, literally they tell you, well, ’cause I ask them, “Hey, can you work on this at home?” Or “Can you come in during lunch, after school, whatever? I’m always here.” And then they drop some bombs on you, like, “Hey, my parents, like, divorced. My mom lives in Mexico.” ‘Cause we live in San Diego. So some students live in Mexico and come to school here in San Diego and they get stuck at the border or, even though they have internet at home, they have to share. It’s like kind of what we experienced during the pandemic, where it’s like, there’s like three kids at home and one computer. Stuff like that. Right? And it’s these stories where you’re like, first of all, it’s very humbling ’cause they’re going through stuff that I never had to go through. I mean, my childhood was not amazing, but compared to what they’re going through, it’s like, “Oh yeah, that exists.” And it kind of like puts you in your place a little bit. It’s also because of the system that I use. There’s no late, really, in my class. Some of the students are like, “I need to subtract points from my grade because I turned it in late.” And I’m like, “No, no, no, no, no. The fact that you’re doing it is quote-unquote punishment enough ’cause you have to do it outside of class, you have to do it at home; you have to do it during lunch. Like, that is, that is not comfortable. You’re still doing it. So why would I punish you by taking a grade away? That doesn’t make sense. You got the work done. That’s all that matters.” I try to be that person that like is understanding. It’s still pushing them to do their best and reminding them and harping on them. And with the spark that I threw in there and fanning that flame of them becoming a better student because I’m supporting them. You’re supporting them. We’re all—our seventh-grade team is incredibly supportive. And then some people might push back, like “That’s not preparing them for the real world.” This is the real world.

Eric Cross (18:20):

There’s a lot of life skills that they’re gonna need…but like, they’re 12 right now! Or 11 or six, you know, whatever it is! Let’s—we can hold off on taxes and the crushing weight of adult reality later on. You got it done! Well-done! I do wanna talk about this thing that is your baby lately, this embryonic thing that you’ve been growing and I’ve been fortunate to be able to watch it since its inception. But you have this class that you created from scratch that’s essentially a STEM class. Two questions: Why did you create the class? And you’ve done some uncommon things. I’m gonna leave it wide open just for you to talk about it because it’s your baby and I’ve been fortunate to be able to watch it from the start. So can you talk about that?

Fabian Hofmann (19:01):

So yeah, so I’m obsessed with Star Wars. I think that’s putting it mildly. I love Star Wars. Always have. My classroom game is called Jedi Academy. And I’ve been playing around with this idea of creating a room that is more immersive. So I put a space, like a window to space, on my wall. I have the Millennium Falcon in my room. I have like a bunch of Resistance stuff or whatever. Anything Star Wars, you can find in my classroom. It’s not like overloaded, but I was very intentional in the things that I put in there, because I want my students to come in and feel like they are playing the game. And one of those things that I used was like smells; I used sounds to try to immerse them more. And then so one day I was like, wouldn’t it be cool to create a classroom that looks literally like a Star Wars set? Like you walked onto a set. Onto a spaceship, onto a rebel base, onto whatever it is. And how can I, how can I make that happen? And then we talked about it and you were like, “Yeah, how about you let the kids do it?” And that’s kind of how the course was born. And now I have students in my classroom who are in the process of designing a classroom based on Star Wars. And they’re gonna build everything. And we’re all learning at the same time. I’ve never done anything like this. I do like STEM, but I’ve never like actually made it a class. And so I contacted a bunch of people on LinkedIn ’cause I was like, it would be cool to talk to an Imagineer and to get like my foot in the door at Disney and then have an Imagineer come in and tell us about what they did. I have this book called The Art of Galaxy’s Edge, which is like the Star Wars land in Disneyland. And I just looked at the list and was like, “Who could be a good person to contact here?” And it said one of them was Eric Baker, and it said, “Executive Creative Director.” And I googled him or I looked for him on LinkedIn and I found him and I was like, “I’m just gonna send him a message. I’m just gonna tell him what I do in my class in history, gamification and all that, and they’re Jedi, and blah, blah, blah.” And he wrote back! Like, he was the only person that wrote back. I wrote a bunch of people and he was like, “Yeah, I’d be super-interested. I don’t know what you want me to do, but I’m down.” And so it created this relationship between me and Eric Baker who used to work for Imagineering, who are like the people at Disney who create the rides in the park and all that. And I talked to him and he gave me some feedback on the room. And then he was like, “Oh, so if you ever want me to talk to students, I’m down.” I was like, “Uh, yes!” And so we had him Zoom in. He talked about his life and how he became one of the people to look for when it comes to theme park design and to create immersive experiences. And I contacted other people on YouTube, like somebody who is like a Star Wars room builder. He’s willing to chat with us about this project. And then, I discovered that there is this thing called Imagination Campus at Disneyland, which they offer workshops on immersive storytelling. And I was like, “Oh, that’s what I want! I want my students to tell a story with my room!” And so I wrote up a proposal. Took a long time, but they signed—our admin signed it off. We kind of financed it. And then, about two weeks ago, you came along, another teacher, and we took 30something students to Disneyland and they did this workshop where they learned all about like how the Imagineers design story elements and put them in the parks. And then we took all of the kids to Galaxy’s Edge. And we took a bunch of photos. We went on the rides together. We had this collective experience. And it was life-changing for a lot of students. Because, I mean, we’re a Title One school; there’s like, we have about 60% free or reduced lunch. And a lot of them had never been to Disneyland. About half of them had never been. Some of them went when they were little. And so just watching their faces, going to Disneyland, watching them walk into Galaxy’s Edge, experiencing all these things, it was just, my mind was just blown. And I like literally, I don’t know if you noticed, but I was just smiling. Literally.

Eric Cross (23:19):

You were loving it.

Fabian Hofmann (23:20):

Yeah. Then we come back and we have these amazing conversations about design and what they noticed and how they created this immersive experience in their world. And we talk about how we can bring this back to our classroom. And parents are sending emails saying, “Oh my God, we’re so happy that you did this for our kids and you’re the coolest teacher.”

Eric Cross (23:39):

You touched on something that I wanted to ask you about. So you stay connected to people that inspire you, I feel like, or you have a pretty broad network of educators and professionals. Like, how much does that play into what you do in the classroom and the ideas that you have, as your network or your community of people?

Fabian Hofmann (23:57):

So the one network that helped me the most is Twitter. And I know people have opinions about Twitter, for good reason. But when I started to gamify, I just started to follow specific hashtags for areas that interested me. And that was gamification; eXPdup, which is like Explore like a Pirate—it’s an acronym. And it just opened up all these people, all these people, all these educators who are out there just like doing cool stuff and sharing it on Twitter. And I started connecting with them. And one of them is on my podcast. We met through Twitter; we started sharing stuff. We started talking about the things that we do. We both happened to have a gamified classroom. And so we connected over this thing Twitter, and now we’re like friends and we’re presenting together at Q and all those places. Teacher Twitter is incredibly supportive and people want to show you the stuff that they work on, just like I do. Like when I have stuff that I worked out, I shared it on there. And it’s so fun to hear back from teachers saying, “Hey, this looks awesome.” It’s just, it makes you feel good and it makes you feel like, “Oh, what I’m doing is not a total waste of time.” <Laugh>

Eric Cross (25:10):

<laugh> Those thoughts do creep in, right? Like, even though you’re doing something awesome and you might think so, we become our own worst critic sometimes, or we always see the things that we can improve and we overlook the things that we’re doing well. Fabian, where can people hear more about you, about gamification, about what you’re doing in the classroom, about how you’re innovating? I know you talk about this stuff with some—and you talk about it with some pretty legit people in the education industry. So can you tell some folks where they can hear more about it?

Fabian Hofmann (25:37):

So you can find me on Twitter at Hofmann edu—one F, two Ns—edu, and then I also host a podcast called Rebel Teacher Alliance. There’s three of us, where we talk all things gamification. But we also talk to teachers who don’t gamify at all. And we just, we just invite people who are interesting, who have stuff to share, who do cool stuff. You can find the podcast on the internet at Rebel Teacher Alliance dot com. Follow us there. If you wanna be a guest, just send a message and we’ll get you on.

Eric Cross (26:10):

Fabian, I’m gonna gush on you right now, but when you came back to Einstein, I was so happy because I knew that you sharpened me; you make me a better science teacher. Your innovation, your passion for kids, your sense of humor, your outside-the-box thinking, all of that. And when you got onto the seventh-grade team and you were here, I just knew that it was going to be awesome. And it has been. And so as a teaching colleague, as a friend, dude, you just rock, man. I’m super proud of you. And thank you for making me better.

Fabian Hofmann (26:40):

Aw, now I’m starting to cry. It’s like, don’t…

Eric Cross (26:43):

<laugh>. All true, dude. All true, my brother.

Fabian Hofmann (26:46):

Thank you.

Eric Cross (26:46):

All true. And thank you for letting me be part of the journey and I will definitely be walking down the hall asking you questions as I try to implement some of these great ideas that you’re doing with kids. Thanks so much for listening. And now we wanna hear more about you. Do you know any inspiring educators? Nominate them as a future guest on Science Connections by emailing STEM at amplifycom.wpengine.com. That’s S T E M at amplifycom.wpengine.com. Make sure to click subscribe wherever you listen to podcasts and join our Facebook group, Science Connections: The Community. Until next time.

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What Fabian Hofmann says about science

“I want my students to come in and feel like they are playing the game. I used smells. I used sounds to try to immerse them more. And then so one day I was like, wouldn’t it be cool to create a classroom that looks literally like a set?”

– Fabian Hofmann

Middle School Educator, Albert Einstein Academies Middle School

Meet the guest

Fabian Hofmann is a middle school International Baccalaureate teacher and host of the Podcast, Rebel Teacher Alliance. He is currently teaching 7th grade History and Multimedia Design just down the hall from Eric Cross at Albert Einstein Academies Middle School in San Diego. To engage students, he uses technology and gamification. Students embark on a year-long journey through a galaxy far, far away to learn the ways of the “Force” and some world history along the way. Follow him on Twitter and check out the Rebel Teacher Alliance podcast.

A man with short gray hair and a beard is smiling at the camera, photographed against a neutral background inside a circular frame with a small yellow sparkle accent, evoking the playful spirit of gamification.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher.

Grade 6

Chapter 1: Numerical Expressions and Factors

Big IdeasDesmos Math 6–A1
Lesson 1: Powers and ExponentsUnit 6
Lesson 10: Powers
Lesson 11: Exponent Expressions (Print available)
Practice Day 2 (Print available)
Lesson 2: Order of OperationsUnit 6
Lesson 11: Exponent Expressions (Print available)
Lesson 3: Prime Factorization
Lesson 4: Greatest Common FactorUnit 5
Lesson 15: Common factors
Lesson 5: Least Common MultipleUnit 5
Lesson 14: Common Multiples
Practice Day 2 (Print available)

Chapter 2: Fractions and Decimals

Lesson 1: Multiplying FractionsUnit 4
Lesson 12: Puzzling Areas (Print available) [Free lesson]
Lesson 13: Volume Challenges
Lesson 14: Planter Planner (Print available)
Lesson 2: Dividing FractionsUnit 4
Lesson 1: Cookie Cutter
Lesson 2: Making Connections (Print available)
Lesson 3: Flour Planner [Free lesson]
Lesson 4: Flower Planters
Practice Day (Print available)
Lesson 3: Dividing Mixed NumbersUnit 4
Lesson 5: Garden Bricks (Print available)
Lesson 7: Break It Down
Lesson 8: Potting Soil
Lesson 9: Division Challenges
Lesson 14: Planter Planner (Print available)
Practice Day
Lesson 4: Adding and Subtracting DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams [Free lesson]
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Lesson 5: Multiplying DecimalsUnit 5
Lesson 1: Dishing Out Decimals (Print available) [Free lesson]
Lesson 2: Decimal Diagrams 
Lesson 3: Fruit by the Pound
Lesson 4: Missing Digits
Lesson 5: Decimal Multiplication
Lesson 12: Budget Vehicles (Print available)
Practice Day 1 (Print available)
Practice Day 2 (Print available)
Lesson 6: Dividing Whole NumbersUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12: Budget Vehicles (Print available)
Lesson 7: Dividing DecimalsUnit 5
Lesson 8: Division Diagrams
Lesson 9: Long Division Launch
Lesson 10: Return of the Long Division (Print available)
Lesson 11: Movie Time [Free lesson] 
Lesson 12:(Print available) Budget Vehicles 
Practice Day 1 (Print available)
Practice Day 2 (Print available)

Chapter 3: Ratios and Rates

Chapter 4: Percents

Chapter 5: Algebraic Expressions and Properties

Chapter 6: Equations

Chapter 7: Area, Surface Area, and Volume

Chapter 8: Integers, Number Lines, and the Coordinate Plane

Chapter 9: Statistical Measures

Chapter 10: Data Displays

Grade 7

Chapter 1: Adding and Subtracting Rational Numbers

Chapter 2: Multiplying and Dividing Rational Numbers

Lesson 1: Multiplying IntegersUnit 5
Lesson 6: Floating in Groups
Lesson 7: Back in Time
Lesson 8: Speeding Turtles
Lesson 10: Integer Puzzles [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Dividing IntegersUnit 5
Lesson 8: Speeding Turtles
Lesson 3: Converting Between Fractions and DecimalsUnit 4
Lesson 13: Decimal Deep Dive (Print available)
Lesson 4: Multiplying Rational NumbersUnit 5
Lesson 7: Back in Time
Lesson 5: Dividing Rational NumbersUnit 5
Lesson 8: Speeding Turtles

Chapter 3: Expressions

Chapter 4: Equations and Inequalities

Chapter 5: Ratios and Proportions

Chapter 6: Percents

Chapter 7: Probability

Chapter 8: Statistics

Chapter 9: Geometric Shapes and Angles

Chapter 10: Surface Area and Volume

Lesson 1: Surface Area of Prisms
Lesson 2: Surface Area of Cylinders
Lesson 3: Surface Area of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 12: Surface Area Strategies (Print available)
Lesson 13: Popcorn Possibilities
Lesson 4: Volumes of Prisms
Lesson 5: Volumes of Pyramids
Unit 7
Lesson 10: Simple Prisms
Lesson 11: More Complicated Prisms
Lesson 13: Popcorn Possibilities
Practice Day 2 (Print available)
Lesson 6: Cross Sections of Three-Dimensional FiguresUnit 7
Lesson 9: Slicing Solids

Grade 8

Chapter 1: Equations

Chapter 2: Transformations

Chapter 3: Angles and Triangles

Chapter 4: Graphing and Writing Linear Equations

Chapter 5: Systems of Linear Equations

Lesson 1: Solving Systems of Linear Equations by GraphingUnit 4
Lesson 8: When Are They the Same?
Lesson 9: On or Off the Line?
Lesson 10: On Both Lines
Lesson 11: Make Them Balance [Free lesson]
Lesson 12: Line Zapper [Free lesson]
Practice Day 2 (Print available)
Lesson 2: Solving Systems of Linear Equations by Substitution
Lesson 3: Solving Systems of Linear Equations by Elimination 
Lesson 4: Solving Special Systems of Linear Equations 
Lesson 6: Scale Drawings

Chapter 6: Data Analysis and Displays

Chapter 7: Functions

Lesson 1: Relations and FunctionsUnit 5
Lesson 1: Turtle Crossing [Free lesson]
Lesson 2: Guess My Rule [Free lesson]
Lesson 2: Representations of FunctionsUnit 5
Lesson 3: Function or Not?
Lesson 5: The Tortoise and the Hare [Free lesson]
Lesson 3: Linear FunctionsUnit 5
Lesson 6: Graphing Stories
Lesson 7: Feel the Burn (Print available) [Free lesson]
Lesson 8: Charge! (Print available)
Lesson 4: Comparing Linear and Nonlinear FunctionsUnit 5
Lesson 4: Window Frames
Lesson 5: Analyzing and Sketching GraphsUnit 5  
Lesson 6: Graphing Stories

Chapter 8: Exponents and Scientific Notation

Chapter 9: Real Numbers and the Pythagorean Theorem

Lesson 1: Finding Square RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 2: The Pythagorean Theorem
Lesson 3: Finding Cube RootsUnit 8
Lesson 2: From Squares to Roots
Lesson 3: Between Squares
Lesson 4: Root Down [Free lesson]
Lesson 4: Rational Numbers 
Lesson 5: Irrational NumbersUnit 8
Lesson 14: Hit the Target
Lesson 6: The Converse of the Pythagorean TheoremUnit 8
Lesson 9: Make It Right

Chapter 10: Volume and Similar Solids

The power of high-quality math assessments

Two women sit at a table looking at an open book together; one woman points at the page as they both smile, engaging in innovative teaching practices for effective literacy instruction.

When students learn math, it’s crucial for them to understand not only right and wrong, but why and how. The same is true of math assessments.

High-quality, asset-based math assessments can show you how each student thinks, where their strengths lie, and what their next learning step should be.

And we need them now more than ever. Math scores have hit their lowest point since 2005, with nearly half of high school seniors scoring below “basic” achievement in 2024. This moment presents our biggest opportunity yet to transform K–12 math assessments.

Keep reading to explore how asset-based assessments help all students succeed—by starting with their strengths.

K–12 math assessments: True or false

Let’s establish some facts about math assessment first:

True or false: Math assessments can tell you only “right” or “wrong.”

False. Asset-based assessments go way beyond simple correct/incorrect scoring, showing you how students work through problems to give you insight into their thinking and what they already know. This provides a much clearer path for next steps.

True or false: Understanding student thinking is the key to improved student performance.

True. The path to math proficiency requires more than just benchmark scores. The better you understand how your students think, the better you can support their growth. When assessments recognize students’ individual strengths and strategies, the data becomes more helpful and complete.

The good news? We don’t have to throw out everything we’re doing, but we do need to enhance it. The current achievement trends aren’t telling us to stop what we’re doing. They’re telling us to do even better.

What high-quality math assessments actually look like

So what makes a math assessment truly powerful? Here are the key ingredients:

They show student thinking. Great assessments don’t just capture right and wrong answers—they reveal the “why” behind student responses. You get to see the logic, the creativity, and the problem-solving strategies each student brings to math. This visibility helps you understand not just what students know, but how they know it.

They welcome different approaches. There’s rarely just one way to solve a math problem. Quality assessments celebrate multiple solution paths and help you understand how each student’s mind works. This flexibility creates more opportunities for students to demonstrate their mathematical understanding.

They work for all learners. Research shows that 3–7% of students experience dyscalculia, meaning that they process numbers differently. The best assessments are designed so every student can show what they really know about math concepts, regardless of how their brain processes numerical information.

They connect to real life. When math problems relate to students’ actual experiences, engagement soars and understanding deepens. Students see math as relevant and useful, not just something they have to endure.

They guide your next teaching move. Instead of functioning like traditional summative assessments that just give you a grade, high-quality assessments tell you exactly what to teach next. They transform assessment from a final judgment into a roadmap for growth.

How asset-based assessment approaches change the game

Here’s where things get really exciting. What if your assessments started by looking for what students can do, instead of what they can’t?

That’s asset-based assessment. And it can change everything.

This approach recognizes that every student walks into your classroom with mathematical knowledge. Even the student who “hates math” or “isn’t good with numbers” has mathematical thinking waiting to be discovered and built upon.

Asset-based assessment strategies help you spot the sophisticated reasoning your students already have, even when they don’t use formal math language yet. Instead of starting with gaps, you start with strengths; instead of deficit thinking, you build from abundance.

When you weave asset-based approaches into your assessment practice through formative assessment lessons, magic happens. Students feel more confident. Their mathematical identities grow stronger. And you get clearer insights into how to help each learner thrive. Perhaps most importantly, these approaches help close achievement gaps by ensuring every student’s mathematical contributions are valued and developed.

The data tells a clear story: Our students need assessment approaches that match not just their current performance, but their true potential.

More to explore

Ready to unlock the full potential of your math assessments? We’ve put together everything you need in our Math Assessment Power Pack, featuring practical tools, proven strategies, and ready-to-use resources that’ll make it simple and easy to enhance your assessments.

S5-02. Uncovering the causes of math anxiety

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’re continuing our season theme of math anxiety, going beyond the basics, diving deeper into what causes it, and how we can help students move forward. In this episode, we talk to Dr. Erin Maloney from the University of Ottawa to better understand what’s actually happening in the brain when a person experiences math anxiety, and how we can take steps to shift student mindsets in a positive direction.
 
Listen now and don’t forget to grab your MTL study guide to track your learning and make the most of this episode!
 
Enjoy this episode and explore more from Math Teacher Lounge by visiting our main page. 

Download Transcript

Dr. Erin Maloney (00:00):

It’s the anxiety itself in many ways that can cause people to underperform.

Bethany Lockhart Johnson (00:06):

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

Dan Meyer (00:10):

And I’m Dan Meyer.

Bethany Lockhart Johnson (00:11):

This is episode two of our new season, all about math anxiety. Who has it? What is it? What do we do about it?

Dan Meyer (00:20):

I’m learning so much, learning a ton.

Bethany Lockhart Johnson (00:22):

I loved our first conversation with Dr. Gerardo Ramirez, episode one, our first episode of the season. Really, our goal with that conversation was just to—we need to talk about the basics of it, for reals. Like, what is math anxiety?

Dan Meyer (00:36):

What is it? How do you measure it? How’s it defined? Super-helpful stuff.

Bethany Lockhart Johnson (00:40):

There’s not only one way that it’s measured. But it’s like, in active research right now, how are folks making sense of it? And I think Dr. Ramirez did such a fantastic job of sharing that with our listeners. And I learned a lot. You learned a lot, Dan?

Dan Meyer (00:56):

I did. And I’m also super-excited to take that knowledge that we have developed together and go and build on top of it and keep on climbing up up the mountain here, and learn more about math anxiety. Which is why we’re super-excited to have a guest on, Dr. Maloney, who is going to help us learn more—especially about what happens to the brain when it’s experiencing math anxiety. There’s some really complex stuff that happens there, including the role of parents and educators in creating and resolving math anxiety. And I think we’ll also learn that the whole situation is a bit of a hot mess. And we’ll try to make it a little bit less messy together.

Bethany Lockhart Johnson (01:34):

Little bit less messy. Dan, if we do nothing else, can we make it a little less messy?

Dan Meyer (01:41):

I sometimes prefer more mess, but in this case I prefer less. So.

Bethany Lockhart Johnson (01:45):

I have a two-year-old, so everything is a mess.

Dan Meyer (01:47):

Your life is mess. Yes. <laugh> Right. Well, I’m excited for you folks to hear this. It was a delightful conversation, so yeah, tune in. We are joined by Dr. Erin Maloney.

Bethany Lockhart Johnson (01:56):

Let’s go. We are joined by Dr. Erin Maloney, associate professor in the School of Psychology at the University of Ottawa, where she directs the Cognition and Emotion Laboratory, as well as serving as the Canada Research Chair in Academic Achievement and Well-being. Welcome to the show, Dr. Maloney. We’re so excited to have you in the Lounge.

Dr. Erin Maloney (02:20):

Yeah, thank you so much for having me. This is fantastic.

Bethany Lockhart Johnson (02:24):

So our last season was all about math and joy. And even when I read your title, I felt more joyful. Like, somebody is thinking about academic achievement, but with well-being in mind. I love it.

Dr. Erin Maloney (02:39):

Aw, thank you.

Dan Meyer (02:40):

Cognition and emotion!

Bethany Lockhart Johnson (02:42):

E-mo-tion!

Dr. Erin Maloney (02:43):

I don’t think they can be separate. I think that you have to think about them together, ’cause they’re so intricately connected.

Dan Meyer (02:49):

Love that. People try, but we love that. Yeah. That’s our vibe here, too.

Bethany Lockhart Johnson (02:52):

People try. That was a big problem with my math anxiety. They just wanted…there was no room for my emotion. They’re like, stop weeping at your desk—

Dan Meyer (03:00):

It’s rearranging neurons….

Bethany Lockhart Johnson (03:01):

—you’re distracting the other children. So would you mind telling us the story of how you even got interested in this topic? You know, when you tell people that you study math anxiety—or, actually, I don’t know how you describe it to them; I’m hopeful you bring in that well-being part—but how did you get here? What do you, what do you, what do you…yeah, tell us! We love it!

Dr. Erin Maloney (03:23):

<laugh> I feel like what you’re actually asking is, “How did you make life choices that got you to here?” <Laugh>

Bethany Lockhart Johnson (03:29):

Justify your life choices! Ready? Go!

Dr. Erin Maloney (03:32):

<laugh> Whoo. OK. So, all right. So we often, in psychology, we joke that instead of doing research, we do “me-search.” And that’s, that’s admittedly true in my case. I was a student who absolutely loved math up until about eighth grade, and then something changed, and all of a sudden I was terrified of math and I had absolutely no sense of self-efficacy in it. Despite trying really hard, I was extremely anxious about it. And so I initially, I set out…my parents were completely convinced that I was absolutely capable of doing mathematics and that I was getting in my own way. And when I went to university, I decided to prove them wrong. So I set out to prove that some people just can’t do math, and that’s the end of it. And, you know, 20 plus years later, my parents were right. And it turns out that many people—well, I would argue virtually everyone—can do math. And that if you are really anxious about it, it can get in the way. And interestingly, you know, in, in the years that we’ve been doing this research, there’s really good strategies that can be used—that hopefully we get a chance to chat about—that can really help reduce the amount of anxiety that students are experiencing. But I really did set out, like the bold teenager that I was, to prove my parents wrong. And that backfired <laugh>. So I know it’s kind of a strange answer, but it’s the truth. So I was really interested in understanding why it was some people just could not do math.

Dan Meyer (05:10):

That makes two for two so far, on guests for this season who did a version of me-search. And I feel like this is pretty common for a lot of researchers. Like, I wanna figure out…my experience as a teacher, the part where you, I think, diverge from a lot of people I knew in grad school, myself included, is that you actually let counter evidence change your perspective on things. Whereas I feel like a lot of us go in: “I know this is true and I’m gonna gather data!” and lo and behold, I’m true! But only now, with the research TM, you know, trademarked research, attached to it. So that’s, really exciting. Thanks for sharing that.

Dr. Erin Maloney (05:43):

No, you’re welcome.

Bethany Lockhart Johnson (05:44):

But don’t people say that the more personal you get, the more universal it is? Right? So if you go and get your doctorate about something that you think is just your experience or in your brain, then people are gonna be gonna be like, “Wait a second; you think that too?” “Wait, that math anxiety isn’t just you?” I don’t know, it sounds like a pretty great path to me. When you tell folks that you study math anxiety or when you’re speaking to folks about your research, do you find that there is a lot of folks who relate to what you’re studying? Or how does that conversation typically go?

Dr. Erin Maloney (06:20):

Yeah, so it is I think an extremely relatable topic. Not in the sense that everyone experiences anxiety about math, but everyone seems to know somebody who’s really anxious about math. Or everyone’s at least aware of the stereotype that like some people are math people and some people aren’t, and that’s just the way it is. So it feels like everyone has feelings about math and everyone seems very happy to share those feelings. So one thing I’ve always found really interesting, and actually, so I, I know you mentioned that you had Gerardo on recently. Gerardo and I have had really interesting conversations about how people are really quick to tell you that they hate math and they can’t do math, and they’re anxious about math. And I’ve yet to have anyone ever tell me they hate reading, they can’t read, they’re really anxious about reading as an adult. So for some reason math seems really different. And in that sense people always seem to be pretty excited to talk about their feelings towards math.

Dan Meyer (07:23):

Yeah, definitely. Been on an airplane or two myself and had those conversations. You know, people asking to be reseated because they found out that I do math for a living or whatever. Or just unburdening themselves, for sure. I’m super-curious: I think that the fact that you are doing the me-search is reason enough to want to dedicate your life to this study. But I am curious: If you were gonna justify to someone else, why is math anxiety important to study? What are its consequences, even outside of math education? What would you say to that?

Dr. Erin Maloney (07:57):

So I think it’s probably not hard to convince people that success in math is important, right? So we know that children who start elementary school behind in mathematics tend to stay behind in mathematics, unless they have any kind of very targeted intervention. We know that children who do worse in mathematics throughout K to 12 education in general get lower-paying jobs when they’re older. We also know that when they do worse than mathematics relative to their peers, there’s fewer jobs that are open to them, relative to if they excelled in math. Right? And so I think in many ways there are really clear consequences for students who are not comfortable with math and who avoid it. But I think one of the really, really interesting things about math anxiety, and maybe part of why I’ve fallen in love with it as a research topic is that it’s the anxiety itself in many ways that can cause people to underperform. So it’s not just the case that people who are bad at math are anxious about it. It’s actually that the anxiety itself can cause you to do worse in math. And that for me is really exciting, ’cause it means that if we can change your mindset, then we can really set you on a path with several more options available to you career-wise. And I think that is really empowering.

Dan Meyer (09:18):

Hmm. Yeah, definitely. And I’d love for you to explore — your laboratory is the cognition and emotion laboratory, which I love, how you’re creating those linkages between how you feel about a thing and what your opportunities or your aptitude for learning it. I’m really curious, can you say more about the, the relationship there? How does feeling anxiety impair your ability to do mathematics?

Dr. Erin Maloney (09:41):

Yeah, so feeling anxiety, typically what you tend to experience is these negative thoughts and ruminations. So you can imagine, you’re somebody who doesn’t really love math, you’re pretty anxious about it; you know, Bethany, maybe you’ve had this kind of experience before. I’m gonna call you out on it. I’ve had it many times, where you sit down to do a math test and all of a sudden you’re not focusing on the actual math test in front of you. You’re focusing on things like the consequences of not doing well on this. Right? Or “my parents are gonna be really disappointed if I don’t pass this test,” or “my teacher is gonna think negatively negative of me,” or sometimes we see things like, “I’m a girl, girls don’t do math.” These types of stereotypes. And what happens is that those thoughts actually tie up really important cognitive resources, like, really important memory resources, that you need to do the math test. And so if you are trying to essentially do two things at once, right? You’re trying to deal with all these negative thoughts that are distracting you and you’re trying to do the math test, then you’re not going to do as well as someone who’s sitting down and doesn’t have all of these distracting thoughts to deal with. And we actually know that from research that we have in our lab right now, where we just ask people like, “Hey, when you did this math test, what kind of stuff are you thinking about?” what we find is that the people who are really anxious about math report a whole bunch of thoughts that are unrelated really to the math test, per se. It’s more about the consequences of doing poorly. And as a result of those thoughts, they actually end up doing worse.

Dan Meyer (11:14):

This has been really helpful to figure out, how the emotional state of doing math affects the ability to do math. And it’s really interesting how you’re saying that the direction of the causality can go from the emotions to the cognition. And I’m just curious then, what is the source of the bad emotions about math? Where does that come from? Is it nature? Is it nurture? Some combination? How do you see it?

Dr. Erin Maloney (11:39):

Yeah, so one, that’s a fantastic question. And there’s been a whole bunch of people all around the world that have been spending a lot of time really trying to pinpoint that down. And I think the answer is that it’s, you know, it’s complex. So most of what it’s looking like right now is that it is a combination of both. So essentially what we find is that kids who start elementary school who are a little bit behind in math—and for the question of why they’re behind, that’s also complex; it could be genetics, it could be just environmental input, before the child ever entered formal schooling kind of thing—but in essence, what we find is that kids that start school behind in mathematics, those are the children who are most likely to develop anxiety about math by the time they’re finished first grade. OK? But we also know that once they’ve developed the anxiety about math, then that’s when they get these thoughts and ruminations that kind of tie up those memory resources, that then is gonna make it harder for them to succeed in math tests. So you get into this sort of vicious cycle, right? Where maybe you start behind a little bit and then you develop the anxiety, the anxiety causes you to underperform relative to what you should be able to, so now you’re even further behind, you get more anxious because you’re not doing as well as you’d like to…but again, kind of coming back to the “Why are the children starting behind in the first place?” Some of that seems to be the role that parents are playing in the household. So some kids come from a household where parents are playing a lot more math games with them, talking about mathematical concepts on a regular basis. Maybe they have older siblings who are, you know, practicing arithmetic and, and mathematical processing in front of them. And so those kids are exposed to more math before they ever even start formal schooling. Those kids seem to do better. And then we also know that the parents’ attitudes matter a lot too. So what we find is that when parents are high in math anxiety themselves, especially when they help their children a lot with their math homework in really early ages, we find that those kids end up being more anxious about math by the end of the school year, and they also end up doing worse in mathematics. So it really does seem to be, you know, kind of a complex set of factors that have something to do with both maybe genetic predisposition to success in math and genetic predisposition to anxiety, but then also the social attitudes and stereotypes about math to which you’re exposed at home that really seem to be coming together to create this anxiety in young children.

Bethany Lockhart Johnson (14:24):

I feel like everything you’re saying is <laugh>…it makes so much sense and yet it’s so often not talked about, right? Because it’s just more like, it gets boiled down to, “Oh, they’re just not a math person,” instead of all these other factors that are at play. And I completely remember the anxiety I felt, whether it was a test or not, walking into my math classroom when I was in ninth grade. And there’s no way I was set up and ready to learn. Right? <Laugh>. And something with—we mentioned Dr. Ramirez, he was talking about validating that anxiety. If teachers validate that like, “Oh, you know what, sometimes you might feel stumped, or this might feel overwhelming.” Even the power in creating space for that in the classroom, right? And acknowledging that it doesn’t—math doesn’t have to “come easy” to you in order for you to have access or make sense, is such a powerful concept. And I love the way that you are looking at all these different factors and saying, “Hey, it’s both simple and also a lot more complicated than we’re we’re making it.” Right?

Dr. Erin Maloney (15:36):

No, and I agree with that sentiment so much. Like, I think, though—one thing I will sort of caution is that I think when teachers are validating the anxiety, or when parents are validating the anxiety, I think there’s a very fine line that needs to be walked where we need to be able to say, you know, “It’s OK to struggle with something. That’s, that is completely OK.” And as we’re, you know, as we’re working towards something that’s really valuable, right? We can, we can work hard at something and by working hard at it, we’re going to get better. And I think that type of validating is really, really important and valuable. I think what we wanna be careful of is not to say things like, “Oh, it’s OK. I also never loved math.” And, you know, “Oh, I was never a math person either.” And so even though we might be bringing comfort to the the child, I think that that’s sending the wrong message. And so sometimes it’s really well intentioned and really not great—

Bethany Lockhart Johnson (16:37):

A hundred percent.

Dr. Erin Maloney (16:38):

—in terms of the messaging. So that’s the only…so just for people listening, the only sort of caution that I would give there is that I think there’s nuances to the validating of the feelings that are important.

Bethany Lockhart Johnson (16:50):

I am so glad you said that because as a kindergarten teacher, I vividly remember—and this is as early as, you know, the kids are five years old, right?—and I remember in a parent-teacher conference, a parent saying, “Oh, I wasn’t a math person either,” or, “Oh, no, ugh.” And they were so quick, like you said, they wouldn’t say that about reading, but they were so quick to talk about their lack of natural math aptitude, right? And, and it was really interesting because you know that even if they’re not saying that specific thing at home, those attitudes are absolutely carrying over at home. And they’re absolutely carrying over to, to how they interact with their kiddo around math and around what’s happening in the conversations about math. And I felt like a lot of times my work as a teacher was also to help support parents through their own math anxiety, and help give them some new language for how they can talk about math. And that math is more than just getting to an answer quickly. Like, let’s talk about, let’s go on math walks, let’s go on number walks, what numbers are around the home? Or oh, is that bigger than this? Do you have more of this? And even those little things, I, my hope was that it was starting to shift the conversation around what math was possible in the home, particularly when you saw that it was the parents who had palpable math anxiety. Right? And how much you know that that’s gonna impact what’s happening when you sit down to do homework together.

Dr. Erin Maloney (18:22):

Yeah. And I love that you have worked to encourage parents to do that. So we do similarly. Like even from a research perspective, where I will often give talks to parents and teachers and we talk about the idea of trying to mathematize everything, right? So just the idea that math is absolutely everywhere, and you know, whether it’s a matter of playing games in the car with your kids where you’re thinking of a number and it’s “My number is higher than 42, but lower than 80, and what number do you think I might be thinking of?” And, and gradually trying to get the child to that number. Or, you know, asking questions like, “What’s your favorite even number and why?” And just little things like that that, that I think can make math fun for kids, that help—I don’t even know how to explain it, but just that idea of bringing joy into it, so it’s not always this heavy subject that kids have to come to. So we definitely try to talk to parents about the idea of, like I said, mathematizing everything. And usually it’s well-received, ’cause often parents find it empowering, right? They’re like, “Oh, well, I could do that! But like, that’s not math!” And you’re like, “No, but it is.”

Dan Meyer (19:33):

Yep.

Dr. Erin Maloney (19:34):

Like, it is! And sometimes parents will say like, “Well, I don’t know how to do fractions.” And you’re like, “OK, but how do you bake?” “Well, I don’t know! I just, like, I know how to do those fractions!” And you’re like, “OK, but that’s the starting point. Let’s work with that.” Like, let’s, you know. And I think a lot of times, it’s reminding the parents that they’re actually far more capable than what they think they are, despite the fact that maybe they struggled with math when they were younger.

Dan Meyer (19:58):

Yeah. This is so interesting. And I feel like part of the challenge around conversations about anxiety and math and how to, how to resolve it and where it comes from, is that it, like, it presupposes a single definition of math. And so, you know, we’re talking about like how to be more mindful about math. But you know, like if kids were walking every day through a treacherous street, you know, the solution might not be become more mindful about that street. It’s just like, we gotta fix the treacherous nature of the street, really. You know, I love that we’re talking also about redefining what math is, making it more playful. That feels like a super-important component here. I’d love to know more about what you know about the role of gender in all of this. Are there differences in the way boys and girls experience math anxiety and how it relates to achievement in math?

Dr. Erin Maloney (20:48):

Yeah, so, there’s really, really interesting research on gender in math anxiety. So in general, we find that girls tend to experience more anxiety about math than boys do. So one hypothesis is that it has to do with just social stereotypes that, you know, girls are, are good at reading; boys are good at math, kind of thing. So there’s some evidence to suggest that that might be playing a role. There’s other evidence to suggest as well that maybe boys actually do experience as much anxiety, they just don’t really own up to it.

Dan Meyer (21:20):

Ooh, yikes.

Dr. Erin Maloney (21:21):

So thoughts are, you know, there’s a bit of an apprehension for males to admit experiencing the anxiety. But I think one of the things that is extremely interesting about it—at least to me—is that we don’t tend to see gender differences in young children. So in early elementary school, even though we’ll see that kids as young as six years old will experience anxiety about math, and that that anxiety is related to how well they do in math and how much they enjoy math, it doesn’t seem to vary as a function of gender at that young age. It doesn’t seem to be related to gender until kids are at about sixth, seventh grade that we really start to see this gender difference coming online. And so that, to me, suggests that it’s probably something more social than biological at play. It probably has something more to do with these stereotypes and stuff. But another really interesting—or at least, I’m biased, but to me—another really interesting line of research that comes into play—and some of this is stuff out of my own lab—so we know that boys in general tend to do better at spatial processing than girls. And we know that spatial processing is really important for math, right? So math and space are pretty connected. And by spatial processing, I mean things like being able to picture something rotating in your mind or, you know, envisioning how these puzzle pieces might fit together. And so we know that boys tend to do better at that type of processing. And the gender difference there seems to be related to gender differences in math anxiety. So there’s some speculation, too, that it might be that as the math starts to become more reliant on spatial processing, that that’s when we see this separation between boys and girls with respect to how much anxiety they feel about math. So a lot of this is to say, I think the answer to the gender question right now is what I think what we would officially call a bit of a hot mess, <laugh> where I think there’s probably more questions than answers. But I think that there’s definitely something going on. And it really seems to be coming on later in elementary school.

Dan Meyer (23:32):

That’s a refreshingly honest admission from a social scientist, that it’s a hot mess and not perfectly clear, <laugh> so I appreciate that. It’s interesting what you said about the spatial reasoning. In our work creating curriculum at Amplify, I find we lean a lot on trying to tie abstract math towards spatial topics. Like, can you estimate a quantity before you calculate it? Can you identify a pattern and where it breaks before you prove it abstractly? And, I dunno, it’s just interesting to me. I’m just thinking out loud about how I feel like math becomes more abstract rather than more spatial. The farther you venture into secondary math…I’m wondering if I misunderstand what you’re meaning by spatial, and the progression of math from K–12.

Dr. Erin Maloney (24:20):

Yeah, so I think you can still have—you can have math be abstract, but still really relying on spatial processing. Right? And I think part of that is maybe a bit of us having different definitions of when we say “spatial.” So in cognitive science, when we talk about spatial representations or spatial reasoning, it’s really like anything you’re picturing in your mind, any time you’re really picturing these things in your mind and manipulating those images at all. So if you imagine, even like at a simple level, but it’s gonna hold when you’re going more complex as well. So doing like equivalence problems, for example, where you have to balance the equations.

Dan Meyer (24:58):

Yeah.

Dr. Erin Maloney (24:59):

Even just being able to envision things kind of moving around that equal sign and bringing one piece of the equation from this side to the other is actually an extremely spatial kind of reasoning. Right? Or when you’re expanding, that’s actually extremely extremely spatial, despite the fact that it might not feel like it initially. Obviously anything in geometry is going to be very spatial. So I think, in that sense, we would argue that the spatial processing is still playing a pretty important role. But it’s maybe a different type of spatial processing than what we’re seeing at a very early level in elementary school. That said, you can completely disagree with me too. ‘Cause I could also just be wrong, and that’s fair. My kids tell me I’m wrong all the time. So I’m used to <laugh> being told that I’m wrong.

Dan Meyer (25:47):

Well, we’re a bit more deferential on this here show, with our guests. So I would not do that. But it makes sense, what you’re saying about how these are things that you manipulate in your mind, whether they are Xs and Ys or numbers and fractions. These are all things that we manipulate. That ties into differences in this spacial reasoning category, it sounds like, which then contributes to math anxiety. And it does start to feel like there’s a lot going on here, is what it feels like.

Bethany Lockhart Johnson (26:14):

You mean hot mess?

Dan Meyer (26:16):

I meant hot mess.

Dr. Erin Maloney (26:17):

Yeah. <laugh>, I think that’s the technical term, right? I’m pretty sure that’s the technical term for it.

Dan Meyer (26:21):

I didn’t know the citation for it. So I didn’t say it. But I knew who in literature named that. But yeah.

Dr. Erin Maloney (26:28):

I’ll write something at some point.

Dan Meyer (26:30):

We’ll cite Maloney, 2022. Yeah. Yes.

Bethany Lockhart Johnson (26:34):

So I will say that one of my dreams in thinking about this season and last season, but particularly this season, since we’re really getting to talk to some researchers who get to think about this, and have really interesting conversations about it all the time…one of my dreams is that we’re bringing—’cause we do have some folks who are researchers that are listening, right? But then we also have teachers and folks who are in the classroom every day, and parents and caregivers listening. And so I think one of the beautiful things about the way that I hear you talking about it is you’re thinking about the research, but it’s so applicable. Right? And I wonder if there’s anything else you can say around it. I wanna reduce that divide, that gap, between the research that’s happening and then what’s happening with the kiddos and in the classroom and at home. And I don’t know if it’s like a magic wand thing where like <laugh> if there were changes you’d wanna see at a societal level, to try to combat math anxiety, but you see where I’m going. You know, it’s like <laugh>….

Dr. Erin Maloney (27:39):

  1. So I’m gonna answer maybe in two ways. So I think the first thing that I’m hearing from you is that idea of diminishing this divide, right? And so one thing I try to keep in mind, as someone who’s a researcher and working in the lab, I will often be called in to talk to teachers and give professional development sessions. And they often want the sage-on-the-stage academic, that stands up there and tells you the answers to things. And one of the first things that I’m gonna admit when I get up there is, “I am not on the front lines.” So what I do in the lab, for me to tell you that that’s gonna work in a classroom of 30 kids who may or may not have eaten dinner that day, and may or may not have snow pants, and may or not…like it’s–

Bethany Lockhart Johnson (28:23):

Mmm, yes.

Dr. Erin Maloney (28:24):

You know, I think we also need to be a little bit reasonable. So I try really hard in my own program of research to make sure that I’m always talking to teachers and to principals and to curriculum designers to make sure that the ideas that I have make sense. In fact, one of the most recent book chapters that I wrote, I wrote in collaboration with a really good friend of mine who’s a principal, an elementary school principal, and a former math consultant. And we wrote it together, to really say like, “Hey, here’s how we can help each other inform how research can inform practice and how practice can also inform research.” ‘Cause he can come to me and say, “I’m doing this. I can’t find anything in the literature to support this, but I’m sure it works!” And we can design something in the lab to test whether or not it seems like it’s gonna work.

Bethany Lockhart Johnson (29:11):

That’s huge. Yeah.

Dr. Erin Maloney (29:12):

Empirically. And so I think that open communication is massive. One thing that we’re doing in my own lab to try to keep that open communication available. So to anyone listening who’s ever tried to get access to a journal article, they’re held behind paywalls, right? So one, the way it works, my understanding of this anyway, is that the journal owns the formatted version of the paper. So what we do is we put up audio recordings of all of the research papers that we ever publish. So I’m pretty sure I own the words as the author, and the journal owns the prettified version that you can buy. So we audio-record all of our papers, so that if teachers or parents ever want to hear the actual science that’s going into some of these decisions, they have access to at least the stuff that we do in our lab. And we also put up an infographic for every paper, just highlighting kind of the main questions and main findings. And we do that because I think that the only way for the information to actually be useful is if it gets into the hands of the stakeholders that actually need that information.

Bethany Lockhart Johnson (30:21):

And is accessible. That’s huge. That’s huge!

Dr. Erin Maloney (30:24):

Yeah. Yeah. So that’s one way that we try to do it. And like I said, the other thing, we try to always be working with principals and with teachers. I joke that the way that I remedied this in my own life…so my husband’s a teacher; it’s like, I just married one! It’s fine! <laugh> I can grill him on a regular basis, and be like, “I wanna try this experiment. Do you think it’s gonna work?” And he can say, like, “It’s not going to. Here’s why.”

Dan Meyer (30:47):

That’s awesome. Marrying a participant—you know, a research participant—is unethical, of course. Would not clear IRB. But turning your partner into a participant? Like, what are you gonna do? That’s great.

Dr. Erin Maloney (30:57):

Yeah, no, that’s fair game.

Dan Meyer (30:58):

Yep.

Dr. Erin Maloney (30:59):

Yeah. So that’s—I think we we compensate each other <laugh>. So, no…so I do joke a little bit about that. He was a teacher simply ’cause he wanted to be one. Not ’cause I needed him to be one. But, I think that communication part is, is really key. That’s one thing. Then the other part of the question or the other sort of piece of the question that I was hearing is that idea of, how do we fix math anxiety. Right? Like, what’s the great, “I’m glad that there’s a whole bunch of time and effort and energy going into trying to understand this, but what, where are we at?” And I think with that, it’s really, really promising. So there’s been a lot of research coming out looking at how best to help children or even adults manage their own anxiety about math. And there’s a few really interesting strategies that seem to be quite effective. So one, and I don’t know if—um, it feels weird calling him Dr. Ramirez, just ’cause I know him well!—but I don’t know if Dr. Ramirez would’ve talked about this when he chatted with you, but he has some really interesting work on expressive writing. Did he chat about that at all?

Bethany Lockhart Johnson (32:07):

He didn’t, but I’ve read some of his work about it and I think it’s so fascinating.

Dr. Erin Maloney (32:11):

Yeah! So, OK, well, I’ll tell you about his work on it.

Bethany Lockhart Johnson (32:13):

Yes, please. Please.

Dr. Erin Maloney (32:14):

Because it’s super-useful. So when we talked about that idea of how anxiety causes these thoughts and ruminations, and they tie up the memory resources that you need, what Gerardo has found is that when you get students to write about their anxiety for about 10 minutes before they do a test, what ends up happening is they end up doing better on the test, relative to if they would not have written about their anxiety at all. And this is particularly true for students who are really high in anxiety. OK? And the idea is that all of those thoughts that they were going to have about the test or the consequences of the test, et cetera, you just kind of get ’em…it’s like a mind dump where you get ’em all onto the page at first before you even go to do the test. And now when you go to do the test, you’re not having to do two things at once. You’re no longer dealing with these thoughts ’cause you got ’em all out on the paper beforehand. And so Gerardo has some really interesting work showing that that works for math anxiety. And then it also works for just testing anxiety in general. And so that’s a strategy that I love. I also—part of what I really love about it is it’s so low-cost, right? You need a paper and a pencil and it’s great. So those are always my favorite strategies, the ones that don’t really cost us anything. So that’s one way of dealing with like the cognitive part of the anxiety. The other thing you can do is try to deal with the anxiety part of the anxiety. So for that, what we find is that the typical strategies that you’re gonna see for anxiety tend to work for math anxiety. So things like focused breathing. Right? Making sure you’re doing deep inhales and exhales. That really diaphragmatic breathing seems to be quite helpful. We know that what we call progressive desensitization is really key. That’s the idea of doing things, you know, starting with the questions that you know how to handle. And then gradually working up to the more difficult questions. So you’re sort of gradually exposing yourself to the more complex stuff. And how that can play out on an actual test at school is, you sit down, and instead of just starting with question number one, you actually read the whole test, see which questions you feel like you know the best, start with those questions, and that helps build your confidence so that you’re better able to tackle the questions that are maybe a little bit outside of where you’re currently at. So that seems to be really helpful. The other part that I will say, too, that’s extremely helpful: So we know that anxiety really ties up those memory resources. And so the more you can make the math automatic, the more immune it’s going to be to anxiety in the moment. And so I know that this part can be a little bit controversial, because we don’t wanna necessarily demotivate children, and kill the enthusiasm for math that we’re trying to cultivate…but really, you know, really committing your arithmetic facts to memory can be extremely helpful. So really learning those times tables, really learning your addition and subtraction facts. ‘Cause what happens is, then when you’re in a situation where you need that information, even if you’re anxious and you’re working with fewer cognitive resources than what you would normally have, you actually don’t need that many cognitive resources to be able to pull something from memory that you’ve memorized. So it really helps to kind of protect you against some of the negative impacts of the anxiety while you’re doing that test.

Bethany Lockhart Johnson (35:37):

And you’re not using all your cognitive resources to figure out seven times eight, because you can really focus on what you’re trying to do with that. Oh, that’s fascinating. Yeah. Yeah.

Dr. Erin Maloney (35:47):

Yes. No, a hundred percent right. And so I know that’s one that, like I said, I know it can be somewhat controversial because it’s…you know, we’ve talked about—or we haven’t talked about in this conversation, but we often talk about—the idea of drilling and killing. Right? So you drill the facts, you kill the, the enthusiasm. But I think that there are ways that we can drill arithmetic facts, or help make them automatic, but still fun, right? It doesn’t have to always be in a high-pressure kind of way.

Bethany Lockhart Johnson (36:16):

Totally. And we’ve talked about fluency, and I’m sure we’ll talk about it more in the Lounge. And that is interesting, that link between anxiety when the fluency isn’t there, that—or, of course we hear about anxiety with timed tests, but the idea of that IS something you can do to reduce it, because you have those facts just at your ready. Right?

Dr. Erin Maloney (36:37):

Yeah. So I actually, again, I’m gonna be a little bit controversial. So I don’t hate timed tests in the way that a lot of people do. But I love time to practice. So I think once we’ve got to a point where children have a fairly decent understanding of skills, of a skill, once they’ve got a fairly decent grasp on it, then I love the idea of the timed practice. So it can be still in a low-pressure situation, where in many ways it doesn’t matter if you get the answer to the question correct. But we’re practicing doing it in a situation in which you might be feeling a little bit of pressure, but it’s not real pressure, if that makes sense. And I think that can be really, really useful for students. And again, it can be done in a fun way, right? It doesn’t have to be these super-intense ways. It can be fun. But I think that in life there are situations in which the time that it takes you to complete a problem matter. And I think that we have to make sure that we don’t get too far away from that.

Dan Meyer (37:40):

Yeah. It feels like we should do an entire other episode thinking about ways to develop that fluency and automaticity that don’t contribute to anxiety, or create further disparities between people who are high math anxiety and low math anxiety. Not a small question, I’m sure. And I appreciate you alluding to all of that. You know, this whole thing, as you said, is quite the hot mess. And I feel like you, Dr. Maloney, have helped us make this a little less messy, in our heads, and hopefully the listeners’ heads. I really appreciate that. I just love…you’ve mentioned lots of resources that you have. You’ve alluded to them: audiobook-style readings of your research, which I need ’cause I just finished, you know, Harry Potter, the seventh book, so I need a new thing to listen to like that. Also infographics. Can you tell our listeners where they can find this work of yours, and if there are any other kinds of resources that you wanna plug for our listeners here?

Dr. Erin Maloney (38:32):

Yeah, for sure. So all of our resources can be found on my lab website. So the address for that is www.ErinMaloney.ca. So there we have, like you said, the infographics and the audio articles and all that stuff. And then we also have a link to a new kids’ book out, actually, that a colleague of mine and I have published recently, that really walks through some of these strategies on combating math anxiety. The book is written as a children’s book, so it’s Peyton & Charlie Challenge Math. But it secretly is a book that would also work for adults. So if you are a parent that’s a little bit anxious about math, or a teacher that maybe is a little bit anxious, and you wanna see how some of these strategies can play out, in that book—we linked to it on the website, but it is available for purchase on Amazon. And the one thing I will say about the book, ’cause this is something that we were pretty proud of, so Sheri-Lynn Skwarchuk, who is a school psychologist, and I wrote the book. And it’s available for purchase at our cost price, so we don’t actually make any money on the book. It was literally just a way of getting some of the science out to people who might be able to benefit from it.

Bethany Lockhart Johnson (39:45):

Reducing that divide!

Dr. Erin Maloney (39:46):

Yeah, well that’s what we’re trying to do! Right? So I think in the U.S., I think it’s like $6 on Amazon. And then in terms of other resources, we’re in the process right now of creating some informational videos and and stuff like that that hopefully will be useful for parents and for teachers, just in terms of understanding a little bit more about the anxiety and understanding how to deal with the anxiety in the classroom more, at home or wherever it might be coming up.

Dan Meyer (40:15):

Well, thanks so much. I really appreciate—we appreciate!—you coming on, and hearing about how you’re trying to bridge so many different barriers from research to practice, and school to home. It’s just really inspiring. And we’d love to have you back on sometime. So thank you so much for joining us.

Bethany Lockhart Johnson (40:29):

I feel like we’ve just hung out! Don’t you, Dan?

Dan Meyer (40:31):

Are we rolling here? Oh my gosh, we’re rolling. I just thought we’re just hanging. Yeah,

Bethany Lockhart Johnson (40:34):

I thought we were just hanging!

Dr. Erin Maloney (40:36):

I know, I do, I really appreciate that it has a very kind of chill vibe to it.

Dan Meyer (40:41):

Chill vibe. Like a lounge.

Bethany Lockhart Johnson (40:42):

It’s the lounge!

Dan Meyer (40:43):

Thank you. You get us; you get us. <laugh>

Bethany Lockhart Johnson (40:45):

Dan Meyer. I was shopping for children’s books, and there was this book, and it was talking about being at home with Mom. And it’s going through all the things that the child did that day with Mom. It’s like, “We played outside, we ran through the sprinklers, we even did some homework.” And it shows them sitting at the table with the homework, that’s clearly math homework, in front of them. And the mom is like, “Harrumph!” Like a very perplexed, anxious face. And there’s all these question marks above her. And it’s just like,

Dan Meyer (41:24):

“There should not be numbers on that paper!”

Bethany Lockhart Johnson (41:25):

Exactly. And the child is like, “Ohhhh,” you know. And I mean, I have to give credit to the illustrator, because they really did capture the clear message of this interaction, which was sitting down to do math homework or think about math together is a source of angst. Right? According to this author and according to too many people. And so I think what’s really important is that we recognize those images when we see them out there and speak back to them, and say, “Hey, wait a second.” Yeah, it can feel like that, and it doesn’t have to. And what’s going on that that’s just the assumed way that it’s gonna feel, to sit down and math together. You know?

Dan Meyer (42:11):

Yeah. It feels like we all have a lot of work to do on the whole math-anxiety front. Dr. Maloney helped us see how parents play a part, educators play a part, society and how they create people plays its own part in how we all define math as a thing where we evaluate student thought or where students play it with their thoughts, has its own huge part as well. So yeah, it was a really fantastic conversation with Dr. Maloney. I hope you folks will check out the show notes, where you will find links to Dr. Maloney’s website. A lot of her work, which as you heard, is very geared towards practitioners and parents and even directly at kids, especially the new children’s book she co-authored, Peyton & Charlie Challenge Math.

Bethany Lockhart Johnson (42:55):

Next time we’re gonna dive even more into the nitty gritty of combating math anxiety. To do that, we’re actually gonna be joined—I am so excited about this—by Dr. Rosemarie Truglio from Sesame Workshop.

Rosemarie Truglio (43:09):

Our core audience are two- to four-year-olds, and they love math. And what’s not to love? Children don’t come with this math anxiety. Math anxiety is learned.

Dan Meyer (43:23):

So excited.

Dr. Erin Maloney (43:24):

Sesame Street was a huge part of my childhood and my toddler doesn’t know it yet, but Sesame Street is coming. It’s coming. Like, we’re we’re gonna introduce Sesame Street to him. We just haven’t yet.

Dan Meyer (43:37):

Sesame Street straight raised me.

Bethany Lockhart Johnson (43:38):

Right?

Dan Meyer (43:39):

Yeah. Don’t tell my parents. But that’s, yeah, that’s true. I’m excited, too. It’s gonna be a blast.

Bethany Lockhart Johnson (43:45):

I’m really excited. I think that the more we dive into this topic—which, again, we’re gonna look at math anxiety from a lot of different angles—and I’m excited to talk to Dr. Truglio about how we can take this research and these conversations that are happening about math and how it can actually impact what’s happening in homes. ‘Cause we wanna help create positive relationships with mathematics, with kids in math. I’m so excited. And I hope you folks keep listening. We love having you here in the Lounge. And if you haven’t already, please subscribe to Math Teacher Lounge, wherever you get podcasts. And if you like what you’re hearing, please leave us a rating and a review. It helps more listeners to find the show, and let other folks know about this show. Recommendations are great. Thanks so much for listening.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Dr. Erin Maloney says about math

“If we can change their mindset, then we can set students on a path to more opportunities and success.”

–Dr. Erin Maloney

Associate Professor in the School of Psychology, Director of the Cognition and Emotion Laboratory, and the Canada Research Chair (Tier II) in Academic Achievement and Well-Being, all at the University of Ottawa

Meet the guest

Erin Maloney is an Associate Professor and Canada Research Chair at the University of Ottawa. Her research sits at the intersection of Cognitive Psychology, Developmental Psychology, and Education and focuses on cognitive and emotional factors that relate to academic achievement. She is a world-renowned expert on the study of math anxiety, conducting research in the lab, in homes, and in classrooms with children, parents, and their teachers. She is passionate about both knowledge mobilization and equity, diversity, and inclusion within education and science.

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About Math Teacher Lounge

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

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Grade 6

Unit 1: Area and Surface Area

Lesson 2: Finding Area by Decomposing and RearrangingShapes on a Plane
Lesson 3: Reasoning to Find AreaLetters
Lesson 4: ParallelogramsExploring Parallelograms, Part 2
Lesson 5: Bases and Heights of ParallelogramsExploring Parallelograms, Part 1
Lesson 6: Areas of ParallelogramsOff the Grid, Part 1
Lesson 7: From Parallelograms to TrianglesTriangles and Parallelograms
Lesson 8: Areas of TrianlgeExploring Triangles
Lesson 10: Bases and Heights of TrianglesOff the Grid, Part 2
Lesson 11: PolygonsPile of Polygons
Lesson 15: More Nets, More Surface AreaRenata’s Stickers

Unit 2: Introducing Rations

Lesson 3: RecipesPizza Maker
Lesson 5: Defining Equivalent RatiosFruit Lab
Lesson 12: Navagating a Table of Equivalent RationsDisaster Preparation

Unit 3: Unit Rates and Percentages

Lesson 1: Anchoring Units of MeasureMany Measurements
Lesson 4: Comparing Speeds and PriceWorld Records
Lesson 5: Interpreting RatesSoft Serve
Lesson 6: Equivalent Ratios Have the Same Unit RatesWelcome to the Robot Factory
Lesson 8: Solving Rate ProblemsMore Soft Serve
Lesson 9: More about Constant SpeedModel Trains
Lesson 11: Representing Percentages with Double Number Line DiagramsLucky Duckies

Unit 4: Dividing Fractions

Lesson 4: How Many Groups? (Part 1)Flour Planner
Lesson 6: Using Diagrams to Find the Number of GroupsFill the Gap
Lesson 13: Rectangles with Fractional Side LengthsPuzzling Areas

Unit 5: Arithmetic in Base 10

Lesson 1: Using Decimals in Shopping ContextDishing Out Decimals

Unit 5: Arithmetic in Base 11

Lesson 2: Using Diagrams to Represent Addition and SubtractionDecimal Diagrams and Algorithms

Unit 5: Arithmetic in Base 12

Lesson 15: Making and Measuring BoxesMovie Time

Unit 6: Expressions and Equations

Lesson 1: Tape Diagrams and EquationsFive Equations
Weight for It
Lesson 3: Staying in BalanceHanging Around
Lesson 4: Practice Solving EquationsHanging It Up
Lesson 5: Represent Situations with EquationsSwap and Solve
Lesson 9: The Distributive Property: Part 1Products and Sums
Lesson 17: Two Related Quantaties, Part 2Subway Fares

Unit 7: Rational Numbers

Lesson 3: Comparing Positive and Negative NumbersOrder in the Class
Lesson 5: Using Negative Numbers to Make Sense in ContextMinimum Wage
Lesson 8: Writing and Graphing InequalitiesTunnel Travels

Unit 8: Data Sets and Distributions

Lesson 5: Using Dot Plots to Answer Statistical QuestionsMinimum Wage
Lesson 6: Interpreting HistogramsThe Plot Thickens
Lesson 11: Variability and MADHoops
Lesson 13: MedianToy Cars

Grade 7

Unit 1: Scale Drawing

Lesson 1: What are scaled copies?Scaling Machines
Lesson 2: Correspond Parts and Scale FactorsMake it Scale
Lesson 3: Making Scaled CopiesScaling Robots
Lesson 5: The Size of the Scale FactorScale Factor Challenges
Lesson 6: Scaling AreaTiles
Lesson 6: Scaling AreaWill It Fit

Unit 2: Introducing Proportional Relationships

Lesson 1: One of These Things is Not Like the OtherPaint
Lesson 5: Two Equations for Each RelationshipTwo and Two
Lesson 10: Introducing Graphs of Proportional RelationshipsDinoPops

Unit 3: Measuring Circles

Lesson 2: Exploring CirclesMeasuring Around
Lesson 7: Exploring the Area of a CircleWhy Pi?
Lesson 9: Applying Area of a CircleArea Challenges

Unit 4: Proportional Relationships and Percentages

Lesson 6: Increasing and DecreasingMosaics
100%
Lesson 7: One Hundred PercentMore and Less
Back in My Day
Lesson 8: Percent Increase and Decrease with EquationsAll the Equations
Lesson 11: Percentage ContextsPercent Machines

Unit 5: Rational Number Arithmetic

Lesson 3: Changing ElevationFloats and Anchors
Lesson 5: Representing SubtractionMore Floats and Anchors
Lesson 6: Finding DifferencesDraw Your Own
Lesson 13: Expressions with Rational NumbersInteger Puzzles

Unit 6: Expressions, Equations, and Inequalities

Lesson 9: Dealing with Negative NumbersKeeping it True
Lesson 13: Reintroducing InequalitiesI Saw the Signs
Lesson 14: Finding Solutions to Inequalities in ContextUnbalanced Hangers
Lesson 15: Efficiently Solving InequalitiesShira the Sheep
Lesson 16: Interpreting InequalitiesBudgeting
Lesson 17: Modeling with InequalitiesWrite Them and Solve Them
Lesson 20: Combining Like Terms (Part 1)Collect the Squares

Unit 7: Angles, Triangles, and Prisms

Lesson 2: Adjacent AnglesFriendly Angles
Lesson 5: Using Equations to Solve For Unknown AnglesMissing Measures
Lesson 7: Building Polygons (Part 2)Can You Build It

Unit 8: Probability and Sampling

Lesson 1: Mystery BagsHow Likely
Lesson 3: What are Probabilities?Prob-bear-bilities
Lesson 4: Estimating Probabilities through Repeated ExperimentsIs It Fair?
Lesson 13: What Make a Good Sample?Crab Island

Grade 8

Unit 1: Rigid Transformations and Congruence

Lesson 1: Moving the PlaneTransformers
Lesson 2: Naming the MovesSpinning, Flipping, Sliding
Lesson 3: Grid MovesMoving Day
Lesson 4: Making MovesTransformation Golf
Lesson 5: Coordinate MovesGetting Coordinated, Part 1
Lesson 6: Describing TransformationsGetting Coordinated, Part 2
Lesson 16: Parallel Lines and Angles in a TrianglePuzzling It Out
Lesson 17: Rotate and TesselateTessellate

Unit 2: Dilations, Similarity, and Introducing Slope

Lesson 1: Projecting and ScalingSketchy Dilations
Lesson 3: Dilations with No GridDilation Mini Golf
Lesson 7: Similar PolygonsSocial Scavenger Hunt

Unit 3: Linear Relationships

Lesson 1: Understanding Proportional RelationshipsTurtle Time Trials
Lesson 5: Introductions to Linear RelationshipsFlags
Lesson 6: More Linear RelationshipsStacking Cups (Optional)
Lesson 8: Translating y=mx+bTranslations
Lesson 9: Slopes Don’t Have to Be PositiveWater Cooler
Lesson 10: Calculating SlopeUps and Downs

Unit 4: Linear Equations and Systems

Lesson 5: Solve Any Linear EquationEquation Roundtable
Lesson 12: Systems of EquationsMake Them Balance
Lesson 13: Solving Systems of EquationsLine Zapper

Unit 5: Functions and Volume

Lesson 1: Inputs and OutputsGuess My Rule
Lesson 5: More graphs of FunctionsTurtle Crossing
Lesson 6: Even More Graphs of FunctionsThe Tortoise and the Hare
Lesson 13: The Volume of a CylinderCylinders
Lesson 15: The Volume of a ConeCones

Unit 6: Associations and Data

Lesson 3: What a Point on a Scatter Plot MeansRobots
Lesson 4: Fitting a Line to DataDapper Cats
Lesson 5: Describing Trends in Scatter PlotsInterpreting Scatter Plots
Lesson 6: Slope of a Fitted LineFind the FIt (called Fit Fights in Desmos Math)
Lesson 7: Observing More Patterns in Scatter PlotsScatter Plot City
Lesson 8: Analyzing Bivariate DataInterpreting Slopes
Lesson 9: Looking for AssociationAnimal Brains
Lesson 10: Using Data Displays to Find AssociationFinding Associations

Unit 7: Exponents and Scientific Notation

Lesson 1: Exponent ReviewCircles
Lesson 6: What about Other Bases?Power Pairs
Lesson 12: Applicatios of Arithmetic with Powers of 10Balance the Scale
Lesson 13: Definition of Scientific NotationSpecific and Scientific (formerly Solar System)

Unit 8: Pythagorean Theorem and Irrational Numbers

Lesson 5: Square Roots on the Number LineRoot Down
Lesson 7: Finding Side Lengths of TrianglesTriangle Tracing Turtle
Lesson 11: Applications of the Pythagorean TheoremTaco Truck

Algebra 1

Intro/Launch

Unit 1: One Variable Statistics

Lesson 12: Standard DeviationFinding Desmo

Unit 2: Linear Equations and Systems

Lesson 4: Equations and Their SolutionsWorking Backwards
Solving Strategies
Same Position
Lesson 5: Equations and Their GraphsShelley the Snail
Five Representations
Lesson 6: Equivalent EquationsSubway Seats
Lesson 7: Explaining Steps for Rewriting EquationsVarious Variables
Lesson 12: Writing and Graphing Systems of Linear EquationsLizard Lines
Lesson 13: Solving Systems by SubstitutionShape It Up

Unit 3: Two Variable Statistics

Lesson 5: Fitting LinesCity Slopes
Penguin Populations
Lesson 6: ResidualsResidual Fruit
Lesson 7: Correlation CoefficientCorrelation Coefficient
City Data
Lesson 8: Using the Correlation CoefficientHow Hot Is It?
Lesson 9: Causal RelationshipsBehind the Headlines

Unit 4: Linear Inequalities and Systems

Lessons 4-6: Graphing Linear Inequalities in Two VariablesPizza Delivery
Lesson 7: Solutions to Systems of Linear Inequalities in Two VariablesQuilts
Seeking Solutions
Lesson 8: Solving Problems with Systems of Linear Inequalities in Two VariablesCarlos’s Fish

Unit 5: Functions

Lesson 1: Describing and Graphing SituationsCraft-a-Graph
Lesson 7: Using Graphs to Find Average Rate of ChangePlane, Train, and Automobile
Lesson 12: Piecewise FunctionsPumpkin Prices
Lesson 15: Inverse FunctionsChip the Robot

Unit 6: Introduction to Exponential Functions

Unit 7: Introduction to Quadratic Functions

Lesson 1: A Different Kind of ChangeRevisiting Visual Patterns, Part 1
Quadratic Visual Patterns
Lesson 10: Graphs of Quadratic Functions in Standard and Factored FormsOn the Fence
Stomp Rockets
Plenty of Parabolas
Two for One
Lesson 11: Graphing Quadratics from the Factored FormParabola Zapper
Shooting Stars
Lesson 14: Quadratic Graphs that Represent SituationsRobot Launch

Unit 8: Quadratic Equations

Lesson 2: When and Why Do We Write Quadratic Equations?Sorting Relationships
Lesson 12-14: Completing the SquareSquare Tactic
Lesson 24: Using Quadratic Equations to Model Situation and Solve ProblemsStomp Rockets in Space

Disclaimer

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

Grade 6

Module 1: Ratios and Rates

Module 2: Fractions, Decimals, and Percents

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

Module 3: Compute with Multi-Digit Numbers and Fractions

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

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

Module 5: Numerical and Algebraic Expressions

Module 6: Relationships in Geometry

Module 7: Relationships Between Two Variables

Module 8: Area

Module 9: Volume and Surface Area

Module 10: Statistical Measures and Displays

Grade 7

Module 1: Proportional Relationships

Module 2: Solve Percent Problems

Module 3: Operations with Integers

Module 4: Operations with Rational Numbers

Module 5: Simplify Algebraic Expressions

Module 6: Write and Solve Equations

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

Module 7: Write and Solve Inequalities

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

Module 8: Geometric Figures

Module 9: Measure Figures

Module 10: Probability

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

Module 11: Sampling and Statistics

Grade 8

Module 1: Exponents and Scientific Notation

Module 2: Real Numbers

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

Module 3: Solve Equations with Variables on Each Side

Module 4: Linear Relationships and Slope

Module 5: Functions

Module 6: Systems of Linear Equations

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

Module 7: Triangles and the Pythagorean Theorem

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

Module 8: Transformations

Module 9: Congruence and Similarity

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

Module 10: Volume

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

Module 11: Scatter Plots and Two-Way Tables

Is this literacy program true to the Science of Reading?

We’ll show you how to tell.

We know how children learn to read. We know how to teach children to read. That’s all thanks to the Science of Reading.

As you likely know, the Science of Reading refers to the pedagogy and practices proven by extensive research to effectively teach children how to read. Learning to read is not innate, but it can be taught—and science tells us how.

That’s why it’s so important to use literacy programs that are truly grounded in the Science of Reading.

But how can you tell which ones are and which ones are not? It can be confusing. Some programs may be partially aligned with the Science of Reading, or use bits and pieces of pedagogy based on it.

But true Science of Reading programs have it in their DNA. And we can show you how to find them.

Explicit and systematic structure

One of the research-based frameworks used in the Science of Reading is the Simple View of Reading.

According to the Simple View, two cognitive capacities are needed for proficient reading: (1) understanding the language (comprehension) and (2) recognizing words in print (decoding).

A true Science of Reading program is built from the start for students to develop these skills. And it’s built to do so in a developmentally appropriate way. That is, program structure matters, too.

Some programs may add supplemental Science of Reading activities to address these needs. Some have been modified to do the same. But that’s not the same as a comprehensive program designed to develop them, explicitly and systematically. That kind of program is truly rooted in the Science of Reading.

The importance of knowledge building

Again, reading depends on both decoding and comprehension. For many years, classroom observation and received wisdom suggested that comprehension should be taught as its own set of skills, while allowing decoding to develop more naturally.

But cognitive science research now shows that early literacy skills are best built deliberately—on a foundation of knowledge. In fact, knowledge-building is not a result of reading and comprehension, but a prerequisite for it. The more you know, the faster you learn.

Some programs rely on the strategy of activating students’ prior knowledge. But not all kids have the same prior knowledge. Diverse backgrounds and experiences mean that not all kids will come to school with the same information about, let’s say, baseball, or the beach.

So a true Science of Reading program will expose students to a diverse array of new topics spanning history, science, and literature. Those topics will be organized in an intentional sequence that builds knowledge coherently within and across grades. And they will make reading accessible to all students.

The foundational skills readers need

Some programs focus on phonemic awareness and phonics. Those are foundational skills, but they’re not all of the foundational skills. The Science of Reading shows that five components are fundamental to reading: phonics, phonemic awareness, vocabulary, fluency, and comprehension.

Students require instruction in all five in order to learn to recognize words and use that knowledge for reading and writing.

As students develop these foundational skills, they develop automaticity. With practice, they are able to recognize words more and more quickly and move from decoding to comprehension.

A true Science of Reading program will include all foundational skills and will deliver the regular practice students need to become automatic decoders.

How Amplify CKLA is built on the Science of Reading

The Science of Reading is in Amplify CKLA’s DNA. The program was built from the ground up:

  • On the Simple View of Reading.
  • To deliver knowledge on an even playing field for all students.
  • With texts that develop all five foundational literacy skills.

With CKLA, students build knowledge through diverse and enriching content domains. They refine foundational skills through explicit, systematic, phonics-focused instruction. And they do it all in one program, with a detailed road map that guides teachers on every step of the reading journey.

Additional resources

5 ways to shift from balanced literacy to the Science of Reading

MTSS vs. RTI in literacy instruction: What’s the difference?

S3 – 03. Math professional learning experiences with Elham Kazemi

Podcast episode poster for "Math Teacher Lounge" featuring Elham Kazemi, a Mathematics Education Professor at the University of Washington.

How do we continue to grow and be more reflective about our own teaching? In this episode, Bethany Lockhart Johnson and Dan Meyer chat with Elham Kazemi to explore how to look at teaching as a collaborative experiment. Moving more toward analyzing student thinking and how that contributes to teaching itself, leaves more space for one’s own understanding of math to grow throughout your career. When one revises their teaching based on the data we’re collecting from students and peers, this allows us to be both teachers and learners forever.

Explore more from Math Teacher Lounge by visiting our main page.

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Dan Meyer (00:04):
Hey folks, welcome to math teacher lounge. My name is Dan Meyer

Bethany Lockhart Johnson (00:07):
And I’m Bethany, Lockhart Johnson.

Dan Meyer (00:09):
And this is the teacher learning week. We’re thinking this week about how we grow as teachers. And to start with, I just wanted to ask Bethany, uh, first Bethany, how are you doing? And second <laugh>. Um, what is, what, what has been your like most favorite and least favorite, most effective least effective professional learning experience when you were a classroom teacher?

Bethany Lockhart Johnson (00:30):
I think for me, most effective was definitely when I could use it right away. Right. Whatever we were talking about, whatever we were learning, like I got to go put it into practice. Sure. Uh, I, I remember we did something where we designed a lesson and then we went and taught it like one person taught it and the rest of the people watched. And then we kind of like got to workshop it, which that was like a one off the fact that we got to go out of our classroom and go observe somebody teaching. It was gold. It was gold. Um, so that was probably the most effective, because there was so much opportunity for reflection and least effective was something that felt like just completely unconnected to, you know, kind of either so theoretical that it wasn’t like touching on what we were navigating right there in the classroom. I don’t know. What about you? What can you think of times that, are you gonna say times you led a PD? Those were the most effective?

Dan Meyer (01:26):
Yeah. My favorite ones are my sessions, of course. But if I had to throw those out for a second, um, yeah, I, I like, I want, I want both, I want it all. I want the, um, the big ideas that take a long time to settle in that also have like small bits that can carve off and use relatively quickly to test my understanding of the ID is, yeah. I’ve had some, some PD where I’m like, this is very relevant to tomorrow. And I also don’t care. Like for instance, like how to use the CD, the, the, like the, the software, you know, on the, on my curriculum, for instance, it’s like, okay, yeah, this is just a little, little too practical. You know what I’m saying? I want some bigger ideas to chew on. Um, I would also say like, I love my favorite PD by a long was writing up thoughts about how the day went and putting that on the internet in a public place that we used to call a blog and where people would come along, cuz there was like 10 blogs and like, tell me like that’s no good.

Dan Meyer (02:16):
Like the thing that you like is not a thing you should like, here’s the thing you should like instead, or try instead, or just this weird community that sprung up, you know, when I was, uh, starting to teach relatively new teacher and uh, I feel like I grew a lot

Bethany Lockhart Johnson (02:28):
Go back to this idea blog. If people would call you, they’d call you on the phone. What, what

Dan Meyer (02:32):
Was they would fax me? They, it would be a fact. So

Bethany Lockhart Johnson (02:35):
Fax,

Dan Meyer (02:36):
I got it. Fax a comment. Yeah. Got it. So, uh, that’s, that’s Bethany and I, and we’re super excited to have people who have a bit broader of a perspective, a bit more of the land than what, what the two of us, um, think about with our own professional learning experiences.

Dan Meyer (02:52):
We’ve invited on an expert. We hope will help us understand alternate ways to do professional learning as teachers to grow as teachers besides, you know, all of us getting into the same room once every, every, uh, few months together, Elm Cosmi is a professor of mathematics education at the university of Washington, Elm studies, how strong professional communities develop in schools and how schools can be organized. So teachers learn from and what their students, this work is informed by equity oriented research on thinking, uh, on children’s mathematical thinking and classroom practice. She is co-author with Allison hints of intentional talk, which focuses on leading productive discussions in mathematics. And she edited coral counting and counting collections with Megan Frankie and Angela tau, which focuses on the importance of counting from preschool to fifth grade. Looking forward to a great chat with Elham, welcome Elham to the show.

Elham Kazemi (03:43):
Thanks for having me, my favorite topic ever to talk with you both about,

Bethany Lockhart Johnson (03:47):
I think something that I just deeply, deeply respected admire is that I feel like you are constantly sharing about how you are learning. You’re continue to learn, continue to, to try out new ideas and you do a very good job of like highlighting things that you’ve learned, whether that’s sharing it through a tweet or sharing it amongst colleagues or peers. And I, I just really appreciate that because I feel like being in the mathematics community with you, I feel like I grow by, I just like paying attention to like, Hey, she’s a learner, she’s done all these amazing things and thinks in these amazing ways and has shifted my thinking in such amazing ways. But she’s saying, Hey, I I’m still learning. So yeah. Hi, thank you. Thank you for your, I don’t know. We’re just glad to have you here.

Elham Kazemi (04:41):
Thanks. I do feel like the perpetual student, like I’ve never left school and I wonder like one day maybe I will, when I grow older, when I grow up, will I ever leave school? Maybe not.

Bethany Lockhart Johnson (04:52):
<laugh>

Dan Meyer (04:53):
Great. Let’s dig in. Yeah. So please tell us you partnered with a school for some professional learning that wasn’t the sort where you would go in and offer brilliant ideas and then leave. But rather it, it seemed like it was more of a job embedded sort, the sort of thing that might have a life of its own after, you know, after the, the grant ends or the program ends. Can you describe what it was you did and what the effect was?

Elham Kazemi (05:15):
I think I wanna first say that everything that I have done and experimented with as really the result of working with fabulous people, teachers, coaches, principals, other, um, colleagues and peers in the field who are constantly trying to work on what good teaching looks like and how you learn to do it. And mostly because we care about kids and we care about what students experience in the classroom. And we want kids to love school, to have school, be a place where they’re known, they’re loved, um, that they look forward to being in every day. And I think there’s that, um, the why that, that, um, per that makes you want to learn is really about the students and being, doing things in service of them. Because when, uh, as one of my colleagues said, when children thrive, teachers thrive. So what does it mean for us to thrive?

Elham Kazemi (06:06):
If we are focused on our kids’ experiences in schools, what we did at this, this particular school and a group of schools is kind of tap into a, all that curiosity and drive that teachers have to do a good job and to use their imaginations well, and to engage the actual ideas that children have in their classroom together, not separately, not like get a great idea and be inspired by it and then go figure it out by yourself, but be inspired by ideas and then try to figure them out together. Because, um, as you both know, very talented teachers, uh, who also have been inspired to change your classroom teaching. Once you figure something out or as you’re figuring it out, there’s all kinds of intricacies. Like I remember when I first learned about three act tasks, I thought what a brilliant idea, but it’s not so simple to try to enact the brilliance of it because you can simplify it too much or you can get stuck and not really know how do you move from one act to the next, or what’s the point of the third act?

Elham Kazemi (07:12):
Do you just like reveal the answer and that’s it. And then you move on. Um, how do you even do design the tasks to begin with all of those things, raise questions and working on them together, uh, and carving up that space and time to work on them together is sorely missing in schools. And so that’s what we were able to do with the schools that I parted and it is find the time and then design the structures so that teachers could, um, <affirmative> think about their teaching together and then also be in the classroom together with kids. So the kids see that we are also learning to be responsive to them. That’s the point. So we have to work stuff out when kids are present, which is the part that usually trips a lot of people up.

Bethany Lockhart Johnson (07:55):
Well, that to me is I think the part that shifted my teaching and continues to is this, it is a culture shift to tell your students, to invite your students into your learning, to tell them I’m, I’m learning too. It was an invitation to, to be vulnerable in a way that I think sometimes teachers are very afraid to be vulnerable. Uh, if they don’t know what the student response is gonna be, or they don’t know, they don’t wanna seem like they don’t know the answers or they don’t know how to figure out a problem. I think that’s a real shift in the, in the culture for, for compared to maybe what we, we experienced growing up.

Dan Meyer (08:33):
I hated not knowing the answer to a math problem. I admitting I, I was uncertain with the mathematics, but to admit that I am like a, a work in aggress as a teacher, feels like an extra admission, an extra layer of humility, which is, I don’t know, it’s a really special thing that you were up to with that school. I’d love to hear like about specific structures that you worked with to help make that transition feel, you know, more natural, more welcoming, more productive.

Elham Kazemi (08:58):
So, I mean, you probably have experienced common planning time, right? This is a thing that often happens for us teachers. I think that common planning time looks a lot sometimes like, uh, what are we gonna do on Monday, Tuesday, Wednesday? Okay. What do we need? What are the materials we need? Who is gonna do that? Will you write this? And that’s what kind of common planning time, and then it’s over. And then you might see each other at lunch and say, well, how did that go? And you’ll talk a little bit about it, but common planning time and learning labs, which is sort of what the, what we call the, the PD that we designed means. Okay. So let’s take three act task. We, we write a little bit about it. We’ve seen a couple, but okay. What would it really mean to plan this particular one?

Elham Kazemi (09:42):
So common planning time is thinking like, how are we gonna launch that first act? What are we actually gonna say? What do we think the kids are gonna say? Why would we say it that way? What if they say something else? Um, and then, okay, so what does it actually sounds like to transition from act one, to act two? What might we say, what would happen with this particular task and actually getting into the details of how you imagine, like, what, what you would do when you were actually planning the specifics of a particular lesson, but leaving it loose enough that you’re not trying to make it perfect. And I think that’s the trick. So, so that you are not so invested, that goes in that particular way or that you fail. If it doesn’t go that way. Um, but that you have something you wanna learn together and trying out this three act task with a particular group of kids so that when you go into the classroom, first of all, you’ve all thought through the full R of the lesson.

Elham Kazemi (10:40):
And you’re curious enough about what’s gonna happen at particular points that you’ve left room for uncertainty and the taking of some risks. So then when you go together into a classroom and kids start to say things that you didn’t anticipate you or, or they start to do something that you’re so jazzed about, that you didn’t anticipate that you’re like, this is the thing we should pursue more. You give each other permission to do that. You’re like, whoa, wait, did you hear what so? And so said, I think we should follow that road and see where it takes us, or, huh. Okay, hold on. And that’s what we call teacher timeouts, where you actually confer briefly and you tell the kids, this is a super special day. We’ve tried to design something. We’re very curious how you are gonna react to it. So we’re gonna try it out. And along the way, we might pause to get your ideas or for us to make some decisions and steer the ship in a, in a new directions and see what happens. So we’re gonna be sitting closely to you among you. Um, and you get to be our teachers today while we teach. That’s how it’s framed.

Bethany Lockhart Johnson (11:46):
Like, what were you seeing in professional development or in that wasn’t happening amongst teachers? Like where, where are the gaps? Because it feels like so much of your work. You’ve just looked in such nuanced ways at how teachers can continue to grow and be more reflective of their own teaching. And I’m just kind of curious where that came from or where you’re seeing the landscape.

Elham Kazemi (12:10):
Yeah, that’s a good question. Well, I, oh, everything I know about, children’s thinking to Megan Frankie and the beautiful body of work called CGI, but, um, one of the things that we noticed, there’s so many great CGI workshops, and even like all the seminars and conference presentations and amazing things that you can design to have engaging work time for teach in, in professional development, outside of their classroom, people get super jazzed, you know, they get, um, uh, they have meaningful experiences, but to contextualize that back into their classrooms with their own students is like where, where often I would see like, wait, the same group of teachers I just saw in my classroom or in either in math methods or in this PD seminar, or even myself, like noticing, like I have seen and thought about stuff a lot. But when I went to go do it with a particular group of kids, holy moly was that so hard. And I saw all kinds of new complexities that I didn’t anticipate. And if I were just left to my own devices, I might very easily say, whew, this seems a little too hard.

Bethany Lockhart Johnson (13:21):
Right,

Elham Kazemi (13:22):
Right. And that’s the thing that I always hated. I was like, oh, if only we had, or you, or if you watched somebody do a demo lesson and you saw something that was like, kind of cool that you wish you had done afterwards. I often this happened in reflections. I wish we had, because we weren’t allowed to interrupt each other during teaching. Cuz somehow that would be rude or that would undermine the teacher’s authority. But that’s only the way we frame it. If we say actually we’re all capable people. So a question we ask ourselves during instruction doesn’t mean you don’t know what you’re doing. It means actually we’re thinking together then the interruptions aren’t about undermining authority. They’re about thinking together.

Dan Meyer (14:04):
There’s a performative aspect to a lot of teaching. Like the like teaching feels like a performance and you don’t, the movie’s playing or there’s a play that’s going on. It feels like inappropriate to interrupt that in any way. Cause the performance is going and I, I love what this that’s. I love what this idea does to kind of, to redefine teaching is not a performance, but this, this co-constructed thing. Or if it’s a performance, it’s a performance, the stars, all of us, like we’re all a part of the cast and always a it’s always the dress rehearsal.

Elham Kazemi (14:30):
<laugh> it is like the dress rehearsal. Although some of my brilliant colleagues with backgrounds in drama and theater, Sarah Kavanaugh and Holly GU and Elizabeth dure, they actually were at a meeting together. And they talked about how this like breaks the fourth wall, you know, mm-hmm, <affirmative> like, which is out of theater, um, where the performer speaks to the audience, you know, I know you’re there and I have something to say to you. Yep. And I was like, well, we should, why can’t we do that in teaching? So we actually wrote a little paper, um, that’s called breaking the fourth wall as a way. That’s so cool as a metaphor for understanding and reframing what these interruptions could meet. Cuz we often get people when we about this for academic audience who say like, aren’t you using the children and what are the children gonna do while you just pause? Are they supposed to freeze? And uh, you know, while you talk about them, but it’s not really that it’s like, Hey students, we’re here because of you. So shouldn’t, we try to involve you and are decision making. To some extent, it’s not like we don’t know what we’re doing, but we’re doing things because we wanna advance your learning.

Bethany Lockhart Johnson (15:40):
I mean, I still remember the first time I did a teacher time out and it, it was, I, it was breaking the four, it was this like, okay, you’re gonna see what happens, kids like, look at my, my tap dances stopped. And you’re you mean like, you know, whoa, wait a second. And I think it is about how you frame it. Right? It’s a celebration of their thinking and you, you use the term ambitious teaching and it, to me that is such a joyful way to think about it.

Elham Kazemi (16:06):
It is risky. And you would never say anything to shame any student, no. Or to shame your colleagues. Clearly it’s not a about that kind of discussion. Right. And they’re so brief. They’re like, it, it seconds. It’s not like you’re wasting time. You’re actually trying to understand what’s happening here. And I’ve just had so many instances where something goes on. Um, like we were doing a growing patterns task in a classroom and the student built the fourth term and they built stuff that did not follow the pattern. And I was so confused. I, I just didn’t understand like what was going on. And one of the kids said, well, if you, if you did follow the pattern, that’s not her words. But you know, she’s like, well, if we built it this way, that would be too obvious. Because if you just, if you saw that and you’re like, oh, that lesson failed.

Elham Kazemi (16:59):
Now we, our kids don’t understand what patterns are. We did it. Like, we gotta pause here and we gotta say, and we’re like, well, what do you mean? Can you say more about that? And basically what they said is that, um, well, first of all, they’re, they’re right. A pattern could change at any time, but it’s like, it would be more interesting if they, they knew how many cubes it would take for the fourth term that it would be nine, but they’re like, Hey, let’s rearrange that nine in some cool new ways. <laugh> cause that’s more interesting. It was like more interesting to them if, if they didn’t keep the pattern. So like, you kind of had to wrestle with that in the moment <affirmative> with them. And that’s how they can actually be partners with you in the teacher, timeout.

Bethany Lockhart Johnson (17:40):
Right. That’s making it about them and their learning. It’s not about that. It’s not about your performance and like looking all shiny and, and I’ve got it all together and I know exactly how this lesson’s gonna go. It that’s so interesting.

Elham Kazemi (17:53):
And sometimes you pause and like some cuz somebody else who’s watching is noticing something about what the kids are doing. And while you’re, if you’re happen to be the person who’s upfront at the time leading, you’ve got so many things going on in your head that some times the person who’s just been sitting on the rug with the kids mm-hmm <affirmative> has noticed something. And they’re like, can I ask something right now? And that’s a great teacher timeout too. Mm. Because they’re interrupting you cuz they’re like, I think I, I wanna see what kids will say. If we ask this question next and those moments have been like amazing because someone has noticed something that another person hasn’t in the room and it’s been very helpful to illuminate how kids are processing something or what two ideas they could connect. That would be really powerful based on what we were hoping to learn that day or do with the kids that day.

Dan Meyer (18:47):
It’s like you have a bonus brain attached to you there in the room. Sounds really powerful. I wonder a couple about the student experience of this. I’m imagine if I was a student in the room and I heard the two teachers like kind of pause, take this time out and like talk about how interesting my thinking was like behind my back a little bit, like trying to strategize about something interesting. I had said, I just imagine I would, I would feel very good about like, that would be a very positive experience for me. Um, but I’m just curious, can you speak to how students reacted when they’re,

Bethany Lockhart Johnson (19:16):
You mean, if you had been a student in the class and you saw two teachers conferring about your work?

Dan Meyer (19:21):
Yeah. Yeah. Like I, my classmates had of thing that was like, it, it kind of like was so novel that it stymied the teachers and then they like had to pause and like talk about what are we doing? Oh, I don’t know. I can imagine that’d be like know a fun feeling. Maybe I just tell more about me than about the kids, but

Elham Kazemi (19:35):
<laugh> it points to like, how would you go about starting to do this work? Right. Because one is you do, you do have to tell kids, Hey, I’m here with so and so and so, and so, and so, and so it might be just two of you. It might be five of you. It might be more and you know how we’ve been working on X thing in class? Well, today we wanted to try this new thing and, but we’re not sure how it’s gonna go and we need, we need your feedback. Right. So here’s something that might happen. We might pause you, you, I mean, you really do directly tell the kids to do that. And then we’re gonna ask you how it felt and we’re gonna share those feelings with one another. So you do that, you do a little exit card or you,

Bethany Lockhart Johnson (20:19):
How, what felt the pause or how,

Elham Kazemi (20:22):
How, yeah. How did it feel that, how did this lesson go or how did a lesson, how did it feel when you heard, you know, ALM and Dan talk to each other, doing this lesson and they might say, Hey, it’s cool. It’s fun. Kids have definitely chimed in, in like, if we ask a question like, should we do this next or this, somebody will pipe in and say, do that, you know, do this thing. Instead. If, if you kind of pipe in to say, can I ask a question? They just turn to you and look at you and answer your question. Right. So, and we always thank them and we just like pump it up. Right? Like this is so cool because this is all about you. And usually when you say today, you’re gonna be our teachers, especially the little kids. They like get all giggly. Totally.

Bethany Lockhart Johnson (21:02):
Right.

Elham Kazemi (21:04):
Love it.

Bethany Lockhart Johnson (21:05):
You know, you, you were sharing about this really unique situation, which I wish it wasn’t as unique where you had the whole school involved, but how did that happen? And what if you don’t have the whole school involved? What if it’s just me in my grade level, who’s like, I kind of wanna try this, but what

Elham Kazemi (21:22):
<laugh>, I think you could start with your, a peer in your school or a colleague in your school. Yeah. I mean, it’s a little seed, right. And it’s a little seed and then you could make it grow. I also believe in starting small and growing, cuz you do have to invite people into a different way of thinking about what it means to learn together. So you need to experience it, um, in order to believe it.

Dan Meyer (21:49):
Yeah. It feels like we would not want to write off any student as like, oh, they just don’t wanna learn. I think a lot of, a lot of us just like don’t buy that, that there’s other reasons why people need that. A teacher shouldn’t like shouldn’t, that’s not true of students that they have been told they can’t learn or there’s various circumstances the same. I, I suppose the same as like should be true is true of teachers. Like no teacher doesn’t want to learn more about teaching is at least a helpful Axiom to use, to approach the work of teacher growth. And so maybe they, yeah, maybe I feel like I’m the only person in my school who wants to do this, but perhaps that’s not actually true. Perhaps it’s just a matter of creating an imagination or the right kind of enticement or I don’t know what, um, but to start small and grow from there makes a lot of sense.

Elham Kazemi (22:32):
I feel now, like it would be weird and a lot harder for me to invite someone to just come in and watch me teach and sit quietly in the back when I don’t know anything about what they’re thinking and wait until afterwards to get their opinion.

Bethany Lockhart Johnson (22:46):
Oh yes.

Elham Kazemi (22:47):
I would be much more willing to co-plan with someone so that we were both on the same page about what we were trying to do and then when you’re in the classroom with me. So that’s the other thing that’s important cuz I don’t think you can just be in the classroom together and I, you know, interrupt each other’s teachers, if you haven’t planned together, cuz you do have to have some common understanding of what are we trying to do here? Oh the

Dan Meyer (23:10):
Intent here.

Elham Kazemi (23:11):
Yeah. So I would definitely say don’t just show up in each other’s classroom and start interrupting each other. <laugh> if you don’t know what the heck is going on. Yeah.

Dan Meyer (23:21):
Yeah. I, I know that’s directed at one person on this call in particular. I hear that.

Elham Kazemi (23:25):
I know who we’re talking about, but you know, I would be way more intimidating for me if I was trying to do a three act task and Dan just came to watch me do it <laugh> and he hadn’t planned with me. He didn’t know why I selected that task. I had no opportunity to talk to him. Then it would be, Hey Dan, would you just like do this with me? Let’s think through this. Why would you do this then? What, what have you normally done? Oh, okay. Why have you done that? Right. And then to like, okay, let’s try it together. Um, and then, and then along the way, if I have questions, you’re there with me. So sometimes there is someone more experience like if right. And sometimes you’re both just like, I just don’t have that much experience with this. I’m learning this for the first time.

Elham Kazemi (24:04):
Right. And the beauty of the math ed community, whether it’s on Twitter or is that we’re kind of pretty accessible to each other. Right. So if I read something and I have a question about it, you bet I’m gonna reach out to the author <laugh> and say, I’ve been thinking about your work and this is what’s been coming up for us. Can you? So like, it definitely happened with hands down conversations. We tried it in the learning lab and we just couldn’t figure out like that. How do you intercede, like into the hands down conversation cuz the kids are supposed to have a conversation. So we had to like give Kaia and her co-author a few specific examples so they could help our thinking so that we could try it again. Right. And make it better. And I think that is, is what it means to be learning in community is that you use the resources more broadly.

Bethany Lockhart Johnson (24:52):
That’s a beautiful reminder too. And it also helps me feel a little better about all the messages I’ve sent you. Like what does this mean? Can you help me with this?

Elham Kazemi (24:59):
<laugh> I mean, that just makes you feel alive. <laugh> I think

Bethany Lockhart Johnson (25:06):
So. I think P part of the beauty of you talking about starting small is that it does give those of us who maybe aren’t seeing that those opportunities for collaboration reflected in our school culture, it gives us kind of some hope for like, wait, don’t just like, think you can’t start. I, how do you, how do you see, how do you see it growing? Or, or do you think like if you could magically <laugh> like wave your wand and, and create some shifts around, around, uh, the culture where folks are feeling isolated or maybe don’t feel like they have the needs to do this work. What could that look like?

Elham Kazemi (25:51):
Yeah. What could that look like? So time, like we need some imagination around the use of time in schools and I have seen some really amazing opportunities where teachers get to co-teach, which means that they really have to co-plan when, um, there’s a break in a regular school session and there’s like an intercession or like a, like an elective that, um, that doesn’t, I haven’t seen it happen a lot in public schools, but I have seen it happen a lot in independent schools where they’ll have like, stop, stop the presses. It’s like a drop everything and read, but it’s like a drop everything and do an R arts week. And then all the kids in the school get shuffled. So they into multiage groupings and the teachers get to plan something special for like the week. But you could start with like a day, which would at least get you to plan something together and try to teach together and be just in each other’s spaces. And I think that might be kind of an interesting way to start where you have to like mess with the schedule somehow. Cuz the schedule is the beast in schools

Bethany Lockhart Johnson (26:59):
Is kind of the first step. Like we are going to create a shared activity, a shared instructional goal, a shared like where do I start?

Elham Kazemi (27:09):
What, where do you start? I mean, there’s so many good books. We all read, start with something that grabs your imagination. That you’re like, if I got to do this in my class, I’d be so jazzed. And I think my kids would love it. Why would they love it? You know, whatever it is. There’s so many good ideas that people are instantly blogging about publishing, um, slow reveal graphs. I love those two. I have like all these things. I was like, I would love to try these out, but I, I gotta do them with somebody cuz I need a sounding board about like how, what does it mean to do it well? And what does it mean to just do it at the surface level and do it a, you know, in a kind of a crappy way. And we don’t wanna do a crappy job. We wanna do a good job, but you have to start, you have to start sometimes in an awkward, crappy way. Like, you know, and get past that stage. Cause often we try a bunch of stuff, eh, and then we drop it. But like you gotta work on it to make it really

Bethany Lockhart Johnson (27:58):
Good. And if you’ve already tried it and it didn’t go so well it’s, this could be an invitation, like, you know, it doesn’t mean give up on the idea. It means like, Hey let, let’s let’s collaborate. Let’s you know, come into my class. Let’s co plan this.

Elham Kazemi (28:10):
So I would challenge people to think about the schedule. <laugh> try to do something just a little bit different. You know, like when we do learning labs, people are like, well, how do you do that? And there’s no money for it. Actually. We just use our money in a slightly different way to make or that everybody four people get a sub, which I know right now, sub shortages is crazy, crazy, but then combine your classes or do something different. Yeah. You know, um, involve people differently somehow in your, in your school environment to get that time,

Bethany Lockhart Johnson (28:43):
Really see this as a priority. This is a, this is there’s is intense value in this time to collaborate. Yeah.

Elham Kazemi (28:51):
Yeah. There’s so many side benefits for, I think for kids and teachers when you’re able to do this.

Dan Meyer (28:58):
Yeah. You’ve heard of folks. Uh, usually our, our math teacher challenge, our lounge challenge has been, uh, pedagogical in nature or a new CU. And uh, this is a different kind of one. This is, uh, go, go be a Rabel Razr go Rouse rabble at your, uh, front office and figure out the right way to get some funding or some time or shuffle a master schedule in such a way that you have collaboration, time to plan to co-teach to interrupt one another and uh, let us know how it goes. We are super excited and super interested in all of that. Thank you, uh, Elham for being with us here today and sharing all of your wisdom about how teachers grow.

Elham Kazemi (29:36):
Thanks for reminding me. You too loved

Bethany Lockhart Johnson (29:38):
It. We’re never done learning. We’re never done learning. Nope.

Bethany Lockhart Johnson (29:44):
Aha. Thank you so much for joining us in the lounge. I think all of us have sat through effective and ineffective professional learning sessions and just helping us to envision of how this can truly help PD can truly transform our classrooms. It is it’s exciting. It’s exciting. And I think we’ve all learned a lot from our conversation. So thank you. Thank you. Thank you. And don’t forget, you can connect with us in the lounge on Facebook at math teacher lounge or on Twitter at MTL show. Let’s keep this conversation going. Keep it going. Thanks so much for joining us. Thanks

Speaker 4 (30:20):
Everybody. <silence>.

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What Elham Kazemi says about math

“ When children thrive, teachers thrive. So what does it mean for us to thrive if we are focused on our kids’ experiences at school?”

– Elham Kazemi

Professor of Mathematics Education, University of Washington

Meet the guest

Elham Kazemi is a professor of mathematics education at the University of Washington. She studies how strong professional communities develop in schools and how schools can be organized so teachers learn from and with their students. This work is informed by equity-oriented research on organizational learning, children’s mathematical thinking, and classroom practice.  She is co-author with Allison Hintz of Intentional Talk, which focuses on leading productive discussions in mathematics. She also edited Choral Counting and Counting Collections with Megan Franke and Angela Turrou, which focuses on the importance of counting from preschool to 5th grade.

Follow Elham on Twitter

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About Math Teacher Lounge: The podcast

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

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

S4 – 02. Bethany and Dan share their math biographies

Promotional graphic for "math teacher lounge," season 4 episode 2, featuring photos and names of math teaching guests Bethany Lockhart and Dan Meyer.

In this episode, co-hosts Bethany Lockhart Johnson and Dan Meyer get personal and share their “math bios”—their early experiences with math and how those experiences turned them into the educators they are today.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:00):

We’re recording. What’s up, everybody. This is Dan Meyer with Math Teacher Lounge.

Bethany Lockhart Johnson (00:08):

And I’m Bethany Lockhart Johnson. We are so excited to be back. Season Four, Episode Two. Hi, Dan.

Dan Meyer (00:16):

Hey, Bethany, how are you doing today?

Bethany Lockhart Johnson (00:18):

I’m so excited to be talking with you! You know, as we record this, our reunion at NCTM is getting closer and closer.

Dan Meyer (00:28):

The NCTM live show is gonna be bonkers. I don’t think people are ready for it. You think you know what we’re about on MTL from listening to us, but the live show is gonna be outta control. You cannot imagine how many clowns and elephants Bethany wants to have at the live show. We’re still—we’re trying to talk her down from like three to one, but we’ll see.

Bethany Lockhart Johnson (00:44):

All I want is the t-shirt cannon. Because I used to go to these baseball games and they would have a t-shirt cannon. And I thought, I wanna operate a t-shirt cannon! So like, if I could be standing on stage aiming t-shirts at people who are jumping up and down requesting a t-shirt? I don’t know. Doesn’t that sound fun?

Dan Meyer (01:01):

Sounds awesome. High point of my college education was catching a t-shirt. No, it was—it was a burrito. It was a burrito cannon. But I think it was just a t-shirt cannon, but it was a burrito cannon. And I caught a burrito at a game and it was probably the most memorable moment of all of college education for me.

Bethany Lockhart Johnson (01:16):

Was the burrito still warm?

Dan Meyer (01:18):

Oh yeah. I think it got—like, I think it might’ve been warm at one point and then it got warmed back up through the muzzle velocity of the cannon. So it was a pretty great system they had going on there. <Laugh> Yeah. <Laugh> Anyway, I’m off topic, but, we’re thrilled to—I’m thrilled to chat with you and we’re thrilled to be listened to by you folks out there in MTL land. In the lounge itself. We got a fun show today.

Bethany Lockhart Johnson (01:40):

So if you listen to Episode One—which if you haven’t, hope you go back and listen to it—if you listen to Season Four, Episode One, you’re gonna hear—we asked Huon, KT, who is this delight of a joyful teacher. We asked her to talk to us about what’s her math bio. And we want to ask all of our guests—like, I wanna go back and ask every single guest we’ve ever had to tell us their math bio.

Dan Meyer (02:06):

Yep.

Bethany Lockhart Johnson (02:06):

Because, while seemingly simple in nature, our students enter our math classroom already having had this relationship with math and these notions about their role in math or what they think about math. And it impacts our school year with them if we’re a teacher. And it impacts our relationship with math as we move through our education and beyond. Right? And I I’m so excited about this question, ’cause I think it also ties into this theme for Season Four, which is joyful math, and diving into “When has math felt joyful? When has it not? Does it feel like—how do we think about how our math bio, our relationship with math, has evolved into a joyful or less joyful place?”

Dan Meyer (02:54):

I get it. And what’s really key here, I think, is that teaching more than other professions is a generational profession. You know what I’m saying? Like, no one is like, “Well, you know, I sold insurance to you and now you’re selling insurance to, you know, my grandkids; that’s amazing!” But people are always posting photos when, like, you teach someone who then becomes a teacher later. Teaching is a generational sort of thing. So the kinds of joyful experiences that we offer or don’t offer students now affect the experiences that students who haven’t even been born yet will have, you know, some 20, 30 years later. That, to me, is a trip. And well-worth exploring, you know, how we got here, mathematically speaking.

Bethany Lockhart Johnson (03:39):

I remember a friend had sent me this image of an assignment that her son got that was asking for their Mathography. They wanted to know about their history of mathematics. And this was their first assignment. And this teacher, I would like to imagine, read them all and used it to inform conversations about students’ relationship with math. And, you know, some of the questions they asked were thinking about whether you consider yourself, quote, unquote, “good at math.” Like “what kind of experiences have you had? What do you like or dislike about math? What is, you know—what do you expect to learn in math this year?” Just asking students to actually pause and examine and reflect on their relationship and then also looking forward to, like, what kind of a classroom community do we wanna create? And I loved that assignment. And yeah, so today’s episode Dan, guess what?

Dan Meyer (04:32):

What’s going on? What’s happening?

Bethany Lockhart Johnson (04:33):

I figured we should ask each other about our math bio.

Dan Meyer (04:39):

I think the people out there would love to know this about us. ‘Cause you know, we’re both awesome. But also what’s really cool here is that like, I don’t know this about you. Like not, not a lot. You know, the folks at Amplify, they kind of assembled me and Bethany together in the same way that record labels assembled pop boy bands, girl bands, that kind of thing, back in the day. You know, grabbing some stars from screen or film and just like throwing ’em together and saying, “All right, now you’re here to perform together.” And so it’s just a really good moment for us to, like, settle back and just know who we’ve been working with for the last three seasons and change here. I love it.

Bethany Lockhart Johnson (05:15):

Well, I don’t know. I don’t actually agree with that, Dan. Because don’t you remember? We knew each other beforehand. And while I would like to think of us as…oh, I’ll say One Direction—well, no, One Direction is now defunct. Who’s another band that got formed by one of those shows and is still together and still—

Dan Meyer (05:33):

BTS! K-Pop, you know! Let’s go!

Bethany Lockhart Johnson (05:35):

K-pop. BTS.

Dan Meyer (05:38):

Let’s go, Bethany <laugh>.

Bethany Lockhart Johnson (05:39):

So can we incorporate some K-pop into the NCTM Math Teacher Lounge live episode? Don’t answer now. Don’t answer now. OK. So not only are we gonna share our math bios, but we want to encourage you listeners to share your math bio with somebody in your life. It could be a child in your life, maybe talking to your kiddo about what was it like. What was math like for you? It could be a student that you have. It could be a partner, a friend, a parent. I mean, the sky’s the limit. Share your math bio. And most of all, share with us. We wanna hear about your math bio and you can share it with us at Twitter, at MTLShow, or in our Facebook group, Math Teacher Lounge.

Dan Meyer (06:26):

Stop on by, please. All right. I’m gonna just share like, just a couple of quick, signposts. Not the full bio. Gotta leave them wondering about something here. But here’s a few quick highlights and lowlights of my math bio and how, maybe, it made me the teacher that I was and the educator I am. Is that cool?

Bethany Lockhart Johnson (06:44):

Wait, I didn’t even, I didn’t ask you yet.

Dan Meyer (06:46):

Ask me what?

Bethany Lockhart Johnson (06:47):

Hey, Dan!

Dan Meyer (06:49):

Is there like a magical word? Like, what’s your math bio? <Laugh> Oh, go for it. No, no, that’s right. They won’t know what I’m talking about. Why is he talking about his math bio? Bethany—

Bethany Lockhart Johnson (06:57):

That whole lead-in that we just gave? They might not know.

Dan Meyer (07:00):

Yeah. We just talked about math bios for the last 20 minutes. But yeah, they might not know what we’re—

Bethany Lockhart Johnson (07:04):

<laugh> So Dan, why don’t you go first? ‘Cause I know you were gonna ask me to go first, but why don’t you go first? Dan? What’s your math bio?

Dan Meyer (07:12):

Oh, wow. Well, thank you for the formal invitation to share my math bio, Bethany Lockhart Johnson. So, I’ll just share—I just wanna share a couple items here, not the full history. Gotta leave ’em—leave a little mystery in there, you know what I’m saying? But here’s a few highlights and lowlights, and I think what it means for me as an educator. So, I was homeschooled for eight years. That was big—did a lot of math learning on my own. Couple of lowlights from that, a lot of highlights, in terms of just like being able to, like, learn at my own rate and just jump on ahead and pursue different wacky things. But I tried to switch into public school in fourth grade and I lasted, um, four hours. I didn’t even go to class. I enrolled and then it was like, boom, I was out of there. Because we went to the school; we met the teacher, saw the room, very nice person and place. But I got the homework assignment and the homework assignment was gibberish. I had no idea what to do and such was this feeling of just, like, despair and hopelessness, I was like, I cannot be a part of this. I remember the assignment. It was about identifying scalene, isosceles, and equilateral triangles. I’ll tell you this: I am quite good at that now. But at the time, like, I didn’t know what those words meant. And you know, at that moment we had Encyclopedia Britannica, could not Google this or even Ask Jeeves or AltaVista this so well back then. It just—it was an entry moment of failure and realizing that so much of math is like a, kind of a social kind of construct. And if you’re not part of that social circle, what can you do? So that was a bummer. Another bummer was eighth-grade math, learned it all by way of videotape. You know, put in the tape and watch—not gonna say the person’s name and not this person’s fault—but it was just like watching someone work on a whiteboard. Kind of a precursor to Khan Academy, kind of a drag. Went to high school—

Bethany Lockhart Johnson (09:02):

Wait, wait, wait, wait. We were—I’m not ready to jump to high school. Wait. Can you pause for just a second?

Dan Meyer (09:06):

Yeah. Rock on.

Bethany Lockhart Johnson (09:07):

I just need you to go back to the triangle thing. So in that moment, what did that mean for you that you had had all these experiences with math and then you encounter math in a completely different sphere, a public school, and it did not have a connection or meaning to you because prior to that, it sounds like it was pretty positive. Right? Explore these things you’re curious about; there’s not, like, a level you need to stick with…

Dan Meyer (09:33):

Yep, yep. Yeah. I think that’s right. Maybe it was a little bit of a classic, like, “Oh, I didn’t have a growth mindset; my mindset was like, ‘Oh, I’m good at math because I am, you know, born that way,’” and all of a sudden, that identity was, you know, thrown into question. And, you know, my foundation was all of a sudden quite shaky. And yeah, that’s—you know, I think I taught a lesson recently where I was like, “Hey, this whole thing with a less-than or equal-to sign and a greater-than or equal-to sign, like what those signs are: it’s just, it’s language. And if it’s confusing to you, it’s not because you’re bad at math; it’s ’cause language is oftentimes confusing ’cause people have to agree on it.” So I dunno, that sort of thing is kind of filtered in, filtered back in periodically, some sympathy for like how a lot of math is like just socially agreed upon ways of working with, you know, numbers, shapes, patterns, that kind of thing.

Bethany Lockhart Johnson (10:20):

OK.

Dan Meyer (10:21):

Anyway.

Bethany Lockhart Johnson (10:21):

  1. And in this home school—I have a lot of questions about that, but I’ll stick to one—were you in a community of people that you talked about these math ideas with? Were you homeschooled solo? You have a sibling, so I think you were together, right?

Dan Meyer (10:39):

Yeah. Yeah. I’ve got a twin sister. So we were, you know, like, right on with each other the whole way through there. And yeah, so we had—but it wasn’t, it wasn’t like a—it was a lot of individual work, with my flavor of homeschooling.

Bethany Lockhart Johnson (10:54):

  1. Got it. And the tapes—wait, before you go to high school, the tapes, the VHS tapes, which I’m just loving this image—

Dan Meyer (11:02):

Yeah.

Bethany Lockhart Johnson (11:02):

Was that a positive experience? Was that because that was an area of math that whoever was homeschooling you wasn’t that comfortable with? Why was it that route for the tapes, and what was that? Was that joyful for you?

Dan Meyer (11:15):

Yeah, definitely not joyful. Yeah, it was like, if you had questions, you couldn’t really ask them of the VHS tape. It didn’t work out so well in that way. And it was a lot of operational-type math. It was, you know—there was no give and take; it was all kind of take. From the video teacher. And yeah, I was doing that because my homeschool teacher, my mom, who is very smart in lots of areas, did not have the math knowledge or confidence, especially to help with math at eighth grade. And that was a big reason why, flash-forward to the next year, went to high school.

Bethany Lockhart Johnson (11:48):

Nice segue. OK.

Dan Meyer (11:50):

<laugh> You caught up to high school…I encountered just like four years of just crazy-good, just bonkers-good math teachers who just really changed a lot for me. Especially, Mr. Bishop and Mr. Cavender, very cool folks who did a lot. And especially, I think Mr. Bishop and Cavender both modeled for me what curiosity from a knowledgeable adult looks like. Like someone who, you know, now I can say to myself, “Oh, they were kind of like putting on an act of being very curious about answers they were hearing for the 2000th time from a student,” let’s say, but what a powerful experience that was for me to feel like, “Oh, wow, my thoughts are interesting to someone besides myself.” I got like, maybe it’s two real highlights that I’ll just point to, from my math bio that made me the math teacher and person that I am. Let’s see here. Maybe three, if you you’ll indulge me. One is just like the idea that you could do math wherever you have your brain, a pencil and a paper. And so I remember like in high school, I was in church with my family and kind of a little bit bored of whatever’s going on. And I just had the Bolton and I like drew a pentagon, a regular one, then a hexagon, a regular one, and kept on drawing, like adding sides to the shape. And it was like, it was becoming a circle. And, you know, I was able to take the area of each of those shapes and say, you know, “What happens as you send the number of sides to infinity?” And watch as the formula for area of a circle, Pi R squared, popped out. And it was kind of a literal religious experience, in that moment, just like, “Wow, like my brain’s so cool and math is so cool and paper and pencil’s so cool.” And so there’s that. Just that kind of experience was pretty awesome. And then I would just say like, I’ve had some really fantastic experiences with math in the world itself. Stuff like—let’s see, this is gonna invite more questions from Bethany, probably, maybe I should avoid—I got, I have a Guinness—I have a Guinness world record that’s almost 20 years old. This Guinness world record is—it’s old enough to drive basically at this point. And almost old enough to drink. But like it was—it was a record for chaining the longest paper clip chain together in 24 hours. And the only way I was able to break that record was through mathematics. Where, like, I would be finishing a box of clips. And I would say to my buddy who was there, “I just finished a box of clips.” And that person would type in the number of clips that I had just done. And then a mathematical formula that I had created would tell me how many—how long the chain was at that point. It was being rolled around a spool. And like, it’s just like, wow. So math just made this possible. You know, math revealed that the record I was trying to beat was beatable, because I did the math on it. It was, like, thousands of feet long in 24 hours. And other folks might be like, “Oh, like, that’s that’s huge!” But me, I was like, “All right, let’s divide this out. You know, divide by 24 hours in a day, divide by 60 minutes an hour, 60 seconds in a minute. Oh, that’s like one clip every four seconds. That’s really slow.” You know, think about that <counts aloud>, “Clip, two, three, four. Clip two, three…” It was just slow. So math helped me, you know, wreck that record. Which to my knowledge still still stands. Don’t get any ideas, Math Teacher Lounge Folks! Is this news to you, Bethany? You haven’t blinked in the last, like, five minutes. I’m curious if this is new.

Bethany Lockhart Johnson (15:20):

It is news to me. And I have so many questions. Because OK, if four seconds was slow, so then what was your like—so then I’m assuming a hundred clips per box? Like, what was the rate, you know, per box? How long did it take you to complete a box? What did this friend like? Did this friend stick with you for the whole 24 hours? Did you really do it for 24 hours? Or once you beat the record, did you rest? How did you account for biological function? Like, needs? Like a restroom?

Dan Meyer (15:51):

<Interrupting> Like what?

Bethany Lockhart Johnson (15:51):

Eating.

Dan Meyer (15:51):

Like what, Bethany? OK.

Bethany Lockhart Johnson (15:52):

Um, Sleep.

Dan Meyer (15:55):

So yeah, maybe we dive into some of the specifics in a different time.

Bethany Lockhart Johnson (15:59):

Just tell me one of ’em. Tell me one.

Dan Meyer (15:59):

I’ll just say. So as to discourage other Math Teacher Lounge listeners from taking this on—back off of the record, folks!—this was back in college, so I was a little more limber back then. But I did one—I think it was 1.8 seconds per clip. For an entire 24 hours. Just like, so just like think about it, would you? If you’re gonna step to me on this one, just think about that, OK? And then, and then, you know, make an informed decision.

Bethany Lockhart Johnson (16:28):

Wait. Wait, wait, I just wanna tell you one thing. I’m picturing somebody with a straw, and like, giving you water as you keep clipping. I’m picturing, like, music, I…

Dan Meyer (16:37):

That’s not far. That’s not far. That’s not far from—yeah.

Bethany Lockhart Johnson (16:40):

So many questions! OK. Go on. Sorry, sorry, sorry. Go on. This is your bio.

Dan Meyer (16:44):

We gotta, I gotta wrap this up. I wanna hear your bio. But, like, I would just say like this move to this sense that math is actually a thing that’s useful for more than just a grade; it’s useful for more than just, you know, the societal, you know, adulation that comes from being a math nerd. That kind of thing. And so that, I think that affected a lot of math teaching for me. And, if I gotta, like, summarize math teaching itself in a journey, it went from like, “Hey kids, aren’t I awesome?” to, “Hey kids, isn’t math awesome?” to “Hey kids, aren’t you awesome?” And like that journey was facilitated by lots and lots of people, you know, a lot of personal growth, but at this point, at one point I was like, “Hey, math can help you get records and whatnot. It’s really useful.” And now I’m like, “Wow, your brain’s just doing just really interesting things. I can help you understand how interesting those things are, and maybe make them more interesting, or interesting in a different way, with some help here.” Let’s put a pin in that. That’s the math bio.

Bethany Lockhart Johnson (17:50):

  1. So I have no doubt that if you ask someone in your life, listeners, for their math bio, that you will discover things about them that you never knew. Literally the questions that I have…I have so many question. And Dan is very good at, you know, bringing me back. Bring me back, like, come on, come on. But I just wanna say, overall, your journey seems pretty joyful. It seems pretty joyful. It seems pretty full of confidence. I don’t wanna say “ego” in a negative way, but I wanna say you were buoyed by these experiences that allowed you to feel like math was a place for you to thrive.

Dan Meyer (18:36):

Right.

Bethany Lockhart Johnson (18:36):

Where you could try out things. You could try it out and just, “I could do that!” Right? Like…your relationship just felt very, like…you felt like you had autonomy, agency, perhaps much like you, you operate in this world. Dan, is that, is that right <laugh>?

Dan Meyer (18:54):

Yeah, I think it’s fair to say. And without telling too much of her story, my twin sister with whom I share most things, including genetics, you know—she had a very different experience in math early on. She’s brilliant. She’s a doctor. And not, you know, the book kind of doctor that I am, but like a real, you know, medical doctor. She’s brilliant. But we were—we encountered different messages about who math was made for, early on in, you know, in our entire math learning. And she—we both digested the messages that we were sent, and took, you know, different, different paths because of them, for sure.

Bethany Lockhart Johnson (19:31):

Funny how that works. I thank you, Dan. I do. For in all sincerity, I appreciate you sharing that. And I think that it’s exciting to hear how it influenced your teaching. It feels like you want to cultivate those experiences for your students. And I’ve been in the room when you’ve presented; I was in a room where you taught a class live. It felt like you were making space for the students to have these aha moments. And it feels like in your work at Desmos, and now Amplify, you’re trying to create these products that allow folks to recreate these amazing math moments. Right? And that it’s for everyone and that it’s accessible and it can be very positive. I feel like I have this new perspective on kind of the energy you bring to your teaching. So thank you for sharing that.

Dan Meyer (20:24):

Yeah. Been a pleasure. Thanks for your questions here, Bethany. And it’s been—it’s been fun to reflect on it. And I do—I do feel very lucky in lots of ways. Privileged. Lucky. I know, like—I think the world has been set up for my success in lots of ways, as who I am. But I do just…yeah, I feel—I want more people to experience what it’s like when you walk into a math classroom and it’s like, “Hey, this place is for you. You have interesting thoughts about this. Let’s get ’em out.” So that’s awesome. I would love to hear about you and how you…I mean, we have taught different kinds of kids. You know, I taught kids who I think were somewhat set in, they’re a little bit more solid at secondary in who they are as a math learner. Like “I know who math is and who I am with math.” And I’m really excited to hear what your math bio allowed you to do with students who were perhaps open to the idea that they are very mathematical or at least not yet closed off to those possibilities. So, yeah. What are some of the high, the, you know, the high and low water marks of the making of Bethany Lockhart Johnson, math teacher? <Laugh>

Bethany Lockhart Johnson (21:24):

Thanks for asking, Dan. <Laugh> I’ve shared aspects of my math bio because I think it really informs the way that I talk to people about math and think about math. And I like to share it because I want folks to consider their own journey with math, as we like engage with problem-solving and sense-making and thinking about the students in our classroom. My dad is a math and computer science major. So he had a computer very early on. I wish he had invested in Apple early on when he had like one of the first Apple computers ever. And, sorry, dad, but it’s true. I do wish you had done that.

Dan Meyer (22:10):

I’m sure he does too.

Bethany Lockhart Johnson (22:11):

Oh, he does. So math and computers and conversations about counting, you know, it felt like it was kind of just normal. Like it was around me. And I went to Montessori, which is a private school that—oh, they have some public Montessori—but it’s very self-directed. And so we would have these kind of charts, these goals for the day that you explored. And so we would explore math in very, I don’t know, very organic ways, with these natural materials. And I feel like I excelled at math, but it wasn’t something that I was conscious of. It was just like, “Oh, well, yeah. Math, it’s, you know, something we do.” And then when I went to—when I left Montessori in fourth grade, I remember that year being a lot of like repetition. I was like, well, we did this. We covered this. And except for the mission project that we hadn’t done, that was all new. And that’s it. For another time I’ll share about that. But <laugh> then, they actually, I was moved with a group of students to the fifth grade math class, ’cause we had already done the work that we were doing. And so, it wasn’t that it felt like it came easily, but it did make sense. What we were doing made sense. And then it all kind of changed. There was a lot of change in my family. There was, like, missed school time. And we moved and I went to a new middle school and I was in this environment with students who—it was like an accelerated program. And so I was in this environment with students who were pretty competitive with each other. And I remember going—and I was not from of a competitive environment; like Montessori is not competitive. It’s not about that.

Dan Meyer (24:02):

Right. Right.

Bethany Lockhart Johnson (24:02):

It’s—it was very strange to me that I would be competing against anyone, even competing against myself. And I, you know, knew how to set goals. But it was a different level of energy. And I felt like, because I wasn’t competitive in that nature, I felt like that kind—I felt on the outside of a lot of the energy. Besides the regular, like, middle-school feeling outside of things. And I remember the first friend that I made. Hi, Susan! She had said to me, this was like maybe our second week of school, she’s like, “Oh, at lunchtime, come with me to math club.” And I was like, “OK.” And I remember walking into that room and I had no idea what was going on. And so that was one of the first times where I was just like, “Whoa, I have absolutely no concept of what they’re talking about or what.” These are my peers. I felt very—it was very—it was strange. It was strange. I was like, “This doesn’t feel like a space for me at all.” When I think ordinarily I was kind of excited about the idea of going to math club at lunch, you know? And over middle school, I kind of just got progressively more and more behind. It started with missing some work and then missing more and then checking out. And, you know, the problem was that I really made it about myself. That, like, it wasn’t something that I was then good at or could do. When really it was that well, pre-algebra, I was having a really hard time in like the rest of my life. And so I wasn’t real present in that class. And so when I got to algebra, it didn’t make a whole lot of sense. And then if I missed Monday, Tuesday, and Wednesday, well, Thursday is gonna be hard, you know? And, it just got progressively harder and harder. So I had this great idea that between eighth grade and ninth grade, I was going to take this accelerated geometry class. ‘Cause that was the ninth grade class, it was geometry. And I would take it. It was like geometry in three weeks or something. So then when I entered high school, I would’ve gotten this like jumpstart. But I wish I had said, “Oh, I’ll take this, and then in ninth grade I’ll take geometry.” So like I’ve already kind of gotten a preview of the material. But instead I went to the 10th grade math, which was like intermediate algebra, trigonometry. I had absolutely no clue what was going on. And I had a very, very difficult time and I wasn’t ready for that class. But it was exacerbated by the fact that this teacher felt very free to let the freshmen in that class know that they shouldn’t be in that class. That this class was for 10th graders.

Dan Meyer (26:49):

Oh wow. Oh, wow.

Bethany Lockhart Johnson (26:51):

And we had a rather contentious relationship. And I will never forget that we were in the hallway, and he says to me, “You don’t belong here.” And I’ve talked to—I’ve talked to a girlfriend of mine about her experiences with this teacher and she has the fondest memories.

Dan Meyer (27:13):

Wow.

Bethany Lockhart Johnson (27:14):

She—in fact, almost everyone I’ve spoken with, you know, if we are talking about past teachers or, “Oh, what was that class like?” I mean, they just have these wonderful memories! And for me, my sense of like belonging was already so on a tight rope anyway, that to have this adult, this teacher, tell me, “You do not belong here,” just crushed me. And in hindsight, I think he was saying like, “This class is too hard for you.” I mean, maybe. <Laugh> But all I heard was “You don’t belong here.” And I extrapolated it to connect to math and to anything having to do with math in general. And it just got worse and worse through high school in the world of math. My next math class was even—I had to repeat that class, and still didn’t understand what was going on, and felt more out of place, and, you know, it’s one of those things that I just kind of had started to accept that, I guess, math isn’t for me. I guess I’m just not a math person. Or whatever these stories are that I started to create and build and find evidence for around me that was informing that this wasn’t for me. And I had always done well in school. I was in, you know, accelerated classes. I felt like I was capable of problem solving. And yet in math, I just felt like I had all of this evidence saying that I didn’t belong there. And so when I went to college, I took whatever two math classes were—you know, I was in performing arts and then I did ethnic studies as well. And I remember you had to take two math classes that were GEs. There were these classes that if you don’t wanna deal with math, you go take those classes. And I was like, “Oh yeah, I’ll take that. I’ll take that.” The gulf widened, you know? <Laugh> And I didn’t feel like anxiety when I had to do things like balance my checkbook or navigate math in everyday spaces. It was just, it would never occur to me that I would like seek out opportunities to engage with math or think about it or talk about it.

Dan Meyer (29:35):

That is—yeah, that’s just so wild, how, I don’t know, like it’s often, from the student’s perspective, it is them in a vacuum with math, and the two of them interact and decide if, you know, if they’re right for each other. But from the grown-up perspective, it’s just, you know, it’s a little bit clearer that your story with math was not just you in math, but you with, you know, various external things happening. With family, various teachers playing their different roles—sometimes, you know, really tragic and horrible roles—and then like the compounding mathematical debt that it feels like you were kind of building up, as challenges in one year didn’t get resolved and moved into the next year and so on. And all that makes me wonder—it makes me, like really, really scared, first of all, because I would bet that your teacher might not even remember that moment, that for you is part of just a pivotal moment in your math story, and how many kids have I played—have I been a part of their story in that way and wouldn’t even recall? You know what I’m saying? So that’s a scary part. And then also I’m just wondering, like, how can we, how can we help kids who are in those moments recognize that, “Oh, this kid is like absent a bunch,” and give them more resources to be successful rather than say, “Well, you just gotta try harder now.” Those are things I’m wondering, hearing your story. Thank you for sharing that. I’d love to know more about how you then became a teacher and what all that did for you as you helped students.

Bethany Lockhart Johnson (31:06):

Well, but to answer what you were saying, it wasn’t that I wasn’t—I was always absent physically, but at least like mentally at that point, because it had become so difficult. It didn’t make sense to me. So I was just really checked out in math class, you know? So in hindsight, you know, as a teacher, for sure I can look back, and especially hearing these stories and these experiences my friend had with this teacher and just like chalks up as one of like her most favorite teachers ever! And you know, he clearly did a great job for so many students. But for me, and I think for some people, they would’ve taken those challenges and, you know, it would have fortified them in a different way or something. But for me, I took it upon myself to mean certain things about myself and about my ability and what I was capable of. And so I think, I think in some ways, you know, yeah, it’s all, it’s all interconnected. You know, when your students walk in the door, they’re not this—the things that are impacting them in their life are coming into the room with them. And I don’t think we can take that for granted and think, “Well, if they just focus hard enough…”

Dan Meyer (32:21):

Yeah.

Bethany Lockhart Johnson (32:23):

So let’s go back to my love of Oprah. You know, Oprah talks about living your best life. And something I really appreciate about Oprah is that she encourages you to examine, like, sticking points, right? Like she doesn’t just say, “Well, this…just pretend nothing ever happened, and everything’s fine!” You know, she really talks about making time for reflection. And I kind of got mad that anytime I thought about math, or math schooling came up. Or, you know, whatever, any time that came up that I just felt UGH about it. And I felt like a failure. And I’m like, “You know what, what if I took a math class? And I’m an adult at this point. I’ve graduated. I have—I’ve left college. I have my degrees. But I said, “What if I took a math class?” So I went down to, the city college and I found out that you have to take this exam, like a placement exam. And I went and took the placement exam. And I remember it’s one of the responsive tests where if you get it right, the next question’s a little harder. And so I’m taking it, panicking, because it’s getting more like…I just, you know. And I remember it placed me in like, whatever, Algebra Something, this class that was far more advanced than I thought I should be in. And I was like, there’s been a mistake! You know, and I went to the counselor and said, you know, “I got these results, but I couldn’t answer a lot of the questions on the test.” She’s like, “No, no, no, that’s how it works.” So I go take this class and the class was hard. And I decided that I was just gonna keep showing up. And every day before class, I kid you not, they had a little math…it was like a math center where you could go in and they had a bunch of tables and you’d sit at the table and you could sit and do your work or whatever. If you had a question, you walked up and put your name on a clipboard and then somebody would come and help you. So I did that, every single—like before every single class I would go in. I’d sit there. I’d do the work. I’d go. And I’d get help. Like somebody would walk over and you know, some kid for whom they’re like this…you know, they’re math—it might be you, Dan! It could be you! It could have been you! You know, would walk over and be like—

Dan Meyer (34:38):

Yeah, I was in Help like that. Naw, it’s awesome. Love, love those people. Yeah.

Bethany Lockhart Johnson (34:42):

And you know, I did it. And I did so well in the class. I did exceedingly well in the class. And I said—

Dan Meyer (34:50):

Take that! Take that, everything! Every other math experience!

Bethany Lockhart Johnson (34:53):

I said, what?

Dan Meyer (34:55):

Yeah!

Bethany Lockhart Johnson (34:55):

Wait a second.

Dan Meyer (34:56):

Yeah.

Bethany Lockhart Johnson (34:57):

And it was that I was present. I was not afraid to look at what didn’t make sense. And if something didn’t make sense, it didn’t mean there was something wrong with me. Whaaaaat?

Dan Meyer (35:10):

Yeah. Yeah.

Bethany Lockhart Johnson (35:10):

So I was just in such a different space. And then I took another math class and that class was even harder. And I did the same thing where I went to the little lab and, you know, and it just buoyed me. And it made me realize that, like, this story, that my experience with it was very powerful and that was a real lived experience, but that it didn’t have to define my relationship with math. But then! I decided I wanted to go back to school to become a classroom teacher. And I totally—this was a couple years after that math class experience. So now, you know, I’m healing my relationship with math through basic positive experiences, da, da, da, you know, doing other work. But fast-forward, for a whole number of reasons, decided to become a classroom teacher. And I freaked out. All of my—like, I’m studying for the GRE and the CSET and all the things you have to the hoops you have to jump through to apply to the masters program and the credential program. And I freaked out. I was so close to quitting, Dan. Because I was convinced that the reason I couldn’t be a classroom teacher is because I wasn’t capable in math. Like I was—it was all that resurfaced. And even though I now had evidence to say something different, to the contrary, it was still so visceral. And I was so scared. But I passed that Math CSET.

Dan Meyer (36:47):

Get it.

Bethany Lockhart Johnson (36:47):

I did well enough on the GRE—

Bethany Lockhart Johnson (36:50):

Yes!

Bethany Lockhart Johnson (36:50):

You know, I finished my credential. I worked really, really hard. I had to work so hard in my student placement, when I was student teaching for a fifth-grade class, ’cause I felt like, “Oh my God!” I mean, now I could do the mathematics, but I couldn’t TEACH it to someone, you know? But I had amazing professors at UCI, and my math professors really like just—and my mentor teacher! shout out to Jennifer! shout out to Phil!—these amazing mentor teachers who just loved teaching and who loved—like you said, you have these teachers in your life who you got to see the way that they listened to students. They taught me about that love of listening to students. And then I fell in love with, you know, CGI, cognitively guided instruction, and started learning all about all of these educators who just wanna learn from students’ thinking. And it was just so powerful. And I realize as a kindergarten teacher that I have this really special role in helping to create space for a positive school experience. Like we get to talk about—I talk about my students as mathematicians; they’re writers; they’re thinkers; they’re problem-solvers. And I also want to make space for parents. Some of them, this is their first kid in kindergarten, and they brought all of their experiences, a lot of it negative, that they had had with mathematics. So I felt like it was such an exciting opportunity to help show parents how they could have conversations about math with their students. That also, I hope helped heal their own anxiety with mathematics.

Dan Meyer (38:41):

Right, right.

Bethany Lockhart Johnson (38:42):

Like, I’ve not even scratched the surface of math learning. But I just have such a changed perspective and relationship with math. And I just fell in love with the sense-making. And I fell in love with the journey of it. I still experience math anxiety about a wide variety of things, but I do love it. And I feel like there’s a space for me in relationship with math. And that really excites me.

Dan Meyer (39:09):

Yeah. Wow. Listen to that folks. We, we don’t deserve her! Bethany Lockhart Johnson! She got some math game and could have gone off there and, you know, become an accountant or something. And she chose to hang with kids and their parents. That’s so wild that you’re like rehabbing parents and their self-conception about mathematics at the same time. I think that is so cool.

Bethany Lockhart Johnson (39:32):

Well, thanks Dan Meyer. I gotta tell you, I don’t know when or if I’ve ever shared that much of my math story. So there is a certain amount of vulnerability there. But thanks for listening. And I’m glad that, you know—I think there’s space for us to talk about these things that we care deeply about, but that can be really complicated.

Dan Meyer (39:56):

Yes. Yes. And I love how you you’ve really sharpened the point on what I feel like I know in my brain, but not my body all the time: That individual teachers are huge. Like, individual teachers, and individual moments of teaching, are just not something to play with. You know, like that kid that’s in fifth grade having a tough time, like there could be a month or a day-long period where all of a sudden, like, you’re just like, “Oh yeah, I’m back in the mix; like, me and math are still buddies.” And there’s also like moments that you had, where like one casual word from a teacher can just really put a huge wedge between you and a discipline that needs and wants you and your intellect in it.That’s a really powerful testimonial. Not just for math, but for teaching, your teaching bio.

Bethany Lockhart Johnson (40:43):

I agree with you. And I also, I also…you know, I think we can’t put this—we are human. Teachers are human. And so I’m sure there’s things I’ve said to students. Twenty-second story: a student stapled his finger in my class. <Laugh> And I remember holding his hand and saying, “Why did you do that?” And I wasn’t yelling at him, but it was like, I am sure the panic in my face…like, that’s what he’s gonna remember about kindergarten. Right? <Laugh>.

Dan Meyer (41:19):

Yeah.

Bethany Lockhart Johnson (41:20):

That. He will remember that. He won’t remember the really cool city project we did. He’s gonna remember his teacher holding his hand, in his face: “Why did you do that?”

Dan Meyer (41:30):

Yeah. Yeah.

Bethany Lockhart Johnson (41:30):

You know, so we’re human. And yes, it was awful that that teacher said that to me. There were a thousand other ways that he could have said whatever it was he was thinking. And that did deeply wound me. But despite his influence—because teachers do have a lot of power and I think they need to examine that power, ongoing—it still doesn’t have to define us. So I don’t wanna put this pressure, like—

Bethany Lockhart Johnson (41:55):

Sure.

Bethany Lockhart Johnson (41:56):

“So never ever say anything negative!” You know, we’re human.

Dan Meyer (42:00):

I feel like that kid is currently on some office-supply podcast talking about “your office-supply bio” and saying, “Let me tell you how I first got really freaked out by staples. Here’s the deal: I only use paper clips. And here’s why.”

Bethany Lockhart Johnson (42:15):

“Here’s why.” But then—callback!—he’s going to stumble upon THIS podcast and think, “And because I’m so adept with paper clips, I can beat that record!”

Dan Meyer (42:30):

Though—aaay! whoa! Settle down!

Bethany Lockhart Johnson (42:31):

BOOM.

Dan Meyer (42:31):

Don’t get any ideas, kid. No way. Uh-uh. I don’t like that at all. That’s not what—that’s not what I want to have happen here. No, thank you.

Bethany Lockhart Johnson (42:41):

Well, I’m spent, Dan. I need a nap.

Dan Meyer (42:45):

Yeah. I need a box of Kleenex. I need a nap. I need a—yeah, for sure, a baba. Uh-huh. Definitely. Hey, so look, I’m not expecting you folks out there in the lounge to kind of give us the same depth or breadth. You know, we are here, of course, for your entertainment. Feast on our stories and dramas. But I would love to know at some point, like, what are a few, a few moments that really came to define you mathematically? Came to influence you as a teacher? I think we would do really well for each other to understand that about all of our processes. So yeah, I would just toss in a plug in for Twitter, @MTLShow, or Facebook, Math Teacher Lounge; it would be fantastic to hear from you.

Bethany Lockhart Johnson (43:24):

Thanks so much for listening.

Dan Meyer (43:25):

Thanks, folks. Bye now.

Stay connected!

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What Dan Meyer says about math teaching

“Teaching, more than other professions, is a generational profession. The kinds of joyful experiences we offer, or don’t offer, now affect the experiences students that haven’t even been born yet will have years later.”

– Dan Meyer

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

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

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

Grade K

Unit 1: Count Sequence and Numbers to 5

Module 1: Represent Numbers to 5 with Objects

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

Unit 2: Count Sequence and Numbers to 10

Module 7: Represent Numbers 6 to 10 with Objects

Module 10: Compare Numbers to 10

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

Module 11: Add To and Take From Within 10

Module 12: Put Together and Take Apart Within 10

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

Module 13: Ways to Make Numbers to 10

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

Unit 3: Geometry

Module 14: Analyze and Compare Three-Dimensional Shapes

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

Module 15: Describe Position of Objects

Module 16: Analyze and Compare Two-Dimensional Shapes

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

Unit 4: Number and Operations in Base Ten

Module 17: Place Value Foundations-Represent Numbers to 20

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

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

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

Grade 1

Unit 1: Ways to Add and Subtract

Module 2: Subtraction Strategies

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

Module 3: Properties of Operations

Lesson 3.6: Determin Equatl and Not EqualReplanting Huli

Module 4: Apply Addition and Subtraction Relationships

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

Module 5: Understand Add to and Take From Problems

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

Module 6: Understand Put Together and Take Apart Problems

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

Module 8: Data

Lesson: 8.2 Represent Data with Picture GraphsShapes Ying Saw

Unit 3: Numbers to 120

Module 10: Count and Represent Numbers

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

Unit 4: Addition and Subtractoin in Base Ten

Module 12: Understand Addition and Subtraction with Tens and Ones

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

Module 13: Two-Digita Addition and Subtraction

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

Unit 6: Measurment

Module 16: Fraction Foundations

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

Grade 2

Unit 1: Numbers and Data

Module 1: Fluency for Addition and Subtraction Within 20

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

Module 1: Fluency for Addition and Subtraction Within 21

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

Module 2: Equal Groups

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

Module 3: Data

Lesson 3.5: Draw bar graphs to Represent DataAwesome Aquariums

Unit 2: Place Value

Module 4: Understand Place Value

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

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

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

Module 6: Use Place Value

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

Unit 3: Money and Time

Module 7: Coins

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

Module 8: Dollar Amounts

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

Unit 5: Three-Digita Addition and Subtraction

Module 16: Three-Digit Addition

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

Unit 6: Measurement

Module 18: Lengths in Inches, Feet, and Yards

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

Module 20: Relate Addition and Subtraction to Length

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

Unit 7: Geometry and Fractions

Module 21: Two- and Three- Dimensional Shapes

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

Grade 3

Unit 1: Understand Multiplication and Area

Module 1: Understand Multiplication

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

Module 2: Relate Multiplication and Area

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

Unit 2: Multiplication and Division

Module 7: Relate Multiplication and Division

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

Module 8: Apply Multiplication and Division

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

Unit 3: Addition and Subtraction Strategies

Module 9: Addition and Subtraction Strategies

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

Module 10: Addition and Subtraction Within 1000

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

Unit 4: Fractions

Module 13: Understand Fractions as Numbers

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

Unit 5: Measurement and Data

Module 18: Represent and Interpret Data

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

Unit 6: Geometry

Module 19: Define Two-Dimensional Shapes

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

Module 20: Categorize Two-Dimensional Shapes

Lesson 20.1: Draw QuadrilateralsMore Quadrilaterals

Grade 4

Unit 1: Place Value and Whole Number Operations

Module 3: Interpret and Solve Problem Situations

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

Unit 2: Multiplication and Division Problems

Module 4: Mental Math and Estimation Strategies

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

Module 5: Multiply by 1-Digit Numbers

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

Unit 3: Extend and Apply Multiplication

Module 8: Extend and Apply Multiplication

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

Unit 4: Fractions and Decimals

Module 10: Algebraic Thinking and Number Theory

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

Module 11: Fraction Equivalence and Comparison

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

Module 12: Relate Fractions and Decimals

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

Module 13: Use Fractions to Understand Angles

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

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

Lesson 14.2: Joining Parts of the Same WholePizza Problems

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

Lesson 15.1: Add and Subtract Fractions to Solve ProblemsMath Pizzeria

Unit 6: Two-Dimensional Figures and Symmetry

Module 18: Symmetry and Patterns

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

Grade 5

Unit 1: Whole Numbers, Expressions, and Volume

Module 1: Whole Number Place Value and Multiplication

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

Module 2: Understand Division of Whole Numbers

Lesson 2.4: Use Partial QuotientsEmptying the Water Tank

Module 5: Volume

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

Unit 3: Multiplying Fractions and Mixed Numbers

Module 8: Understand Multiplication of Fractions

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

Module 9: Understand and Apply Multiplication of Mixed Numbers

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

Unit 4: Divide Fractions and Convert Customary Units

Module 10: Understand Division with Whole Numbers and Unit Fractions

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

Unit 5: Add and Subtract Decimals

Module 13: Decimal Place Value

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

Unit 6: Multiply Decimals

Module 15: Multiply Decimals and Whole Numbers

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

Unit 7: Divide Decimals and Convert Customary Units

Module 17: Understand Decimal Division Patterns

Lesson 17.1: Understand Decimal Division PatternsPowers of 10 Parade

Unit 8: Graphs, Patterns, and Geometry

Module 19: Graphs and Patterns

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

Grade 6

Unit 1: Number Systems and Operations

Module 1: Integer Concepts

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

Module 3: Fraction Division

Lesson 1: Understand Fraction DivisionFlour Planner
Fill the Gap

Module 4: Fluency with Multi-Digit Decimal Operations

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

Unit 2: Ratio and Rate Reasoning

Module 5: Ratio and Rates

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

Module 6: Apply Ratios and Rates to Measurement

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

Module 7: Understand, Express, and Compare Percent Ratios

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

Unit 3: Expressions, Equations, and Inequalities

Module 8: Numerical and Algebraic Expressions

Lesson 3: Write Algebraic Expressions to Model SituationsProducts and Sums

Module 9: Solve Problems Using Equations and Inequalities

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

Module 10: Real-World Relationships Between Variables

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

Unit 4: Relationships in Geometry

Module 11: Polygons on the Coordinate Plane

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

Module 12: Area of Triangles and Special Quadrilaterals

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

Module 13: Surface Area and Volume

Lesson 1: Explore Nets and Surface AreaRenata’s Stickers

Unit 5: Data Collection and Analysis

Module 14: Data Collection and Displays

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

Module 15: Measure of Center

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

Grade 7

Unit 1: Proportional Relationships

Module 1: Identify and Represent Proportional Relationships

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

Module 2: Proportional Reasoning with Percents

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

Unit 2: Rational Number Operations

Module 3: Understand Addition and Subtraction of Rational Numbers

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

Module 4: Add and Subtract Rational Numbers

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

Unit 3: Model with Expressions, Equations, and Inequalities

Module 7: Solve Problems Using Expressions and Equations

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

Module 8: Solve Problems Using Inequalities

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

Unit 4: Geometry

Module 9: Draw and Analyze Two-Dimensional Figures

Lesson 2: Draw Circles and Other FiguresCan You Build It

Module 10: Analyze Figures to Find Circumference and Area

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

Unit 5: Sampling and Data Analysis

Module 13: Use Statistics and Graphs to Compare Data

Lesson 3: Compare Means Using MAD and Repeated SamplingCrab Island

Module 14: Understand and Apply Experimental Probability

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

Module 15: Find Theoretical Probability of Simple Events

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

Grade 8

Unit 1: Transformational Geometry

Module 1: Transformations and Congruence

Module 2: Transformations and Similarity

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

Unit 2: Linear Equations and Applications

Module 3: Solve Linear Equations

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

Module 4: Angle Relationships

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

Unit 3: Relationships and Functions

Module 5: Proportional Relationships

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

Module 6: Understand and Analyze Functions

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

Module 7: Systems of Linear Equations

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

Unit 4: Statistics and Probability

Module 8: Scatter Plots

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

Module 9: Two-Way Tables

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

Unit 5: Real Numbers and the Pythagorean Theorem

Module 10: Real Numbers

Lesson 2: Investigate RootsRoot Down

Module 11: The Pythagorean Theorem

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

Unit 6: Exponents, Scientific Notation, and Volume

Module 12: Exponents and Scientific Notation

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

Module 13: Volume

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

Algebra 1

Intro/Launch

Unit 1: Real Numbers and Connections to Algebra

Module 2: Linear Equations and Inequalities in One Variable

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

Unit 2: Linear Functions and Equations

Module 3: Linear Equations in Two Variables

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

Module 4: Linear Functions and Models

Lesson 4.3: Characteristics of Linear FunctionsCraft-a-Graph

Module 5: Relationships Among Linear Functions

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

Unit 3: Build Linear Functions and Models

Module 6: Fit Linear Functions to Data

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

Module 7: Discrete Linear Functions

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

Module 8: Piecewise-Defined Functions

Lesson 8.1: Graph Piecewise-Defined FunctionsPumpkin Prices

Unit 4: Linear Systems

Module 9: Systems of Linear Equations

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

Module 10: Linear Inequalities

Lesson 10.2: Graph Systems of Linear InequalitiesQuilts
Seeking Solutions

Unit 5: Exponential Functions and Equations

Module 11: Exponential Functions and Models

Lesson 11.1: Exponential Growth FunctionsCarlos’s Fish

Unit 6: Build Exponential Functions and Models

Module 13: Fit Exponential Functions to Data

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

Module 14: Discrete Exponential Functions

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

Unit 8: Quadratic Functions and Equations

Module 17: Use Graphing and Factoring to Solve Quadratic Equations

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

Module 18: Use Square Roots to Solve Quadratic Equations

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

Unit 9: Function Analysis

Module 20: Function Analysis

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

Unit 10: Data Analysis

Module 22: Numerical Data

Lesson 22.1: Data Distributions and Appropriate StatisticsFinding Desmo

Disclaimer

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.

Welcome, Amplify ELA families!

We’re excited to welcome you and your student to the Amplify ELA program for the new school year, and to provide you with exceptional learning opportunities through ELA. We’ve assembled the following resources and guides to help you support your student and enable them to have the most productive experience with our platform throughout the year.

Para la versión en español, haga clic aquí.

Illustrated collage with people playing sports, riding bikes, and a thoughtful person’s portrait, framed by natural elements and a rocket launching, next to an "EdReports Review Year 2020" badge.

What is Amplify ELA?

Amplify ELA helps students in grades 6–8 read and understand complex texts that encourage them to grapple with interesting ideas and find relevance for themselves. Amplify ELA is a blended program that includes both digital and print materials, but can also be used as a print-only version. Students using Amplify ELA read text passages closely, interpret what they find, discuss their thinking with peers, and develop their ideas in writing. The lesson structure is easy to follow, but flexible enough to allow for a variety of learning experiences and varied enough to keep students engaged. 

Features include:

  • Functionality that allows individual students to work at their own level while also being challenged appropriately.
  • Built-in tools that allow teachers to track and respond to student work.
  • The digital Amplify Library, which contains more than 700 downloadable, full-length fiction and nonfiction books.
  • The Vocab App, which uses game-like activities to help students master keywords from the program’s texts. (Students using print materials will see keywords highlighted.)
  • Independent writing assignments called Solos, available on mobile devices.
  • Interactive projects called Quests that accompany certain units to provide additional practice with analytical reading, writing, speaking, and listening skills.

Getting started

How you can support the child in your care:

  • If possible, read with your student daily; even 15 minutes of reading together each day can make a huge impact. You can read aloud sections of the text together—many middle grade students enjoy performing sections of dialogue by taking on the role of a character in a play, or adding some dramatic flair to a poem with which they are working. If your student struggles with reading aloud, you might try reading the text to them with expression, then having them read it back to you. For additional practice, there are an array of fluency activities in the program’s Flex Days. Ask your student to help you find these activities.
  • Find moments to discuss what they are reading and discovering. Examples of questions you could ask: What stood out to you from what you read today? Were any sentences or words confusing? What was most surprising? What do you think the writer was trying to communicate? Do you agree with the writer’s ideas or descriptions? What connections can you make between what you are reading and your own life, or other issues you’ve heard about?
  • Listen to your student read their written responses or have them share with a friend over the phone or video chat. 
  • Browse the Amplify Library with your student to find books they’ll enjoy and be able to read fluently and independently.
  • Review this Protecting Kids Online website by the Federal Trade Commission addressing digital safety.

Accessing texts in the Amplify Library

We encourage students to utilize the core texts from the Amplify Library while at home! Please follow these steps to download a text for offline reading:

1. Navigate to the Program & Apps menu at the top of your screen and scroll through to find the Amplify Library icon. When you select it, the Amplify Library will open in a new tab.

A digital menu displays various educational tools and resources, with "Amplify ELA" highlighted at the top and the "Library" option outlined in orange.

2. If prompted, follow the directions to set up a pin for the Amplify Library; otherwise, proceed to the next step.

A pop-up window prompts the user to create a four-character PIN of lowercase letters and/or numbers for offline reading, with Cancel and Submit buttons.

3. In the upper right corner of your screen, search for the book you would like to download. Example: The Secret of the Yellow Death: A True Story of Medical Sleuthing.

A digital library search page displays "yellow death" in the search bar with no results found for title, authors, or genre. Book covers are visible in the left sidebar.

4. Select the Download button.

A digital library interface displays the book "The Secret of the Yellow Death" by Suzanne Jurmain, showing its cover, synopsis, and options to read or download.

5.  If you lose connection while still in the Amplify Library, you can continue to access and read the downloaded book(s). If the page refreshes without internet access, or you try to login on another device without internet access, you will lose access to the downloaded book(s) until the internet connection is restored. 

To retrieve your downloaded texts: 

  1.  In the Amplify Library app, open the My Library drop-down menu in the upper left corner.
  2. Select Downloaded. 
  3. Choose the text you wish to read from all of your pre-downloaded texts.
A dropdown menu under "My Library" shows options: Recently Read, Favorites, Downloaded (highlighted), and All Books. Below, a Recently Read section displays three book covers.

Materials overview

Not every school will operate the same way, but students attending schools that have both the print and digital editions of the program will likely have the following print materials at home:

  • Student Edition: This includes all of the readings and activities necessary for instruction throughout the year. Students can read the selections both digitally and in print, annotating in either format. The lessons in the print Student Edition reflect each digital lesson, but have been modified to work effectively in print. 
  • Writing Journals: This provides space for students to respond to Writing Prompts and complete other written assignments. 

In the case that students are without access to devices or the internet, they can continue to complete key reading and writing assignments using the print Student Editions and student Writing Journals.

Teachers can also access, print, and mail student Novel Guides for up to 12 commonly taught novels. Six of these novels are available in the Amplify Library, and most should be available in a public library.

Unit overviews

Below are quick overviews of each unit your student will be working through in their grade throughout the year. Included along with each unit is a downloadable guide that provides a more in-depth look at what content is covered and how you can help your student advance their understanding of the topics.

  • Unit 6A: Dahl & Narrative  
    • Students begin with narrative writing to quickly boost their writing production, learn the foundational skill of focus, and become comfortable with key classroom habits and routines they will use all year. Students then apply their new observational focus to some lively readings from Roald Dahl’s memoir Boy and learn how to work closely with textual evidence.
  • Unit 6B: Mysteries & Investigations
    • Students read like an investigator to embark on a multi-genre study of the mesmerizing world of scientific and investigative sleuthing. At the end of the unit, students write an essay explaining which trait is most useful to problem-solving investigators.
  • Unit 6C: The Chocolate Collection
    • The Aztecs used it as currency. Robert Falcon Scott took it to the Antarctic. The Nazis made it into a bomb designed to kill Churchill. The 3,700-year-long history of chocolate is full of twists and turns, making it a rich and rewarding research topic. In this unit, students explore primary source documents and conduct independent research to better understand the strange and wonderful range of roles that chocolate has played for centuries around the world.
  • Unit 6D: The Greeks
    • Greek myths help us understand not only ancient Greek culture but also the world around us and our role in it. Drawing on the routines and skills established in previous units, these lessons ask students to move from considering the state of a single person—themselves or a character—to contemplating broader questions concerning the role people play in the world and the communities they inhabit within it.
  • Unit 6E: Summer of Mariposas
    • The borderlands between the United States and Mexico are the place of legends, both true and fictional. Summer of the Mariposas, by Guadalupe Garcia McCall, plants a retelling of the Odyssey into this setting, launching five sisters on an adventure into a world of heroes and evildoers derived from Aztec myths and Latinx legends. On the journey, the sisters reconcile the dissolution of their parent’s marriage and find new strength in their identity and connection to Aztec lineage. Students consider how McCall uses the structure of the hero’s journey to celebrate women, heritage, and a broad definition of family. Students also have the opportunity to compare these characters’ fictional journey into Mexico to a description of one boy’s true journey into the United States.
  • Unit 6F: The Titanic Collection 
    • In this research unit, students learn to tell the difference between primary, secondary, and tertiary sources; determine if a given source is reliable; and understand the ethical uses of information. Students then construct their own research questions and explore the internet for answers. They also take on the role of a passenger from the Titanic’s manifest to consider gender and class issues as they research and write narrative accounts from the point of view of their passenger.  
  • Unit 6G: Beginning Story Writing
    • In this unit, students get to practice their creative writing skills and learn the elements of storytelling and character development, as well as the importance of vivid language. Students gain a sense of ownership over their writing as they experiment with the impact of their authorial choices on sentences, language, character traits, and plot twists.
  • Grade 6: Grammar
    • In this unit, students complete self-guided grammar instruction and practice that teachers assign to them throughout the year. Sub-units are organized by key grammar topics, so teachers can assign the content that best meets their student’s needs while making sure students work with the key grammar topics for their grades.
  • Unit 7A: Red Scarf Girl & Narrative
    • In this study of a highly engaging memoir of a young woman growing up in China during the Cultural Revolution, students quickly learn the history and politics of this tumultuous period by focusing on the story of someone living through the upheaval. As students follow her journey through a world turned upside down, they will track the changes in her feelings and motivations over time.
  • Unit 7B: Character & Conflict
    • By reading the play A Raisin in the Sun and the short story “Sucker,” students explore how people facing hardships can inflict unintentional harm on the people around them. The two narratives work together to provide opportunities for students to analyze characters’ responses to conflict and the author’s development of ideas over the course of a piece of fiction.
  • Unit 7C: Brain Science
    • Could you survive an iron rod through your skull? Phineas Gage did, and his gruesome-but-true story allows students to build background information and analyze other informational texts, including the contemporary The Man Who Mistook His Wife For A Hat and the relevant Demystifying the Adolescent Brain.
  • Unit 7D: Poetry & Poe
    • Poe’s texts always offer so much to notice, decipher, talk about—and creep us out. Since things are not always what they seem, students must use close reading skills to question whether they should believe what Poe’s narrator is telling them … or not.
  • Unit 7E: The Frida & Diego Collection
    • Mexico’s most famous and provocative artists, Diego Rivera and Frida Kahlo, were an extraordinary couple who lived in extraordinary times. They were both soul mates and complete opposites. Their multifaceted lives and work offer students rich and fascinating subjects to study as they examine primary source documents and conduct independent research.
  • Unit 7F: The Gold Rush Collection
    • In this research unit, students choose from a large collection of primary and secondary sources to learn about the wide range of people who took part in the California Gold Rush. They also take on the role of someone who lived during the gold rush and write journal entries from their perspective.
  • Unit 7G: Intermediate Story Writing
    • In this unit, students get to practice their creative writing skills and learn the elements of storytelling and character development, as well as the importance of vivid language. Students gain a sense of ownership over their writing as they experiment with the impact of their authorial choices on sentences, language, character traits, and plot twists.
  • Grade 7: Grammar
    • In this unit, students complete self-guided grammar instruction and practice that teachers assign to them throughout the year. Sub-units are organized by key grammar topics, so teachers can assign the content that best meets their student’s needs while making sure students work with the key grammar topics for their grades.
  • Unit 8A: Perspectives & Narrative
    • This unit aims to teach students to read like writersThey practice paying attention to the craft of writing and to the moves a good writer makes to shape the way we see a scene or feel about a character—to stir us up, surprise us, or leave us wondering what will happen next. Students closely read examples of rich, layered narrative nonfiction, analyze the techniques each author uses to make their writing resonate, and practice applying these techniques to their own narrative writing.
  • Unit 8B: Liberty & Equality
    • In this unit, students look at the words of a range of creators—from poet Walt Whitman to abolitionist Frederick Douglass to President Abraham Lincoln—to see how their writing contributed to an extreme shift in social organization: a whole new concept of what it means for people to be considered “equal.” They also study multiple perspectives on the Civil War, including the memoir of a girl who was enslaved, a confederate girl’s diary, and a nonfiction account of the young boys who served as soldiers during the war. 
  • Unit 8C: Science & Science Fiction
    • Students read Gris Grimly’s Frankenstein, a graphic novel that adds captivating illustrations to an abridgment of the 1818 edition of Mary Shelley’s book. Paired with Shelley’s text, Grimly’s haunting—and, at times, horrific—representations of Frankenstein’s creature push students to wrestle with some of the text’s central themes: the source of humanity and the root of evil. Students then write an essay in which, after arguing both sides of the question, they determine whether or not Frankenstein’s creature should ultimately be considered human.
  • Unit 8D: Shakespeare’s Romeo & Juliet
    • Romeo and Juliet combines romance with action, offering a wide range of themes and scenes for students to read about and act out. Your middle schoolers are at the right age to identify with the lovers’ strong feelings—and also old enough to think critically about the choices Romeo and Juliet make.
  • Unit 8E: Holocaust: Memory & Meaning
    • This unit uses a range of primary source articles, images, and videos, as well as literary nonfiction and graphic nonfiction, to study what made the atrocities of the Holocaust possible. Students investigate how propaganda was generated and employed to create a political environment that ultimately corrupted a society. The Olympics are seen through the lens of an international propaganda campaign, providing cover for Nazis to begin eliminating non-Aryans from their culture. The final sub-unit examines the outcomes of Nazi doctrine and the impact on Jewish victims and survivors.
  • Unit 8F: The Space Race Collection
    • In this unit, students to put their research and close-reading skills to the test to distinguish between reliable  and unreliable sources, explore primary documents, and conduct independent research to better understand the space race that took place between two of the world’s superpowers. This dramatic story offers students a rich research topic to explore as they build information literacy skills, learn how to construct their own research questions, and explore the internet for answers.
  • Grade 8: Grammar
    • In this unit, students complete self-guided grammar instruction and practice that teachers assign to them throughout the year. Sub-units are organized by key grammar topics, so teachers can assign the content that best meets their student’s needs while making sure students work with the key grammar topics for their grades.
  • Unit 8G: Advanced Story Writing
    • In this unit, students get to practice their creative writing skills. They’ll learn the elements of storytelling and character development, and the power of vivid language to grab readers and pull them into a story.

Additional activities

Quests: 

You may notice your student working with peers on the same interactive project over several days, trying to solve a mystery or explain a historical event. That’s what happens when a teacher assigns a Quest: an in-depth week-long exploration that requires collaboration and deepens engagement with texts and topics.

Vocab App:

The Vocab App helps students master vocabulary words through game-like activities that challenge them to think through morphology, analogy, and synonyms/antonyms, and to decipher meaning through context.

Have a question about Amplify ELA?

Visit our help library to search for articles with answers to your program questions. 

For additional curriculum support, please contact your student’s teacher.

S3 – 06. Bethany and Dan take on Twitter!

Promotional graphic for Math Teacher Lounge Season 3, Episode 6, featuring Bethany Lockhart Johnson, Educator, and Dan Meyer, Director of Research at Desmos.

In this episode, Bethany and Dan take a look at several tweets that caught the most fire on Twitter during the 2021-2022 school year. The pair answer questions about viral teaching methods, the best teaching advice you can give in three words, and if students should use pencils or pens in class. Join them as they take on those questions and several others in a fast-paced episode.

Explore more from Math Teacher Lounge by visiting our main page

Download Transcript

Dan Meyer (00:02):

Hey folks. Welcome back to the Math Teacher Lounge. I’m your co-host, Dan Meyer.

Bethany Lockhart Johnson (00:07):

And I am Bethany Lockhart Johnson. And I’m your co-host, Dan! Hi!

Dan Meyer (00:12):

We’re co-hosts! Hey! Great to see you.

Bethany Lockhart Johnson (00:13):

Dan, this is the last episode of Season 3. Three seasons!

Dan Meyer (00:19):

It’s gotta have a cliffhanger. What will the cliffhanger be? You know?

Bethany Lockhart Johnson (00:22):

The cliffhanger is that we love having guests! It’s one of our most favorite things, because selfishly, we love to talk to all of these amazing folks who are doing this interesting research and thinking about amazing things. But for this last episode, it’s just you and I, Dan. Cliffhanger!

Dan Meyer (00:40):

Yeah. I like this. I like this. So the cliffhanger was last episode, and people are all like, “So who’s the last guest gonna be of the season before we roll out into summer?” And yes, as Bethany said, we love all the fascinating guests we’ve had on throughout these last few seasons. And we realized…who is more fascinating to each other than both of us? You know, let’s talk to each other about things, right? <Laughs> You get that! You get that! Or am I alone here in this? We had this idea about what we should talk about here, and that’s this: I am on Twitter a lot. I’m @DDMeyer on Twitter; throw me a follow; might follow back; who knows? I don’t tweet much. Bethany, what’s your handle on Twitter? Let ’em know.

Bethany Lockhart Johnson (01:22):

I’m @LockhartEdu, and I was much more active pre-mamahood. But I’m still up in there. Go ahead.

Dan Meyer (01:30):

Yep. In there. Yeah, great. So I’ve been keeping track of the hottest conversations in math education Twitter, the conversations that the most people who kind of describe themselves as math teachers in their bios and whatnot have been replying to. We’ve got some little things working in the background, keeping track of this sort of thing. And so we are gonna bring you folks some of those extremely hot conversations, and even better than the questions—which we hope you’ll reply to and tag us in your replies—even more than those questions, we’ll bring you our answers—our answers!—to those questions. Can you believe that? We’ll fully settle these questions! Won’t we, Bethany? My gosh, won’t we?

Bethany Lockhart Johnson (02:15):

Jeez Louise! No! Dan Meyer, the point is not our final word on it! The point is this episode, we’re furthering the conversation. We wanna hear from listeners about what do you think?

Dan Meyer (02:25):

Right. You’re right. You all need someone in your life like Bethany who will help you become the best version of yourself. So here’s the deal. We have several questions in a few different categories. We’re gonna bust through some quick ones, pretty quick. And, uh, there’s some meaty ones as well. Let’s get into it! The first questions come to you all, and us, courtesy of MTL guest Howie Hua, who has a renowned knack for just creating math memes, but also conversation starters that really capture the curiosity and answers of of a grateful nation. So Howie’s first question, which I’ll pose to Bethany, is, “What’s your favorite number?” Bethany? And why is it your favorite number?

Bethany Lockhart Johnson (03:14):

Oh, I love it. OK. Well, the first thing that came to my mind is 12. ‘Cause It’s a highly divisible number. I mean, 2, 6, 3, 4—I love it. And it coincides with the day and month of my birth. Which, like, the double-digit…come on, 12, 12, 12, 12. I dunno, am I giving away, like, my bank security code <laugh> or anything by saying that?

Dan Meyer (03:41):

Yeah. What’s your favorite PIN?

Bethany Lockhart Johnson (03:43):

Let me change my PIN. Yeah, it’s just such a happy, happy number. Well, 12 is, you know, 10 and 2. Two more. Anyway. Love it. What about you, Dan? What’s your favorite number and why?

Dan Meyer (03:55):

I’m into it. I’m into it. I think I would choose 16. Because it’s the first number for me when it was like, “Oh, you can keep on making numbers forever!” Where I’m like, OK, 2times 2 is 4. Great. That’s kind of an elemental expression in mathematics. Four times 2 is 8. OK. But then, 8 times 2 is 16, and it’s like, “Oh, you can just keep doubling that thing over and over and over again!” And I can recall feeling pretty excited that numbers are just like, out there for the finding. For the taking. Cool stuff.

Bethany Lockhart Johnson (04:33):

I’m sorry. Wait, I have to interrupt. You went 2 times 4 is 8 and you didn’t go 4 times 4 is 16? You went 8 times 2 is 16? You wanted to keep the 2 the same?

Dan Meyer (04:49):

Yup. Yup. You can keep on doubling. You can keep on doubling numbers and it just keeps on going.

Bethany Lockhart Johnson (04:53):

More evidence that our brain works very differently.

Dan Meyer (04:56):

We learn more about each other…let me keep this rolling with Howie questions. OK? Howie says, “If you could co-teach with one teacher from Twitter, who would you choose?”

Bethany Lockhart Johnson (05:06):

Oh, oh, it has to be a teacher?

Dan Meyer (05:11):

Or anybody, I guess. I mean, like, I know you love Oprah.

Bethany Lockhart Johnson (05:15):

Can I co-teach with Oprah?

Dan Meyer (05:16):

Yup, yeah, so there we are. <Laugh> Yup. OK. Fair enough. We have to work Oprah into every single episode.

Bethany Lockhart Johnson (05:23):

I’d just love to sit and like, we’d read together, we’d read to the students, and then we’d talk…I mean, obviously it’d be Oprah. But if we’re thinking more of like MTBoS, like math Twitter blogosphere-land, I suppose the person I would wanna co-teach with honestly would probably be Allison Hintz. One of our former guests as well. Her book, Mathematizing Children’s Literature, with Antony Smith, that book—I just love the idea of sitting and doing a read-aloud and then diving into some juicy math that’s inspired by what comes out of that read-aloud. So yes, that’s who I pick. Allison! Let’s co-teach!

Dan Meyer (06:00):

<Laugh> Shout-out to Allison.

Bethany Lockhart Johnson (06:01):

What about you?

Dan Meyer (06:03):

I would choose MTL guest Idil Abdulkadir—because, and this relates to Allison and also Elham Kazemi—they talked about, in our episode about teacher time-outs. And I’m choosing someone who I think is—like I’ve never seen Idil teach, but I work with Idil at Desmos and think she’s fantastic. But what I really want in a co-teacher is someone that I can say, “Whoa, time out, do you see what’s going on here? This is really interesting. What should we do next about this?” And have a little strategy sesh in front of the kids and no one gets freaked out by that. And I think that that’d be a pile of fun. Idil seems like she’d be receptive to that kind of interaction, teacher to teacher. So that’s my vote right there.

Bethany Lockhart Johnson (06:48):

Opportunity for you to grow your own practice, Dan.

Dan Meyer (06:52):

Yeah, yeah, exactly. 100%.

Bethany Lockhart Johnson (06:56):

So Dan, I actually have a question for you from Howie. If we’re on the Howie tweet train, I have one from Howie too.

Dan Meyer (07:04):

Howie had some fire tweets, some fire tweets this current year. Yep.

Bethany Lockhart Johnson (07:08):

Dan, I wanna know: Do you prefer doing math in pen or pencil?

Dan Meyer (07:16):

Ooh, yeah. Oh, I see that Howie says, “I don’t mean to start any drama, BUT,” and then asks the question–

Bethany Lockhart Johnson (07:23):

But!

Dan Meyer (07:24):

I think that Howie lives for drama. I think he knows he’s messy. He lives for drama. He knows what he’s doing this with this question here. He knows.

Bethany Lockhart Johnson (07:32):

DRAAAAMAAAA!

Dan Meyer (07:32):

He knows what he’s doing. Yup. So I would just say it depends. Is that cheating? Like if I’m doing math to learn, or if we are learning in that process, then I want to use pen, actually. I wanna see the tracks of the thinking. And if we’re doing it for presentation, like if I’m presenting something, I wanna…I guess that’s an area where I’d be fine to not erase things. I don’t wanna prep it so it’s, you know…I guess you could use pen for presentation also. Just pen. Period. But I wanna see the tracks of the thinking if we’re doing some learning versus presentation. What about you?

Bethany Lockhart Johnson (08:09):

Well, I heard the voice in my head telling one of my kindergartners, “No, you cannot do that in sparkly pen. You need to do it in pencil.” And I was like, “Wait, whose voice is that?” It was one of my math teachers telling me I couldn’t do it in pen! Why couldn’t this kid do it in pen? Sure! Do it in a sparkly pen! So I wanna say do it in pen. And since usually pen is what I have around…I mean, I do crosswords in pen, Dan.

Dan Meyer (08:36):

Wow, wow. With a piece of paper and math, you have lots of room to re-revise and cross off…but those little, little boxes on the crossword, that says a lot about your commitment to pen.

Bethany Lockhart Johnson (08:46):

I got really good at making an A into an H or a P or whatever we need. So I would say, “Hey, if you’re in the room with your kiddos and you’re doing math, if somebody wants to do pen, let them do pen.” But I do know that I’ve seen teachers say you need to do pen so that I can see all of your thinking. So I think I hear what you’re saying. But do you think it should be like a classroom rule or something?

Dan Meyer (09:13):

Oh, no, no, no. I mean, I’m gonna ask you like, “How’d you get to this destination?” And I wanna know process somehow, and I think you’ll get tired of having to explain it verbally rather than just, like, showing. Just don’t erase stuff. Don’t scratch stuff off. Let’s let’s see how you’re getting there. That is what I’m into.

Bethany Lockhart Johnson (09:30):

Thanks, Howie, for that trio of thought-provoking tweets, because I genuinely wanted to know what Dan thought and what our listeners think. I mean, Dan, I gotta say: Howie, you say you don’t wanna cause drama, but I gotta say I’m with Dan on that—

Dan Meyer (09:50):

Got the gift. Got the gift for drama. We’re still friends though. So I’m happy about that. Our next section, I got a few more questions queued up here and these ones relate to advice for educators, advice for yourself. Good advice, bad advice, that kind of thing. So let’s jump in. I would love to know—this one’s from Pernille Ripp—I’m very curious, Bethany, what is the worst teaching advice you have gotten in your life, ever?

Bethany Lockhart Johnson (10:19):

<Laugh> Ooh. OK. Um, worst teaching advice was: “That’s OK, just move on anyway.” And that was in terms of pacing. It was like, students needed to do a deeper dive and the teacher who I was chatting with said, “No, no, it’s fine; it’s fine; just move on. Just move on to the next chapter.” That was probably the worst advice, because no, I don’t think that’s what I should have done at all! <Laugh>

Dan Meyer (10:48):

Right.

Bethany Lockhart Johnson (10:48):

But I was a first-year teacher and I was trying to figure it out. And I learned that that was not good advice. And I understand the pressure of pacing. But it was totally antithetical to the type of listening to my students that I want to do in my craft. And this teacher meant well, but that was not good advice, teacher! <Laugh> What about you, Dan? What is the worst teaching advice?

Dan Meyer (11:13):

I dig that. That feels similar to one of the replies to Pernille here. Frances Klein says, “Never let them know you’ve made a mistake” being particularly bad advice. You know, just this like idea of like moving along, covering your tracks, not backtracking or admitting mistakes, those all feel kind of a piece. The worst advice I think I’ve ever received, and I wasn’t given this often, but it’s echoed by a lot of the commenters here on this tweet, which is “Don’t smile until X, Y, or Z,” where X, Y, and Z are like Christmas, October, December, January. Just the idea that you’ve gotta develop—

Bethany Lockhart Johnson (11:54):

Wait, what?

Dan Meyer (11:55):

<Laugh> Did you never hear this from anybody? Don’t smile until Christmas? Perhaps this is more—

Bethany Lockhart Johnson (11:59):

I’m a kindergarten teacher! Can you imagine? If I don’t smile the second they walk in? The tears?! The parents’ tears?! The kids’ tears?! If I’m just like, stoic?

Dan Meyer (12:07):

Yeah. Well.

Bethany Lockhart Johnson (12:08):

So explain it to me.

Dan Meyer (12:10):

Well, the idea is, is that, you know, for older kids, they’re scoping you, they’re clocking you for weakness, they’re looking at you, they’re looking to take advantage. And so “don’t smile until Christmas” is like, hey, you can always relax. You can always relax your discipline, but you can’t UN-relax it if you start out, you know, Mr. Happy Pants Meyer. Which—

Bethany Lockhart Johnson (12:33):

Smile perceived as weakness.

Dan Meyer (12:36):

Yeah. Very obviously poor advice. Eventually you come to realize that like having a rapport and a relationship that is trusting and warm and demanding, that has high expectations, that’s the best kind of classroom management. Not some kind of persona built around intimidation or stoicism, that kinda thing. So, terrible, terrible advice!

Bethany Lockhart Johnson (13:01):

I feel like I did have a few of those math classes. Yeah.

Dan Meyer (13:04):

Yeah, exactly. <Laugh> You loved them, right? They were like your favorite math classes. It was a blast, right?

Bethany Lockhart Johnson (13:11):

<Laugh> So we have to ask the opposite. Thank you, Daniel Willingham, who said, “What’s the best advice you got?” But hold on, Dan, he didn’t just want the best advice. He wanted the best advice in three words.

Dan Meyer (13:26):

Oh yeah. He doesn’t, he doesn’t want a book or dissertation or even a blog post or even a tweet. He wants just three words.

Bethany Lockhart Johnson (13:32):

I think maybe that might have been to me. <Laugh>

Dan Meyer (13:34):

This is someone who’s doesn’t have much time for this advice, wants it distilled down. I’m just obviously stalling here as I try to think about this. I don’t know, there’s just like so much nuance lost here. I would say, listen to students, listen to students. I can’t say more that, I guess. I guess I’m done. I can’t say more than that there. But you’re in a bad place if you’re not listening carefully to students. How about you?

Bethany Lockhart Johnson (14:04):

  1. Mine is “Ask…lots…questions.”

Dan Meyer (14:11):

Nice. ‘Cause I filled in the word! I filled in the word! I was able to kinda infer that. I did that. I got that.

Bethany Lockhart Johnson (14:17):

Wait, wait, wait, wait! I could have said many! Wait, I could have said “Ask many questions.”

Dan Meyer (14:22):

Strong, strong.

Bethany Lockhart Johnson (14:25):

So yeah. You know, no isolation, like don’t put yourself in a bubble. Ask, not just, not just your students, but the teachers! Ask a lot of questions. You don’t have to have it all figured out.

Dan Meyer (14:34):

Into it. Very much into it.

Bethany Lockhart Johnson (14:37):

Thanks. Daniel. Thanks, Pernille.

Dan Meyer (14:40):

Yeah. Daniel and Pernille, Both great questions there about advice, best and worst. Another fire tweet popped up earlier this year from Dr. Khristopher Childs, which was “Name one thing every educator should stop doing.”

Bethany Lockhart Johnson (14:57):

Oh, I don’t know. This kind of ties into my best advice about asking questions.

Dan Meyer (15:03):

Stop not asking questions?

Bethany Lockhart Johnson (15:06):

<Laugh> Avoid the isolation. I really love this idea of when we can, popping into each others’ classrooms, co-teaching, building this collaborative nature. Elham Kazemi, in our interview, talked about this idea of, like you said, the teacher time-outs, learning from each other. So I feel like if we could stop isolating ourself…and I don’t mean at lunch—sometimes you need to not be in the teacher lounge at lunch. Like if you need a minute, take the minute! But in general, as a practice, how can we not be isolated and instead be learning with, and from, each other? How can we stop the isolation? That’s what I would hope every educator would stop doing. What about you, Dan?

Dan Meyer (15:54):

I think that educators should…this is gonna require a little bit of elaboration. I think educators should stop taking responsibility for things that are not in their zone of influence. I think that as a society we are asking teachers to do more and more, to become more and more of a central fixture holding together with chewing gum and twine all the various parts of a student’s life. From their health, their fitness, emotional health, that we feed students at school. It becomes very tempting, I think, there’s a lot of pressures to blame outcomes, disparate and unjust outcomes later on in life, on teachers. And teachers should just flatly refuse. And to yeah, understand what the job has been set up to do. What it’s good for. And do that with excellence and intent and a lot of effort. And then not take responsibility for the rest of it.

Bethany Lockhart Johnson (16:53):

If I asked five different people about the definition of what a teacher should be doing, I would get five different answers. So I think it’s really interesting that you say that because yeah, many, many hats, which I think, yes, can lead to burnout. Can lead to all sorts of things. We’re asking schools to be all things to all, all people. Interesting. I’m gonna think about that more. I need to hear folks’ response on that, Dan.

Dan Meyer (17:18):

Mm-Hmm. I’m curious too. I mean, yeah, there are definitely things that are in teachers’ responsibility and some that are not. That’s a tough one.

Bethany Lockhart Johnson (17:26):

OK, for help, name an example of each. And what’s something that you think every teacher should not and should be doing. ‘Cause I feel like my brain goes to some things like, you know, I had teachers who were saying, “Well, I don’t wanna have my kids have to have breakfast in my classroom in the morning. That shouldn’t be my responsibility to serve breakfast in the morning.” But I’m like, “But then your kids are eating and they’re gonna be able to learn and be more focused.” Should that be the teacher’s responsibility? I’m not saying it necessarily should, but I’m saying…I don’t know. It gets murky for me.

Dan Meyer (18:06):

Yeah, for sure. I mean, I think that we should, as a country, have a really generous social welfare net so that everyone has food at home. Where a school is not the place where some students have to go to in order to receive nutrition and nourishment. That seems sad to me. And uncommon in developed nations. I think that teachers should watch out for, should be responsible for, the mathematical development of the students they teach, up to a point, they should be responsible for learning math and creating relationships in their classes. I don’t think that teachers should accept responsibility for larger kinds of outcomes, like the health of a democracy or international competition, who goes to the moon first. That kind of thing has historically been placed at the feet of teachers. And it’s tempting when you’re a teacher, I think, to take on that responsibility because it kind of develops your social importance. And I just say, we should say no to that. And get compensation, not in terms of social importance, but rather like in spendable dollars and monies.

Bethany Lockhart Johnson (19:10):

I’m learning more about you, Dan. And you know, this is what I’ve gotten from that answer: If you’re gonna dream, dream big. Right?

Dan Meyer (19:17):

Is that what you got from that? I don’t know. I think I’m trying to dream realistically.

Bethany Lockhart Johnson (19:23):

No, like if we’re gonna say, “Maybe teachers shouldn’t be responsible for serving breakfast in the morning,” well, because we want every child to have access to nutritious and filling food at home and time to eat it in the morning, right? It’s bigger than just, “I don’t want the teacher to have to do this.” So we’re dreaming big. We’re saying this should be the LEAST that students have access to, right?

Dan Meyer (19:53):

Yeah. Yeah. I’m here now. I’m with you. I like that dream. Where we take care of folks in their lives outside of schools. So schools don’t have to be the one linchpin for every kind of social outcome. Like currently a lot of them run through a school ’cause we don’t do a good job of setting up other ways to meet those needs. And we should.

Bethany Lockhart Johnson (20:16):

And we’re also recording this in, what, two weeks, a week, after a tragedy where students and teachers were killed in the classroom. And I think both of us are taking some deep breaths and recognizing that there’s a lot of debate that is happening about what teacher’s role should be in preventing this in the future. And I don’t know if you’ve done drills in your classroom that are supposed to help mitigate disaster, but you know—collective deep breaths— <laugh> is where we’re at right now.

Dan Meyer (20:52):

Yep. The idea of “we should arm teachers” is another example of no, we should not do that. We should solve the tendency towards violence outside of the classroom so that teachers and students can teach and learn. That sounds awesome to me.

Bethany Lockhart Johnson (21:06):

Collective deep breath. Whew. OK. So what else you got for me, Dan?

Bethany Lockhart Johnson (21:33):

Ooh. So I feel like I’ve heard that in many teaching PDs. “I Do, you do, we do.” Actually I feel like I’ve seen like more “I do, we do, you do.” Like graduated release. I do it, then we’ll do it a little bit together, and then now you have permission to do it. And I feel like in directed draw, that’s a hundred percent true. Like I’m gonna show you this and then you draw it. And then you cut here and then you do it. If we’re trying to create this, like I’m teaching this new art technique. But in mathematics, I feel like that’s really not what I want my classroom to look like. I want to support my students and set them up for sense-making, and then I want them to try it out and I don’t want them to solve it the way it first comes to mind for me. I wanna see how they make sense of it and how they solve it. And then I want us to share it with each other so we can grow together. So I think time and place for “I do, you do, we do,” or “I do, we do, you do.” Or shoo-be-doo-be-doo-be. Yeah. You?

Dan Meyer (22:44):

I’ve got nothing. I have nothing to add. I thought that was just an excellent summary of a classroom I would love to be a part in, love to teach. I think it’s a certain tool in the toolbox that I think is overused. But it’s also a tool that can be useful in the case of certain kinds of operations. There are some operations that do benefit from “let me just show you how, like one way you might do this.” I don’t know. I’m like helping my kid whack a nail into a board and there’s a moment where it’s like, “Hey, actually, lemme just show you one way you can do this,” and do it, and then that’s helpful in some moments. But for so much of math, a lot of math does not relate to the operational kinds of fluency. And in those instances, it’s a little bit…it’s not a useful tool, I don’t think, for those kinds of skills and ideas.

Bethany Lockhart Johnson (23:34):

I’m thinking of tool talks in my classroom. So in kindergarten, many of the tools that we use in math and just in class in general, are new to the students. And if I tell them, this is exactly how you should use this tool, then I feel like I’m taking a lot of the sense-making away from them. But if I introduce the tool, show them how to use the tool safely, show them this is not a safe way to use the tool, chewing on this is not safe. That’s not how we use this tool. This is how we take care of it, et cetera. But then support different modes of using the tool that are gonna help them use it to solve problems and make sense, I think…but I guess—Dan, have you heard “I do, you do, we do,” or is it “I do, we do, you do”?

Dan Meyer (24:22):

I’m with you. And I think that it got clarified post-tweet. But yeah, it typically is “I do, we do, you do,” the gradual release of responsibility it’s often called. And I, I have heard people do what you described, which is…what is it? It’s “You do, we do, I do”? Like an inversion of that? Like have people do a thing that I can do that’s not too, too abstract for them, and then like “We all do something together, and then I’ll offer a summary of what we learned,” is one way that goes. I like that tool as well.

Bethany Lockhart Johnson (24:53):

I think particularly, at least I’ve seen in elementary classrooms, there’s sometimes this fear of letting students just try it out before I’ve really showed them, “but this is how it has to be.” And what I am most excited about is supporting students and creating a classroom environment where students don’t need my permission or need my direct “this is the only way to do it.” Instead, it’s like, yes, there’s lots of things we model. But there’s also like, “Hey, what do you think? How do you think this should be used?” And the joy of that exploration.

Dan Meyer (25:30):

Yeah. There’s a feeling of efficiency that comes from “I do, we do, you do,” for some kinds of math, but it’s undercut in my experience by what it cultivates in the students, which is “I’ve gotta wait until the teacher does before I can do anything.” So it pays off real diminishing returns over time. And it’s, just for me, an exhausting way to teach. Always being the bottleneck for new learning is a total drag.

Bethany Lockhart Johnson (25:55):

Ooh, what a great way to describe it. You do not wanna be the bottleneck. You want to be…what’s the other thing? The facilitator? What’s the opposite of a bottleneck? The flowing river? The…The…Help me!

Dan Meyer (26:10):

Hit us up in the replies. I dunno. The opposite of a bottleneck. That’s what you wanna…you wanna not be the opposite? No, you want, yeah. We got this here. We’ll figure it out. We’ll get back to you. <Laugh> OK. Well, folks, those were a few of this year’s fire tweets. It’s been fantastic chatting with you—

Bethany Lockhart Johnson (26:29):

Dan.

Dan Meyer (26:29):

—Bethany, About all those—

Bethany Lockhart Johnson (26:32):

Dan. You know, my favorite thing to do is interrupting you, Dan. I have to interrupt you because we can’t end fire tweets, Dan, without including a tweet from you.

Dan Meyer (26:43):

Oh, that’s true. I do have my moments. Yeah, we should. We really should. <Laugh> Do you have one in mind?

Bethany Lockhart Johnson (26:50):

No. Dan. Yes. I loved…you tweeted recently, “How many years have you been teaching?” Which, OK. “What Has been like the most influential? Like, what, OK, blah, blah, blah.” <blathering noises> You tweeted, “How many years have you been teaching? And at this point, what has most influenced how you teach?” And you gave some ideas: A methods course, PD sessions, curriculum, TV and movies, et cetera, et cetera. And I love that you put that out there because this episode is coming out as we’re wrapping up another school year. And it also got me thinking about summer and what teachers sometimes do during the summer, but what we might need to do this summer for self-care. But I’m really curious. I love that tweet. And I’m curious, Dan, what did folks say was the thing that had most influenced their teaching and what’s most influenced your teaching?

Dan Meyer (27:49):

Ooh, yeah. People’s responses to this one were really fantastic. I came into this, I was flying to the Association of Mathematics Teacher Educators conference. And I just found myself wondering, so, the pre-service year, the one year of, like, you’re learning how to teach, is how we did it in California. Like how much of that has still infused my practice? And in what ways? I don’t think I think about that stuff consciously, but I think that did like set me up with a lot of images that I would be unpacking for going on two decades now working in education. I think conversations with people, I think observing classes, I don’t think that like the one-day PDs, the one-day development days throughout the year, four times per year, I don’t think those stuck to me much. I think that this summer, I have learned so much, just an embarrassment of riches, from non-educational sources. From other disciplines. From storytelling, for instance. From how people have constructed movies I like. I am proud of the way…one of the aspects of my character that I’m proud of—it takes a lot to admit this, as I’m sure you understand, Bethany—but to integrate lots of wacky stuff and pick from it and use that to affect my practice and teaching has been really positive. So for this summer, I hope that people read a good beach book and just kinda let your teaching mind rest a little bit. And in doing so, create some openings for new ideas about education from other parts of the world. Kids! Having kids has been helpful. I don’t know! Just everything! It’s such a big job, education. Everything has so helpful. What about you? What’s an influence on your practice that might surprise me or other folks out there in MTL land?

Bethany Lockhart Johnson (29:52):

Well, I don’t know about surprise. I mean, I definitely feel similarly, like methods courses absolutely impacted my teaching. But I feel like opportunities where I was able to observe other teachers and where I was able to have conversations with folks about their practice, that has deeply impacted me. And books I’ve read. I mean, honestly, I’ve learned so much from sharing with other teachers. Like, for example, maybe I’ll bring student work and we’ll talk about it. And we kind of create this conversation together about how we wanna come back to the students based on the work we see. Those type of moments where we’re collaborating and we’re bringing multiple perspectives to the table, that I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day. So that continues to surprise and delight me. And thinking about this summer, I think there’s a lot of creativity and joy that can come out of the marination process, when you’re just kind of sitting back and healing yourself, whether through sleep or sunshine or time with friends and family or whatever that looks like for you. I think there’s a lot of creativity that can come from that place of fertile, you know, wellness. I never think of that as wasted time. I think of that as getting the soil ready for all that’s gonna come in the fall. And that being said, I also think it could be a fun time to dip your toes into something that you are excited to read, that you might not have a chance to read during the school year that could be teaching-related. So it’s like very low pressure, like, “Oh, I’ve really wanted to read more by this author. I’ve wanted to read this article. I’ve wanted to dip into this topic.” And not with a pressure, but just with a curiosity. And, yeah, I think so often we as teachers love learning, and to give yourself space to learn in whatever that looks like can be a real gift.

Dan Meyer (32:09):

Yes. And if you need book recommendations, hit the MTL back catalog of episodes. Loads of folks that we interviewed have real good books out.

Bethany Lockhart Johnson (32:16):

Yes!

Dan Meyer (32:16):

Think about it. Think about it.

Bethany Lockhart Johnson (32:22):

One quick recommendation: Again, gotta plug Antony Smith and Allison Hintz’s book. I read Mathematizing Children’s Literature before we did the interview, but this summer I wanna read all the children’s books that they mention. I just wanna go to the library and read all those children’s books. I wanna read them to my son. I wanna read ’em to myself. So, you know, diving into some good YA, children’s books, just, like, TLC. Dan, thank you for such a rich season and a chance to have so many interesting conversations. It is genuinely a joy to learn with and from you.

Dan Meyer (33:00):

Likewise. And always hope to see you folks on Twitter now and then. Let us know what you’re up to this summer at MTLShow on Twitter or in our Facebook group, Math Teacher Lounge. We’ll be there tuning in now and then. It’s been a treat interacting with you folks over this last season. Take care and until the new season, so long.

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What Bethany Lockhart Johnson says about math

“I’ve learned so much from sharing with other teachers… Those type of moments where we’re collaborating and bringing multiple perspectives to the table, I think, has really often shifted me out of my first initial reaction or what I thought I was going to do in the classroom the next day.”

– Bethany Lockhart Johnson

Meet the guests

Dan Meyer

Dan Meyer taught high school math to students who didn’t like high school math. He has advocated for better math instruction on CNN, Good Morning America, Everyday With Rachel Ray, and TED.com. He earned his doctorate from Stanford University in math education and is currently the Dean of Research at Desmos, where he explores the future of math, technology, and learning. Dan has worked with teachers internationally and in all 50 United States and was named one of Tech & Learning’s 30 Leaders of the Future.

Bethany Lockhart Johnson

Bethany Lockhart Johnson is an elementary school educator and author. Prior to serving as a multiple-subject teacher, she taught theater and dance and now loves incorporating movement and creative play into her classroom. Bethany is committed to helping students find joy in discovering their identities as mathematicians. In addition to her role as a full-time classroom teacher, Bethany is a Student Achievement Partners California Core Advocate and is active in national and local mathematics organizations. Bethany is a member of the Illustrative Mathematics Elementary Curriculum Steering Committee and serves as a consultant, creating materials to support families during distance learning.

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About Math Teacher Lounge: The podcast

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

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

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

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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!

Download Transcript

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.

Stay connected!

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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.

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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: Numbers

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

Unit 2: Number Operations

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

Unit 3: Proportionality, Ratios, and Rates

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

Unit 4: Equivalent Expressions

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

Unit 5: Equations and Inequalities

Unit 6: Relationships in Geometry

Unit 7: Measurement and Data

Grade 7

Unit 1: The Number System

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

Unit 2: Ratios and Proportional Relationships

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

Unit 3: Expressions, Equations, and Inequalities

Unit 4: Geometry

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

Unit 5: Statistics

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

Unit 6: Probability

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

Grade 8

Unit 1: Real Numbers, Exponents, and Scientific Notation

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

Unit 2: Proportional and Nonproportional Relationships and Functions

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

Unit 3: Solving Equations and Systems of Equations

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

Unit 4: Transformational Geometry

Unit 5: Measurement Geometry

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

Unit 6: Statistics

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

S2-05: Moving students forward with project-based learning

A promotional image for the podcast "Science Connections" featuring guest Janis Lodge and the topic "Moving students forward with project-based learning." Season 2, Episode 5.

In this episode, Eric Cross sits with K–5 educator Janis Lodge to chat about building on her own science curriculum to create meaningful project-based learning experiences. Janis shares her work teaching Gifted and Talented Education (GATE), and how to use those practices to help accelerate the learning of all students. Eric and Janis also talk about making time for science within K–5 classrooms. Explore more from Science Connections by visiting our main page.

DOWNLOAD TRANSCRIPT

Janis Lodge (00:00):
To me, the reward of having those kids feel like they accomplished something and the way that they can take ownership of it and go in so many different directions, I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it.

Eric Cross (00:18):
Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Janis Lodge. Janis is a third-grade teacher in Orange County, California, with a specialization in gifted and talented education. Recently, Janis was awarded the Orange County Council for the Gifted and Talented Education Classroom grant. This grant funds a project that provides an extension to her third-grade science unit about environments and survival. Through this project, students will think like a biomimicry engineer as they design a robot that is inspired by an innovation found in nature. In this episode, we discuss how she uses interdisciplinary teaching practices to make time for science learning; why gifted and talented education strategies can benefit all students; and her process for creating a problem-based lesson that ultimately earned her a grant for her classroom. And now, please enjoy my conversation with Janis Lodge. One, welcome! Thanks for being here.

Janis Lodge (01:14):
Of course, I am happy to do it. I’m excited for the opportunity.

Eric Cross (01:17):
Of course! Yeah. Elementary school teachers in science, I feel like there’s so many things to have conversations about. And some of the things that you’ve really focused on, I think, are, really, really important. But I wanna start off with your journey of you becoming a teacher in the classroom. And so, would you kind of give your background, your origin story? How did you end up as a third-grade teacher?

Janis Lodge (01:37):
Well, my story is definitely not a traditional story. Before I was a teacher, I was actually living in Maui, Hawaii. I moved there right after college. I went to Chico State in Northern California. And I got a degree in graphic design. And after I graduated, well, I should give a little bit of a backstory. My last summer before graduating, I spent the whole summer in Maui and I just fell in love with it. So when I graduated, I decided instead of applying for jobs in Northern California, I’m just gonna put some resumes out in Maui and see if I can get a job. And I did. I ended up getting a job doing graphic design and marketing for a kite surf company out there. And I ended up just staying for seven years on the island. And after about seven years, I kind of got a little bit of island fever and decided I wanted to come back to California. I wasn’t sure exactly what I wanted to do, but I just had this calling that I need to do something a little more fulfilling with my life. And I started thinking about different ideas and dreams I had. And I actually started thinking about when I was younger, right? I had this dream. If you were to ask me when I was 10 years old what I wanted to be when I grow up, it would be elementary school teacher.

Eric Cross (02:48):
Really?

Janis Lodge (02:48):
Believe it or not. When I was younger, I transformed my bedroom into a classroom. My stuffed animals were my students. I just thought I’m gonna be the next best teacher ever. And you know, as I went through life and kind of went in different directions, I kind of lost sight of that dream a little bit. But for some reason, when I decided to change careers, I just remembered that. And so I just decided to go get my teaching credential and see if it worked out. And it was probably the best decision I made. I feel like everything just fell perfectly into place. I ended up getting a job at an amazing school, and now, five years later, I’m a third grade teacher.

Eric Cross (03:28):
So one of the questions I have to ask, and talking to elementary school teachers, this comes up a lot: How do you make time for science as an elementary school teacher who’s teaching everything? And let me kind of premise this with, at least for those of us in California, and I’m sure the rest of the states too, but we know this; There’s kind of this pressure with pacing and then even, depending on what school you’re at, math and English tend to get the bulk of things. And maybe there’s this perception also of like, well, I gotta teach math and English, and sometimes science gets put to the back burner for different reasons.

Janis Lodge (03:57):
Well, you’re exactly right. The beginning of the year, we were provided with a pacing from the district. And you know, they try to keep us on track, saying, “You should be starting Unit 2 at this time.” But other than that, there’s really no specific guidelines of how many days we’re supposed to be teaching or for how long. But one kind of secret that I’ve discovered is that I can weave science into the other subjects, specifically with language arts. So quite often what I do is I take a look at the language arts standard, and if it’s identifying the key details and the main idea, well I can do that with the science books used from the curriculum. So I’ll just pull those readers and we’ll do the exact same skill, start with the same standard, but we’ll use the content from science. By doing that, we call that kind of like interdisciplinary study. And the students really enjoy that more, too, because they’re using the same skills but they’re diving deeper into the content.

Eric Cross (04:54):
Right.

Janis Lodge (04:55):
And so also that helps build the background knowledge. So then when it comes to time where, if I want to do a science lab or a science investigation, now they already have that background knowledge ’cause we already dove deep into the reading and they can apply that pretty quickly right away into their lab or whatever activity they’re doing.

Eric Cross (05:12):
Can you give an example maybe of how you might pull out something that might be a skill that you’re trying to develop, maybe in an English content, but you would pull that out in a science lesson, maybe? What would you do?

Janis Lodge (05:25):
We’re actually doing that right now. So we’re in our second unit of science and they’re studying inheritance and traits and they’re looking at different organisms to see how they have adaptations to help them survive in their environment. So coincidentally part of the literacy skills is to look at multiple sources, do research, and summarize and make analysis of what they’re reading. And so we have different varied resources. I have websites; I have books, ebooks, videos, and pictures. And they’re choosing which four sources they want to use. And then, then they’re coming up with a summary at the end and then putting together a Google Slides presentation based on whatever organism that they chose.

Eric Cross (06:05):
Did you have a science background before becoming an elementary school teacher?

Janis Lodge (06:11):
Um, none. Besides what I, you know, took in high school and college.

Eric Cross (06:16):
Did you find it easy to kind of lean into the science, or was it something you just kind of jumped into and said, “All right, I’m gonna get after it”?

Janis Lodge (06:23):
What’s interesting is if, you know, throughout my education, my favorite subjects were English and reading and writing and art. And quite honestly, science wasn’t my favorite subject. But I think because of that, that inspires me to come up with creative ways of presenting the information to them and making it exciting and engaging for them, because I don’t want them to feel that way. I want them to be excited about all subjects. And I think that’s the beauty of combining the different subjects like I mentioned before. Like I say, you know, “What would a scholar do? Think like a wildlife biologist. And like with my project, think like a biomimicry engineer.” And so it kind of shifts their thinking. Like, it’s not just, “Oh, we have to study science.” It’s like, “No, you are the scientist; you are a meteorologist; or you are an author. How would an author write about this? How would an illustrator capture this in a photo or a comic strip?” And so, when you really combine those disciplines, you can take it to another level. So even if science isn’t their favorite subject, like maybe it wasn’t for me growing up, they can still take something they’re passionate about and apply the science content to it and they really resonate with them.

Eric Cross (07:37):
You leaned into your strengths. Which are more like, coming into it, you had all these kind of creative strengths. You have that background as a graphics designer. You were into the arts. But then with those strengths, did that kinda give you more confidence to dive into the science work, because you approached it from your assets that you were already coming to the table with?

Janis Lodge (07:55):
Yeah.You said it perfectly. If you look at it from a different lens, there’s all these different ways you can approach science.

Eric Cross (07:59):
I find it in my own science class, too. We’re all teaching the same standards. But how I approach it is through Eric Cross’s kind of personality and understanding and my angle, and another teacher might do it a different way. But we’re all leading to the same destination.

Janis Lodge (08:14):
Exactly.

Eric Cross (08:15):
That kind of leads me to my next question, and this is having to do with the project that you just alluded to. The biomimicry project. So you did a biomimicry project. Would you consider that like a project based-learning assignment?

Janis Lodge (08:26):
Well, this will be the third year that I’ve taught this unit. And when I wrapped it up last year, it’s through the Amplify Science program, and they do a wonderful job of having a lot of investigations and really thinking like a biomimicry engineer. But the final part of the unit was to design a robot inspired by a giraffe, to eliminate invasive plants in a particular environment. And the project part of it at the end was to create a model using Popsicle sticks and pipe cleaners. And then the other part of it was a digital simulation where they would put in different shape structures of teeth, and kind of reconfigure the shape of the mouth. And then they’d put in what they think is effective, and then the computer would say, oh, you’re 98% successful or 70% successful. And I remember at the end of it the students were like, “OK, well when do we make the robots?” And I thought, “Well, we’re just doing the simulation, or we’re just doing this model out of Popsicle sticks; we’re not actually gonna make a robot.” And they just seemed so disappointed. And that’s kind of how the wheels started turning my head like, “Well, what if they actually could make a robot? The only thing stopping me is I don’t have the materials to do it.” So, shortly after that unit wrapped up, coincidentally I saw the email about this grant opportunity that was being offered through the Orange County Council for Gifted Education. And they said, If you have a project that you wanna get funded that would promote GATE strategies within the classroom, then you can submit this proposal. So that’s how the ball got rolling for that proposal. And I researched different robotics kits and different companies and I found one that was really user-friendly for third graders, and not so difficult for me to learn as well.

Eric Cross (10:10):
You’re a risk taker. Like, I’m already seeing this as I’m talking to you. Is that just who you are or do you have a network? Like what keeps you taking these risks?

Janis Lodge (10:18):
I don’t really consider it a risk, because it’s exciting for me. Like I said, I don’t know that much about robotics, but the idea of learning more and then teaching that to my students is exciting. And you know, there was a little bit of risk ’cause I’m deviating a little bit from the curriculum, from the standard lesson, but to me, the reward of having those kids feel like they accomplished something, and the way that they can take ownership of it and go in so many different directions, and on top of that, develop coding skills and computer science skills and robotic skills, to me it was just like I cannot take that away from them. That’s such an opportunity that if I have the means to do it, I have to just take it and run with it. So I think just being inspired by the potential outcomes of what could happen is what made me take that risk.

Eric Cross (11:05):
Did you just kind of create this from scratch? Did you work with a team of people? How did you come to the point where you were ready to present this for the grant?

Janis Lodge (11:12):
Pretty much from scratch. Like I said, the Amplify unit, it does teach them about robotics that were inspired by nature. So some of the materials that they read, and there’s some videos that show really great examples. There’s like a robotic arm that was inspired by an elephant trunk. There’s a book that shows what this field is, biomimicry engineer, they actually show like what they do in that field. And I thought this is a perfect way to apply it because the curriculum’s already pretty much set it up for me; now I just have to add this one final component to it. And essentially it becomes project-based learning at that point, because they’re taking their knowledge and their skills that they’ve learned up to that point. Even the unit that we’re doing doing right now is building up to it. So it’s kind of that final—instead of giving them a test at the end and saying, “OK, tell me what you learned about inheritance and traits and environments,” they can actually take that knowledge and apply it to an innovation or creation that comes out of their own mind, which is so much more powerful.

Eric Cross (12:11):
Do they connect to any other learning goals as they’re doing these projects?

Janis Lodge (12:15):
Well, I think first and foremost, the 21st century skills that from day one I tell them, the four Cs: collaboration, creativity, communication, and critical thinking. All of those are woven in through this lesson. From the beginning, we talked about the whole engineering design process. So from the beginning, they start with a question and oftentimes that actually can be the hardest for them to think about, “What’s a scientific question or a problem that I wanna solve?” If they’re passionate about, maybe, a sport or the environment or something within their school, I go, “There it is. OK, that’s the problem. How can you design something inspired by nature to solve that problem?” And then, from there they go into the planning and the designing and the testing and then the improving. So going through that engineering design process, I think, is what really makes them feel like they are the engineer going through this. And they can make mistakes. They can take risks. A lot of my students I’ve found are afraid to take risks. They wanna make sure they succeed. And they need that challenge to know that if they do fail, that’s OK. We can just revisit this. We can test it. We can look at it in a different way.

Eric Cross (13:27):
You maybe wonder about, how do you assess something like this?

Janis Lodge (13:30):
I think that’s where all those stages along the way are important. Because I wanna make sure that they have a plan and that it’s based on the knowledge that they’ve gained in the unit. I think one of the other things about project-based learning is the final product of how they demonstrate their mastery. And in my classroom I oftentimes give them a choice of how they’re gonna present that to me. So maybe they’re going to write it out like an essay. Maybe they’re gonna create a Google slide. Maybe they’re gonna make a video. Maybe they’re going to—obviously in this part they will have the model, but they’ll have to have some way to explain it to me. And I think giving them that choice gives them the opportunity to show it in the way that’s meaningful to them.

Eric Cross (14:14):
And are you using like a rubric when you’re grading these assignments? Or, how do you actually grade it?

Janis Lodge (14:20):
Yes. So we have a rubric that’s provided to us for the written component that all the students will do at the end. But I can take that same rubric and see if they’ve applied that to the project. So even the verbiage wouldn’t really need to change. I think it’s still important that the students are able to demonstrate this in written form and so all of them will still complete that written component, but to also give them the opportunity to show that in the modality of their choice. I think is really important too.

Eric Cross (14:48):
Right. And you have some students that feel much more comfortable being able to present orally versus—

Janis Lodge (14:53):
Exactly.

Eric Cross (14:53):
—versus writing versus maybe doing a video. I mean, we see that in middle school and in high school too. Students show their knowledge or their understanding of a topic depending on the medium in different ways, and some better than others. Some may find that they can communicate it a lot better orally, but when pen goes to paper or fingers go to keyboard, you might grade it completely different, ’cause they’re not able to transfer what’s in their mind into writing. And the way you’re doing it, and giving that student choice, they probably have so much more buy-in, I’d imagine, because they get to pick what they get to do.

Janis Lodge (15:21):
Right.

Eric Cross (15:22):
You said something earlier and I wanna come back to it. So you mentioned GATE, and GATE is not something that I hear a lot in my world, but it was something I heard a lot when I was in school. There were kind of all of these perceptions and ideas about GATE. You’re a GATE teacher, correct?

Janis Lodge (15:38):
Right.

Eric Cross (15:39):
What is GATE, and what is it like being a GATE teacher? What are the misconceptions, if any, that you might have heard or come across?

Janis Lodge (15:46):
Well, so GATE stands for Gifted and Talented Education. And first and foremost, I think a misconception is that we’re just kind of doing whatever we want; we come up with our own lessons and teach a totally different curriculum. Which is definitely a myth. Because we start with the exact same standards as any other third grade class that you’d walk into. That’s definitely where we start. But I think in addition to the standards, we also implement what are called GATE standards: So they’re Depth, Complexity, Acceleration, and Novelty. And there’s a lot of tools that we use in the classroom, different strategies. You’ll see things like the prompts of Depth and Complexity. We’ll use things like “think like a disciplinarian”; I’m doing “think like a biomimicry engineer.” But really, all they are are just thinking tools and strategies to elevate students thinking and kind of go below that surface level of the content to dive deeper. It also provides opportunities for acceleration. So for example, our last science unit, it was on magnetic force, and there was a handful of students that just grasped the concepts right away, and they’re ready for something else. They’re ready for more rigor. They need some challenge. And so at that point I can kind of pull that group aside and provide some differentiation for them. And I said, “OK, well, you understand the concept of magnetic force, balanced forces. So now what I want you to do is think about something that you’re really passionate about, and how could you use magnetic force somewhere in that field—again to solve a problem, problem-based learning—and present it to me?” So they create this form, it’s like a “think like a disciplinarian” frame, and one of them was “think like a hockey player.” And he’s trying to think of a way that he can incorporate magnetic force. Anyway, I could go on and on. But basically it’s finding what these students’ passions are. And I do that with all my students. And I should probably preface this by saying that even though these are standards that I implement in my classroom because it’s a GATE classroom, these are practices and tools that can be applied to any learner, at any age. And they really just enrich the education for all students.

Eric Cross (18:02):
So your classroom is, is a mixed classroom. There’s GATE students and then general—

Janis Lodge (18:05):
Right.

Eric Cross (18:07):
—students, non-GATE students, in the same class. It’s interesting because I imagine GATE is kind of scaffolding up to a higher level, but then, you also said something that I’ve noticed when I’m creating scaffolds for my students to support them, who may not be at a grade level, maybe in reading or literacy or math, those same scaffolds can help all students.

Janis Lodge (18:27):
So yeah, I don’t just go, “OK, you’re my GATE students; I’m gonna use these practices on you.” I use it for the whole class. But I’m also surprised by having that mix of these different learning styles. A lot of times students are inspired by other students, or, you know, we have this big thing about one of the prompts is Multiple Perspectives. I try to do that as much as I can, because students are inspired by the ideas of their peers. And quite often, if they hear it from a peer, it could be exactly what I just said, but they heard their student say it in a different way and it just clicks and they’re like, “Wow, I get that.”

Eric Cross (19:00):
I think a lot of teachers struggle or, or maybe feel ill-equipped, to support higher-level students. Did you get trained to be a GATE teacher? First lemme ask that question: Did you get special training for this?

Janis Lodge (19:13):
Yes. I went through a course, I think it was like a six-week certification course, through my district.

Eric Cross (19:19):
OK, so you got a special training, which—I’ve been in the classroom for nine years; I teach at a university as an adjunct professor; but I’ve never been trained on teaching gifted or accelerated students. And I’m kind of wondering now, like, do you feel like it made you a better teacher?

Janis Lodge (19:33):
Absolutely.

Eric Cross (19:34):
And if so, how do I get to do this?

Janis Lodge (19:36):
Well, it’s through the county. I mean, anybody can get trained and certified how to teach this way. But, just like you said, I think coming out of that, my eyes were just open, and my biggest takeaway is that these practices, even though they are designed for gifted and talented, it really kind of reshaped my thinking about how I, number one, present material to the students, that I’m doing it in an engaging way, and I’m not just lecturing at them; there’s opportunities for them to collaborate and communicate and use multiple resources. So, you know, how I’m teaching has changed. And then also, how I’m providing opportunities for them to demonstrate their learning. And a lot of that is project-based learning, because once they have the knowledge and skills they need to do something with it. I mean, that’s really the true definition of innovation, is taking the skills or taking something that you’ve learned, and now go with it. Run with it.

Eric Cross (20:32):
How can we take what you’ve learned and then kind of spread it, so teachers have this in their toolkit, too? Like for me, I have multiple ways to be able to support reading and literacy and math and tools and sentence frames. And my students who have special learning plans, I have a have a lot of tool sets for that. I wanna build my tool sets for this other area for my students who want to continue, who wanna run, or go beyond, or even stretch themselves. I think we need to take some of the things that you’re doing and not make them kind of like this exclusive group, but also let’s share it with everyone, ’cause if everybody can access it—

Janis Lodge (21:03):
I agree.

Eric Cross (21:03):
—we might see a lot more potential or a lot more opportunities for students who might not otherwise have them.

Janis Lodge (21:08):
And one thing: My school, I’m really proud to say that my principal has seen that. You know, he’s like, “Well why are we just keeping this in the GATE classroom?” So he’s working on getting all of our teachers certified.

Eric Cross (21:19):
No, I love what you’re doing and your principal sounds, sounds awesome for doing that and recognizing that this can benefit more students than just the ones who, you know, pass the Raisin Test, I think it’s what it was called when I was taking it, or whatever it is back then.

Janis Lodge (21:31):
Exactly.

Eric Cross (21:32):
We’ve talked about project-based learning, the GATE classroom…I kind of wanna come back to you as we wrap up. Thinking about, like, the jobs that you and I do, and the people that listen to this podcast, we have one of the few jobs that people remember us for a lifetime. And I wanna ask you, who was someone that was maybe inspirational in your educational career, that inspired you, or is maybe one of the most memorable? You might have several…but who is someone that was memorable to you in your career, and why? Why were they memorable to you?

Janis Lodge (22:02):
Yeah. Well, obviously, when I was younger, I was definitely inspired by all my teachers. The fact that I turned my bedroom into a classroom…I just was just in awe of this profession. But I think one that really resonated with me was my junior year in high school. I was taking a newspaper class and the teacher was Mrs. Kavanaugh, and she really taught us everything from writing the articles to the editing, to putting the pages together. And I remember in that class I was working on this program called QuarkXPress. I don’t even know if it exists anymore. But I was just fascinated with putting all these pieces together that we’d worked on for so long and getting the articles, picking the pictures, the illustrations and the titles. And I remember her looking at me saying, “You really enjoy this, don’t you?” And I said, “Yeah.” And she said, “Well, I have a computer graphics elective class that you should take next year.” And I thought, “OK, I’d love to do this, this opportunity to expand my knowledge and my skills.” So because of that, I took the computer graphics class the next year and I just remember throughout the whole time, she was just constantly encouraging me and acknowledging my skills. And I find myself doing that as a teacher as well. ‘Cause that really resonated with me. And it’s funny, this summer I was going through some boxes of some old stuff from high school, and I found this handout that I had made, because I remember my senior year of high school, she said, “Janis, you know what? You’re doing such a great job; we have these new, incoming students coming into the newspaper class, and I’d love for you to actually teach them how to do this pagination on this QuarkXPress program. I want you to put something together and actually teach it to them.” I thought, “Wow, she believes in me that much that she’s gonna let me teach this to the incoming students.” But I think my takeaway from that was that she gave me the opportunity to take those skills and actually do something with them, to apply them right away.

Eric Cross (23:53):
Mrs. Kavanaugh. Miss Kavanaugh. Shout-out to Miss Kavanaugh. As you told that story, I heard you as a teacher because I’m hearing she’s applying these GATE strategies in that situation. That’s what that’s what I heard.

Janis Lodge (24:08):
Yeah, absolutely.

Eric Cross (24:09):
She personalized this learning. She created a specialized opportunity. You presented to a real audience that was authentic. It had this personalization in it and this rigor and this challenge and it made a huge impact. And it’s just amazing to listen to you and hear this come full-circle, and now you’re doing this with little ones. And I just wanna thank you for your time in doing the interview, sharing your story with how you became a teacher, your students, the projects that you do. And just like so many teachers, going the extra mile for your kids and bringing in these really important 21st century skills; they’re gonna be so much better off for it. And I know it makes my job easier when I get them in the classroom, so thank you.

Janis Lodge (24:49):
Yeah. Well, thank you for the opportunity.

Eric Cross (24:51):
My pleasure. Thanks so much for listening and we wanna hear more about you and the educators who inspire you. You can nominate them as a future guest on Science Connections by emailing STEM@amplify.com. That’s S -T-E-M at amplify dot com. And be sure to click subscribe, wherever you listen to podcasts, and join our Facebook group, Science Connections: The Community. Until next time.

Stay connected!

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We’ll also share new and exciting free resources for your classroom every month!

What Janis Lodge says about science

“The reward of having kids feel like they accomplished something and take ownership is such an opportunity [with project-based learning] that I have to run with it. Being inspired by the potential outcomes of what could happen is what made me take that risk.”

– Janice Lodge

3rd Grade Teacher, De Portola Elementary

Meet the guest

Janis Lodge is a third grade teacher in Orange County, California. Her career in education started six years ago when she decided to follow her passion of making a positive difference in the lives of young scholars. Prior to teaching, Janis lived in Maui, Hawaii for seven years, working in the field of graphic design, marketing, and hospitality. She has found that her interest in innovation, project-based learning, and inquiry-driven exploration has helped shape her into the educator she is today. STEAM is integrated regularly into her classroom, and her students continually develop 21st century skills through a variety of unique projects. ​​Janis is also a PAL (Peer Assistance Leadership) Advisor for her school, where she helps young leaders (4th-6th graders) cultivate their leadership skills and empowers them to make a positive difference in their school and community. Janis was recently awarded the Orange County Council for the Gifted & Talented Education Classroom Grant, which will provide an extension to the third grade Amplify Science Unit: Environments and Survival.

A woman with long blonde hair smiles at the camera; she is inside a circular frame with a small decorative star in the corner.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

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Making reading comprehension connections

A smiling girl in a green shirt sits at a desk with an open book, holding a pencil, highlighting the importance of literacy benchmarks. A yellow background with a book icon is shown behind her.

Comprehension isn’t just a process, or just a product—it’s both. And connecting reading and understanding is what most teachers are working on every day.

That fundamental connection was the focus of our recent Science of Reading Webinar Week: Comprehension Connections—Building the Bridge Between Reading and Understanding, a five-day, expert-filled series that unpacked what really drives comprehension, from early decoding to middle school mastery.

Here’s a quick look at what you’ll learn when you watch—and a few ideas you can use right away.

Day 1: What Is Reading Comprehension, Anyway?

Speaker: Susan Lambert, Ed.D., Chief Academic Officer, Literacy, Amplify; Host of Science of Reading: The Podcast

“Reading comprehension is more than just language comprehension. It’s language comprehension on the page, which makes it much more complex.” — Susan Lambert, Ed.D.

If you ask ten teachers to define comprehension, you might get twelve answers. Lambert opened the week by grounding everyone in the Science of Reading, including the Simple View of Reading and the Reading Rope. Skilled reading, she reminded viewers, is the result of multiple strands—decoding, language comprehension, and knowledge—woven together over time.

The takeaway? The most effective approaches don’t teach comprehension strategies—such as “find the main idea”—in isolation. Rather, they connect word recognition to meaning through rich texts, conversation, and writing. Whether you’re teaching second-grade reading comprehension or sixth-grade reading comprehension, students need the same thing: a clear path from sounding out words to making sense of ideas.

Day 2: Comprehension and Knowledge Building: A Two-Way Street

Speakers: Sonia Cabell, Ph.D., Sigmon Endowed Professor of Reading Education, Florida State University

HyeJin Hwang, Ph.D., Assistant Professor, Department of Educational Psychology, University of Minnesota Twin Cities

“Better background knowledge leads to improved reading comprehension, which in turn enables readers to learn more from text, thereby building additional knowledge.” —HyeJin Hwang, Ph.D.

In their session, Sonia Cabell and HyeJin Hwang explored one of the clearest findings in reading research: Comprehension and knowledge develop together. Cabell began by explaining how comprehension (including oral language, background knowledge, vocabulary, syntax, and verbal reasoning) forms one of the essential strands of the Reading Rope.

Students can’t activate knowledge they don’t yet have. Teachers need to help them build it early, and intentionally. Cabell’s research found that integrating literacy and content instruction produced gains in vocabulary and content knowledge.

Likewise, Hwang’s two large-scale longitudinal studies showed that better knowledge instruction leads to better reading, which leads to even more knowledge. These findings held true across languages and grade levels, underscoring the universal value of content-rich instruction.

Classroom takeaways:

  • Plan literacy units around connected science or social studies topics to build coherent knowledge.
  • Use content-rich interactive read-alouds with discussion before, during, and after reading.
  • Ask inferential comprehension questions (“Why?” “How?”) that require students to connect ideas using their own words.
  • Encourage quick writing or drawing tasks that help students show what they’ve learned.

Day 3: Where and How to Measure Comprehension to Drive Improvement

Speakers: Danielle Damico, Ph.D., Executive Director of Learning Science, Amplify

Gina Biancarosa, Ed.D., Ann Swindells Chair in Education, University of Oregon

“Reading comprehension is both a process and a product.” —Danielle Damico, Ph.D.

Too often, comprehension is measured only as a finished product—how well students answer questions after reading—without revealing how they built understanding along the way. This session explored what comprehension actually involves: reading words accurately, understanding their meaning, applying background knowledge, and making inferences. As researcher Sharon Vaughn, Ph.D., has described, these interconnected skills all work together as students learn to read.

Biancarosa showed how looking at comprehension as a complex process helps teachers see student thinking in action. She described the major types of inferences—lexical, bridging, gap-filling, and causal—and the importance of understanding how students connect ideas and construct meaning.

Try this:

  • Treat comprehension as ongoing thinking, not a one-time test score.
  • Use brief think-alouds or class discussions to get a look at how students connect ideas.
  • Match assessments to the precise question you’re trying to answer.
  • Let assessment guide instruction—data should lead directly to next steps.

Day 4: Comprehension in Middle School: More Important Than Ever

Speaker: Deb Sabin, Chief Academic Officer, Amplify ELA

“Writing done right encodes knowledge. And discourse done right gets into the realm of higher-order thinking.” —Deb Sabin

By the time you’re teaching fourth-grade reading comprehension through sixth-grade reading comprehension, decoding should be automatic. At this stage, the upper strands of the Reading Rope—vocabulary, background knowledge, and syntax—move to the forefront. In this session, Deb Sabin highlighted how comprehension in middle school relies on academic knowledge, disciplinary vocabulary, and structured discourse—and how it truly blossoms when reading, writing, and speaking reinforce one another.

Classroom moves that help:

  • Pair writing with reading: Even short, text-based responses consolidate knowledge in long-term memory.
  • Use structured discussion (“accountable talk”), where students cite text evidence and build on one another’s ideas.
  • Center rich, grade-level texts that challenge thinking and vocabulary.

Speaker: Julie A. Van Dyke, Ph.D., Clinical Assistant Professor, Yale University Child Study Center; Research Scientist, Yale-UConn Haskins Global Literacy Hub

“Teach phonics for decoding. Teach syntax for understanding.” —Julie A. Van Dyke, Ph.D.

In the final presentation of the series, Julie Van Dyke explored an often-overlooked element of comprehension: syntax—the way words combine to create meaning. Van Dyke argued that syntax is to comprehension what phonics is to decoding.

She illustrated how the Science of Reading and the Reading Rope locate syntax within the language-comprehension strands—critical to understanding who did what to whom in complex sentences. Explicitly teaching sentence structure helps all learners, including multilingual/English learners, access higher-level meaning.

Simple practices can make a difference:

  • Have students paraphrase tricky sentences. (Starter question: “Who’s doing the action?”)
  • Pull strong sentences from your class texts to show how structure shapes meaning.
  • Encourage students to mirror those structures in their own writing.

What linked all five sessions together? The understanding that comprehension develops when teachers connect the code, the language, and the knowledge. Whether students are decoding in second grade or crafting essays in sixth, they thrive when we help them move from reading to understanding—step by step, strand by strand.

Watch all five on-demand recordings.

More to explore:

Overview Video

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
The logo for The Lawrence Hall of Science, University of California, Berkeley, features blue text on a light background and is recognized by educators using Amplify Science for middle school science programs.

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

DO

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

TALK

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

READ

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

WRITE

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

VISUALIZE

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS, and support students in mastering the standards.

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.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3-D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Amplify Science California supports 3-D learning with more materials than any other program.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

A laptop displays a PowerPoint presentation in presenter view, with slides about observing objects in plastic containers and related sensory instructions.

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free TG!

A laptop screen shows an energy simulation, with surrounding text and diagrams explaining the Earth's system and energy flow.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

What comes in each grade level kit? Click the links below to see the grade-specific lists of all materials included in each kit.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t1.jeffersoncounty@demo.tryamplify.net
  • Enter the password: Amplify1-jeffersoncounty
  • Click the Science icon.
  • Click on the Program Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform,watch the below navigational video.

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: s1.jeffersoncounty@demo.tryamplify.net
  • Enter the password: Amplify1-jeffersoncounty
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

Resources to support your review

Eureka Math²

Level K

Module 1: Counting and Cardinality

Topic A: Classify to Make Categories and Count

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

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

Lesson 3: Sort by Same ColorMatching Groups

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

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

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

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

Module 2: Two- and Three- Dimensional Shapes

Topic A: Analyze and Name Two-Dimensional Shapes

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

Module 3: Comparison

Topic C: Compare Sets Within 10

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

Module 4: Composition and Decomposition

Topic A: Explore Composition and Decomposition

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

Topic B: Record Composition and Decomposition

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

Module 5: Addition and Subtraction

Topic A: Represent Addition

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

Topic B: Represent Subtraction

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

Topic C: Make Sense of Problems

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

Level 1

Module 1: Counting, Comparison, and Addition

Topic A: Count and Compare with Data

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

Module 2: Addition and Subtraction Relationships

Topic A: Reason About Take From Situations

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

Topic B: Relate and Distinguish Addition and Subtraction

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

Topic C: Find an Unknown Part in Change Unknown Problems

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

Module 3: Properties of Operations to Make Easier Problems

Topic B: Make Easier Problems to Add

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

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

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

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

Topic A: Grouping Units in Tens and Ones

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

Topic D: Addition and Subtraction of Tens

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

Level 2

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

Topic A: Representing Data to Solve Problems

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

Topic C: Estimate, Measure, and Compare Lengths

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

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

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

Module 2: Addition and Subtraction Within 200

Topic A: Simplifying Strategies for Addition

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

Module 5: Money, Data, and Customary Measurement

Topic A: Problem Solving with Coins and Bills

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

Topic B: Use Customary Units to Measure and Estimate Length

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

Topic C: Use Measurement and Data to Solve Problems

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

Level 3

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

Topic A: Conceptual Understanding of Multiplication

Lesson 2: Interpret equal groups as multiplication.Equal Groups

Topic C: Properties of Multiplication

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

Topic D: Two Interpretations of Division

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

Module 2: Place Value Concepts Through Metric Measurement

Topic A: Understanding Place Value Concepts Through Metric Measurement

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

Topic C: Simplifying Strategies to Find Sums and Differences

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

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

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

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

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

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

Module 4: Multiplication and Area

Topic A: Foundations for Understanding Area

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

Topic B: Concepts of Area Measurement

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

Module 6: Geometry, Measurement, and Data

Topic D: Collecting and Displaying Dat

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

Level 4

Module 1: Place Value Concepts for Addition and Subtraction

Topic A: Multiplication as Multiplicative Comparison

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

Module 2: Place Value Concepts for Multiplication and Division

Topic E: Factors and Multiples

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

Module 4: Foundations for Fraction Operations

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

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

Topic D: Add and Subtract Fractions

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

Topic F: Repeated Addition of Fractions as Multiplication

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

Module 5: Place Value Concepts for Decimal Fractions

Topic A: Exploration of Tenths

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

Topic B: Tenths and Hundredths

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

Topic C: Comparison of Decimal Numbers

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

Level 5

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

Topic B: Multiplication of Whole Numbers

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

Topic C: Division of Whole Numbers

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

Module 2: Addition and Subtraction with Fractions

Topic A: Fractions and Division

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

Module 3: Multiplication and Division with Fractions

Topic B: Multiplication of Fractions

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

Module 5: Addition and Multiplication with Area and Volume

Topic C: Volume Concepts

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

Topic D: Volume and the Operations of Multiplication and Addition

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

Level 6

Module 1: Ratios, Rates, and Percents

Topic A: Ratios

Lesson 2: Introduction to RatiosPizza Maker

Topic B: Collections of Equivalent Ratios

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

Topic D: Rates

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

Module 2: Operations with Fractions and Multi-Digit Numbers

Topic B: Dividing Fractions

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

Topic C: Dividing Fractions Fluently

Lesson 9: Dividing Fractions by Using Tape DiagramsPuzzling Areas

Topic D: Decimal Addition, Subtraction, and Multiplication

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

Topic F: Decimal Division

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

Module 3: Rational Numbers

Topic A: Integers and Rational Numbers

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

Module 4: Expressions and One-Step Equations

Topic B: Expressions and Real-World Problems

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

Topic C: Equivalent Expressions Using the Properties of Operations

Lesson 13: The Distributive PropertyProducts and Sums

Topic D: Equations and Inequalities

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

Module 5: Area, Surface Area, and Volume

Topic A: Areas of Polygons

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

Topic B: Problem Solving with Area

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

Topic C: Nets and Surface Area

Lesson 12: From Nets to Surface AreaRenata’s Stickers

Module 6: Statistics

Topic A: Understanding Distributions

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

Topic B: Mean and Mean Absolute Deviation

Lesson 7: Using the Mean to Describe CenterToy Cars

Level 7

Module 1: Ratios and Proportional Relationships

Topic A: Understanding Proportional Relationships

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

Topic C: Scale Drawing and Proportional Relationships

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

Module 2: Operations with Rational Numbers

Topic A: Adding Rational Numbers

Lesson 2: Adding IntegersFloats and Anchors

Topic B: Subtracting Rational Numbers

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

Topic E: Numberical Expressions with Rational Numbers

Lesson 25: Writing and Evaluating Expressions with Rational NumbersInteger Puzzles

Module 3: Expressions, Equations, and Inequalities

Topic A: Equivalent Expressions

Lesson 1: Equivalent ExpressionsCollect the Squares

Topic B: Unknown Angle Measurements

Lesson 7: Angle Relationships and Unknown Angle MeasuresFriendly Angles

Topic C: Solving Equations

Lesson 11: Dominoes and DominoesKeeping it True

Topic D: Inequalities

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

Module 4: Geometry

Topic A: Constructing Geometric Figures

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

Topic C: Circumference and Areas of Circles

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

Module 5: Percent and Applications of Percent

Topic A: Proportion and Percent

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

Topic C: More of Less Than 100%

Lesson 10: Percent IncreaseAll the Equations

Topic D: Applications of Percent

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

Topic E: Problems Involving Percent

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

Module 6: Probability and Populations

Topic A: Calculating and Interpreting Probabilities

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

Topic B: Estimating Probabilities

Lesson 7: The Law of Large NumbersIs It Fair?

Topic C: Random Sampling

Lesson 11: Populations and SamplesCrab Island

Level 8

Module 1: Scientific Notation, Exponents, and Irrational Numbers

Topic A: Introduction to Scientific Notation

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

Topic B: Properties and Definitions of Exponents

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

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

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

Module 2: Rigid Motions and Congruent Figures

Topic A: Rigid Motion and Their Properties

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

Topic B: Rigid Motions and Congruent Figures

Lesson 8: Sequencing the Rigid MotionsTransformation Golf

Topic C: Angle Relationships

Lesson 12: Lines Cut by a TransversalPuzzling It Out

Module 3: Dilations and Similar Figures

Topic A: Dilations

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

Topic B: Properties of Dilations

Lesson 5: Figures and DilationsSocial Scavenger Hunt

Module 4: Linear Equations in One and Two Variables

Topic A: Linear Equations in One Variable

Lesson 3: Solving Linear Equations with Rational CoefficientsEquation Roundtable

Topic D: Slope of a Line

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

Topic E: Different Forms of a Linear Equation

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

Module 5: Systems of Linear Equations

Topic A: Solving Systems of Linear Equations Graphically

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

Topic B: Solving Systems of Linear Equations Algebraically

Lesson 6: Solving Systems of Linear Equations without GraphingLine Zapper

Module 6: Functions and Bivariate Statistics

Topic A: Functions

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

Topic B: Linear and Nonlinear Functions

Lesson 9: Increasing and Decreasing FunctionsThe Tortoise and the Hare

Topic C: Bivariate Numerical Data

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

Topic D: Bivariate Categorical Data

Lesson 18: Bivariate Categorical DataFinding Associations

Topic E: Volume

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

Algebra 1

Module 1: Expressions, Equations and Inequalities in One Variable

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

Module 2: Equations and Inequalities in Two Variables

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

Module 3: Functions and Their Representations

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

Module 4: Quadratic Functions

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

Module 5: Linear and Exponential Functions

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

Module 6: Modeling with Functions

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

Grade 6

Module 1: Composing and Decomposing

Topic 1: Factors and Multiples

MATHbookLesson 1: Taking Apart Numbers and ShapesProducts and Sums
MATHbookLesson 5: Yours IS to Reason Why!Fill the Gap

Topic 2: Area, Volume, and Surface Area

MATHbookLesson 1: All About That Base….and HeightExploring Triangles
Triangles and Parallelograms
MATHbookLesson 2: Slicing and Dicing: Composit FigureShapes on a Plane
Letters

Topic 3: Decimals

MATHbookLesson 1: You Have a PointDishing Out Decimals
MATHbookLesson 2: Get In LineDecimal Diagrams and Algorithms
MATHbookLesson 4: Dividend In the HouseMovie Time

Topic 4: Fraction by Fraction Division

MATHiaLesson 1: Representing Fraction DivisionFlour Planner

Topic 5: Area of Triangles and Quadrilaterals

MATHiaLesson 2: Developing Area FormulasExploring Parallelograms,
Part 1
MATHiaLesson 3: Calculating Areas of Various FiguresExploring Parallelograms,
Part 2

Off the Grid, Part 1
Off the Grid, Part 2

Topic 6: Composite Figures

MATHiaLesson 2: Calculating Area of Composite FiguresPile of Polygons

Topic 8: Surface Area of Regulat Prisms and Pyramids

MATHiaLesson 1: Determing Surface Area Using NetsRenata’s Stickers

Module 2: Relating Quantitites

Topic 1: Ratios

MATHbookLesson 2: Going StrongPizza Maker
MATHbookLesson 3: Different but the SamePizza Maker
MATHbookLesson 4: A trip to the MoonFruit Lab

Topic 2: Percents

MATHbookLesson 2: Warming the BenchLucky Duckies

Topic 3: Using Tables to Represent Equivalent Ratios

MATHbookLesson 1: Many ways to MeasureMany Measurements
Model Trains
MATHbookLesson 2: What is the Best Buy?World Records
MATHbookLesson 3: A Trip to the MoonWelcome to the Robot Factory
MATHiaLesson 2: Using Tables to Determine Equivalent RatiosDisaster Preparation
MATHiaLesson 3: Problem Solving with Equivalent Rations and Rates using TablesDisaster Preparation

Topic 9: Introduction to Unit Rate

MATHiaLesson 2: Determining and Comparing RatesSoft Serve
More Soft Serve

Module 3: Determining Unknown Values

Topic 2: Equations

MATHbookLesson 2: Double TalkWeight for It
MATHbookLesson 3: Play It in ReverseWeight for It
MATHbookLesson 4: One, None, or a TonTunnel Travels
MATHbookLesson 5: Getting RealFive Equations
Swap and Solve

Topic 3: Graphing Quantitative Relationships

MATHbookLesson 3: Planes, Trains, and PaychecksSubway Fares

Topic 6: Solving One-Step Addition and Subtraction Equations

MATHiaLesson 1: Exploring One-Step Equations with Double-Number LinesHanging Around

Topic 7: Solving One-Step Multiplication and Division Equations

MATHiaLesson 1: Using Double Number Lines to Solve One-Step Multiplicaiton EquationsHanging Around

Topic 8: Solving One-Step Equations with Decimals and Fractions

MATHiaLessons 1-4:Hanging Around

Module 4: Moving Beyond Positive Quantities

Topic 1: Signed Numbers

MATHbookLesson 1: Signed NumbersCan You Dig It?

Topic 1: Introduction to Negative Numbers

MATHiaLesson 2: Representing Integers on Number LinesOrder in the Class

Module 5: Describing Variability of Quantities

Topic 1: The Statical Process

MATHbookLesson 3: SkyscrapersThe Plot Thickens

Topic 2: Numerical Summaries of Data

MATHbookLesson 1: In the MiddleToy Cars
MATHbookLesson 3: March MADnessHoops

Topic 2: Analyzing Numeric Data Displays

MATHiaLesson 1: Creating Dot PlotsMinimum Wage

Grade 7

Module 1: Thinking Proportionally

Topic 1: Circles and Ratios

MATHbookLesson 1: Pi: The Ultimate RatioMeasuring Around
MATHbookLesson 2: That’s a Spicy Pizza!Why Pi?
MATHbookLesson 2: Circular ReasoningArea Challenges
MATHbook
Lesson 4: Pound for Pount, Inch for Inch
Scaling Machines
Tiles
Scaling Robots

Topic 2: Proportionality

MATHbookLesson 1: Poultry in MotionPaint
MATHbookLesson 6: Minding Your Ps and QsTwo and Two

Topic 3: Proportional Relationships

MATHbookLesson 1: Markups and MarkdownsAll the Equations
100%
MATHbookLesson 4: More Ups and DownsMosaics
More and Less

Topic 3: Scale and Scale Drawing

MATHiaLesson 1: Critical Attributes of Similar FiguresScale Factor Challenges
MATHiaLesson 3: Calculating Measurements Using ScaleMake it Scale
Will It Fit

Topic 4: Ratio Representations

MATHiaLesson 2: Determining Characteristics of Graphs of Proportional RelationshipsDinoPops

Topic 11: Introducing Proportions to Solve Percent Problems

MATHiaLesson 2: Solving Simple Percent ProblemsBack in My Day

Topic 13: Percent Increase and Percent Decrease

MATHiaLesson 1: Calculating Percent Change and Final AmountsPercent Machines

Module 2: Operating with Signed Numbers

Topic 1: Adding and Subtracting Rational Numbers

MATHbookLesson 1: Math FootballFloats and Anchors
MATHbookLesson 2: Walk the LineMore Floats and Anchors
MATHbookLesson 4: What’s the Difference?More Floats and Anchors

Topic 5: Rewriting Expressions

MATHiaLesson 2: Evaluating Simple Numberic Expressions with IntegersInteger Puzzles

Topic 6: Using Number Properties to Interpret Expressions with Signed Numbers

MATHiaLesson 2: Operating with Signed DecimalsDraw Your Own

Module 3: Reasoning Algebraically

Topic 1: Two-Step Expressions and Equations

MATHbookLesson 4: Formally YoursKeeping it True

Topic 2: Multiple Representations of Equations and Inequalities

MATHbookLesson 3: Solving Inequalities with Inverse OperationsUnbalanced Hangers
MATHbook
Lesson 4: Deep Dive
Budgeting
Write Them and Solve Them

Topic 1: Rewriting Algebraic Expressions

MATHiaLesson 2: Rewriting Algebraic Expressions Involving Integer CoefficientsCollect the Squares

Topic 8: Solving Inequalities with Inverse Operations

MATHiaLesson 3: Solving Two-Step InequalitiesI Saw the Signs
Shira the Sheep

Module 4: Analyzing Populations and Probabilities

Topic 1: Introduction to Probability

MATHbookLesson 1: Rolling, Rolling, Rolling…How Likely
Prob-bear-bilities
MATHbookLesson 2: Give the Model a ChanceIs It Fair?

Topic 3: Drawing Inferences

MATHbookLesson 2: Tiles, Gumballs, and PumpkinsCrab Island

Module 5: Constructing and Measuring

Topic 1: Angles and Triangles

MATHbookLesson 2: Special DeliveryFriendly Angles
MATHbookLesson 3: Consider Every SideCan You Build It

Topic 1: Special Angle Relationships

MATHiaLesson 2: Exploring Angle RelationshipsMissing Measures
MATHiaLesson 3: Solving for Angle MeasuresMissing Measures

Grade 8

Module 1: Transforming Geometric Objects

Topic 1: Rigit Motion Transformaitons

MATHbookLesson 1: Patty Paper, Patty PaperTransformers
MATHbookLesson 2: Slides, Flips, and SpinsSpinning, Flipping, Sliding
MATHbookLesson 3: Lateral MovesGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 4: Mirror, MirrorGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLasson 5: Half Turnsa and Quarter TurnsGetting Coordinated, Part 1
Getting Coordinated, Part 2
MATHbookLesson 6: Every Which WayTransformation Golf

Topic 2: Dilations

MATHbookLesson 1: Pinch-Zoom GeometrySketchy Dilations
MATHbookLesson 2: Rising, Running, Stepping, ScalingDilation Mini Golf
MATHbookLesson 3: From Here to ThereSocial Scavenger Hunt

Topic 3: Line and Angle Relationships

MATHbookLesson 2: Crisscrsoss ApplesaucePuzzling It Out

Topic 1: Rigid Motion in the Coordinate Plane

MATHiaLesson 1: Experimenting with Rigid MotionMoving Day

Module 2: Modeling Linear Relationships

Topic 1: From Proportions to Linear Relationships

MATHbookLesson 2: Jack and Jill Went Up the HillTurtle Time Trials
MATHbookLesson 4: Up, Down, and All AroundTranslations

Topic 2: Modeling Linear Relationships

MATHbookLesson 2: Been There, Done That, Got the T-shirtWater Cooler
MATHbookLesson 3: Dining, Dancing, DrivingFlags
Ups and Downs
MATHbookLesson 4: Derby DayStacking Cups (Optional)

Topic 3: Systems of Linear Equations

MATHbookLesson 1: Crossing PathsMake Them Balance
MATHbookLesson 2: The Road Less TraveledLine Zapper

Topic 11: Solving Linear Equations with Variables on Both Sides

MATHiaLesson 3: Solving with Variables on Both Sides with RationalsEquation Roundtable

Module 3: Developing Function Foundations

Topic 1: Introduction to Functions

MATHbookLesson 1: Patterns, Sequences, Rules…Guess My Rule
MATHbookLesson 2: Once Upon a GraphTurtle Crossing
MATHbookLesson 4: Over the River and Through the WoodsThe Tortoise and the Hare
Scatter Plot City
Interpreting Slopes

Topic 2: Patterns in Bivariate Data

MATHbookLesson 1: Pass the SqueezeRobots
MATHbookLesson 2: Off the ChainDapper Cats
MATHbookLesson 3: Mia is Growing Like a WeedFind the FIt (called Fit Fights in Desmos Math)
MATHbookLesson 4: The Stroop TestInterpreting Scatter Plots
MATHbookLesson 5: Would You Rather…?Finding Associations

Topic 4: Drawing Lines of Best Fit

MATHiaLesson 1: Estimating Lines of Best FitInterpreting Slopes
MATHiaLesson 2: Using Lines of Best FitAnimal Brains

Module 4: Expanding Number Systems

Topic 2: Pythagorean Theorem

MATHbookLesson 1: The Right ConnectionTriangle Tracing Turtle
MATHbookLesson 4: Catty CornerTaco Truck

Topic 1: The Real Number System

MATHiaLesson 2: Graphing Real Numbers on the Number LineRoot Down

Module 5: Applying Powers

Topic 1: Exponents and Scientific Notation

MATHbookLesson 1: It’s a Generational ThingCircles
MATHbookLesson 2: Show What You KnowPower Pairs
MATHbookLesson 3: The Big and Small of ItSpecific and Scientific (formerly Solar System)
MATHbook
Lesson 4: How Much Larger?
Balance the Scale

Topic 2: Volume of Curved Figures

MATHbookLesson 1: Drum Roll, Please!Cylinders
MATHbookLesson 2: Conse of SilenceCones

Algebra 1

Module 1: Searching for Patterns

Topic 1: Quantities and Relationships

Lesson 3: f of x, Recognizing Functions and Function FamiliesCraft-a-Graph
Pumpkin Prices

Topic 2: Sequences

Lesson 1: Is there a Pattern Here?Visual Patterns
Revisiting Visual Patterns, Part 1
Lesson 2: The Password is Operations!Sequence Carnival
Revisiting Visual Patterns, Part 2
Lesson 3: Did You Mean: Recursion?More Visual Patterns

Topic 3: Linear Regressions

Lesson 1: Like a GlovePenguin Populations
Lesson 2: Gotta Keep It Correlatin’Correlation Coefficient
How Hot Is It?
Behind the Headlines
City Data
Lesson 3: The Residual EffectResidual Fruit
Lesson 4: To Fit or Not To Fit? That Is the Question!City Slopes

Module 2: Exploring Constant Change

Topic 1: Linear Functions

Lesson 1: Connecting the DotsPlane, Train, and Automobile

Topic 2: Solving Linear Equations and Inequalities

Lesson 1: Strike a BalanceWorking Backwards
Solving Strategies
Same Position
Lesson 2: It’s Literally About Literal EquationsSubway Seats
Various Variables
Shelley the Snail
Five Representations
Lesson 3: Not All Statements Are Made EqualPizza Delivery

Topic 3: Systems of Equations and Inequalities

Lesson 1: Double the FunShape It Up
Lizard Lines
Lesson 3: Throwing ShadeSeeking Solutions
Lesson 4: Working with ConstraintsQuilts

Module 3: Investigating Growth and Decay

Topic 1: Introduction to Exponential Functions

Lesson 2: The Power WithinCarlos’s Fish

Topic 2: Using Exponential Equations

Module 4: Describing Distributions

Topic 1: One-Variable Statistics

Lesson 2: A Skewed RealityFinding Desmo

Module 5: Maximizing and Minimizing

Topic 1: Introduction to Quadratic Functions

Lesson 1: Up and Down or Down and UpQuadratic Visual Patterns
On the Fence
Stomp Rockets
Plenty of Parabolas
Robot Launch
Lesson 2: Endless Forms Most BeautifulParabola Zapper
Two for One
Shooting Stars
Lesson 4: You Lose Some, You Lose SomeSorting Relationships

Topic 2: Solving Quadratic Equations

Lesson 4: The Missing LinkSquare Tactic
Lesson 5: The Quadratic FormulaStomp Rockets in Space

Disclaimer

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

Science of Reading dos and don’ts

For classrooms and districts making the shift, understanding what a true Science of Reading curriculum looks like can be challenging. How do you know which instructional practices to adopt, which to avoid, and which ones are the real deal?

We’ve outlined five practices to start implementing today.

1. Use decodable readers.

Early readers need regular practice with grade-level text . Learning to read is not innate and must be taught through explicit, systemic instruction. Early readers need regular practice with grade-level text, especially text that’s connected to each day’s phonics instruction to helps students apply what they’ve learned.

Move away from level readers and curricula that have:

  • A focus on predictable text or below-grade-level text.
  • Decodable readers that don’t follow a clear phonics scope and sequence aligned to instruction.

2. Provide all students with dedicated phonics instruction.

Learning to read is not an innate skill. It must be taught through explicit, systematic instruction. An effective approach to phonics instruction provides enough time for teaching, application, and practice.

Shift from mini-lessons and curricula that have: 

  • Phonics instruction given only on an as-needed basis. When phonics is on an as-needed basis, students don’t get what they need to prevent reading difficulty.
  • Students alternating between limited phonics, guided reading, writing, and vocabulary practice in a mini-lesson.

3. Help students with phonics-based scaffolds.

Learning to decode builds neural pathways that are critical to automatic reading. Students need practice sounding out words, not doing guesswork.

Transition away from three-cueing or word guessing and curricula that have:

  • Prompts that encourage students to guess through three-cueing (e.g., “What word would make sense,” “what’s in this picture”).
  • Predictable books that enable pattern memorization.

4. Teach content.

Language comprehension is as important as decoding. The more background knowledge students receive, the more prior knowledge and vocabulary they can bring to texts.

Limit use of isolated comprehension strategies and curricula that have:

  • Limited time spent on each topic, or isolated topics introduced without connection to each other.
  • Comprehension skill practice without a strong content foundation (e.g., asking students to “find the main idea” or “determine the author’s purpose” in disconnected texts).

5. Follow a clear instructional path.

Clear instructional paths offer explicit guidance and cohesive structure, the most beneficial—yet overlooked—elements of teaching reading effectively. A definitive instructional path (rather than a patchwork) enables components to build upon each other. This gets students the support they need right away, so they don’t have to wait for intervention.

Withdraw from “choose your own adventure” models and curricula that have:

  • A model that provides multiple instructional pathways, which often lead to inconsistencies.
  • So many pieces to their programs that it’s unclear how to implement each effectively.

Centering students in math curriculum adaptations

Starting with a high-quality math program

In her research article, “Examining Key Concepts in Research on Teachers’ Use of Mathematics Curricula”, Janine Remillard described curriculum use as a dynamic and ongoing relationship between teachers and resources—a relationship shaped by both the teacher and characteristics of the resource.

I have found that while certain characteristics can make a math curriculum high-quality, it is only through its relationship with teachers that it creates truly meaningful math experiences for students.

In my own teaching experiences and now back in classrooms with teachers, I am convinced that no matter how well-constructed a lesson, it only gets better as teachers plan collaboratively and center their students.

Shaping lessons for the students in your classroom can be challenging because there is not one right way or time to adapt a lesson, and the reasons we adapt vary.

Sometimes we make relatively small tweaks to the wording of a prompt, a question the teacher should pose, or the timing of an activity.

Other times we make more substantial changes to the task or task structure in order to more clearly move toward the learning goal based on what we are seeing and hearing from students.

And then there are the times we realize in the midst of an activity we should have made an adaption in our planning.

I recently taught a 5th grade fractions lesson that provided a perfect example of the dynamic nature of the work.

Engaging in a math curriculum activity

This particular lesson falls at the end of the fraction addition and subtraction unit.

The Warm-Up of this lesson is a Number Talk, which made sense to the 5th grade teachers and I, given the unit focus.

We reviewed the mathematical concepts and problems in our planning session, anticipated that students might find common denominators, and agreed that the synthesis discussion around denominator choice aligned with the problems. 

Four addition problems with fractions—1/8 + 5/8, 1/8 + 6/16, 1/8 + 1/3, and 1/8 + 5/12—are arranged vertically to support math students and center student ideas in the math curriculum.

While we anticipated that students would successfully add, the number choices in the string led students to solve each one the same exact way, with the only difference being whether they stated their sum in simplest form or not.

Halfway through, we could see the majority of the students were getting bored and it was hard to infuse curiosity and excitement around denominator choice because students had already generalized a way of finding a common denominator—which at this point in the unit was great!

In the midst of the Number Talk, we paused and debated pivoting our focus to the problems in relation to one another rather than denominator choice. But we knew that doing that would add extra time to the lesson, when we needed the majority of the time for the activities that followed.

So we wrapped it up and moved on, knowing we had time to discuss our choice in an upcoming planning session.

Adapting in ways that center student ideas

After class, I couldn’t stop thinking about revisions I would make if we had the opportunity to plan it all over again. Because although the problems in the string supported mental calculation and aligned with the lesson activities, the students needed something different at this point in their learning.

After reflecting with colleagues, we decided the timing of that particular Number Talk for these students was too late in the unit and wondered if a different routine would have made it more engaging.

Using that Number Talk as a rough draft (shout out to Mandy Jansen), I played around with different number choices and routines we might use in a second take on that lesson. 

If we wanted to stick with the same task structure, we could adjust the numbers to create a new Number Talk or True or False? routine that more explicitly encouraged relational reasoning and use of the properties.

For example, the following problem strings still attend to denominators when adding fractions but also open up the space for more interesting and engaging student discourse. 

Number Talk

Four horizontal equations invite math students to add fractions with different denominators—1/8 + 5/8; 1/8 + 1/2; 1/8 + 1/2 + 9/24; and 1/8 + 1/2 + 9/24 + 6/4—centering student ideas as part of a dynamic math curriculum.

True or False?

Four lines of math equations with fractions involve addition, comparison, and equality symbols—featuring denominators like 8, 16, 3, 7, and 24—centered on student ideas to enhance the math curriculum for eager math students.

If we wanted to use a different structure altogether, we could try the Which One Doesn’t Belong? routine to provide opportunities for students to notice other interesting aspects.

In this activity, students share reasons why one of four items—in this case, equations—doesn’t belong. There is no single right answer because each object could both belong and not belong, depending on the student’s criteria. (If you’ve never tried this routine, it’s a must!)

A set of four boxes labeled A to D, each showing a math equation involving the addition of two fractions and their simplified sum—perfect for centering student ideas and matching student needs in any math curriculum.

Because I couldn’t wait until this lesson next year to see what students would do with one of these ideas, I asked them to write about the Which One Doesn’t Belong? The variation among their ideas was exciting.

While I could still see attention to the denominators as in the original Warm-Up, students were now describing their ideas in much more unique ways. If this had been the original Warm-Up, it’s not hard to imagine how much more engaged students would have been—and how much more teachers would have learned about their thinking. 

A worksheet from the math curriculum asks which fraction equation doesn't belong; all options are shown worked out, and a handwritten note concludes that none are wrong if you do the math, centering student ideas and matching student needs.
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A
Student response 2 to the "Which One Doesn't Belong Question" This students picks option B
Student response 2 to the "Which One Doesn't Belong Question" This students picks option B
Student response 2 to the "Which One Doesn't Belong Question" This students picks option C
Student response 2 to the "Which One Doesn't Belong Question" This students picks option D
Student response 2 to the "Which One Doesn't Belong Question" This students picks option A and D

Learning from within the work of teaching

Curriculum materials have shaped my teaching and learning since the beginning of my time in the classroom. They then became the focus of my work at Illustrative Mathematics and now in my current work at Amplify.

I am a strong advocate for high-quality curriculum materials, and at the same time, I also believe that every curriculum can always be improved to better meet the needs of students and teachers.

I continually recognize and appreciate the time I get to spend planning, teaching, and reflecting with teachers about their dynamic and ongoing relationship with curriculum materials.

These opportunities to learn from within the work of teaching are invaluable inputs to our current work at Amplify, where we have the exciting opportunity to improve the characteristics of math resources currently in schools. 

Want to learn more from Kristin Gray? Watch her webinar!

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Create transformation that lasts.

Embarking on educational change takes heart, intention, and determination. It also requires proven strategies and practical tools. With data, resources, and countless stories of successful implementations to guide us, we can take the first step toward true transformation together.

A woman with long dark hair is smiling while sitting at a desk in a classroom. Children in the foreground look toward her. The wall has colorful paper decorations.
Three women sit at a table in a library, engaged in conversation with notebooks and pens in front of them.

Principles for Educational Change Management

Whether you’re looking for transformative change in math, literacy, or science instruction, some essential principles apply across the board. As a teacher, administrator, or community leader, you’ll find these guiding principles can help you manage your new curriculum implementation and help each student reach their potential.

Corey Beil, Instructional Interventionist
“This goes out to the interventionists, coaches, and administrators … support your staff. Lead staff trainings, provide push-in support, model and co-teach so that the staff will see that this is not ‘just another initiative.’ Remember, this is the start of a long, powerful journey. Take small steps, do them well, then use data to move on to the next small step.”

— Corey Beil, Instructional Interventionist

Quakertown Community School District, PA

Leading instructional shifts across all disciplines

Two women review material on a tablet next to a document titled "Literacy Change Management Playbook," featuring a flowchart illustrating k-12 education concepts and the implementation of high-quality instruction materials.

Make the shift to the Science of Reading.

Learn the key steps that will drive the success you need.

learn more

Two pages of a math change management playbook for grades K–12, featuring a cover with teachers and a sample interior page with illustrations of children and math concepts for effective curriculum implementation.

Change in math is different.

Managing change in math doesn’t have to mean starting over. It starts with a few simple shifts.

learn more

Cover and inside page of a document titled "Science Change Management Playbook," featuring photos of adults and children engaged in educational activities with high-quality instruction materials for k-12 education.

Be a science inspiration.

Intentional shifts help transform students into concerned global citizens ready to take on the world. Find out how.

learn more

Let data guide your transformation.

The right data at the right time is crucial in planning lasting instructional change. With specific metrics to guide your implementation, you’ll know exactly how to monitor your progress. Download our literacy assessment infographic as a model for the key data questions to ask at critical points in the school year.

Two people sitting at a table in a bright room, engaging in a discussion with papers and a laptop in front of them.

Achieve implementation success.

Ready to navigate educational implementation with confidence? The following resources will help you discover practical strategies for decision-making, managing change, and engaging stakeholders.

A PDF page titled "The implementation journey" showing five steps, with step one, "Set the vision," highlighted and described in detail at the bottom—ideal for guiding new curriculum in schools or supporting k-12 education initiatives.

Discover five steps to successful implementation.

Balancing decision-making, data collection, and transparent communication doesn’t have to be overwhelming. Discover the five essential steps to making implementation manageable.

learn more

Cover page of a PDF titled "Transforming Leadership: Leveraging Implementation for Impact," showing a woman smiling and talking to others in a meeting room, highlighting the importance of high-quality instruction materials in curriculum implementation.

Think like a leader.

Strategic leadership requires more than sharp management skills. Find out how the leadership brain model can help you, as a district leader, connect initiatives with your broader vision.

learn more

Cover of a PDF titled “Transforming leadership: Leveraging implementation for impact,” featuring two children working together at a laptop, highlighting the importance of curriculum implementation in K-12 education.

Turn plans into results.

Educational change requires intentional effort. Key leadership imperatives can provide the framework you need for effective implementation.

learn more

Woman with wavy, shoulder-length hair and glasses, wearing a black blazer over a patterned top, smiling in front of a plain light-colored background—dedicated to supporting K-12 education and effective curriculum implementation.

What district leaders are saying

“In the past we’ve adopted a resource and we’ve left it to the teachers and the buildings to use and to put into practice. I was determined that we needed to do more than just that for both our teachers and our students. That is really where…the leadership brain concept has come into play. [It] provided the framework and key questions that I needed so that I could reflect, process, and determine what was next throughout the first year of implementation.”

—Lori Riehle, Assistant Director of Curriculum, Northwest Local School District, OH

Woman with long brown hair wearing a patterned jacket and black top stands in front of a beige siding wall, reflecting the confidence seen in leaders of K-12 education and curriculum implementation, looking directly at the camera.

What district leaders are saying

“Through the guidance and collaboration of the Amplify Team, our stakeholders participated in thoughtful conversations, relevant hands-on learning, and the development of clear guidelines for moving forward [with Amplify CKLA]. This process led to the creation of our district commitments, which, together with the six leadership imperatives, remain central to the progress we continue to make today.”

—Kristina Tucker, Coordinator of English Language Arts and Social Studies, Richland School District, WA

Woman with wavy brown hair wearing a brightly patterned blouse, large round earrings, and a necklace, smiling at the camera against a white background—perfect for illustrating curriculum implementation in schools.

What district leaders are saying

“[My advice to other leaders is to] stop trying to fix everything at once. Dig deep with systematic analysis to find your one high leverage problem; then build your entire system around solving it. You can have all the coaching and support in the world, but if you’re not focused on the right problem, those systems won’t translate to classroom impact.”

—Susan Rawlings, Assistant Principal, Charleston County School District, SC

Educational leaders share their success.

Find out how educational leaders have transformed their districts through successful implementation, revealing the commitment and strategic approach that led to real academic improvements.

A document titled "Building sustainable implementation" by Amplify, detailing Richland School District's approach to collaborative commitments for k-12 education, with an orange "PDF" label on the top right.

Change needs commitment.

Change is achievable when everyone commits to the process. See how one district turned collaboration into a successful implementation of Amplify CKLA.

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A document titled "From system to classrooms" discusses Charleston County School District’s efforts to improve teacher resources and support, featuring a Q&A with a district leader. An orange "PDF" label is overlaid.

Existing strengths need focused direction.

Strong district foundations require intentional focus. Learn how systematic analysis helped one district turn comprehensive resources into meaningful impact for teachers.

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A PDF titled "From solo leadership to distributed ownership" explores how a school district engaged stakeholders for sustainable curriculum implementation. Amplify logo appears at the bottom.

Shared responsibility transforms implementation.

Managing implementation alone limits success. Discover how one district leader used stakeholder mapping to create shared leadership and building-level ownership.

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Cover page of a PDF titled "Driving impact through implementation science," featuring a simple line drawing of a head and an orange label reading "PDF." Ideal for those seeking high-quality instruction materials in K-12 education.

See implementation in action.

Learn how one district achieved positive test results across grades 1–5 within their first year of adopting Amplify CKLA.

learn more

Cover page of a PDF titled "Driving impact through implementation science," featuring an outline of Washington state, with the Richland School District highlighted and a focus on curriculum implementation in schools.

Strategic change delivers results.

Results happen when change is managed strategically. Check out how one district turned thoughtful planning into successful Amplify CKLA adoption.

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Cover page of a PDF titled "Driving impact through implementation science," featuring a line drawing and orange banner reading "District Success Story." Highlights high-quality instruction materials in K-12 education. Amplify logo at the bottom.

Curriculum evaluation leads to confident decisions.

Explore how one district implemented Amplify CKLA (after piloting seven different programs!) and achieved powerful kindergarten reading gains.

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Cover page of a PDF titled "Driving impact through implementation science," featuring an outline of South Carolina and highlighting Charleston County School District's curriculum implementation and teacher resources.

Regular communication fosters growth.

Structured coaching support transforms implementation outcomes. Find out how regular communication helped one district achieve consistency and sustained student growth with Amplify CKLA.

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Cover page of a PDF titled "Driving impact through implementation science," featuring an outline map and text about Knox County Schools' academic achievement using Amplify CKLA's high-quality instruction materials.

Preparation creates lasting results.

Comprehensive training creates the foundation for sustained success. Read about how strategic summer preparation and ongoing professional learning helped one county achieve significant academic improvements.

learn more

Winter Wrap-Up 01: Problem-solving and facilitating classroom discussions

Promotional graphic for Math Teacher Lounge podcast, episode 1, featuring Fawn Nguyen, Christy Thompson, and Kassia Omohundro Wedekind discussing classroom problem-solving and discussions.

As we prep for an exciting new season of Math Teacher Lounge: The Podcast, hosts Bethany Lockhart Johnson and Dan Meyer are looking back at the amazing speakers and conversations from past episodes and sharing some of their favorites!

First up: A season 2 double feature of the power of problem-solving with Fawn Nguyen and Facilitating Classroom Discussions with authors Christy Hermann Thompson and Kassia Omohundro Wedekind.

Fawn is a specialist on Amplify’s advanced math team and a former math teacher and math coach—so she knows her stuff! You’ll hear about her five criteria for good problem-solving problems, and the power and importance of exposing all students to problem-solving.

Then, we’ll move into Bethany and Dan’s conversation with Christy and Kassia to learn how hands-down conversations allow students to become better listeners and the steps you can take to implement hands-down conversations in your classroom.

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. My name is Dan Meyer.

Bethany Lockhart Johnson: (00:03)

And I’m Bethany Lockhart Johnson. Hello! Happy New Year! Hello, Dan Meyer.

Dan Meyer: (00:09)

HNY, Bethany. HNY to you and to all of the listeners out there in Math Teacher Lounge. HNY is the abbreviation that I use sometimes.

Bethany Lockhart Johnson: (00:18)

Oh, is that what that is? Is that—I wasn’t sure what that was. If on my birthday you send me HBD…no.

Dan Meyer: (00:25)

Yeah.

Bethany Lockhart Johnson: (00:25)

No. Unacceptable.

Dan Meyer: (00:27)

I will. No, you want the full thing. To demonstrate my care for your birthday, I gotta spell the whole thing out. I’m just trying to stay relevant. You know, I’m just trying to stay relevant and youthful. So I’m using The Abreevs.

Bethany Lockhart Johnson: (00:38)

The Brevvies.

Dan Meyer: (00:40)

To the extent of even abbreviating the word “abbreviation.” . So, any New Year’s resolutions you wanna share with the listeners, Bethany? While you think, I’ll just share mine real quick here. This is the year of the perfect Wordle streak for yours truly, Dan Meyer. I’m going the full 365. Watch. Watch me do it, folks. I’m naming it here. Live on air. recorded on air. Perfect Wordle year. What you got for the listeners, Bethany?

Bethany Lockhart Johnson: (01:10)

Let’s see. It’s raining very hard here in Southern California, and my newest resolution is to embrace nature. My child wants nothing more than to go and splash in all the puddles.

Dan Meyer: (01:22)

Nice.

Bethany Lockhart Johnson: (01:23)

And be amongst the mud. And what I’m gonna keep telling myself—and so far, so far, I’ve been doing pretty good with this—thrive, child. Splash. Squish. We can dry you off. You will not melt. So I want to keep finding opportunities. Like, for instance, my response is, “It’s pouring rain. Let’s stay under covers and let’s read this book together!” And his response is like, banging on the windows, like, “Please let me go outside.” So I myself have some rain boots. I’m going to go forth and splash with my child. So hopefully you’ll see me doing that a bit more.

Dan Meyer: (02:08)

Love that.

Bethany Lockhart Johnson: (02:09)

Ask me what I’m doing. I’m outside, splashing in nature.

Dan Meyer: (02:12)

I don’t wanna put words in your mouth, but I have felt a bit like parenting is a means for rounding out aspects of my own personality that I have felt are—or habits or hobbies that are lacking. Like, I’ve never been real outdoorsy or into camping, but I don’t want that to limit my own kids’ aspirations or interests. So let’s do the thing that’s not super natural for me, for their own sake. Which is kind of what I’m hearing a little bit from you, which—that sounds exciting.

Bethany Lockhart Johnson: (02:35)

Do you wanna go camping together? Like, our families?

Dan Meyer: (02:38)

Uhhh. Let’s take this one off the air. I also love something that’s more relevant to a teachers audience that you said, that I think is super interesting, is how there’s ways that we can make the jobs harder for ourselves, that are optional. And what I hear from you is like, “I’m just not gonna freak out. We’re getting wet. We’re getting soggy. And I’m just not gonna freak out.” And I just think that that’s interesting to think about, the things that we take on, you know, that’s optional. Freaking out is optional, sometimes. And there’s other areas, I think, for parenting or for teaching, where it’s like, “Oh, do I really need to choose this particular battle?” And to reconsider that.

Bethany Lockhart Johnson: (03:19)

And in that spirit, our whole Wordle episode that we talked about? Do you remember you talked about how beautiful Wordle mistakes are, and how you keep learning from mistakes? I mean, you obviously want the final correct answer, but just, you know, when you get on a losing streak, Dan, I hope you’ll continue to pat yourself on the back.

Dan Meyer: (03:38)

Well, I will not be taking on a losing streak, or even lose one day. This is what’s gonna happen here. I’m just speaking that and putting it out in the universe.

Bethany Lockhart Johnson: (03:49)

Speak it!

Dan Meyer: (03:50)

But if it happens, I will be taking a long break from all human interaction. And lamenting, as I do.

Bethany Lockhart Johnson: (03:59)

Camping. Dan’s off in the woods, weeping.

Dan Meyer: (04:01)

That’s right. That’s right. Yeah. Well, we wanna share with you folks—an exciting programming note is that we are currently working very hard on producing a special fifth season of this podcast. You thought the other seasons were special? Let me tell you, this fifth season gives new meaning to the word “special.” And we can’t wait to tell you more about that. But in the meantime, Bethany, you wanna tell ’em what we’re up to in the meantime?

Bethany Lockhart Johnson: (04:26)

Well, Dan and I went back and we were having a conversation about some of our most favorite conversations, or the conversations that people bring up to us. Like, when we were at the CMC conference, or NCTM, folks, when we talk about the podcast, they’re like, “Oh, I loved this one.” “Oh, I love this one.” And that, to me, I don’t know, that is exciting. And so, while we’re putting together this new season over these next few weeks, we’re gonna feature a few of our favorite conversations from our first four seasons. Dan, four seasons!

Dan Meyer: (04:59)

We’ve been at this for four seasons! And I do want to just emphasize something you said, Bethany: that all of our conversations are our favorite conversations. They’re all our special children. What we just felt like you, the listeners, did not quite learn enough from some of these, and so we really needed you to hear them again to make sure you got everything that you should get out of them. So, let’s tell ’em who’s up first. And who’s up first is a conversation we had about problem-solving with Fawn Nguyen, who’s an advanced math team specialist here at Amplify. Been a former math coach, math teacher. Just really done the work, is what I’d say about Fawn.

Bethany Lockhart Johnson: (05:38)

If you have been listening to this podcast, you’re like, “Whoa, whoa. Wait, I have not missed an episode. I didn’t hear Fawn’s interview.” That is because we used to be video only, not podcasts. So this conversation with Fawn was from, what, our second season?

Dan Meyer: (05:55)

Yeah.

Bethany Lockhart Johnson: (05:56)

And we were on video. And another thing about it is it was, this is a conversation that, when folks talk about problem-solving, a lot of the responses we’ve gotten are like, “Wait, I’ve never thought of problem-solving this way.” In fact, you’ll hear us say that exact thing . So we really appreciated the time with Fawn. And yeah.

Dan Meyer: (06:17)

Enjoy it, folks. Especially enjoy Fawn’s—I think a four-part?—definition of problem-solving, a word that’s often kind of mushily defined. And Fawn really goes into, I think, precision and depth on it. So hope you folks enjoy it.

Dan Meyer: (06:35)

Give a wave, Fawn, to the camera. Would you? Cool. Fawn has been a teacher for a very long time. She is someone who could have left the classroom at any point and taken any number of jobs in the math-teaching universe. But I’ve always admired that Fawn has taught kids for a very long time, and that has given her, in my view, just a lot of clarity on what is important to her about students. I’ve seen her not get upset or obsessed with certain kinds of small niche issues that a lot of us, like, they get a lot of us down in the classroom, sometimes. And she’s maintained a laser focus on among many other things, problem-solving as a virtue in mathematics classrooms. So, please welcome Fawn to our show. Fawn, thanks so much for being here.

Fawn Nguyen: (07:18)

Hey, thank you so much. Thank you. I am so excited and honored that you guys invited me for this, Bethany and Dan.

Bethany Lockhart Johnson: (07:24)

Thank you for being here.

Fawn Nguyen: (07:26)

I love you, Bethany. Dan, I can tolerate, but I love you.

Dan Meyer: (07:30)

I really worked myself up there on that complimentary opening for you, and that’s how you get me back, here? OK. Problem-solving is fully on the consciousness of math teachers. Every math teacher knows that they need to say, like, “Yeah, oh, problem-solving. Yes. Love it. Do it. I dig it.” But even so, I feel like it’s become kind of a buzzword. Like, it’s not always obvious what that means…or am I doing problem-solving, really? So we’re curious: As someone who is a problem-solving expert, who is asked all over the world to talk about problem-solving: How do I know if I’m doing problem-solving in my classroom?

Fawn Nguyen: (08:12)

This is not my definition of it, but—nor am I an expert, by the way, Dan, thank you! but I try really, really hard and work on it!—my definition—or it’s not my definition, but I like it because it’s short and honest—is “problem-solving is what we do when we don’t know what to do.” And so—

Bethany Lockhart Johnson: (08:32)

Ooh!

Fawn Nguyen: (08:32)

—with that mind-frame, I’m hoping teachers think more about what they task. Because I think it gets mislabeled a lot, as to what is problem-solving. If the kids already know what to do, there’s a solution path. Then it’s not problem-solving.

Dan Meyer: (08:48)

Yeah. So what are examples then? An example of, like, I might call something problem-solving, but it it fails that particular definition that you just proposed there. Very short, very honest definition.

Fawn Nguyen: (08:59)

Just, it needs to have constraint and contradiction to what the kids think naturally. It should come as a surprise. There’s an element of surprise in it. There’s tension.

Dan Meyer: (09:11)

Maybe if there’s harder numbers or, you know, decimals or fractions in the same kind of procedure…I can feel myself thinking, “Yeah, this is hard. This is problem-solving. Problem-solving equals hard. But we already know what to do.”

Fawn Nguyen: (09:27)

Or just word problems. That’s the most common thing. As soon as it just has words attached to the math, it becomes problem-solving. But that’s just coding it to me. That’s just coding it with words, wrapping it around. It doesn’t mean anything until we read through and see if there’s true problem-solving in it.

Bethany Lockhart Johnson: (09:45)

Like, what’s the moment that it becomes problem-solving? In the way that you envision it?

Fawn Nguyen: (09:53)

Well, I think there’s the bigger problem-solving of really bringing a task…I wanna call it left field. It just—we rarely ever, if ever, see it in the regular coursework, but it can also be problem-solving if we just take what we expect the children to do at the end of the unit, how about we front-load that? To me, that’s also problem-solving. And I’m trying to encourage teachers to do that last problem first. The task writers put more thought—not that they don’t do the rest of it!—but you know, this is a special one, because they label it “challenge,” or “enrichment,” or “are you ready for more?” I’ve seen those. And so it is this really special problem. And I would love for us to think about “do that first.” Because my biggest fear is that because it comes at the end, that not all the children are involved. And so that to me is the saddest part. Because we might not get to it, right? In mathematics, we always think, “OK, well, let’s do these problems and then we don’t have time for the rest.” But I think that’s your richest task right there, is at the very end. So why don’t we front-load it, start it, and it’s OK—of course it’s OK!—that we don’t all get it. But the exposure to all students is so important. Talk about, you know, equity. Talk about that, everybody gets the same thing. If everyone dug into that first one with everybody’s collaboration, and we get to share that, and then we leave it, because “Yeah, OK, now we learn more of the other stuff, right? That hopefully support. And then we can go back. And now everybody had a chance to go get into it, and then we can come back to it as, as many problems, we need to go back to it.”

Bethany Lockhart Johnson: (11:37)

And that feels so powerful. Because it feels like—as a teacher, I’m thinking it would also inform my work, how I approach the unit, and how I approach the next steps. Right? Like, what kind of work would we be doing if I let it, if I allow it, to change the way that I approach the unit.

Dan Meyer: (11:58)

Yeah. What you’re describing is so powerful, and really asks a lot of the task designers as well, I think. There are problem-solving tasks that really require, like, abstract knowledge of the way formulas and variables fit together. And what I love about what Amplify is doing with their problem-solving, what you’re helping them do, is that they start with a true low floor that can draw in every student. And they might get stuck at different places; that’s fine. But everyone has a way in. That’s exciting.

Fawn Nguyen: (12:24)

It’s a big deal for me to have this opportunity and this trust, to integrate problem-solving into the curriculum, make it intentional. It’s difficult to implement. It is, to be honest. Because for me, what is a good task? This makes one of my four criteria: One is, it is non-routine. It is simply stated. Simply stated—that’s like your low floor. And then has multiple solutions. And the fourth: This makes it. Because that the teacher enjoys solving it. And so you have to enjoy solving it to bring it. Because so that way I can say to my kids, “This is my gift.” It really is, Because, you know, it has so much fun and joy. And I appreciate the struggle. And I wanna illustrate an example. For example, let’s say Dan and I are classmates. And I know that Dan gets A’s on his tests and the lowest score he ever got was an 89%. I, on the other hand, just sitting right next to him, I average D. I have a D average on everything. While Bethany, our amazing and wonderful teacher, brings in a problem. And when she brings it in, she says, “I worked on this problem. I found this problem; I worked on it; and I struggled with it. And it was amazing. I enjoyed it so much, I’m sharing it with you.” And all of a sudden it’s like, “OK!” And I”m sitting there, right? My teacher loves this problem so much; she’s bringing it in to share with us. And now, all of a sudden, it’s not, you know…and I know she only gives us non-routine. When she talks about problem-solving, it’s non-routine. So it’s not directly tied to the textbook that I’ve been struggling with. So it gives me a chance, it gives me a chance to contribute. To think differently. And now, suddenly I look forward to working with Dan, because in this space, in this problem-solving space, Dan is no longer Mr. Know-It-All. And so that’s what I mean by—I am saying this a hundred times, and I will not stop saying it—problem-solving levels the playing field. Our world is filled with unsolved problems. Are you kidding me? Right? We look around us, we have so many things that are not solvable, or people are working on it, and yet in mathematics, what happens? The bell rings; we start; and we solve everything during that time, and we leave. And that’s…yeah. No! No! We need to wrestle with problems.

Dan Meyer: (15:04)

And that was our conversation with Fawn Nguyen, which we first released way back in November, 2021. You folks can follow Fawn on Twitter at Fawn P Nguyen. Um, that’s @ F A W N P N G U Y E N.

Bethany Lockhart Johnson: (15:18)

So our episode today is a double feature. We are featuring another conversation that we loved from Season Two. This is a conversation with Christy Hermann Thompson and Kassia Omohundro Wedekind. They’re authors of the book, “Hands Down, Speak Out: Listening and Talking Across Literacy and Math.” And I don’t know if you remember, but not only did we have a conversation with them, but we did a whole book study on Facebook, a Facebook Live book study, over the course of several months. And it was one of my most favorite things. And then they did a webinar at the end. So our conversation with them on the podcast for me felt like such a beautiful dive into their book. And you know, I’ve said it before, you think you have something down in the classroom, you’re like, “Oh, hand-raising, I’ve got that down.” You think you have it down, but then somebody says, “OK, but have you ever considered thiiiis?” You know, and it just—

Dan Meyer: (16:17)

NOT that??

Bethany Lockhart Johnson: (16:18)

, Not that? Something totally different? And I loved talking with them. They’re a lot of fun. And I loved the book.

Dan Meyer: (16:23)

Wonderful conversation, great book. Very provocative ideas. Yeah. As someone who’s like, “OK, classroom management, I gotta get the hand-raising going…”. In the classroom before we talked, they offered a really potent challenge to some really standard classroom management ideas. Yeah. Loved it.

Bethany Lockhart Johnson: (16:40)

And this conversation also offers some really practical tips for facilitating student conversations. So we think you’ll enjoy it. Here’s our conversation with Christy and Kassia.

Bethany Lockhart Johnson: (16:53)

So today we are talking about “Hands Down, Speak Out: Listening and Talking Across Literacy and Math, K—5.” And we have the authors here, Kassia Omohundro Wedekind and Christy Hermann Thompson. Before we begin, let’s define what a hands-down conversation is. A hands-down conversation is just another way to structure discourse in your classroom. So in a typical classroom, you might see students raising their hand and waiting on a teacher to call on them before they share their ideas or engage in discussion. But in a hands-down conversation, it’s students’ ideas and voices that are taking the lead, and teachers are stepping back and focusing on listening and facilitating. Hello! Welcome to the Lounge.

Kassia Omohundro Wedekind: (17:44)

Thank you. We’re excited to be here. We’re fans of Season One. So we’re ready to go.

Dan Meyer: (17:50)

I was a secondary teacher but I still found so much to love about the book. I think facilitating conversations is just generally challenging, and perhaps even more so in math, where answers feel so tightly dialed-in, in lots of ways. But I loved it. I would love for you to just explain to our audience, what is a hands-down conversation and how does that contrast with what might be standard practice for some people? For some classes?

Christy Hermann Thompson: (18:13)

We just started using the term hands-down conversation because we wanted to differentiate the fact that there are different times to have different types of dialogue in the math classroom, in the literacy classroom. And we use this as one of our tools. Right? It’s not that every day, all day long, we’re very against hand-raising and should never see that again. We find that having this as one of our tools will be where we make really clear to the students that this is a moment where we’re turning it over to you to negotiate the space and make the decisions about when your voice comes in and who speaks next. You know, carry on kind of like that dinner table or that playground or, you know, whatever is your natural habitat for talk. And bringing that into the classroom and then hoping that it also someday transfers back out of the classroom back into the real world.

Bethany Lockhart Johnson: (19:09)

For the teachers who feel like that’s terrifying to have students just start speaking, and speaking without any sort of control or my little equity sticks, my little popsicle sticks, or my popcorn, or whatever other thing they’re using, what would you say is the first step?

Christy Hermann Thompson: (19:25)

So I think recognizing and naming that fear is part of it. And then saying to yourself, “What’s the worst that could happen here?” You know, I think the worst that could happen is that nobody talks and it’s totally silent. Or on the other hand, everybody talks at the same time. And both of those things will happen! And so what? It’s gonna be messy. And if you just acknowledge that it’s gonna look messy, and that’s part of growing; that every child as they learn—and every adult—is messy as they grow.

Kassia Omohundro Wedekind: (19:59)

And we have to see what kinds of things will happen in a hands-down conversation. Like there’s no prerequisite. You just start and then you see what happens. And those are the signs that tell you, “What can help this community grow as talkers and listeners? If everyone’s talking at the same time, and they’re kind of pushing each other over with their words by saying, “I have something to add!” “I have something to add!” or something like that, that’s a common thing that sometimes happens at the beginning. Then you know that the next step is to do some work about how to hold your thoughts back, how to add, wait for a space in the conversation to talk. And those are all things we need people to know out in the world.

Bethany Lockhart Johnson: (20:41)

So can you give an example of a micro-lesson that…well, first, what do you define as a micro-lesson? And then, what’s an example of one that maybe somebody who wants to dip their toe into the world of hands-down conversations that they could try?

Christy Hermann Thompson: (20:56)

The reason we call them micro-lessons is because we wanted to differentiate from the term mini lesson, which is out there and tends to describe about 10 or 15 minutes that might take place at the beginning of a work period of time. And this is much smaller than that. We usually follow a pretty predictable structure of naming. Here’s this thing that’s so helpful when we’re having conversations, and we love to especially be able to name something that a student had done: “Kaylee did this yesterday and it really helped us.” So what we might call that is, “And then here’s how Kaylee and other people might do that. They might do something like this.” And, you know, having a little anchor chart, so there’s a visual reminder of that skill. “So when we’re having a conversation today, you could try…”. And that’s basically a micro-lesson, just in a nutshell.

Kassia Omohundro Wedekind: (21:51)

When I was doing these hands-down conversations and I had more space for myself to listen as a teacher, I’m like, “Well, look at those kids, like, slumped onto the ground, like, pulling the carpet apart, but they’re having this amazing conversation!” And so I learned that listening is a lot broader. So in this lesson that I’m thinking about, we just talk with kids about what are lots of different ways that listening can look like. Sometimes with younger kids, I’ll take pictures of them listening in different ways and we’ll notice things about them together. And then we invite them to talk with their Turn and Talk partner about like, “How do you like to be listened to?” Or “Tell me about how you listen.” And just kind of broaden that. And really, I like to think that like the micro-lessons are for the kids, but also I’m saying those things to say them for myself. Like, “Remember, you don’t have to insist that kids are staring each other down in the eyes all the time. Like, “It’s OK when they’re doing other things. There’s other ways of listening.” So I think I’ve learned as much from the micro-lessons each time I do them as the kids that I’m trying to help grow as listeners and talkers, as well.

Dan Meyer: (23:00)

You folks have a lot of really eloquent ideals you express, around democratic classrooms and engagement. But you also have just some very tangible, practical…even down to, like, how a teacher positions their body in space and the way they use their eyes to connect. I think it would be really helpful for teachers to hear that it’s not just they’re signing on to a manifesto of sorts, but there’s ways they can act their way into the beliefs that you both expressed here.

Christy Hermann Thompson: (23:26)

When I’m starting hands-down conversation work, if I put myself a little bit outside of the circle and look down, and give myself a clipboard, it, it helps me bite my tongue and it helps me give better wait time and see what the kids are doing before I have that tendency to jump in and teach and do lots of teacher-y things.

Bethany Lockhart Johnson: (23:48)

Kassia and Christy, thank you so much for joining us. We are so excited to have this conversation and to share your work. This is exciting. And I feel like this conversation is just the beginning of a deeper dive into this book.

Kassia Omohundro Wedekind: (24:01)

Thanks for having us.

Christy Hermann Thompson: (24:02)

Thank you.

Dan Meyer: (24:03)

Thank you both.

Bethany Lockhart Johnson: (24:06)

Thanks so much for listening to our conversations with Fawn Nguyen and Christy Hermann Thompson and Kassia Omohundro Wedekind, both of which were released in 2021, part of our second season. And, you know, we hoped you enjoyed listening to it for a first, second, maybe third, fourth time.

Dan Meyer: (24:24)

Let’s be real. There’s some real fans out there.

Bethany Lockhart Johnson: (24:26)

We loved it then. We love it now!

Dan Meyer: (24:28)

Yep, yep, yep. Please keep in touch with the show by following us on Twitter at MTL Show, and join our Facebook group, the Math Teacher Lounge community. We’d love to hear from you there. And please stay tuned for more info on what we’re cooking up here in the Math Teacher Lounge. Thank you folks for listening. Take care, Bethany.

Bethany Lockhart Johnson: (24:47)

Bye now.

Stay connected!

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What Fawn Nguyen says about math teaching

“It’s a big deal for me to have the opportunity and this trust to integrate problem-solving into the curriculum.”

– Fawn Nguyen

Specialist, Math Advance Team, Amplify Desmos Math

Meet the guests

Fawn Nguyen

Fawn began her work with Amplify in 2022 as a Math Advance Team Specialist. She was a math coach for a K-8 school district for three years, and a middle school teacher for 30 years before that. Fawn has also received a number of accolades as an educator.

Christy Thompson

Christy Thompson is a Literacy Coach in Fairfax County Public Schools in Virginia. She has spent her teaching and coaching career particularly focused on listening to and learning from the talk of our youngest students.

Kassia Omohundro Wedekind

Kassia Omohundro Wedekind spent many wonderful years as a classroom teacher and math coach in Fairfax County Public Schools in Virginia and now splits her time between being an independent math coach and an editor at Stenhouse Publishers. Her favorite days are spent in classrooms learning from the many ways children talk, listen and negotiate meaning together.

Three women are pictured separately in circular frames, each smiling and facing the camera, against a white background with overlapping pastel shapes—perfect for highlighting math teacher lounge discussions or sharing essential math teacher resources.
A graphic with the text "Math Teacher Lounge with Bethany Lockhart Johnson and Dan Meyer" on colored overlapping circles.

About Math Teacher Lounge: The podcast

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

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

Amplify ELA Community Review Site

Welcome to the Amplify ELA community review site for Idaho Falls School District. This site is designed to help you learn about Amplify ELA—a core English Language Arts curriculum for Grade 6.

Your district leaders want to hear from you! Please share your thoughts by completing this district survey.

Looking for Grades K–5 materials? Click here.

What is Amplify ELA?

Amplify ELA helps kids in grades 6–8 read and understand complex texts that encourage them to grapple with interesting ideas and find relevance for themselves. Amplify ELA is a blended program that includes both digital and print materials, as well as a print-only version. Students using Amplify ELA read text passages closely, interpret what they find, discuss their thinking with peers, and develop their ideas in writing. The lesson structure is easy to follow, but flexible enough to allow for a variety of learning experiences and varied enough to keep students engaged. 

Features include:

  • Functionality that allows individual students to work at their own level while also being challenged appropriately.
  • Built-in tools that allow teachers to track and respond to student work.
  • The digital Amplify Library, which contains more than 700 downloadable full-length fiction and nonfiction books.
  • The Vocab App, which uses game-like activities to help students master keywords from the program’s texts. (Students using print materials will see keywords highlighted).
  • Independent writing assignments called Solos, available on mobile devices.

Unit Overviews

Students begin with narrative writing to quickly boost their writing production, learn the foundational skill of focus, and become comfortable with key classroom habits and routines they will use all year. Students then apply their new observational focus to some lively readings from Roald Dahl’s memoir Boy and learn how to work closely with textual evidence.

Unit 6A: Dahl & Narrative Caregiver Letter

Students read like an investigator to embark on a multi-genre study of the mesmerizing world of scientific and investigative sleuthing. At the end of the unit, students write an essay explaining which trait is most useful to problem-solving investigators.

Unit 6B: Mysteries & Investigations Caregiver Letter

The Aztecs used it as currency. Robert Falcon Scott took it to the Antarctic. The Nazis made it into a bomb designed to kill Churchill. The 3,700-year-long history of chocolate is full of twists and turns, making it a rich and rewarding research topic. In this unit, students explore primary source documents and conduct independent research to better understand the strange and wonderful range of roles that chocolate has played for centuries around the world.

Unit 6C: The Chocolate Collection Caregiver Letter

Greek myths help us understand not only ancient Greek culture, but also the world around us and our role in it. Drawing on the routines and skills established in previous units, these lessons ask students to move from considering the state of a single person—themselves or a character—to contemplating broader questions concerning the role people play in the world and the communities they inhabit within it.

Unit 6D: The Greeks Caregiver Letter

The borderlands between the United States and Mexico are the place of legends, both true and fictional. Summer of the Mariposas, by Guadalupe Garcia McCall, plants a retelling of the Odyssey into this setting, launching five sisters on an adventure into a world of heroes and evildoers derived from Aztec myths and Latinx legends. On the journey, the sisters reconcile the dissolution of their parent’s marriage and find new strength in their identity and connection to Aztec lineage. Students consider how McCall uses the structure of the hero’s journey to celebrate women, heritage, and a broad definition of family. Students also have the opportunity to compare these characters’ fictional journey into Mexico to a description of one boy’s true journey into the United States.

Unit 6E: Summer of the Mariposas Caregiver Letter

In this research unit, students learn to tell the difference between primary, secondary, and tertiary sources; determine if a given source is reliable; and understand the ethical uses of information. Students then construct their own research questions and explore the internet for answers. They also take on the role of a passenger from the Titanic‘s manifest to consider gender and class issues as they research and write narrative accounts from the point of view of their passenger.

Unit 6F: The Titanic Collection Caregiver Letter

In this unit, students get to practice their creative writing skills and learn the elements of storytelling and character development, as well as the importance of vivid language. Students gain a sense of ownership over their writing as they experiment with the impact of their authorial choices on sentences, language, character traits, and plot twists.

Unit 6G: Beginning Story Writing Caregiver Letter

In this unit, students complete self-guided grammar instruction and practice that teachers assign to them throughout the year. Sub-units are organized by key grammar topics, so teachers can assign the content that best meets their student’s needs while making sure students work with the key grammar topics for their grades.

Grade 6: Grammar Caregiver Letter

Materials overview

Amplify ELA is a blended program, which means your student will be interacting with both print and digital materials.

Print materials

Student Edition

Includes all of the readings and activities necessary for instruction throughout the year. Students can read the selections both digitally and in print throughout the year, annotating in either format. The lessons in the print Student Edition reflect each digital lesson, but have been modified to work effectively in print.

Writing Journals

Where students respond to Writing Prompts and complete other written assignments.

Novel Guides

Teachers can also access, print, and mail student Novel Guides for up to 12 commonly taught novels. Six of these novels are available in the Amplify Library, and most should be available in a public library.

Digital materials

Quests

You may notice your student working with peers on the same interactive project over several days, trying to solve a mystery or explain a historical event. That’s what happens when a teacher assigns a Quest: an in-depth week-long exploration that requires collaboration and deepens engagement with texts and topics.

Vocab App

The Vocab App helps students master vocabulary words through game-like activities that challenge them to think through morphology, analogy, and synonyms/antonyms, and to decipher meaning through context.

Support your child at home

How you can support the child in your care

  • If possible, read with your student daily; even 15 minutes of reading together each day can make a huge impact. You can read aloud sections of the text together—many middle grade students enjoy performing sections of dialogue by taking on the role of a character in a play, or adding some dramatic flair to a poem with which they are working. If your student struggles with reading aloud, you might try reading the text to them with expression, then having them read it back to you. For additional practice, there are an array of fluency activities in the program’s Flex Days. Ask your student to help you find this activity.
  • Find moments to discuss what they are reading and discovering. Examples of questions you could ask: What stood out to you from what you read today? Were any sentences or words confusing? What was most surprising? What do you think the writer was trying to communicate? Do you agree with the writer’s ideas or descriptions? What connections can you make between what you are reading and your own life or other issues?
  • Listen to your student read their written responses or have them share with a friend over the phone or video chat. 
  • Browse the Amplify Library with your student to find books they’ll enjoy and be able to read fluently and independently.
  • Review this Protecting Kids Online article by the Federal Trade Commission addressing digital safety.

Program access

Before accessing the program, watch the below video to learn even more about Amplify ELA! Then scroll down and follow the login instructions provided.

Take a closer look at the program with the Idaho Falls Community demo account! Follow these simple instructions to access our program digitally.

  • Click the ELA Digital Platform button.
  • Select Log in with Amplify.
  • Enter this username: t1.ifela6@demo.tryamplify.net
  • Enter this password: Amplify1-ifela6
  • Select any unit to explore.

Where to go for help

Whether you have questions about your technology or want to know more about the program, Amplify’s Support Team is here to help!

Contact Support via telephone at (833) 97-Care-8 (833-972-2738) or caregiver@amplify.com.

Our support hours are Monday – Friday, 7 am – 9 PM ET, and Sunday, 10 – 6 ET.

What’s included in our literacy curriculum for 6–8

Amplify ELA is a blended literacy curriculum designed specifically for grades 6–8. The heart of every lesson is the text. Our core English Language Arts curriculum enables teachers to teach skills through texts and develop their students’ muscles for building meaning through reading. With Amplify ELA, students learn to attack any complex text and make observations, grapple with interesting ideas, and find relevance for themselves.

Year at a glance

Each grade includes six core units centered on literary or informational texts, delivered in several forms of media. In addition to these main units, students will engage with targeted Grammar lessons and a dedicated Story Writing unit, plus two to three immersive learning experiences called Quests.

Dahl & Narrative

1 assessment lesson
4 sub-units | 28 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Mysteries & Investigations

1 assessment lesson
5 sub-units | 32 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Chocolate Collection

1 assessment lesson
5 sub-units | 25 lessons | 4-6 weeks

The Greeks

Myth World Quest

1 assessment lesson
4 sub-units | 25 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Summer of the Mariposas

1 assessment lesson
2 sub-units | 27 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Titanic Collection

1 assessment lesson
5 sub-units | 25 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Red Scarf Girl

1 assessment lesson
4 sub-units | 31 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Character & Conflict

1 assessment lesson
4 sub-units | 29 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Brain Science

Perception Academy Quest

1 assessment lesson
4 sub-units | 25 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Poetry & Poe

The “Who Killed Edgar Allen Poe” Quest

1 assessment lesson
5 sub-units | 29 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Frida & Diego Collection

1 assessment lesson
5 sub-units | 25 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Gold Rush Collection

1 assessment lesson
5 sub-units | 25 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Perspectives & Narrative

1 assessment lesson
4 sub-units | 27 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Liberty & Equality

1 assessment lesson
6 sub-units | 38 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Science & Science Fiction

1 assessment lesson
3 sub-units | 29 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

Shakespeare’s Romeo & Juliet

1 assessment lesson
2 sub-units | 22 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Holocaust: Memory & Meeting

1 assessment lesson
6 sub-units | 21 lessons | 4-6 weeks

A man with a mustache looks through a microscope at a slide, with abstract yellow lines in the background.

The Space Race Collection

1 assessment lesson
5 sub-units | 25 lessons | 4-6 weeks

Units at a glance

Amplify ELA lessons follow a structure both grounded in regular routines and flexible enough to allow for a variety of learning experiences. Lesson structures vary from day to day, ensuring that students are always engaged.

Learn more in the Amplify ELA Grade Overview.

Unit 6A

Dahl & Narrative

Students begin with narrative writing to develop foundational Focus skills and establish key classroom routines. Teachers use this work to create targeted feedback cycles and build a vibrant community centered on diverse experiences. Students then apply observational skills to Roald Dahl’s Boy: Tales of Childhood, learning to work closely with textual evidence.

Unit 6B

Mysteries & Investigations

Students read like an investigator to embark on a multi-genre study into the mesmerizing world of scientific and investigative sleuthing. The Secret of the Yellow Death: A True Story of Medical Sleuthing by Suzanne Jurmain, and Sir Arthur Conan Doyle’s Sherlock Holmes stories take place in the late 19th century, when medical diagnostics and criminal investigations were still evolving into scientific fields.

Unit 6C

The Chocolate Collection

Students explore primary documents and research the diverse cultural roles chocolate has played over 3,700 years, from its various uses in ancient Mexico to issues with modern production. Along the way, they build information literacy skills, craft research questions, and collaborate in Socratic seminars. Students also learn how to construct an evidence-based argument and use those skills to write pieces aimed at convincing readers about chocolate preferences, school lunch policies, and recommendations for local candy stores.

Unit 6D

The Greeks

Students closely explore and analyze three stories from Greek mythology: “Prometheus,” “Odysseus,” and “Arachne.” Drawing on the routines and skills established in previous units, these lessons ask students to move from considering the state of a single person to contemplating broader questions concerning the role people play in the world and the various communities they inhabit.

Unit 6E

Summer of the Mariposas

Students read Summer of the Mariposas by Guadalupe García McCall, a contemporary Latino retelling of The Odyssey. Following five sisters on their journey into Mexico and back, students explore this reimagining of the hero’s journey as they encounter Mexican folklore and Aztec legends along the way. Students analyze character development, compare the novel to Homer’s original, research Aztec mythology, explore symbolism, and engage in collaborative discussions before writing an essay about what makes the heroes successful.

Unit 6F

The Titanic Collection

Students explore primary documents and conduct research to understand the 1912 Titanic disaster, building information literacy skills by examining artifacts such as dining menus, ship photos, telegraph transcripts, and newspaper accounts. Each student is assigned a passenger from the manifest and writes a narrative account from that person’s perspective, considering different views. Students also participate in Socratic seminars to examine the complicated issues within the Titanic story.

Unit 7A

Red Scarf Girl & Narrative

Students begin with narrative writing to develop foundational Focus skills while teachers establish targeted feedback cycles and build a classroom community centered on diverse experiences. After exploring how they describe their own experiences and emotions, students apply the same close attention to analyzing details in Ji-li Jiang’s Red Scarf Girl: A Memoir of the Cultural Revolution.

Unit 7B

Character & Conflict

Students analyze characters’ responses to conflict and examine how authors use character interactions to develop theme and perspective. They read Carson McCullers’ “Sucker” and Lorraine Hansberry’s A Raisin in the Sun, both texts that explore how families facing hardships can support and harm one another. Students observe complex character growth and discuss issues of identity, family obligations, and differing notions of success.

Unit 7C

Brain Science

Students explore narrative nonfiction and informational texts about brain science to understand what it means to be human and how their developing brains impact daily experiences. They also build awareness of their cognitive strengths and analyze the structures of informational texts and scientific arguments. Key texts include Phineas Gage, Inventing Ourselves: The Secret Life of the Teenage Brain, and Oliver Sacks’ The Man Who Mistook His Wife for a Hat.

Unit 7D

Poetry & Poe

Students learn visualization techniques to read like a movie director, beginning with poems by D.H. Lawrence, Federico García Lorca, and Emily Dickinson to form mental images. They then read three Edgar Allan Poe texts, creating storyboards and analyzing narrative elements to learn about unreliable narrators. Students also participate in the murder-mystery Quest “Who Killed Edgar Allan Poe?” and write an essay arguing whether they can trust a narrator in the unit’s texts.

Unit 7E

The Frida & Diego Collection

Students explore primary source documents and research on Mexican artists Diego Rivera and Frida Kahlo, learning how they drew inspiration from Latin American folklore, politics, and customs. Along the way, students build information literacy by generating research questions and visual analysis skills through close reading of key paintings. They also compare the artists’ descriptive writing to Shakespeare’s and analyze figurative language. The unit culminates in a research project showcasing their interpretation of Frida and Diego’s work and legacy.

Unit 7F

The Gold Rush Collection

Students explore primary documents and conduct research on the California Gold Rush, building information literacy skills and constructing research questions. They also learn about the diverse people who participated, compare fictional and historical accounts, and participate in Socratic seminars. Students write narrative accounts from specific perspectives and complete a culminating research assignment combining essay and media project elements.

Unit 8A

Perspectives & Narrative

Students learn to read like writers, paying attention to craft and writing moves that shape reader experience and developing Focus and Showing skills as they build collaborative classroom routines. Students study three narrative texts, exploring themes of belonging and identity through close reading. They also practice alternating between analytic and narrative writing, and conclude with an essay arguing whether the mothers in Amy Tan’s “Fish Cheeks” are role models. 

Unit 8B

Liberty & Equality

Students study Civil War-era writings that debate the meaning of “all men are created equal,” exploring various perspectives on American ideals. Key texts include Walt Whitman’s Leaves of Grass, Frederick Douglass’ Narrative, and Harriet Ann Jacobs’s Incidents in the Life of a Slave Girl. The unit culminates with an essay examining Douglass’s arguments and Lincoln’s Gettysburg Address to consider what America means by “all men are created equal.”

Unit 8C

Science & Science Fiction

Students read Gris Grimly’s Frankenstein, a graphic novel adaptation of Mary Shelley’s novel, exploring themes of creator responsibility, societal influence, and the risks of scientific inquiry. They trace Victor’s sympathy for his creation, rewrite scenes from the creature’s perspective, and debate whether Victor owes the creature a companion. The unit concludes with an essay determining whether the creature should be considered human.

Unit 8D

Shakespeare’s Romeo & Juliet

Students read five excerpts from Shakespeare’s Romeo and Juliet to learn key elements of Shakespearean English through close reading. They practice memorizing and reciting the famous “Prologue,” put on stage performances, translate Shakespeare’s language into contemporary terms, and study the Shakespearean sonnet form. The unit concludes with an essay arguing whether love or hate is responsible for Romeo’s death.

Unit 8E

Holocaust: Memory & Meaning

Students use close reading to explore memoirs and primary sources that address two key Holocaust questions: How do societies become participants in atrocity, and what are our responsibilities as witnesses? Students analyze multiple perspectives through texts, including Alexander Kimel’s “I Cannot Forget,” Irene Butter’s Shores Beyond Shores, 1936 Olympics propaganda, and excerpts from Maus and Night.

Unit 8F

The Space Race Collection

Students explore primary documents and conduct research on the Space Race. They build information literacy skills, construct research questions, and learn about diverse participants from Soviet cosmonauts to American heroes like Buzz Aldrin and Katherine Johnson. Each student researches an assigned cosmonaut or astronaut and writes space blog entries from their perspective. Students also complete a capstone research essay and media project.

Print & digital components

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

A diagram shows the Amplify ELA curriculum with examples of the digital teacher edition on a tablet, print teacher edition pages, and a teacher projection of an artwork on a screen.

Teacher materials

Teacher Edition

Available digitally and in print, the Teacher’s Edition contains all the information teachers need to facilitate classroom instruction, including detailed lesson plans, video teacher tips, presentation slides, standards alignment, Exit Tickets, real-time differentiation strategies, and robust reporting.

Student materials

Student Edition

Available digitally and in print, student materials guide middle schoolers through complex texts and writing by engaging them with high-quality narrative and informational texts—providing videos, audio supports, and a digital experience that captures their attention. They also keep all of their writing in one place with a personal Writing Journal.

A collection of Amplify ELA materials including a print student edition, a digital student edition on a laptop, a writing journal, and an Arachne literature module.

Explore more programs

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

Amplify and SFUSD Partnership

We recognize and respect the unique differences of each of our partnering districts—and that includes San Francisco USD.

Out of the box, Amplify Caminos offers districts a rich, comprehensive, research-based SELA experience. That said, no two districts are exactly alike. To that end, we are committed to working with San Francisco USD to ensure that Amplify Caminos addresses the needs of your community. This includes providing implementation guidance and support, as well as collaborating with your staff to determine which domains need to be modified or exchanged.

What is Amplify Caminos?

Amplify Caminos is a core Spanish language arts program for grades TK–5 that delivers:

  • Authentic instruction built from the ground up for the Spanish language.
  • A unique research-based approach truly built on the Science of Reading.
  • A combination of explicit foundational skills with meaningful knowledge-building.
  • Embedded support and differentiation that gets all students reading grade-level texts together.
  • Opportunities for students to see the strengths and experiences that all people share while also celebrating each others’ unique identities and experiences.



Watch the video below to learn more about Amplify Caminos for Grades K–2.



Watch the video below to learn more about Amplify Caminos for Grades 3–5.

How does Amplify Caminos work?

Amplify Caminos is built on the science of how kids learn to read—in Spanish.

Amplify Caminos is all about helping you teach students how to read, all while giving them authentic and engaging reasons to read. That’s why Amplify Caminos develops foundational skills and builds knowledge in tandem.

  • Knowledge: Through complex and authentic Spanish read-alouds with an emphasis on classroom interactivity, oral comprehension, and contextual vocabulary, students start to build their awareness of the world around them—and the way the reading skills they’re building give them access to it.
  • Skills: Starting with the sounds at the core of the Spanish
    language, students practice their phonemic awareness, handwriting skills, vocabulary, spelling, and grammar. Through daily practice, students become aware of the connection between reading and writing, building confidence as they go.
Illustration depicting the flow of genetic information, represented by ribbons transitioning from dna to rna, connected to various educational images and diagrams.

Respecting the development differences between grade ranges, Amplify Caminos teaches foundational skills and background knowledge as two distinct strands in grades K–2, and combines them into one integrated strand in grades 3–5.

Grades K–2:
Every day, students in grades K–2 complete one full lesson that explicitly and systematically builds foundational reading skills in the Amplify Caminos Lectoescritura strand, as well as one full lesson that builds robust background knowledge to access complex text in the Amplify Caminos Conocimiento strand. Through learning in each of these strands, students develop the early literacy skills necessary to help them become confident readers and build the context to understand what they’re reading.

Grades 3–5:
In grades 3–5, the Amplify Caminos Lectoescritura and Conocimiento strands are integrated in one set of instructional materials. Lessons begin to combine skills and knowledge with increasingly complex texts, close reading, and a greater writing emphasis. Students can then use their skills to go on their own independent reading adventures.

What do Amplify Caminos students explore?

Amplify Caminos builds students’ knowledge about the world.

In addition to teaching all students to crack the written code (which is vital for equity), the Amplify Caminos program helps students see the strengths and experiences we all share while celebrating their own unique identities and experiences.

This is accomplished through the exploration of topics and text that feature people who resemble students and familiar situations or experiences while also exposing them to people whose appearances, lives, beliefs, and backgrounds differ from their own.
 

Engaging domains

Amplify Caminos builds knowledge coherently across subjects and grades.

Throughout the program, students use their skills to explore domains that relate to storytelling, science, and the history of our world as seen through the eyes of many different groups.

Carefully selected to build from year-to-year, our grade-appropriate topics help students make and deepen connections while also reading, writing, and thinking creatively and for themselves.

Curriculum flowchart for Kindergarten to Grade 5, showing subject progression in language, science, and social studies, with highlighted and connected units.

New Knowledge Research Units for Grades K–5

Our brand-new Knowledge Research units carry forward Amplify Caminos’ powerful and proven instructional approach while also:

  • Adding more diversity. The rich topics and highly visual components featured in these units provide students with even more “windows and mirrors” and perspectives as they work to build knowledge.
  • Adding more authentic literature. Each new research unit revolves around a collection of high-interest authentic trade books that will spark more curiosity and inspire more inquiry.
  • Adding more flexibility. Units can be implemented for extended core instruction during flex periods, district-designated Pausing Points, or enrichment periods.

Units cover a variety of rich and relevant topics:

With these new units, students will soar to new heights with Dr. Ellen Ochoa, Amelia Earhart, and the Tuskegee Airmen. They’ll feel the rhythm as they learn about Jazz legends Miles Davis, Tito Puente, and Duke Ellington. And they’ll explore the far reaches of the world with Jacques Cousteau, Matthew Henson, and Eugenie Clark.

  • Grade K: El arte y el mundo que nos rodea
  • Grade 1: Cuentos de aventuras: relatos desde los confines de la Tierra
  • Grade 2: ¡A volar! La era de la aviación
  • Grade 3: Jazz y más
  • Grade 4: Energía: pasado, presente y futuro
  • Grade 5: Más allá de Juneteenth: de 1865 al presente

Units will be made available in English and Spanish, and will include the following components:

Why we added this unit:
“Every child is an artist,” said Picasso, meaning that every child uses art to explore and understand the world around them. El arte y el mundo que nos rodea honors that truth by introducing Kindergarten students to some of the ways in which artists have explored and understood the world around them.

This domain introduces students to artists from different time periods, countries, and cultures. Throughout the unit, students learn about different kinds of art and how artists use the world around them as they make art. They also connect this to what they have already learned about the earth, plants, and animals in other Caminos domains: GranjasPlantas, and Cuidar el planeta Tierra. In addition, students connect this to what they have learned about sculptors in the Presidentes y símbolos de los Estados Unidos domain. As they explore different artists and artistic traditions, they develop their ideas about how humans are connected to each other and to the world around them.

As you read the texts in this unit, students may observe ways in which the characters or subjects are both similar to and different from students. This is a good opportunity to teach students awareness and sensitivity, building on the idea that all people share some things in common, even as they have other things that make them unique. This unit also offers an excellent opportunity to collaborate with your school’s art teacher, as many lessons have suggested activities to help students understand the kind of art they are studying.

Within this unit, students have opportunities to:

  • Use details to describe art.
  • Identify three ways to create art.
  • Identify characteristics of cave art.
  • Sequence the steps of making pottery.
  • Describe how artists can create work connected to the world around them.
  • Describe what makes Kehinde Wiley’s portraits unique.
  • Explain how the texture of a surface can affect artwork created on it.
  • Explain what a sculpture is.
  • Describe what makes James Turrell’s artwork about the sky unique.
  • Explain what a museum is and what kinds of things you can see or do there.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • Georgia O’Keeffe por Erica Salcedo
  • Yayoi Kusama: De aquí al infinito por Sarah Suzuki
  • Tejedora del arcoíris por Linda Elovitz Marshall
  • Las tijeras de Matisse por Jeanette Winter
  • El museo por Susan Verde
  • Quizás algo hermoso: Cómo el arte transformó un barrio por F. Isabel Campoy

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
This domain introduces students to adventure stories set around the world and challenges students to dig into the adventures through research. By listening to the Read-Alouds and trade books, students increase their vocabulary and reading comprehension skills, learn valuable lessons about perseverance and teamwork, and become familiar with gathering information for research.

In this unit, students study the careers of real-world explorers Dr. Eugenie Clark and Sophia Danenberg, marvel at the inventions of Jacques Cousteau, think critically about how teamwork and collaboration can make greater adventures possible, learn about the science and technology that enable adventures, and research some of the ways humans have confronted challenges at the edges of the world, from the oceans below to space above.

Each lesson in the domain builds students’ research skills as they ask questions, gather information, and write a paragraph about their findings. Students share what they have learned about adventures in an Adventure Gallery Walkthrough. By taking on the persona of one of the adventurers they meet in the Read-Alouds and trade books, students deliver their final paragraphs as if they are a “speaking portrait” of that person. Students are invited to dress up as that adventurer if they desire.

In addition, teachers can set aside time outside the instructional block to create the picture frames students will hold as they present to the Adventure Gallery Walk guests. Frames can be made from shirt boxes, cardboard, construction paper, or any art supplies that are on hand. This might be an opportunity to collaborate with the school’s art department if resources are available. Another option is to ask students to make their frames at home with their caregivers. On the day of the Adventure Gallery Walk, students will be the hosts and take on specific jobs, such as welcoming the guests, describing their work throughout the unit, and pointing out the areas of study on the domain bulletin board. You can find a complete list of student jobs in Lesson 13.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in the previous grade.

  • Rimas y fábulas infantiles (Kindergarten)
  • Cuentos (Kindergarten)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Cuentos de aventuras: relatos desde los confines de la Tierra. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • My Name Is Gabito/Me llamo Gabito por Monica Brown
  • Galápagos Girl/Galapagueña por Marsha Diane Arnold
  • My Name Is Gabriela/Me llamo Gabriela por Monica Brown
  • El viaje de Kalak por María Quintana Silva y Marie-Noëlle Hébert
  • Señorita Mariposa por Ben Gundersheimer
  • Sharuko, el arqueólogo peruano/Peruvian Archaeologist Julio C. Tello por Monica Brown
  • Abuelita fue al mercado por Stella Blackstone

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
With this domain, students head up, up, and away with an introduction to the soaring history of aviation. Students learn the stories of early aviators, such as the Montgolfier brothers, the Wright brothers, Aida de Acosta, and Amelia Earhart.

During the unit, students study the science of flight, including the physics concept of lift, and research the social impacts of the world of flight. Finally, students let their research skills take flight as they explore key figures from the world of aviation.

The lessons in this domain build on earlier Grade 2 Caminos domains about the westward expansion, early Greek civilizations, and Greek myths, and lay the foundation for learning about other periods of world history in future grades.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered earlier in the year.

  • La civilización griega antigua (Grade 2)
  • Mitos griegos (Grade 2)
  • La expansión hacia el oeste (Grade 2)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in ¡A volar! La era de la aviación. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • ¡A volar! Todo sobre aviones por Jennifer Prior
  • Amelia sabe volar por Mara dal Corso
  • Héroes de la aviación que cambiaron el mundo por Dan Green
  • El niño que alcanzó las estrellas por José M. Hernández
  • La niña que aprendió a volar por Sylvia Acevedo
  • Buenas Noches Capitán Mamá por Graciela Tiscareño-Sato

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
This domain teaches students about the vibrant music, poetry, and culture of the Jazz Age in the United States. Students learn about famous writers and musicians like Langston Hughes, Louis Armstrong, Billie Holiday, Melba Liston, Tito Puente, and Miles Davis. They study how the jazz art form took root in the South, then spread to the North to become the sound of the Harlem Renaissance, eventually connecting people around the world in musical expression.

During this unit, students perform guided research to further explore both the history of jazz and what jazz is today. They develop research skills and then use those skills to find deeper connections between the stories and music of the Jazz Age and music today. As students learn about the world of jazz, they collaborate and share ideas with their classmates. They also practice sharing feedback focused on their written work, and, at the end of the unit, students present their research to the group.

The lessons give students opportunities to dive into the rhythms and stories of jazz, utilizing the knowledge sequence in this unit to:

  • Collaboratively generate research questions about jazz, jazz musicians, contemporary musicians from the state where they live or have lived, and the evolution of jazz music.
  • Utilize Read-Alouds, independent reading, and partner reading to learn about the Jazz Age, the Harlem Renaissance, jazz music, and biographies of celebrated jazz musicians and writers.
  • Research the answers to their generated questions, gather information, write a short research essay about a famous jazz musician, write a short essay about a contemporary musician from the state where they live or have lived, and give a presentation about their research.

How this unit builds knowledge:
Within this unit, students have opportunities to:

  • Ask relevant questions and make pertinent comments
  • Identify details in texts
  • Determine key ideas of texts by evaluating details
  • Make text-based inferences
  • Generate questions based on prior knowledge and gathered information
  • Synthesize details across texts to demonstrate comprehension
  • Discuss and explain an author’s purpose
  • Identify and cite reliable primary and secondary sources of information
  • Compose a well-organized and focused informative essay
  • Make connections between topics
  • Present information using appropriate media

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • ¡Esquivel! Un artista del sonido de la era espacial por Susan Wood
  • Ray Charles por Sharon Bell Mathis
  • Tito Puente, el Rey del Mambo por Monica Brown
  • Me llamo Celia, la vida de Celia Cruz por Monica Brown
  • ¡Azúcar! por Ivar Da Coll

In this unit, students also read the poem “Harlem” by Langston Hughes. (Available for free through the Academy of American Poets website and the Poetry Foundation website, with recorded audio available through the website for John Hancock College Preparatory High School.)

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
With this domain, students become tomorrow’s problem solvers in this study of energy in the United States. Analytical reading skills are developed by examining the challenges of early energy innovators. Students then read about current energy practices and young energy change-makers across the world.

Throughout the unit, students conduct research into different sources of energy and present a proposal, putting them in the shoes of future energy innovators. They also use the knowledge sequence in this unit to:

  • Collaboratively analyze texts to identify cause-effect and problem-solution relationships.
  • Generate questions and conduct research about energy.
  • Write an opinion essay making their case for a fuel of the future.
  • Create energy proposals using primary and secondary resources.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in previous grades as well as earlier in the year.

  • Plantas (Grade K)
  • La historia de la Tierra (Grade 1)
  • ¡Eureka! Estudiante inventor (Grade 4)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Energía: pasado, presente y futuro. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • La historia de los combustibles fósiles por William B. Rice
  • El niño que domó el viento por William Kamkwamba y Bryan Mealer

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
Within this domain, Students learn about General Granger’s announcement in Galveston, Texas on June 19, 1865, a day marked in history as Juneteenth. Texts and multimedia sources will support foundational knowledge-building about the end of slavery in the United States. A review of the first freedom announcement, President Lincoln’s Emancipation Proclamation, provides students with background knowledge to further emphasize the significance of Juneteenth in American history.

This unit also takes students on a journey beyond Juneteenth, as they study specific contributions of African Americans from 1865 to the present day. Students participate in a virtual field trip to Emancipation Park in Houston, Texas and use the knowledge sequence in this unit to:

  • Collaboratively generate research questions about Juneteenth, The Great Migration, innovators and inventors, education, the humanities, activists, and allies.
  • Use Read-Alouds, independent, and partner reading to learn about African American contributions from 1865 to the present.
  • Research to find answers to their generated questions, gather information, and write a four-chapter Beyond Juneteenth book.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in previous grades.

  • Los nativos americanos (Grade K)
  • Una nueva nación: la independencia de los Estados Unidos (Grade 1)
  • La Guerra Civil de los Estaods Unidos (Grade 2)
  • La inmigración (Grade 2)
  • Los nativos americanos (Grade 5)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Más allá de Juneteenth: de 1865 al presente
. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • Martí’s Song for Freedom/Martí y sus versos por la libertad escrito por Emma Otheguy
  • ¡Celebremos Juneteenth! escrito por Carole Boston Weatherford
  • Side by Side/Lado a Lado: The Story of Dolores Huerta and Cesar Chavez/La Historia de Dolores Huerta y César Chávez escrito por Monica Brown
  • Canto de alabanza para el día: Poema para la ceremonia inaugural del mandato de Barack Obama escrito por Elizabeth Alexander, traducido por Rodrigo Rojas

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Diverse texts

Amplify Caminos puts a variety of texts in the hands of students every day.

Amplify Caminos includes both transadaptations and authentic texts written by Latin American and Spanish authors. In addition to featuring a diverse range of authors and topics, our texts represent individuals and characters with a broad range of identity factors, including socioeconomic status, age, ability, race, ethnicity, country of origin, religion, and more.

Amplify Caminos texts include:

  • Authentic literature: Authentic literature exposes students to a variety of text types and perspectives to deepen their knowledge of fascinating topics in social studies, science, literature, and the arts. Authentic texts support text-to-self, text-to-world, and text-to-text connections for readers.
  • Decodable Student Readers: Amplify Caminos is built on the conviction that equitable instruction is vital to an effective program. Decodable Student Readers at grades K–2 are newly re-designed to celebrate students’ diverse experiences and feature individuals with a broad range of identity factors, including socioeconomic status, age, ability, race, ethnicity, country of origin, religion, and more.
  • ReadWorks® texts: Amplify and ReadWorks have partnered to deliver high-quality texts curated to support the Amplify Caminos Knowledge Sequence and to extend student learning. Texts include high-interest nonfiction articles in topics in social studies, science, literature, and the arts. These texts are accompanied by vocabulary supports and standards-aligned formative assessment opportunities. Teachers can monitor their students’ progress using the ReadWorks reporting features.
Three book covers displaying children's books in spanish, each featuring colorful and stylized illustrations related to cultural stories.

Amplify Caminos Trade Book Collection Guide

Each book in our authentic literature collection was selected specifically to support and enhance the content of the K-2 Conocimiento Strand. These anchor texts are intended for use as an introduction to each domain—engaging students, piquing their curiosity, and building initial background knowledge—before diving into the deeper content of the domain Read-Alouds.

Every trade book has an instructional guide that includes the following:

  • Author and illustrator
  • Book summary
  • The Essential Question of the Knowledge domain, connecting the book to the domain
  • Key Tier 2 and Tier 3 vocabulary words found in the book
  • A group activity to reinforce and extend students’ knowledge and understanding
  • A performance task to help gauge students’ comprehension of concepts in the text
  • Writing prompts to expand understanding and critical thinking
  • Text complexity ratings and descriptors for quantitative, qualitative, and reader/task categories

Download the Amplify Caminos Trade Book Collection Guide for Grades K–2.

Detailed information about text complexity ratings and descriptors; additional uses for the books before, during, and after domain instruction; and the complete list of domains and books for each grade level can be found in the More About the Books section of this guide.

What makes Amplify Caminos different?

Built on the Science of Reading

Built out of the latest research in the Science of Reading, Amplify Caminos delivers explicit instruction in both foundational literacy skills (systematic phonics, decoding, and fluency) and background knowledge in grades K–2 with an integrated approach to explicit instruction in grades 3–5.

Three connected orange blocks labeled

Explicit systematic skills instruction

The skills instruction in Amplify Caminos was distinctly developed with the Spanish language in mind. Its foundational lessons are specific to the language, rather than a direct translation from Amplify CKLA’s English skills instruction.

Reading instruction begins with the vowels first, then the most common consonants, and finally the least common consonants. Students will blend and segment sounds to form syllables, and syllables to form words.

Although Spanish has a highly predictable orthography, there are a few silent letters (h is always silent, u is silent after g or q), as well as letters that can make different sounds, depending on the letters that follow them. For that reason, syllables with these letters are taught somewhat later in the progression. The same is true for syllables with infrequently occurring consonants, such as z, k, x, and w.

Coherent knowledge instruction

While students are learning how to read, the Conocimiento strand gives them authentic and engaging reasons to read.

Amplify Caminos uses spiral learning to reinforce every student’s ability to develop skills like reading, writing, speaking, and listening in Spanish that can be transferred to English. As students engage with their lessons, they explore the similarities and differences in grammar, vocabulary, writing, and language use between Spanish and English. This bridge helps students learning two languages to strengthen their knowledge in both.

Through cross-curricular content, students explore units that relate to storytelling, science, and the history of our world in a holistic and thoughtful way. With these units, you’ll bring the world to your students, showing them how reading can become an exciting, rewarding, and useful part of their lives.

A collage of illustrated book covers, including themes of Don Quixote, space exploration, and anthropomorphic animals in various scenarios, all enriched with Spanish language elements.

Embedded differentiation for all learners

Amplify Caminos provides built-in differentiation strategies and supports in every lesson.

  • Apoyo a la enseñanza y desafío: Support and Challenge suggestions in every lesson provide assistance or opportunities for more advanced work toward the goal of the lesson.
  • Notas culturales: These point-of-use notes provide additional information about the traditions, foods, holidays, word variations, and more from across the Spanish-speaking world.
  • Apoyo adicional: Every lesson in the Lectoescritura (Skills) Strand provides additional support activities suggested to reinforce foundational skills instruction. These activities can be given to any student who requires extra help, including students with special needs.

Systematic and cohesive writing instruction

Writing instruction in Amplify Caminos builds systematically and cohesively within and across grades.

In Grades K-2, writing mechanics—including handwriting and spelling—are taught in the Amplify Caminos Lectoescritura strand. Starting in Grade 1, instruction includes four steps in the writing process: planning, drafting, editing, and publishing and features lessons that have modeling, collaboration, and sharing. As students gain skills and confidence, they are able to take on more of these steps independently. Students learn to use planning techniques, including brainstorming and graphic organizers.

Beginning in Grade 4, the Amplify Caminos writing process expands to also include sharing and evaluating. In Grades 4 and 5, the writing process is no longer conceptualized as a series of scaffolded, linear steps (an important change from the Grade 3 writing process). Rather, students move between components of the writing process in a flexible manner, similar to the process mature and experienced writers follow naturally.

young male students writing with a pencil

Amplify Caminos’ writing instruction provides a clear progression through the text types in each grade.

Because Amplify Caminos has two strands of lessons in Grades K-2, Lectoescritura and Conocimiento, students are exposed to both narrative and informational texts throughout the year. In Grades 3-5, the integrated units feature study in literary, informational, or a mix of both types of texts, depending on the content of the unit.

  • Grades K–2 introduce and establish the key elements of each text type, allowing students to gain comfort and confidence writing narratives, opinions, and informative texts. This enables students to practice thinking about content in different ways, offering more depth and breadth to their understanding of core content and of the writing text types.
  • By Grade 3, students will have gained significant practice in narrative, opinion/argumentative, and informational/explanatory forms of writing and will continue to apply those skills through Grade 5.

How does Amplify Caminos integrate with the other parts of the literacy system?

Amplify Caminos + mCLASS® Lectura

Achieve complete parity between English and Spanish assessments with mCLASS Lectura for K–6. mCLASS Lectura allows teachers to connect with their Spanish-speaking students face-to-face, one-on-one, and in the language most comfortable to them. The result? Valid and reliable student data reports
available in both English and Spanish, enabling teachers to pinpoint where their Spanish-speaking or emergent bilingual students really are in their skill development and what instruction to prioritize.

Reading assessment validated for benchmark, progress monitoring, and dyslexia screening

Amplify Caminos + Amplify Reading

Amplify Reading is an engaging, adaptive digital program that extends the learning in Amplify Caminos. Amplify Reading offers support to a large sub-group of English learners (ELs) through Spanish voice-over. Spanish voiceover instructions are available in vocabulary and sentence-level comprehension games so ELs can build their vocabulary, language, and critical comprehension skills before moving into analyzing complex texts

Spanish Support

Demo access and sample materials

Ready to explore on your own? First, watch the videos below to learn about the program’s components and how to navigate the digital platform.

Physical materials walkthrough video



Digital navigation video

Demo access

Next, follow the instructions below to access your demo account.

Laptop screen displaying a login page for
  • Click the CKLA and Caminos Demo button below.
  • Select Log in with Amplify.
  • To explore as a teacher, enter this username: t1.sfusdreviewer@demo.tryamplify.net
  • To explore as a student, enter this username: s1.sfusdreviewer@demo.tryamplify.net
  • Enter the password: Amplify1-sfusdreviewer
  • Click the Programs and apps menu
  • Select CKLA Teacher Resource Site
  • Select the desire grade level
  • Use the toggle to switch between English (CKLA) and Spanish (Caminos) resources.

Sample materials

Finally, click on the grade levels below to explore your requested sample units.

Each book in our authentic literature collection was selected specifically to support and enhance the content of the K-2 Conocimiento Strand. These anchor texts are intended for use as an introduction to each domain—engaging students, piquing their curiosity, and building initial background knowledge—before diving into the deeper content of the domain Read-Alouds.

Every trade book has an instructional guide that includes the following:

  • Author and illustrator
  • Book summary
  • The Essential Question of the Knowledge domain, connecting the book to the domain
  • Key Tier 2 and Tier 3 vocabulary words found in the book
  • A group activity to reinforce and extend students’ knowledge and understanding
  • A performance task to help gauge students’ comprehension of concepts in the text
  • Writing prompts to expand understanding and critical thinking
  • Text complexity ratings and descriptors for quantitative, qualitative, and reader/task categories

Download the Amplify Caminos Trade Book Collection Guide for Grades K–2.
Detailed information about text complexity ratings and descriptors; additional uses for the books before, during, and after domain instruction; and the complete list of domains and books for each grade level can be found in the More About the Books section of this guide.

Additional resources

Grade 6

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

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

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

Unit 3: Ratio Reasoning: Ratio Concepts and Equivalent Ratios

Unit 4: Ratio Reasoning: Unit Rates and Percent

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

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

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

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

Grade 7

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

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

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

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

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

Unit 5: Proportional Reasoning: Percents and Statistical Samples

Unit 6: Geometry: Solids, Triangles, and Angles

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

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

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

Grade 8

Unit 1: Geometric Figures: Rigid Transformations and Congruence

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

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

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

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

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

Unit 4: Functions: Linear and Nonlinear Relationships

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

Unit 5: Integer Exponents: Properties and Scientific Notation

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

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

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

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

Frequently asked questions

The following FAQ contains the answers to some of the most common questions that we receive from pilot teachers like you.

Still have questions? Your dedicated pilot support coordinator would be happy to help. His or her contact information can be found in the pilot support brochure you received during your pilot implementation training. If you prefer, request that your pilot support coordinator gets in touch with you by completing this form.

A teacher discusses educational content in front of a whiteboard while students in the classroom raise their hands eagerly.

Program questions

It’s true. Our teacher’s guide does not look like the typical guide that comes with a traditional textbook. Here’s why: we aren’t a traditional textbook program. Rather, we’re a next generation curriculum designed to support a shift to a whole new way of teaching science.

With this shift, your district will be faced with supporting a wide-variety of needs from a wide-variety of teachers. For that reason, the resources required to successfully implement a new program will vary considerably from teacher to teacher. That’s precisely why our Teacher’s Reference Guide is chock full of so many rich and varied resources. From scientific background knowledge to suggested teacher talk, standards maps to materials lists, and lesson preparation notes and classroom management tips to strategies for differentiating instruction, this guide is truly meant to serve as an instructional reference.

For everyday instructional use, we recommend that busy classroom teachers use Classroom Slides, which are now available for most K–5 units and will be coming soon for grades 6–8.

Also known as our hands-free TG, Classroom Slides are a brand-new teaching resource that makes delivering daily instruction easy and fun. With a fully customizable PPT available for every lesson of the program, teachers can put down the Teacher’s Guide and focus on what matters most—their students.

Classroom Slides are:

  • Available offline, which means no more sweating unreliable internet connections.
  • Streamlined for easy lesson delivery, including lesson visuals, activity instructions and transitions, animations, investigation setup videos, technology support, and more.
  • Fully editable, allowing teachers to incorporate their own flavor, flair, and favorite resources.

Our development team is working as quickly as possible to make Classroom Slides available to all teachers. That said, at this time they are only available for the first and second units of each grade K–5, with the remaining units being released over the next few months. Due to the popularity of Classroom Slides at the elementary level, development for grades 6–8 is now underway, with all units scheduled for completion by the 2020-2021 school year.

Not to worry. Amplify Science California was developed with plenty of wiggle room built right into the program. This means that you can relax knowing that there’s ample time to get it all done.
 
Most curricula provide 180 days of lessons despite knowing that the typical classroom can’t possibly complete everything in a given school year. Rather than asking you to wade through unnecessary content, we designed a program that addresses 100 percent of the California NGSS in just 66 days at grades K–2 and 88 days at grades 3–5, and 146 days at grades 6–8.

While we took great care in ensuring cohesiveness across units and grade levels, we also know that the ability level of your students changes from year to year. As a result, you need a program that provides adaptable and flexible pacing, and that empowers you to make instructional decisions in the moment.

As you evaluate how well Amplify Science California can accommodate your pacing needs, consider the following:

Progress Builds: Our Progress Builds describe the way in which students’ understanding of the central phenomenon should develop and deepen over the course of a unit. Each Progress Build defines several levels of understanding, with each level integrating and building upon the knowledge and skills from lower levels. Because these Progress Builds are directly tied to the program’s system of assessments, teachers are armed with the data they need to make informed decisions about when to move on, when to slow down, and when to revisit a concept and dive deeper.

A chart titled Animal and Plant Defenses Progress Build outlines three levels of understanding about survival strategies in animals and plants.

Multiple at-bats: Rather than introducing a concept on Monday, testing for mastery on Friday, and knowing students will forget everything by the next Tuesday, we set out to help students build meaningful and lasting knowledge that they can retain and transfer over the course of the entire unit. We accomplish this by giving students multiple opportunities (a.k.a. “at-bats”) to encounter, explore, and experience a concept. Said another way, Amplify Science California is actually made up of a series of multi-modal “mini-lessons”. This intentional cyclical and iterative design mirrors the 5Es, allows teachers the flexibility to speed up or skip ahead once students have demonstrated mastery, and empowers students to learn concepts more deeply than any other program. 

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.

Extension activities: When some students are ready to move on and others are not, our unit extension activities can be a big help. Found in the Lesson Brief section of both the digital and printed Teacher’s Guide, these activities ensure that advanced learners remain engaged and challenged while teachers help the rest of the class build the foundational knowledge they need to be successful later in the unit.

What’s important to remember is that more hands-on doesn’t necessarily mean better, at least according to the California NGSS. That’s because only two of the eight Science and Engineering Practices (SEPs) are directly related to hands-on learning. 

Just as scientists gather evidence from many types of sources, so do students in the Amplify Science California program. Like scientists, students gather evidence from physical models, digital models, texts, videos, photographs, maps, and data sets. By doing so, we provide students more opportunities than any other program to practice using all of the practices called out in the California NGSS Framework.

NGSS 8 Science Practices

  1. Asking questions
  2. Developing and using models
  3. Planning and carrying out investigations
  4. Analyzing and interpreting data
  5. Using mathematics and computational thinking
  6. Constructing explanations
  7. Engaging in arguments from evidence
  8. Obtaining, evaluating, and communicating information

While all of our units engage students in gathering evidence from a rich collection of sources, the reliance on different types of evidence (and evidence sources) varies according to unit. For instance, some units lend themselves to meaningful hands-on experiences, while in other units the phenomena students are investigating are too slow, too dangerous, or too big to be observed directly. In those units, students rely more heavily on other evidence sources such a physical models or simulations.

Unit types in grades K–5
In each K–5 grade, there is one unit that emphasizes investigation, one that emphasizes modeling, and one that emphasizes design. In addition, in grades 3–5, there is also one unit that emphasizes argumentation.

Unit types in grades 6–8
Each 6–8 grade features three types of units: LaunchCore, and Engineering Internships. Each year has one Launch unit, six Core units, and two Engineering Internships.

For teachers who wish to supplement the lessons with even more hands-on activities, optional “flextension” activities are included in many units.

As a blended curriculum, districts who adopt Amplify Science California are outfitted with a variety of print and digital resources as well as hands-on materials kits. To explore the specific components of the program, visit our What’s Included page.

As our customers will tell you, when you adopt Amplify Science California, you aren’t just buying a science curriculum, you’re joining a family. As such, along with materials, your adoption of Amplify Science California also includes care and support through a variety of staff and resources, including: customer support specialists, pedagogical support specialist, implementation specialists, professional learning specialists, educational partnership managers, and more.

Technical questions

To ensure that your hardware and network meet the minimum technical requirements for optimal performance and support of your digital curriculum products please see Amplify’s customer requirements page.

Absolutely! While 1:1 scenarios are great, they aren’t required. That’s because all Amplify Science California lessons were designed with device sharing in mind, and never assume that every student has a separate device. 

When the use of practice apps is called for in a lesson, you have several options:

  • If internet access is unavailable—“Preload” the digital tool on your device or devices for use offline.
  • If limited student devices are available—Have students do the activities in pairs or small groups.
  • If no student devices are available—Project the digital tool to the class and either “drive” the digital tool yourself or invite students to “drive” by using your device.

learning.amplify.com gives you access to the digital Teacher’s Guide and also gives your students (grades 68) access to the digital student experience.

apps.learning.amplify.com/elementary gives your students (grades 25) access to any practice apps referenced in the instruction. The teacher will either need to log in using their credentials, or have student accounts set up.

Tech headaches are never fun. However, implementing the following tips can help you keep the tech gremlins away.

  • Display the student URLs near the classroom display materials.
  • Before you start a unit, download all unit and lesson resources using the Offline Guide found in the Unit Guide of your digital Teacher’s Guide. In the event that connectivity issues strike, you will still be able to conduct your lessons without interruption.
  • Use Chrome or Safari if possible as these are our preferred browsers.
  • Disable pop-up blockers on all devices being used to support lessons.
  • Be prepared for some webpages to open in a new tab and for PDF files to download automatically.
  • Check and test your connections to any projection devices that you might be using throughout the lesson.
  • Display the student URLs near the classroom display materials.

Amplify Caminos for SFUSD

Amplify Caminos is an authentic elementary Spanish language arts program. Like its English language counterpart, Amplify CKLA, Amplify Caminos provides explicit, systematic foundational skills instruction sequenced with deep knowledge-building content to foster comprehension. When used with Amplify CKLA, Amplify Caminos provides full parity across English and Spanish that’s suitable for any dual language implementation model.

Colorful illustration featuring a child in traditional Andean clothing, tropical plants, a volcano, a toucan, a horse rider, and the word "Gracias!" written in Spanish.

Amplify and SFUSD Partnership

We recognize and respect the unique differences of each of our partnering districts—and that includes San Francisco USD.

Out of the box, Amplify Caminos offers districts a rich, comprehensive, research-based SELA experience. That said, no two districts are exactly alike. To that end, we are committed to working with San Francisco USD to ensure that Amplify Caminos addresses the needs of your community. This includes providing implementation guidance and support, as well as collaborating with your staff to determine which domains need to be modified or exchanged.

What is Amplify Caminos?

Amplify Caminos is a core Spanish language arts program for grades TK–5 that delivers:

  • Authentic instruction built from the ground up for the Spanish language.
  • A unique research-based approach truly built on the Science of Reading.
  • A combination of explicit foundational skills with meaningful knowledge-building.
  • Embedded support and differentiation that gets all students reading grade-level texts together.
  • Opportunities for students to see the strengths and experiences that all people share while also celebrating each others’ unique identities and experiences.

Watch the video below to learn more about Amplify Caminos for Grades K–2.

Watch the video below to learn more about Amplify Caminos for Grades 3–5.

How does Amplify Caminos work?

Amplify Caminos is built on the science of how kids learn to read—in Spanish.

Amplify Caminos is all about helping you teach students how to read, all while giving them authentic and engaging reasons to read. That’s why Amplify Caminos develops foundational skills and builds knowledge in tandem.

  • Knowledge: Through complex and authentic Spanish read-alouds with an emphasis on classroom interactivity, oral comprehension, and contextual vocabulary, students start to build their awareness of the world around them—and the way the reading skills they’re building give them access to it.
  • Skills: Starting with the sounds at the core of the Spanish
    language, students practice their phonemic awareness, handwriting skills, vocabulary, spelling, and grammar. Through daily practice, students become aware of the connection between reading and writing, building confidence as they go.
A diagram illustrating reading development as intertwined strands: language comprehension and word recognition, progressing from basic skills to increasingly strategic and automatic reading.

Respecting the development differences between grade ranges, Amplify Caminos teaches foundational skills and background knowledge as two distinct strands in grades K–2, and combines them into one integrated strand in grades 3–5.

Grades K–2:
Every day, students in grades K–2 complete one full lesson that explicitly and systematically builds foundational reading skills in the Amplify Caminos Lectoescritura strand, as well as one full lesson that builds robust background knowledge to access complex text in the Amplify Caminos Conocimiento strand. Through learning in each of these strands, students develop the early literacy skills necessary to help them become confident readers and build the context to understand what they’re reading.

Grades 3–5:
In grades 3–5, the Amplify Caminos Lectoescritura and Conocimiento strands are integrated in one set of instructional materials. Lessons begin to combine skills and knowledge with increasingly complex texts, close reading, and a greater writing emphasis. Students can then use their skills to go on their own independent reading adventures.

What do Amplify Caminos students explore?

Amplify Caminos builds students’ knowledge about the world.

In addition to teaching all students to crack the written code (which is vital for fairness), the Amplify Caminos program helps students see the strengths and experiences we all share while celebrating their own unique identities and experiences.

This is accomplished through the exploration of topics and text that feature people who resemble students and familiar situations or experiences while also exposing them to people whose appearances, lives, beliefs, and backgrounds differ from their own.

Engaging domains

Amplify Caminos builds knowledge coherently across subjects and grades.

Throughout the program, students use their skills to explore domains that relate to storytelling, science, and the history of our world as seen through the eyes of many different groups.

Carefully selected to build from year-to-year, our grade-appropriate topics help students make and deepen connections while also reading, writing, and thinking creatively and for themselves.

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

New Knowledge Research Units for Grades K–5

Our brand-new Knowledge Research units carry forward Amplify Caminos’ powerful and proven instructional approach while also:

  • Adding more content for students from all walks of life. The rich topics and highly visual components featured in these units provide students with even more “windows and mirrors” and perspectives as they work to build knowledge.
  • Adding more authentic literature. Each new research unit revolves around a collection of high-interest authentic trade books that will spark more curiosity and inspire more inquiry.
  • Adding more flexibility. Units can be implemented for extended core instruction during flex periods, district-designated Pausing Points, or enrichment periods.

Units cover a variety of rich and relevant topics:

With these new units, students will soar to new heights with Dr. Ellen Ochoa, Amelia Earhart, and the Tuskegee Airmen. They’ll feel the rhythm as they learn about Jazz legends Miles Davis, Tito Puente, and Duke Ellington. And they’ll explore the far reaches of the world with Jacques Cousteau, Matthew Henson, and Eugenie Clark.

  • Grade K: El arte y el mundo que nos rodea
  • Grade 1: Cuentos de aventuras: relatos desde los confines de la Tierra
  • Grade 2: ¡A volar! La era de la aviación
  • Grade 3: Jazz y más
  • Grade 4: Energía: pasado, presente y futuro
  • Grade 5: Más allá de Juneteenth: de 1865 al presente

Units will be made available in English and Spanish, and will include the following components:

  • Teacher Guide
  • Student Activity Books
  • Image Cards
  • Trade Book Collection
  • Digital Components (for Grades K–3 and Grade 5 only)

Why we added this unit:
“Every child is an artist,” said Picasso, meaning that every child uses art to explore and understand the world around them. El arte y el mundo que nos rodea honors that truth by introducing Kindergarten students to some of the ways in which artists have explored and understood the world around them.

This domain introduces students to artists from different time periods, countries, and cultures. Throughout the unit, students learn about different kinds of art and how artists use the world around them as they make art. They also connect this to what they have already learned about the earth, plants, and animals in other Caminos domains: GranjasPlantas, and Cuidar el planeta Tierra. In addition, students connect this to what they have learned about sculptors in the Presidentes y símbolos de los Estados Unidos domain. As they explore different artists and artistic traditions, they develop their ideas about how humans are connected to each other and to the world around them.

As you read the texts in this unit, students may observe ways in which the characters or subjects are both similar to and different from students. This is a good opportunity to teach students awareness and sensitivity, building on the idea that all people share some things in common, even as they have other things that make them unique. This unit also offers an excellent opportunity to collaborate with your school’s art teacher, as many lessons have suggested activities to help students understand the kind of art they are studying.

Within this unit, students have opportunities to:

  • Use details to describe art.
  • Identify three ways to create art.
  • Identify characteristics of cave art.
  • Sequence the steps of making pottery.
  • Describe how artists can create work connected to the world around them.
  • Describe what makes Kehinde Wiley’s portraits unique.
  • Explain how the texture of a surface can affect artwork created on it.
  • Explain what a sculpture is.
  • Describe what makes James Turrell’s artwork about the sky unique.
  • Explain what a museum is and what kinds of things you can see or do there.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • Georgia O’Keeffe por Erica Salcedo
  • Yayoi Kusama: De aquí al infinito por Sarah Suzuki
  • Tejedora del arcoíris por Linda Elovitz Marshall
  • Las tijeras de Matisse por Jeanette Winter
  • El museo por Susan Verde
  • Quizás algo hermoso: Cómo el arte transformó un barrio por F. Isabel Campoy

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
This domain introduces students to adventure stories set around the world and challenges students to dig into the adventures through research. By listening to the Read-Alouds and trade books, students increase their vocabulary and reading comprehension skills, learn valuable lessons about perseverance and teamwork, and become familiar with gathering information for research.

In this unit, students study the careers of real-world explorers Dr. Eugenie Clark and Sophia Danenberg, marvel at the inventions of Jacques Cousteau, think critically about how teamwork and collaboration can make greater adventures possible, learn about the science and technology that enable adventures, and research some of the ways humans have confronted challenges at the edges of the world, from the oceans below to space above.

Each lesson in the domain builds students’ research skills as they ask questions, gather information, and write a paragraph about their findings. Students share what they have learned about adventures in an Adventure Gallery Walkthrough. By taking on the persona of one of the adventurers they meet in the Read-Alouds and trade books, students deliver their final paragraphs as if they are a “speaking portrait” of that person. Students are invited to dress up as that adventurer if they desire.

In addition, teachers can set aside time outside the instructional block to create the picture frames students will hold as they present to the Adventure Gallery Walk guests. Frames can be made from shirt boxes, cardboard, construction paper, or any art supplies that are on hand. This might be an opportunity to collaborate with the school’s art department if resources are available. Another option is to ask students to make their frames at home with their caregivers. On the day of the Adventure Gallery Walk, students will be the hosts and take on specific jobs, such as welcoming the guests, describing their work throughout the unit, and pointing out the areas of study on the domain bulletin board. You can find a complete list of student jobs in Lesson 13.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in the previous grade.

  • Rimas y fábulas infantiles (Kindergarten)
  • Cuentos (Kindergarten)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Cuentos de aventuras: relatos desde los confines de la Tierra. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • My Name Is Gabito/Me llamo Gabito por Monica Brown
  • Galápagos Girl/Galapagueña por Marsha Diane Arnold
  • My Name Is Gabriela/Me llamo Gabriela por Monica Brown
  • El viaje de Kalak por María Quintana Silva y Marie-Noëlle Hébert
  • Señorita Mariposa por Ben Gundersheimer
  • Sharuko, el arqueólogo peruano/Peruvian Archaeologist Julio C. Tello por Monica Brown
  • Abuelita fue al mercado por Stella Blackstone

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
With this domain, students head up, up, and away with an introduction to the soaring history of aviation. Students learn the stories of early aviators, such as the Montgolfier brothers, the Wright brothers, Aida de Acosta, and Amelia Earhart.

During the unit, students study the science of flight, including the physics concept of lift, and research the social impacts of the world of flight. Finally, students let their research skills take flight as they explore key figures from the world of aviation.

The lessons in this domain build on earlier Grade 2 Caminos domains about the westward expansion, early Greek civilizations, and Greek myths, and lay the foundation for learning about other periods of world history in future grades.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered earlier in the year.

  • La civilización griega antigua (Grade 2)
  • Mitos griegos (Grade 2)
  • La expansión hacia el oeste (Grade 2)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in ¡A volar! La era de la aviación. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • ¡A volar! Todo sobre aviones por Jennifer Prior
  • Amelia sabe volar por Mara dal Corso
  • Héroes de la aviación que cambiaron el mundo por Dan Green
  • El niño que alcanzó las estrellas por José M. Hernández
  • La niña que aprendió a volar por Sylvia Acevedo
  • Buenas Noches Capitán Mamá por Graciela Tiscareño-Sato

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
This domain teaches students about the vibrant music, poetry, and culture of the Jazz Age in the United States. Students learn about famous writers and musicians like Langston Hughes, Louis Armstrong, Billie Holiday, Melba Liston, Tito Puente, and Miles Davis. They study how the jazz art form took root in the South, then spread to the North to become the sound of the Harlem Renaissance, eventually connecting people around the world in musical expression.

During this unit, students perform guided research to further explore both the history of jazz and what jazz is today. They develop research skills and then use those skills to find deeper connections between the stories and music of the Jazz Age and music today. As students learn about the world of jazz, they collaborate and share ideas with their classmates. They also practice sharing feedback focused on their written work, and, at the end of the unit, students present their research to the group.

The lessons give students opportunities to dive into the rhythms and stories of jazz, utilizing the knowledge sequence in this unit to:

  • Collaboratively generate research questions about jazz, jazz musicians, contemporary musicians from the state where they live or have lived, and the evolution of jazz music.
  • Utilize Read-Alouds, independent reading, and partner reading to learn about the Jazz Age, the Harlem Renaissance, jazz music, and biographies of celebrated jazz musicians and writers.
  • Research the answers to their generated questions, gather information, write a short research essay about a famous jazz musician, write a short essay about a contemporary musician from the state where they live or have lived, and give a presentation about their research.

How this unit builds knowledge:
Within this unit, students have opportunities to:

  • Ask relevant questions and make pertinent comments
  • Identify details in texts
  • Determine key ideas of texts by evaluating details
  • Make text-based inferences
  • Generate questions based on prior knowledge and gathered information
  • Synthesize details across texts to demonstrate comprehension
  • Discuss and explain an author’s purpose
  • Identify and cite reliable primary and secondary sources of information
  • Compose a well-organized and focused informative essay
  • Make connections between topics
  • Present information using appropriate media

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • ¡Esquivel! Un artista del sonido de la era espacial por Susan Wood
  • Ray Charles por Sharon Bell Mathis
  • Tito Puente, el Rey del Mambo por Monica Brown
  • Me llamo Celia, la vida de Celia Cruz por Monica Brown
  • ¡Azúcar! por Ivar Da Coll

In this unit, students also read the poem “Harlem” by Langston Hughes. (Available for free through the Academy of American Poets website and the Poetry Foundation website, with recorded audio available through the website for John Hancock College Preparatory High School.)

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
With this domain, students become tomorrow’s problem solvers in this study of energy in the United States. Analytical reading skills are developed by examining the challenges of early energy innovators. Students then read about current energy practices and young energy change-makers across the world.

Throughout the unit, students conduct research into different sources of energy and present a proposal, putting them in the shoes of future energy innovators. They also use the knowledge sequence in this unit to:

  • Collaboratively analyze texts to identify cause-effect and problem-solution relationships.
  • Generate questions and conduct research about energy.
  • Write an opinion essay making their case for a fuel of the future.
  • Create energy proposals using primary and secondary resources.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in previous grades as well as earlier in the year.

  • Plantas (Grade K)
  • La historia de la Tierra (Grade 1)
  • ¡Eureka! Estudiante inventor (Grade 4)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Energía: pasado, presente y futuro. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • La historia de los combustibles fósiles por William B. Rice
  • El niño que domó el viento por William Kamkwamba y Bryan Mealer

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Why we added this unit:
Within this domain, Students learn about General Granger’s announcement in Galveston, Texas on June 19, 1865, a day marked in history as Juneteenth. Texts and multimedia sources will support foundational knowledge-building about the end of slavery in the United States. A review of the first freedom announcement, President Lincoln’s Emancipation Proclamation, provides students with background knowledge to further emphasize the significance of Juneteenth in American history.

This unit also takes students on a journey beyond Juneteenth, as they study specific contributions of African Americans from 1865 to the present day. Students participate in a virtual field trip to Emancipation Park in Houston, Texas and use the knowledge sequence in this unit to:

  • Collaboratively generate research questions about Juneteenth, The Great Migration, innovators and inventors, education, the humanities, activists, and allies.
  • Use Read-Alouds, independent, and partner reading to learn about African American contributions from 1865 to the present.
  • Research to find answers to their generated questions, gather information, and write a four-chapter Beyond Juneteenth book.

How this unit builds knowledge:
This unit builds upon the following Caminos units that students will have encountered in previous grades.

  • Los nativos americanos (Grade K)
  • Una nueva nación: la independencia de los Estados Unidos (Grade 1)
  • La Guerra Civil de los Estaods Unidos (Grade 2)
  • La inmigración (Grade 2)
  • Los nativos americanos (Grade 5)

The specific core content targeted in these domains is particularly relevant to the Read-Alouds students will hear in Más allá de Juneteenth: de 1865 al presente
. The background knowledge students bring to this unit will greatly enhance their understanding of the trade books used in this unit.

Trade books in this unit:
Instruction in this unit revolves around the following collection of high-interest authentic trade books. One copy of each trade book is included with the unit materials.

  • Martí’s Song for Freedom/Martí y sus versos por la libertad escrito por Emma Otheguy
  • ¡Celebremos Juneteenth! escrito por Carole Boston Weatherford
  • Side by Side/Lado a Lado: The Story of Dolores Huerta and Cesar Chavez/La Historia de Dolores Huerta y César Chávez escrito por Monica Brown
  • Canto de alabanza para el día: Poema para la ceremonia inaugural del mandato de Barack Obama escrito por Elizabeth Alexander, traducido por Rodrigo Rojas

Sample materials:
Take a sneak peek at the rich instruction and engaging activities for this unit by viewing the PDFs below.

Wide-ranging texts

Amplify Caminos puts a variety of texts in the hands of students every day.

Amplify Caminos includes both transadaptations and authentic texts written by Latin American and Spanish authors. Our texts feature a wide variety of authors, topics, individuals and characters representing many different socioeconomic statuses, ages, abilities, races, ethnicities, countries of origin, religions, and more.

Amplify Caminos texts include:

  • Authentic literature: Authentic literature exposes students to a variety of text types and perspectives to deepen their knowledge of fascinating topics in social studies, science, literature, and the arts. Authentic texts support text-to-self, text-to-world, and text-to-text connections for readers.
  • Decodable Student Readers: Decodable Student Readers at grades K–2 are newly redesigned to include students from all walks of life and educational backgrounds. They feature characters with a broad range of backgrounds, experiences, ages, races, religions, and more.
  • ReadWorks® texts: Amplify and ReadWorks have partnered to deliver high-quality texts curated to support the Amplify Caminos Knowledge Sequence and to extend student learning. Texts include high-interest nonfiction articles in topics in social studies, science, literature, and the arts. These texts are accompanied by vocabulary supports and standards-aligned formative assessment opportunities. Teachers can monitor their students’ progress using the ReadWorks reporting features.
Three children's book covers in Spanish are shown: "La Flor de Oro," "El conejo en la Luna," and "El secreto de las hormigas," each featuring illustrated artwork.

Amplify Caminos Trade Book Collection Guide

Each book in our authentic literature collection was selected specifically to support and enhance the content of the K-2 Conocimiento Strand. These anchor texts are intended for use as an introduction to each domain—engaging students, piquing their curiosity, and building initial background knowledge—before diving into the deeper content of the domain Read-Alouds.

Every trade book has an instructional guide that includes the following:

  • Author and illustrator
  • Book summary
  • The Essential Question of the Knowledge domain, connecting the book to the domain
  • Key Tier 2 and Tier 3 vocabulary words found in the book
  • A group activity to reinforce and extend students’ knowledge and understanding
  • A performance task to help gauge students’ comprehension of concepts in the text
  • Writing prompts to expand understanding and critical thinking
  • Text complexity ratings and descriptors for quantitative, qualitative, and reader/task categories

Download the Amplify Caminos Trade Book Collection Guide for Grades K–2.

Detailed information about text complexity ratings and descriptors; additional uses for the books before, during, and after domain instruction; and the complete list of domains and books for each grade level can be found in the More About the Books section of this guide.

What makes Amplify Caminos different?

Built on the Science of Reading

Built out of the latest research in the Science of Reading, Amplify Caminos delivers explicit instruction in both foundational literacy skills (systematic phonics, decoding, and fluency) and background knowledge in grades K–2 with an integrated approach to explicit instruction in grades 3–5.

Flowchart showing "Language comprehension" times "Word recognition" equals "Skilled reading," with text in both Spanish and English inside orange boxes.

Explicit systematic skills instruction

The skills instruction in Amplify Caminos was distinctly developed with the Spanish language in mind. Its foundational lessons are specific to the language, rather than a direct translation from Amplify CKLA’s English skills instruction.

Reading instruction begins with the vowels first, then the most common consonants, and finally the least common consonants. Students will blend and segment sounds to form syllables, and syllables to form words.

Although Spanish has a highly predictable orthography, there are a few silent letters (h is always silent, u is silent after g or q), as well as letters that can make different sounds, depending on the letters that follow them. For that reason, syllables with these letters are taught somewhat later in the progression. The same is true for syllables with infrequently occurring consonants, such as z, k, x, and w.

Coherent knowledge instruction

While students are learning how to read, the Conocimiento strand gives them authentic and engaging reasons to read.

Amplify Caminos uses spiral learning to reinforce every student’s ability to develop skills like reading, writing, speaking, and listening in Spanish that can be transferred to English. As students engage with their lessons, they explore the similarities and differences in grammar, vocabulary, writing, and language use between Spanish and English. This bridge helps students learning two languages to strengthen their knowledge in both.

Through cross-curricular content, students explore units that relate to storytelling, science, and the history of our world in a holistic and thoughtful way. With these units, you’ll bring the world to your students, showing them how reading can become an exciting, rewarding, and useful part of their lives.

Embedded differentiation for all learners

Amplify Caminos provides built-in differentiation strategies and supports in every lesson.

  • Apoyo a la enseñanza y desafío: Support and Challenge suggestions in every lesson provide assistance or opportunities for more advanced work toward the goal of the lesson.
  • Notas culturales: These point-of-use notes provide additional information about the traditions, foods, holidays, word variations, and more from across the Spanish-speaking world.
  • Apoyo adicional: Every lesson in the Lectoescritura (Skills) Strand provides additional support activities suggested to reinforce foundational skills instruction. These activities can be given to any student who requires extra help, including students with special needs.

Systematic and cohesive writing instruction

Writing instruction in Amplify Caminos builds systematically and cohesively within and across grades.

In Grades K-2, writing mechanics—including handwriting and spelling—are taught in the Amplify Caminos Lectoescritura strand. Starting in Grade 1, instruction includes four steps in the writing process: planning, drafting, editing, and publishing and features lessons that have modeling, collaboration, and sharing. As students gain skills and confidence, they are able to take on more of these steps independently. Students learn to use planning techniques, including brainstorming and graphic organizers.

Beginning in Grade 4, the Amplify Caminos writing process expands to also include sharing and evaluating. In Grades 4 and 5, the writing process is no longer conceptualized as a series of scaffolded, linear steps (an important change from the Grade 3 writing process). Rather, students move between components of the writing process in a flexible manner, similar to the process mature and experienced writers follow naturally.

young male students writing with a pencil

Amplify Caminos’ writing instruction provides a clear progression through the text types in each grade.

Because Amplify Caminos has two strands of lessons in Grades K-2, Lectoescritura and Conocimiento, students are exposed to both narrative and informational texts throughout the year. In Grades 3-5, the integrated units feature study in literary, informational, or a mix of both types of texts, depending on the content of the unit.

  • Grades K–2 introduce and establish the key elements of each text type, allowing students to gain comfort and confidence writing narratives, opinions, and informative texts. This enables students to practice thinking about content in different ways, offering more depth and breadth to their understanding of core content and of the writing text types.
  • By Grade 3, students will have gained significant practice in narrative, opinion/argumentative, and informational/explanatory forms of writing and will continue to apply those skills through Grade 5.

How does Amplify Caminos integrate with the other parts of the literacy system?

Amplify Caminos + mCLASS® Lectura

Achieve complete parity between English and Spanish assessments with mCLASS Lectura for K–6. mCLASS Lectura allows teachers to connect with their Spanish-speaking students face-to-face, one-on-one, and in the language most comfortable to them. The result? Valid and reliable student data reports
available in both English and Spanish, enabling teachers to pinpoint where their Spanish-speaking or emergent bilingual students really are in their skill development and what instruction to prioritize.

A laptop screen displays a slide describing the Lectura data-driven instructional cycle with sections for Assessment, Reporting, and Instruction, each illustrated with sample interface screenshots.

Amplify Caminos + Amplify Reading

Amplify Reading is an engaging, adaptive digital program that extends the learning in Amplify Caminos. Amplify Reading offers support to a large sub-group of English learners (ELs) through Spanish voice-over. Spanish voiceover instructions are available in vocabulary and sentence-level comprehension games so ELs can build their vocabulary, language, and critical comprehension skills before moving into analyzing complex texts

Language selection screen with options for English and Spanish, and an illustrated girl saying “¡Hola!” in a speech bubble. The heading reads “Idiomas.”.

Demo access and sample materials

Ready to explore on your own? First, watch the videos below to learn about the program’s components and how to navigate the digital platform.

Physical materials walkthrough video

Digital navigation video

Demo access

Next, follow the instructions below to access your demo account.

  • Click the CKLA and Caminos Demo button below.
  • Select Log in with Amplify.
  • To explore as a teacher, enter this username: t1.sfusdreviewer@demo.tryamplify.net
  • To explore as a student, enter this username: s1.sfusdreviewer@demo.tryamplify.net
  • Enter the password: Amplify1-sfusdreviewer
  • Click the Programs and apps menu
  • Select CKLA Teacher Resource Site
  • Select the desire grade level
  • Use the toggle to switch between English (CKLA) and Spanish (Caminos) resources.

Sample materials

Finally, click on the grade levels below to explore your requested sample units.

Additional resources

S1-02: Community and joy within K–8 science instruction: Desiré Whitmore

Promotional graphic for "Science Connections" Season 1, Episode 2 featuring Desiré Whitmore, focusing on community and joy in K–8 science instruction.

In this episode, we join Eric Cross as he sits down with physicist and science education specialist, Desiré Whitmore. Listen in as Desiré explains her work at the Exploratorium, a public learning laboratory. Eric and Desiré discuss finding passion in science, the importance of meeting students we’re they’re at, and K–8 science instruction with real-life connections. Desiré chats with Eric about her work on supporting the science of teaching science content at the Exploratorium museum.

Explore more from Science Connections by visiting our main page.

Download Transcript

Desiré Whitmore (00:00):

I think it’s really amazing when we can realize as teachers, like, no, our job is not to just enforce rules on our students, right? Our job is to help students to achieve more learning.

Eric Cross (00:37):

Welcome to Science Connections. I’m your host, Eric Cross. My guest today is Desiré Whitmore. Desiré has held positions as a science curriculum specialist with Amplify Science, a professor of laser and photonics technology at Irvine Valley College, and is now the senior physics educator in the Teacher Institute at the Exploratorium in San Francisco. Her current work is focused on providing support and professional development to middle and high school science teachers to help them teach through inquiry. In this episode, we discussed Desiré’s pathway into physics, the impact of educators in her life, and the importance of representation for students in the classroom. I’m so excited for you to meet my physicist friend, Dr. Desiré Whitmore. All right. So just like a superhero, STEM superhero, you have an origin story and so—

Desiré Whitmore (01:36):

How long is this podcast gonna be? ‘Cause, you know, I can talk for days, so you—

Eric Cross (01:40):

I know, I know! But it’s, it’s…so, OK. We can give us a highlight. So, you know, 30 minutes. But what would be the origin story? You can start from any point in time, but what’s that journey like?

Desiré Whitmore (01:51):

I’m gonna start at the beginning, when I was really young, just because I think it’s important. Neither of my parents were college-educated. My mother didn’t finish high school. My father went back and got a GED later. But my father’s grandmother, her name was Claudia Pairs, and she was a teacher, right? So when I was a kid, she actually kind of raised me from, I don’t know, until I was around seven or eight. And so she was very important in who I became, I think because she taught me that college is important and she taught me to think. She taught me to ask questions. She taught me how to ask questions. Just the Exploratorium likes to do. Which is why I fit so well here. She taught me to always wonder and always think about things. And I remember as a kid, she taught me to count and read and write when I was, like, three. And she would always have bubbles at her house. And I was obsessed with bubbles. I thought bubbles were the coolest thing in the world. And just how you can take your breath and create this thing that now you can see, and it’s your breath, right? It’s your breath inside of a bubble and it’s flying around and it has all these cool colors, and then it would fly up and then eventually just pop. And you’re like, where did it go? Now my breath is just up there. Not understanding, as a kid, but my breath is always everywhere. I didn’t understand any of that, but I understood that my breath was inside of a bubble. That’s my earliest memory of thinking about science, was from that. And she was not a science teacher. She was—I don’t even know what she taught. I think she was an elementary school teacher, maybe. She died when I was 12. So I don’t have super-strong memories or of understanding who she was, only that she raised me and what she taught me as a kid. But that in itself really helped me because then when I was in the environment that I was in at home with my parents, which was not at all the environment she provided for me, I always had the things she taught me in my head, right? So I was always asking questions. My mother hated it. I was always taking things apart and putting them back together. So I used to take apart TVs and VCRs and vacuum cleaners and telephones, and my mother’s like, “Oh my God, I’m gonna murder you.” And she tried a couple times, too.

Eric Cross (04:25):

Did you ever put ’em back together and realize you had extra parts? You’re like, oh, hi.

Desiré Whitmore (04:29):

Oh yeah. All the time. Yeah. Yeah. VCRs have a lot of extra pieces. You’re like, “What do you even…it still works. It’s fine.” <laugh> You know? And vacuum cleaners too. They had a lot of extra parts, <laugh> all the time. And TVs. I should not have been playing with TVs. But like I said, I didn’t have a lot of parental, guidance as a child. So, like, whatever—I’m opening up TVs.

Eric Cross (04:54):

There’s a lot of open inquiry going on in your household. Yeah. Unsupervised.

Desiré Whitmore (04:59):

Unsupervised. But I didn’t know what it was or what it meant as a kid. I mean, I used to put things in the microwave. I did so many microwave experiments as a child, trying to cook different foods or melt different things. And so I think those kinds of experiences, where I was allowed to just be curious, kind of shaped who I am today. And then I kind of got into…you know, when I was in school, I loved math. In 10th grade, I had my first Black teacher, he was my chemistry teacher. His name was Mr. Strickland. And I was like, chemistry is cool, dude. And he was not the best teacher, but he was fun. Like you were saying, he was me, and he was talking to us the way I speak. And he was so like, just kind of chill and happy-go-lucky, I guess. But he wasn’t…he hadn’t taught chemistry in a long time. So he wasn’t a very good teacher. And me and one other kid in the class were in love with chemistry. And so we would read the book and do all the homework and he’d be in class lecturing and we’re like, “That’s not right, Mr. Strickland, like, what are you talking about?” And then he’d be like, “Oh, really, Desiré? Do you wanna teach the class, then?” And I’d be like, “Yeah.” And so I would go up and I would teach my chemistry class in high school, because the teacher was trying to make an example out of me. But he was also, I think, willing to be like, “I really don’t know.” And I really appreciated that. That he wasn’t just like, “I know all of the answers and you’re wrong.” Like, he wasn’t being a jerk, right? Like, the fact that I said, “Yes, I do wanna teach it,” and he actually let me do it? That’s pretty dope. And then I liked physics in my senior year in high school, but I didn’t think it was where I was gonna go or anything. I loved music and I loved math. Those were my two subjects.

Eric Cross (06:51):

What was it about math that resonated with you?

Desiré Whitmore (06:55):

I think it helped me understand the world a lot better. I didn’t have strong science teachers, I guess, growing up. It was a lot of reading out of books or watching laser discs in class. That’s how old I am.

Eric Cross (07:12):

Laser discs.

Desiré Whitmore (07:13):

Laser discs. And you know, so there wasn’t a lot of…I moved around a lot as a kid. I didn’t have this straight curriculum. You know, in one year, in the third grade, I went to three different schools.

Eric Cross (07:25):

Mm. Oh wow.

Desiré Whitmore (07:26):

It was kinda hard for me to latch onto school. But with math, because I could look at math and actually understand the world in it, I could see how math can be used to describe how things work.

Eric Cross (07:40):

I almost imagine, especially with so much transition in your life, it helped make sense of things. You had a lot of transition going on, but you were able to understand the world through the process of math. And then this early exposure, it kind of reminds me my own story too. Because there were these books that would do these cross sections of a cruise ship or a machine; that’s what got me really into engineering. Kind of How Stuff Works. I would watch that on Nova, How Stuff Works. I’d always be fascinated. Even Sesame Street had a segment where they would show you crayons and how the dye was added. You remember that?

Desiré Whitmore (08:19):

Yep. Yeah.

Eric Cross (08:20):

Young Desiré, doing photronics…photronics?

Desiré Whitmore (08:24):

Photonics.

Eric Cross (08:24):

Photonics. Photonics at home with the microwave and all these other things.

Desiré Whitmore (08:29):

Sure. How ’bout that.

Eric Cross (08:30):

<laugh> Right. And then loving math. So, early, I could see this combination, sort of this alchemy, happening inside you. And then, how did that lead to you becoming a physicist?

Desiré Whitmore (08:46):

It’s not as straightforward as it seems it should be. It’s obvious to everyone. <laugh>. But it wasn’t obvious to me. ‘Cause I wanted to be a lawyer. You know, because my parents weren’t educated, they didn’t really know…both of my parents and their subsequent spouses when they broke up—so my parents and my stepparents—are all bus drivers. And so they don’t know what options are. Right? So for them it’s like, “You have to be—you can be a doctor. You can be a lawyer. ‘Cause you’re smart. I know you’re smart, so you’re gonna be one of those things.” And I was like, “I don’t wanna be a doctor. That’s not actually interesting to me.” I did wanna be a teacher when I was younger, because I knew that my grandmother was one. But yeah, I went in and I was like, “I’m gonna be a lawyer. I’m gonna be a lawyer.” And then I go to college and I was like, ‘Eh, I don’t. I hate writing.” <Laugh> Like, I love reading, but I don’t writing. So I don’t think I wanna be a lawyer. I love music and I love math. I was originally going to major in music and math, but then I went to community college because I missed my opportunity to go to university for…long story. And so I’m at community college and I was like, “You know what? I’m gonna just do something new. I’m gonna be a marine biologist.” So my major was marine biology, and then they’re helping me pick out my classes. And they had zero math there. And I was like, “Pardon me. I think there’s a mistake, but I’m not taking any math.” And they were like, “No, you’re done with all your math. For marine biology, you only need calculus. And you took all of that in high school, so you’re done.” And I was like, “No, this is not gonna work for me, dude.” So I continued taking calculus anyway and moving on in math. And then I realized that biology wasn’t what I needed, but I did love my chemistry and I loved my physics classes. So I asked those teachers—chemistry, physics, and math teachers in community college, my professors—”I don’t wanna be a marine biologist and I don’t wanna be a lawyer. What do I do? What do you think I could study? I really like chemistry and math and physics.” And so all of them, all three of these professors told me, “Oh, it sounds chemical engineering would be good for you, so you should be a chemical engineer.” And I was like, “OK, cool. No problem.” That’s what I did. So I got my degree in chemical engineering. Right. And I finished community college, studying chemical engineering. I was like, “This is really cool. This is a lot of fun. I love engineering.” And then I transferred to UCLA as a chemical engineering major. And I was like, “I hate this.” <Laugh>. “I hate it a lot.” It was just…

Eric Cross (11:07):

What was it about chemical engineering that you were just not feeling anymore? What was it that just made you go, “nope”?

Desiré Whitmore (11:12):

It didn’t—at least the way it was taught to me—it wasn’t as as…exploratory, I guess. There wasn’t a lot of theory in it. There was just a lot of “OK, pull out a ruler and you’re gonna draw a thing and then this is how you’re gonna build a reactor.” And it didn’t seem very scientific to me. The science was missing. And don’t get me wrong, I understand, now that I have a degree in chemical engineering, that it’s not that chemical engineering is not scientific. But it’s that you build up the science and then you don’t focus on it. You focus on the engineering aspect of it. Which is, you have the science and the scientists will work on that aspect. But then how can WE do kind of larger batch chemistry. And for me, that was just less interesting. It was a lot of pushing buttons and just plug-and-play equations stuff. Instead of diving into first principles of why things happen in chemical engineering. There was no “why things happen”; it was “this is what happens, so this is the next step.”

Eric Cross (12:25):

You had to go so far into your academic career to realize that this is what chemical engineering is. And we were talking about representation, and not having examples or parents; your families were bus drivers. My mom was a receptionist and executive assistant, things like that. And I was the first of many, like you…we kind of had to go through and invest all this time and money to finally get to this place to realize, “This ain’t it.”

Desiré Whitmore (12:58):

This is not for me, yeah.

Eric Cross (12:59):

This is not for me. That was a long journey to get to that point.

Desiré Whitmore (13:03):

It was. Especially because I went through community college and I took a long time in community college, ’cause I was working full-time. So I was working full-time, going to community college. Took me a while. And then I finally get to UCLA. I’m like, “Yeah, I’m finally gonna get my degree and go make money!” And then I was like, “Ooh, no.” I mean, I could go and make money, don’t get me wrong. I could have graduated and made a ton of money. But I was not happy at all and I did not enjoy what I was doing. So, while I was in undergrad, I realized I don’t wanna do chemical engineering anymore. But what do I wanna do? But then I was taking…I took a quantum mechanics class. And that class blew my whole mind. And I was like, “This is the coolest thing that I’ve ever learned in my life, and this is what I wanna do.” And so I went and talked to my professor and I was like, “Can I work for you? Can I do research? Because this is amazing and I wanna do this.” I felt it was too late for me. I had been in school for so long and I was already kind of burnt out. So I was, “I’m not going to change my major. That’s just outta the question for me right now. It costs so much money for this degree and I don’t have—I’m not just gonna waste my time and keep working all these jobs.” So I had three jobs in college. And it was like, I worked at Radio Shack, I did research for this professor, and I worked in the library, the chemistry and physics library.

Eric Cross (14:28):

I love the fact that we’ve talked about laser discs; you said Radio Shack; and we talked about the analog internet of the encyclopedia salespeople. And I know all of those things. And I’ve been through all of those things together.

Desiré Whitmore (14:43):

Just in case people don’t know how old I am. <Laugh>

Eric Cross (14:47):

For our listeners who are way younger, yeah, this is how we grew up. This is how we—these things are extinct now. There’s this element of this kind of cultural connection. I think that we experience that. It kind of it flies under the radar. People don’t really realize it until you’re in an environment that’s different from what you’re used to. And you realize that, “Oh wow. this is not what I’m used to.” And the things that I’m finding funnier, the things that I connect with, it’s not what everybody else connects with. And as a teacher, it’s the same thing, right? Like, we go in the classroom and you know, you and I are rapping about laser discs and Radio Shack and I’m trying to talk to my kids about it. And they’re like, “Yo, Cross, what is that? Are you gonna give us a history lesson? What are these things?”

Desiré Whitmore (15:35):

Yeah.

Eric Cross (15:36):

And I found myself having to stay connected to pop culture, because I teach 12- and 13-year-olds all day. And it’s great for keeping things relevant for my students. But when I talk to my friends that are my peers, they’re like, unless they’re a teacher, they’re like, “I got no idea what you’re talking about.”

Desiré Whitmore (15:55):

Yeah. I have a friend who’s also a middle-school teacher and she’s always coming to me with all this. I’m like, “What are you talking about?” She did the Glow-up Challenge, but she did the Glow-down Challenge. So she invented a new thing. She’s like, “No, I couldn’t do Glow Up ’cause that’s too much. So I did the Glow-Down Challenge.” And it’s the cutest thing ever. And the students think it’s amazing. And I’m like, “That’s awesome. But I have no idea what the point of that is.” <Laugh>

Eric Cross (16:21):

And there’s this theme, too, that when we talk about teaching kids STEM, there’s this soft part of it, this relational piece of it that you mentioned, of this connective aspect that in a certain way kind of even superseded the content knowledge that your teacher even had at that point, where you’re going up and teaching the class. But just the fact that someone looked like you or spoke like you or connected with you in a certain way made a big difference to who you are as…well, the trajectory of where you went.

Desiré Whitmore (16:57):

Yeah.

Eric Cross (16:57):

“I like chemistry. It resonates with me.” And it’s something I think can get lost. And I think just to kind of a good segue, I use Amplify my classroom, and one of the reasons why is because of the representation that is in these videos. And you were part of crafting this for…was it the fifth grade?

Desiré Whitmore (17:21):

I mean, it was K–8. So I was—

Eric Cross (17:23):

OK, so you were doing the whole thing.

Desiré Whitmore (17:24):

Yeah, I was a part of the K–8 science team. My title was science curriculum specialist. But in reality I was hired to do the engineering internships, mostly. Which are middle school. And to be a sim developer. So sims K–8. I worked on several of them in both middle school and elementary. Yeah.

Eric Cross (17:47):

What was that like for you? When you were designing curriculum? ‘Cause as a teacher, it’s, you know, I think with teachers it’s kind of…I would consider myself, if I was gonna use hip hop as a metaphor, I’m more of a DJ than an MC. Where I wanna remix things that exist, versus, I don’t wanna write the lyrics in freestyle. So I don’t want to go and write the curriculum completely; I wanna take something that’s solid and then I want to go ahead and remix it. You are great at both. What was the process for you, being on that team, designing? How did you go about making, “OK, we’re gonna create this experience for kids”?

Desiré Whitmore (18:25):

It was, it was amazing. I learned so much, so much. It was the best job I had before I came to the Exploratorium. The process was amazing, because it wasn’t just me, right? It wasn’t just me. It was a whole team. And each unit had its own team. So we had a scientist, which I was the scientist we had. So we had a scientist; we had a literacy specialist, because it was really important to increase science literacy so that students understand not just that science exists, but “What are the terms that are used in science and how can I speak and act a scientist? What are the things that scientists actually do in their real life?” Then we had an assessment specialist and then we had a simulation specialist. And so, on the units that I was on, sometimes I was both the sim developer and the scientist, or sometimes I was just the sim developer and I got to work alongside another scientist, which was always fun. And so it was really nice, because I was working alongside master teachers. People who had been teaching for years, and they were able to help me better understand. ‘Cause I’ll come in and I’ll be like, “Yeah, there’s a unit on light waves, let’s come in and teach this unit on light waves!” <laugh> I was the sim developer and scientist on that unit, and there was another scientist working on the unit, but they were like, “Well, Desiré literally builds lasers, so I think she should be the science developer.” So we kinda had two science developers on that one, which was fun. But I come in and she’ll come in and she’ll be like, “Yeah, I think this is where we wanna go and this is what we wanna teach.” I’m like, “No way! Like, that’s not accurate, right?” And so I can come in, but then I’m coming in with all this crazy lingo, right? I’m up here. But then also I have taught kids about lasers and optics and photonics my whole career. So I’m also very capable of bringing it down to where kids need it to be. What I don’t know is how effective that is, right? When to do it and when not to do it. When to bring the level up; when to bring the level down. And so working alongside these other teachers and assessors really helped me to do that. And so for me it was just two years of deep learning experience. I learned—every single day at work, I learned something new. Which is something that I value and I’ve wanted in my career, my whole life. We made active decisions in that room. Like, “We want to interview scientists who are scientists of color or who have different abilities or who have different representations in all kinds of ways.” Right? And then we also have these fake internships, or not even the internships, but just in the general units. And we actively wrote scripts for those. And we actively wrote in those scripts, like, “This is a Black woman. This is an Indian woman. This is a Jewish man in a wheelchair.” Like, we specifically dictated exactly who we wanted in these videos, because we knew that representation was super-important and we knew that we wanted students to be able to connect.

Eric Cross (21:35):

Right. One of the things, I appreciate what I’m hearing a lot in that is the amount of intentionality that went into this. But even now as you’re reliving it, you’re still almost iterating on how could we improve it or how can we make it different or reach more people. And I think that goes towards when we’re talking about including more people and inclusion. Like, it’s not a binary thing. You’re always modifying; you’re always iterating; you’re always redesigning and improving to be more inclusive, to reach more students. Because you know, to your point, part of it is, “Yes, we wanna do this really awesome science curriculum,” but the other part of it is there’s more to it than just your content. And I think now more than ever…I use—we just finished the food bar unit. Metabolism. And in there there’s a simulator. They always ask me when I show the videos, “Are these, are these real people? Are these real situations?” And I tell ’em, “Well, the story is real, but these are all fictional actors. But what’s actually happening happens. It’s real.” And they get really into it. And I think one of the other things is with your simulations—especially the engineering units—there’s no one right answer. And so my students who want to go, “Mr. Cross, I wanna make the best bar! Perfect 10, best taste, cheapest!” And I’m like, “All right, good luck!”

Desiré Whitmore (23:06):

Yeah. Go do that.

Eric Cross (23:09):

Casue there’s something called trade-offs! It could happen! And they’re like, they’re trying. They get into the code. They try to open up the Inspect Element, when they feel like hackers.

Desiré Whitmore (23:17):

Yeah, they do. But these kids like, they’re so smart and they’re so resourceful. And I’m just thinking like, maybe that’s how we challenge them more, right? Sometimes we can give them these kinds of things where it’s like, “Go and create a program, ’cause that’s the level you’re at <laugh>. Go and create this program to do something similar that’s related to the work that we’re doing.”

Eric Cross (23:38):

I’ve had some of my own students redesign—I have one student who redesigns every assessment I give him. I give the project; I give the options for the final goal; and he always chooses—if I give three options, he always chooses option four. If I choose two options, he’s choosing option three. And so he’ll go into Google Sheets, he’ll pull all the data and then he’ll construct his own kind of spreadsheet with all the probabilities of different things.

Desiré Whitmore (24:06):

You tell this kid to make a GitHub right now <laugh> so that he can get a job as soon as he’s done with high school. <laugh>.

Eric Cross (24:12):

He’s amazing. And we did this one project where students had to design a Netflix show to show their understanding of metabolism. And they had to do four episodes. So I gave him a template. It’s not from me; it’s from, I think, EdTechPicks.org or something. And it looks like the whole Netflix splash page. They took photos, did the whole deal. He created NOTflix. Everyone else did Google Slides. His Google Slides was interactive. So when you clicked on different boxes, it actually took you to the next splash page of that show. I mean, it was….

Desiré Whitmore (24:48):

That’s fantastic.

Eric Cross (24:49):

It was, it was. I recorded his presentation. It was brilliant.

Desiré Whitmore (24:53):

But that’s amazing. And that speaks to your strengths as a teacher and why you’re an amazing teacher. Because you see the students and what they’re trying to do and you work with them; you meet them where they are. Right? There are so many teachers who would just be frustrated with that student. And it’d be like, “No, these are not your options. Your option was to do what I told you to do.” And there are many teachers who would do that. And I think it’s really amazing when we can realize as teachers, “No, our job is not to just enforce rules on our students. I mean, that is part of the job, because that’s what school was when it was created. But our job is to help students to achieve more learning in what we’re trying to do. And so the fact that you are so good with this student and that you encourage him to go above and beyond when he can, I think it’s so amazing.

Eric Cross (25:49):

Well, that brings me to my favorite group, organization, and the phase of your career of where you are now: The Exploratorium. And I wanted to kind of rap, talking about what you do now. Because the Exploratorium—I tell people, they go, what is that place? And maybe you can tell us what it is and then what you do. But for me, I’ll just tell everybody: It’s Disneyland for science teachers. And I love going there. I not only love going there because of what I receive from it professionally. Many of the PDs, I don’t even call ’em PDs—just communal learning experiences, that I’ve had that have been led by you and Lori and, and Tammy and the rest, and everybody that’s there have been incredible. And I have so much fun. Emotionally, I get excited when I go. When I’m on the plane, I’m like, “Here we go!” And then we go and we’re making fudge or we’re blowing darts with marshmallows across the room in the theme of Boba Fett. There’s just these rad things that are going on there. And it’s not like anything I’ve ever experienced before. So maybe we can close with talking about what the Exploratorium is, what you do there, for people who’ve never been and have been a part of it.

Desiré Whitmore (27:19):

I’m gonna give you what my definition of the Exploratorium is.

Eric Cross (27:21):

That’s what we want.

Desiré Whitmore (27:22):

So, the actual definition is, we are a public learning laboratory. We are known as the Museum of Art, Science and Human Perception. Cool. But, like, what does that all mean? Right? And I think your description of the Disneyland for science teachers, I think that’s a perfect description. ‘Cause for me, I tell people like, “Oh, I wanna go to the happiest place on earth.” And for me, that is the Exploratorium. And yes, I work there, and yes, it’s still true for me. So the Exploratorium is this huge museum. It’s an interactive science museum. And art—we have a lot of art. And it’s all about learning through doing. It’s not about learning science by going up to an exhibit and reading the little paper next to it. It’s like, no, you go up to an exhibit and you interact with it and you teach yourself science. The goal of the Exploratorium is really to help people understand that learning science, doing science, isn’t reserved for only scientists. Doing science is something that everyone in the world should and does do. And so helping people understand that everything we do is science is kind of the point of the Exploratorium to me.

Eric Cross (28:35):

Even the building itself…one of the other cool things too is, for people that don’t know, it’s the size of Costco or two.

Desiré Whitmore (28:43):

Yeah. Yeah.

Eric Cross (28:44):

It’s immense! And even the building itself teaches. Like, you have that whole workshop, dead-center in the middle of the floor where they’re designing things. It’s like inside-out. And then I remember going to the one experience where I think it was Eric who showed us that it’s one of the few facilities that is actually cooled by the Bay water. And there’s only a couple of those in the state that can do that. And it has a platinum rating, something wild that. So even just the building itself…everything that if they can extract every ounce of science teaching in that, it’s in there. And you are in a very important program for me. And can you talk a little bit about maybe what you’re doing in T.I.?

Desiré Whitmore (29:33):

So I am in the Teacher Institute. I’m a physicist in the Teacher Institute. And the Teacher Institute is a group of teachers and scientists. And our job is to basically support middle school and high school science teachers and teacher leaders in the state of California, but science teachers around the world, in their pursuit of science teaching. And by support, I mean we provide professional development. We provide other things, communities of practice, and we go and do workshops in certain places. We go to India to teach Tibetan monks and nuns science. And we go to Costa Rica to teach teachers all over the country of Costa Rica about science. And so our job is really, to help science teachers feel more secure in their science teaching and help to retain them in the field, because a good science teacher is so important in helping our students thrive. And so our job—and we take this very seriously—is to help science teachers thrive. And we are made up of PhD scientists and veteran classroom teachers. So we have on the one side teachers who have been teaching middle school or high school for years. One of my coworkers, Zeke, who I work with the most, he was a high school physics and environmental science teacher for 21 years before coming to the Exploratorium. And then me, I was never a classroom teacher. I was a professor; I was a physics professor at a community college, and I was a researcher. So my deep knowledge of physics and current knowledge of physics—or knowledge of current physics—combined with Zeke’s extremely experienced pedagogy is really how we work together as a team. And it’s not just Zeke, right? We’ve got a geologist on the team, Eric Muller. We’ve got Tammy, who’s a middle-school bio teacher. We’ve got, Julie Yu, who is a chemical engineer, PhD, and also a prior middle school teacher, former middle school teacher. We’ve got Hilleary Osheroff, who was a PhD biologist who used to work at the American Museum of Natural History. We’ve got Lori Lambertson, who was a middle-school math teacher. And so, you know, we all come together to bring our experiences both in and out of the classroom and in and out of the research lab to provide teachers with the best inquiry-driven stuff we can. And we’re very—we’re so equity-focused, because we believe that that’s important, right? We know that the impact of our work is, I think, why most of us are here. It’s why I’m here. In undergrad, my grad school, and my postdoc, I would go into classrooms. I would go into science museums and teach science to people. And I probably reached out to maybe…over that whole time, I would say a couple thousand people, right? Maybe a couple thousand people total. That’s great. But over 15 years of reaching out and only reaching a couple thousand people, that’s rough, right? And now I’m at the Exploratorium, and I know that if I reach one teacher, right? If I can teach one teacher…let’s say you. How many students do you have in your classes a year?

Eric Cross (33:11):

Two hundred a year.

Desiré Whitmore (33:12):

You have 200 students a year that you teach. So if you teach for 10 years, that’s 2000. That’s 2000 students. So I have, by teaching you today, assuming that I’m actually teaching you something that’s gonna be useful for you—

Eric Cross (33:29):

You do! And you are!

Desiré Whitmore (33:30):

You are going to be impacting these 2000 students over the next 10 years. And of course you’re gonna be in teaching for much longer than that. But let’s just say in 10 years, that payoff is so much higher, right? And you’re one teacher. But I have 30 of you in my workshop! And so if all of these 30 teachers each teach 2000 kids over the next 10 years, then I’m actually doing something. I’m actually changing the way that students see science, through changing the way that you see science. Right? And so I take my job very seriously, as we all do. Like, we’re so invested in our teachers. And it’s not that we don’t care about students, ’cause we absolutely do. But we understand that without good teachers, students aren’t going to be able to thrive, as often as they would otherwise. I was able to do it somehow. But I’m one. There are so many other kids who could have gone into science who didn’t because they felt they never connected to it. So our job is to try to help teachers connect to it. And an important part of that is allowing you all to experience science as a learner. We want you to play and have joyful experiences. We want you to enjoy science and to try to think about it from the perspective of your students. Walk in their shoes. So that when you then go back to your classroom, you are able to think about like, “Oh yeah, you know, my students totally asked the same question that I asked, or that another teacher asked in the workshop because they had the foresight to think about that’s what my students would ask.” Right?

Eric Cross (35:02):

Well, I think it’s really effective to create empathy for the learner. Because I find myself in that position. I don’t know if some kind of memory displacement field happens to me when I sit in those workshops, but Hillary will ask a question that I know the answer to and I’m like, “I don’t want to answer the question. I don’t—I might be wrong.” And I teach the subject! And I embody what it’s like to be a student. And when I leave, I might have to go back and reference exactly what the lesson was, but I remember how I felt when I didn’t know. And very rarely as teachers do we get put in positions like that. And so it helps me be in the position of my students emotionally, of what it’s like. Even even the intentionality of how do you ask questions and not showing an affect on your face when somebody says the right answer or the wrong answer.

Desiré Whitmore (35:55):

Well, I’m still learning that. I’m not great at it. Julie is the mast.

Eric Cross (35:59):

Julie’s got it nailed.

Desiré Whitmore (36:00):

I’m still trying to learn from her. She’s amazing. And I really would like to get there one day. But I’m still not there. I’ll be like, “Oh! Oh! Well, that’s…”. I have a terrible poker face. So I’ll be like, “Oh yeah, but you think that? Maybe…”. That’s a piece of it that’s really important, right? It’s this not giving away the answer, even when you have the right answer. Allowing people to ask the questions and explore and become invested in the problem, before giving away the answer. That’s something that I learn here at the Exploratorium. And like I said, I learn every day. And it’s something that I think is so important for us as teachers to learn and try to implement. Because oftentimes you’ll come and you’ll have students who are like, “I’m too stupid. I don’t know the answer.” And then somebody else will say the answer, and then the student is like, “Yeah, I was right. I’m too stupid.’” But it’s like no! But if you have that student actually think about it, then the student—once they do hear the right answer—they might be like, “Oh yeah, that would make sense.” Instead of “I’m stupid.” It’s like, no, this is, “I explored this and I figured it out on my own.”

Eric Cross (37:08):

Things keep coming back to how this experience and the process of them learning science even outweighs the content of it. ‘Cause the content is almost easier to share, it’s easier to get, you can look it up really quickly. But in your story and in many other people’s stories, the exposure, the experience, how they’re going through that process—I know that’s something that I’ve learned a lot in just watching. Not teaching science, but actually the science of teaching. Sitting in the workshops and watching how we’re treated as students, how you interact with us, and then being able to take that back to the classroom. And just to add onto the value that it’s created, I think one thing that it’s also done is given us community. And in addition to being able to impact students, it’s also been able to build resilience in teachers. Because we as teachers can feel very isolated. And especially now when things are incredibly difficult, and every teacher’s experiencing Covid and shutdowns and low staffing across the country in different ways, when you don’t feel you have community or people that you can connect with, it just makes everything feel exponentially harder. And you’ve done a great job at being able to build community with us in our community of practice. The Exploratorium has been able to do that. And it’s something that I’m super-grateful for probably more than anything else is that through these last two years, being able to connect really made me feel like, “OK, we’re gonna be able to do this.” And it’s not just about Cross or my other teacher in eighth grade or my sixth grade teacher who’s doing this. That message, I think, is really, really important. I wanna ask this: Was there a teacher or an experience that impacted you or inspired you throughout your educational career? You know, kindergarten all the way to college? Was there a moment or a person or anything that that really stuck with you, that you felt maybe influenced who you became? Met you where you were at? I know you mentioned your chemistry teacher at that point, but is there anyone else, or was it that person that was really the person who sticks out for you?

Desiré Whitmore (39:21):

There actually have been a few. Of course, the first is my great-grandmother, Claudia Pairs. But I think in the fourth and fifth grade I had the same teacher. She stayed with us going from fourth to fifth grade. And fourth grade was a new school for me. New town. I was the only Black child in the school, me and my sister. And my teacher recognized that I had no real help at home, I guess? And she really kind of…she saw that I was really smart. She would give me extra assignments when she could tell I was bored. It meant that someone outside of my house cared about me in a way that I didn’t feel cared about at home. Her name is Ms. Comet. Mrs. Comet.

Eric Cross (40:11):

Like…comet?

Desiré Whitmore (40:13):

Yeah. Mrs. Fran Comet. And I’ve tried looking her up as an adult and I can’t find her. But I work with so many teachers, and I know how hard teaching is and how degrading it can be…or demoralizing, I guess, to not be appreciated. And so I know what it feels to me when a student has reached out and shown me like, “Hey, I’m now in dental school,” or “I’m now getting a PhD in science,” and I’m just like….

Eric Cross (40:40):

I got a message this morning on Instagram from a student. And none of my students use their real names in their Instagram handles. So I got a message from Moonshine. <Laugh> And I was a seventh grade teacher. And through deduction, deductive reasoning, I figured out who it was. This person’s now in college and they responded in that…you know, you get one of those every once in a while. And I feel it just fills your tank. It’s just so important that we—it’s funny because, kind of to your point, we don’t realize who or how we’re making impacts on people. And in what ways. We just know that we are. And I tell other teachers, I said, “You have one of the few professions where you fall asleep worrying about other people’s kids.” And it’s the words that we speak, the things that we do, people are always watching. I know, no pressure, right!? Hopefully, someone listening can find Ms. Comet.

Desiré Whitmore (41:37):

Ms. Comet. Teacher at Buena Vista Elementary School back in the ’80s. But your talk about this impact, it reminds me of the thing I wanted to say, but I didn’t. But I’m gonna tell you right now. I mentioned how science was not a priority when I went to school, in my hometown. That’s Lancaster, California. But recently I got a phone call from a family friend and she was so excited. And she called me to tell me that her daughter was super-excited when she picked her up from school. Because I was in her classroom. She said, “Auntie Desiré was in my class today! And she works on lasers! And she does spectroscopy! And I wanna learn about spectroscopy now. So can we call Auntie Desiré?” And I was like, “Wait, what?” My friend was kind of confused. She’s like, “Desiré didn’t tell me she was in town.” She had no idea why her daughter was saying I was in her classroom, ’cause I was not physically there. And then I had to put the pieces together and I was like, “Oh my God, your daughter’s in eighth grade already.” It made me feel really old, ’cause I know this girl from a little baby. But I was like, “Oh my God, that’s the eighth grade unit on light waves for Amplify that I wrote, and I’m featured as the scientist.” Because we have real scientists in the units. And they featured me in that one, in my laser lab. And so this little girl who knows me really well, who lives in my hometown, is seeing representation in science. She doesn’t necessarily know I’m a scientist. She knows that—I don’t know what she knows about me. She just knows I’m Auntie Desiré and, you know, I like gumbo at Christmas. That’s what she knows about me. <Laugh>. And so she comes back and she’s so excited ’cause now she knows so much more about me. And she knows that if I can do it and I came from where she’s at, she can do it too. And she was super-excited. And I was just…it brought me to tears. I was just crying in the car. I was driving <laugh> at the time and I was like, “This is amazing. Work that I did is teaching you and all of your friends in this tiny little town that you live in. And that to me is so important because now this little girl knows that, like, she knows me as just a normal human right. Who likes Star Trek and Star Wars and The Owl House. And now she’s over here like, “Oh my gosh, this normal human wrote the science curriculum that I’m learning from.” Which I think is just so fantastic. And it really brought home for me kind of the importance of my work and why I’m doing what I’m doing. And that’s pretty awesome. And I get messages from Instagram, you know, from teachers who are like, “Hey, did you work on this? ‘Cause you were featured in the video, but did you write this light waves unit?” And I’m like, “Yeah.” And they’ll tell me, “I have students, this is their favorite unit. I’ve gotten notes from students saying, ‘This was my favorite unit in all of middle school.’” And I’m like, “Ohhhhhh!”<Laugh>

Eric Cross (44:33):

That story just gives me chills. Because I just can imagine how surreal that must feel. And you’re directly making that impact on those kids. And I’m glad that you shared that story so that everyone can hear it, because it’s a powerful story and I lived—I feel I was living it through you, just now, as you were discussing it.

Desiré Whitmore (44:54):

Yeah.

Eric Cross (44:54):

And I feel that way in the classroom to a small degree, because I get to have—when my students create posters of scientists that we don’t typically see, I’ve got you on my list of scientists, and I’m they’re like…And I’m like, “I can call her!” Like, “Mr. Cross, you KNOW her?!” I’m like, “Yeah, she’s a friend of mine! I was talking to her the other day!” And they’re like, “Whoa. She works with lasers?!”

Desiré Whitmore (45:17):

<Whispers> I do.

Eric Cross (45:18):

Desiré. I’ve held you for so long and—

Desiré Whitmore (45:23):

Yes, I’m sorry! I told you, I talk so much! I’m a teacher!

Eric Cross (45:26):

No! No, no, no, no. It was great! I wanna honor your time. Can you tell everybody where they can find out more about you again?

Desiré Whitmore (45:33):

So first off, you can find me on Twitter at Darth Science, D A R T H S C I E N C E, and you can also find me at Instagram at Dr. Laser Chick: D R dot laser chick. Even though I don’t post on Instagram that much. I also have a website, which is laser chick dot net. I’m still working on it. It’s not the best website yet. But, you know, it’ll, it’ll be better in the future.

Eric Cross (46:02):

Would you be willing to come back later on in the year and do a part two?

Desiré Whitmore (46:07):

Oh, for sure. Yeah. So I can actually finish telling you the story of how I got into physics! ‘Cause I totally didn’t. ‘Cause I’m all over the place.

Eric Cross (46:15):

So, everybody, cliffhanger! Next time she comes back, she’ll continue to tell us the story. Desiré, thank you so much.

Stay connected!

Join our community and get new episodes every other Tuesday!

We’ll also share new and exciting free resources for your classroom every month.

What Desiré Whitmore says about science

“I think it’s really amazing when we can realize as teachers… our job is not just to enforce rules on our students… our job is is to help students achieve more learning.”

– Desiré Whitmore

Senior Physics Educator, aka “LaserChick”, Exploratorium

Meet the guest

A Southern California native, Desiré earned an associate of science from Antelope Valley College, a bachelor of science in chemical engineering from UCLA, and a master of science and Ph.D. in chemical and material physics from UC Irvine. Her research focused on developing very fast laser and microscope systems that could capture molecules vibrating and rotating in real time. She was a postdoctoral fellow at UC Berkeley, where she designed and built attosecond lasers (the fastest laser pulses, which emit x-ray light, ever measured). At the Lawrence Hall of Science she wrote an all-digital K–8 science curriculum (Amplify Science), which aligned to the NGSS, with the Learning Design Group (LDG). Desiré left LDG to teach hands-on laser technology and physics courses at Irvine Valley College before joining the TI staff. She is the proud mom of Stella, a four-year-old boxer-pit mix. In her spare time, Desiré is restoring her 1967 VW bug.

Person with curly hair wearing a blue jacket, smiling at the camera with a blurred background.

About Science Connections

Welcome to Science Connections! Science is changing before our eyes, now more than ever. So…how do we help kids figure that out? We will bring on educators, scientists, and more to discuss the importance of high-quality science instruction. In this episode, hear from our host Eric Cross about his work engaging students as a K-8 science teacher. Listen here!

High-impact, evidence-based programs that help students make gap-closing gains in reading and math

Amplify Tutoring engages students and drives measurable academic gains. We partner with districts to ensure that children become confident, proficient readers and mathematical thinkers.

A student and an adult sit at a table, both looking at a laptop screen. The background features blue and yellow geometric shapes with a star icon.

About Amplify Tutoring

Grounded in evidence-based practices and taught by caring, consistent tutors, our high-impact tutoring programs use high-quality instructional materials and data-driven mCLASS® products to support and engage students.

  • Personalized, data-driven instruction
  • Research-backed solutions tailored to support your Multi-Tiered System of Supports (MTSS) framework
  • Customizable—before, during, or after school; year-long, semester-long, and summer programming
  • Comprehensive, hands-on program management and staffing support

Amplify Literacy Tutoring supports K–6 readers through engaging, systematic instruction aligned to the Science of Reading and driven by mCLASS DIBELS® data.

Amplify Math Tutoring accelerates student achievement in grades 3–5 and builds students’ confidence in speaking, writing, and thinking mathematically.

More than a program: a true partner

Hear directly from district leaders and educators who’ve experienced the Amplify Tutoring difference. In these candid conversations, they share how we partner to deliver solutions for schools, gains for students, and support for teachers.

What district leaders and teachers are saying

“Students’ enthusiasm for Amplify Tutoring is evident! From the moment they sit down for their session, you can see how motivated and engaged they are while working with their tutor and peers. … It is very helpful that the tutors provide real-time feedback to students, and it has allowed them to be more confident and committed to their own learning paths.”

—Jennifer Quartano, Teacher, NYC Public Schools

What district leaders and teachers are saying

“There has been an increase in many students’ scores. The students are always excited to participate and the small group instruction truly is making a difference … I am passionate about reaching students who require support. This initiative was very much needed in our school. Thank you, Amplify Tutoring!”

—Denise Bishop, Assistant Principal, Prince George’s County Public Schools

What district leaders and teachers are saying

“I appreciate the support and quick response we have received from Amplify Tutoring this year. We have seen lots of growth with our fourth graders with phonics, decoding, vocabulary, and comprehension that we likely would not have seen without the program!”

—Heather Wasburn, Instructional Coach, Springfield City Schools

Bar chart showing that students with 2–3 literacy tutoring sessions per week outperform national growth norms across grades K–5, compared to students not in tutoring.
Bar chart showing percent correct in performing multi-digit arithmetic for Grades 3, 4, and 5 before and after Amplify Math Tutoring; scores improved in Grades 4 and 5 after tutoring.

Our impact

Amplify Tutoring accelerates learning for students who need it most. Students in Amplify Tutoring are more likely to achieve outsized academic gains than similarly at-risk peers in the same schools who are not enrolled in the program.

A hexagonal badge labeled "National Student Support Accelerator Tutoring Program Design, Amplify Tutoring 2024-2027," recognizing high impact tutoring programs that boost reading competency.

Amplify Tutoring has been awarded the National Student Support Accelerator (NSSA) Tutoring Program Design Badge by Stanford University!

Learn more

Reliable, easy-to-read data

With valid and reliable mCLASS assessments and real-time reporting always within reach, everyone involved in a child’s learning journey—from teachers and tutors to school leaders and families—can support student growth.

  • Teachers have visibility into students’ data and all tutoring lesson content.
  • School and district administrators receive regular tutoring attendance and progress-monitoring reports.
  • Caregivers receive Home Connect letters and activities to help their child practice foundational skills at home.
Screenshot of mCLASS Home Connect dashboard displaying reading assessment data, scores, and activity details with charts and text descriptions.

High-quality instructional materials that power Amplify Literacy Tutoring

Amplify Literacy Tutoring includes high-quality resources to support students’ growth.

Targeted lessons generated by precise data

mCLASS Intervention is a research-backed, ESSA rated program that targets instruction based on students’ mCLASS DIBELS 8th Edition assessment results. With engaging lessons aligned to the Science of Reading that adapt based on students’ progress monitoring results, mCLASS Intervention streamlines time-consuming data analysis for teachers and makes sure that tutoring focuses on the literacy skills students need.

A line graph displays students' letter-sound fluency scores from June to May, showing progress toward a custom goal of 90, with benchmark and performance data points.
A screenshot of the mCLASS Reading assessment dashboard showing student scores, benchmarks, and assessment categories for Bolton Grade 1.

Transparency into student performance

mCLASS DIBELS 8th Edition is our nationally normed benchmarking and progress monitoring assessment tool to measure students’ foundational literacy skills. Students take the benchmark assessment three times a year and progress monitoring occurs every 7–10 lessons in between.

Proven impact for students who need it most

Boost Reading delivers targeted, adaptive practice that meets students where they are, while teachers get simple and meaningful insights into student progress. The program consistently moves students toward grade-level proficiency with just 30 minutes of use per week. Students can continue learning through Boost Reading between tutoring sessions or at home.

High-quality instructional materials that power Amplify Math Tutoring

Amplify Math Tutoring includes high-quality resources to support students’ growth.

Intervention Mini-Lessons aligned to core instruction

Amplify Desmos Math Mini-Lessons provide targeted intervention for students who require additional support or need more time. These lessons are aligned to the most critical topics throughout a unit; they enhance conceptual understanding while improving procedural fluency and application.

Two overlapping math worksheets on a white background with blue and orange squares; worksheets show graphs, equations, and instructional text about graph rotations.

Valuable insights into student mathematical thinking

mCLASS Math is our benchmarking and progress monitoring assessment tool. Students take the benchmark assessment three times a year; progress monitoring occurs every 7–10 lessons in between.

Personalized practice—anytime and at home

Fact fluency practice provides students with regular practice beyond rote memorization. The program is used during tutoring sessions and is available on non-tutoring days. Students also have access to Boost Math’s independent learning activities, to continue practicing between tutoring sessions or at home.

A woman and a boy sit at a table, looking at a tablet together. The background includes blue and orange graphic elements with a clipboard icon.

Consultation and collaboration

Amplify Tutoring tailors our support for educators, schools, districts, caregivers, and state-level leaders, helping to realize the promise of high-impact tutoring programs. Through collaborative partnerships at every level, Amplify Tutoring engages communities in driving academic improvement and boosting attendance.

Our services can include:

Program design consultation: Amplify Tutoring offers expert program design consultation services to help schools and districts create effective and scalable high-impact tutoring programs.

Tailored onboarding: We provide customized training sessions for school, district, and state leaders, ensuring that Amplify Tutoring services are integrated smoothly into existing systems.

Ongoing professional development and coaching: Our program management includes continuous training, coaching support, and office hours with pedagogical experts to fortify the program’s success and adaptability.

Caregiver engagement: We offer resources and support for families and caregivers, including tips for at-home support, helping them stay informed and involved in their child’s progress.

Seamless communication and support: We provide transparent communication and engage all stakeholders—district and school leaders, teachers, caregivers, and students—to keep everyone aligned and informed.

Data reporting: We provide detailed reports and analytics to district and school leaders, giving them the power to monitor progress, make data-driven decisions, and celebrate successes.

Amplify Tutoring is part of a connected early literacy and math suite.

Our literacy and math suite programs are designed to support and complement each other in a Multi-Tiered System of Supports (MTSS). Learn more about our related programs.

Texas ELAR Literacy Adoption

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The next chapter in the Science of Reading

Introducing Amplify CKLA 3rd Edition, a K–5 core literacy program within Amplify’s literacy suite. For more than a decade, Amplify CKLA has transformed classrooms nationwide with its intentional knowledge building and systematic skills instruction. Available for the 2025–2026 school year, the 3rd Edition builds on this successful foundation to better support all students in becoming confident readers, writers, and thinkers. Together, let’s write the next chapter in the Science of Reading.

An astronaut floats in space near the Moon, with a speech bubble displaying

Amplify CKLA serves

150,000+

Classrooms

4,000,000+

Students

50

U.S. States and D.C.

Our approach

Improve outcomes with a program built on a decade of research, and that meets the strongest ESSA Tier I criteria.

Diagram illustrating the Simple View of Reading model, depicting language comprehension and word recognition pathways converging into skilled reading, with processes becoming increasingly strategic and automatic—a foundational concept in literacy curriculum for elementary education.

Grounded in the Science of Reading

As the original Science of Reading program, Amplify CKLA puts research into action with explicit, systematic foundational skills instruction and a proven knowledge-building sequence. In collaboration with education experts and practitioners, we provide powerful resources that deliver real results.

Background knowledge drives results

Amplify CKLA follows the Core Knowledge Sequence, a content-specific, cumulative, and coherent approach to knowledge building. This approach improves reading scores and closes achievement gaps by establishing a robust knowledge base that strengthens comprehension.

In Amplify CKLA 3rd Edition, we’ve enriched our Knowledge Sequence with a wider range of perspectives and high-quality texts in new and enhanced units.

An infographic showing the steps to pronounce

Build foundational skills for long-term success.

Students progress from simple to complex skill development starting with phonological and phonemic awareness. Instruction in Grades K–2 explicitly teaches the 150 spellings for the 44 sounds of English, following an intentional progression to ensure student success.

In our 3rd Edition, we’ve added dedicated Grades 3–5 foundational skills instruction that can either support core lessons or function as an intervention, based on student needs.

Daily writing deepens learning.

Grounded in the Science of Writing—the research on how kids learn to write—instruction is explicit, daily, and woven into the curriculum’s rich content. It covers both transcription (handwriting and spelling) and composition (organizing ideas into narratives) with high-impact activities like sentence-level combining and expanding, and pre-writing exercises. Writing and reading instruction are integrated so students simultaneously strengthen their communication skills, comprehension, and confidence.

A child in a green shirt smiles while writing in a notebook at a classroom desk, engaged in their k–5 literacy curriculum, with another student visible in the background.
An open laptop displaying a children's story titled

High-quality, diverse texts

Amplify CKLA students are immersed in a variety of texts—complex read-alouds, decodable chapter books, trade books, and content-rich readers—that reflect varied experiences and connect to learning goals.

Readers are 100% decodable for Grades K–2, empowering students to directly apply what they’ve learned. Novel Study units for Grades 3–5 offer a mix of contemporary and classic literature, and Culminating Research Units in every grade include a set of authentic texts and trade books.

Reach all learners with differentiated support.

Scaffolds and challenges, developed in collaboration with education experts, make content available to every student—including multilingual and English learners. With strategies embedded right in the curriculum, teachers can deliver in-the-moment, individualized instruction to meet all student needs.

For a dedicated English language development program aligned to Amplify CKLA, explore Language Studio.

Children sit on the floor in a classroom, some raising their hands, smiling and engaged. The lively atmosphere reflects the effectiveness of the k–5 literacy curriculum being implemented.

What’s included

The comprehensive resources in Amplify CKLA 3rd Edition support effective literacy instruction in every classroom.

Image of a laptop displaying an assessment report, surrounded by books about astronomy, an illustration of the moon, and a
Various educational materials, including textbooks, workbooks, a picture book, documents, and a laptop displaying a slide titled

Easy-to-use teacher materials

Amplify CKLA teachers are empowered to deliver effective instruction with the following print and digital resources:

  • Teacher Guides (K–5)
  • Assessment Guides (K–5)
  • Authentic texts and trade books (K–5)
  • Knowledge Image Cards (K–2)
  • Knowledge Flip Books (K–2, digital)
  • Ready-made and customizable Presentation Screens (K–5, digital)
  • Remediation and intervention resources (K–5)
  • On-demand professional development (K–5, digital)

Immersive Amplify CKLA student resources

Amplify CKLA students stay engaged with the following print and digital resources:

  • Decodable readers (K–2)
  • Student Readers and novels (3–5)
  • Student Activity Books (K–5)
  • Poet’s Journal and Writer’s Journal (3–5)
  • eReaders (K–5, digital)
  • Sound Library featuring articulation videos and songs (K–2, digital)
  • Assignable Practice Games (K–5)
An open laptop displaying a poem and a person, alongside two educational booklets and a green butterfly, depicts the essence of a rich core knowledge language arts curriculum. The background includes simple graphic elements enhancing the scene.
A collection of six book covers including

Rich literary experiences

All of the high-quality, diverse texts in Amplify CKLA connect to the curriculum, fostering your students’ curiosity and helping them learn to read with confidence.

  • Trade Book Collections (K–5) inspire student research in each grade’s Culminating Research Unit.
  • Classic and contemporary literature (3–5) delight students in Novel Study Units.
  • Increasingly complex Student Readers (K–5) develop students’ literacy across grades.

Hands-on phonics materials

Multisensory phonics and foundational skills resources engage students with fun, varied approaches that promote mastery and build independence.

  • Chaining Folders and Small Letter Cards (K)
  • Read-Aloud Big Books (K–1)
  • Large Letter Cards (K–2)
  • Sound Cards (K–2)
  • Image Cards (K–3)
  • Blending Picture Cards (K)
  • Consonant and Vowel Code Posters and Spelling Cards (1–2)
  • Sound Library (K–2, digital)
Image includes various vowel sounds and combinations on flashcards and worksheets, along with a playful illustrated mammal, all part of a comprehensive literacy curriculum for elementary students.

All-in-one digital platform

Our comprehensive platform simplifies your day-to-day tasks and makes it easier to plan and deliver lessons.

  • Ready-made and customizable Presentation Screens
  • Auto-scored digital assessments
  • Standards-based reporting
  • Assignable Practice Games
  • Sound Library
  • eReaders

Professional Development

Move beyond traditional program training with Amplify’s digital PD Library, designed to fully support your shift to the Science of Reading and Amplify CKLA. Deepen your understanding with:

  • Program and planning resources
  • Model lesson videos from real classrooms
  • Guidance on using Amplify’s literacy suite to provide multi-tiered support
Two women are seated at a table with papers and a laptop. One woman is working on the literacy curriculum for elementary grades, while the other is smiling.

Ready to continue your learning journey?

We also offer live, tailored professional learning sessions by expert partners to expand your Science of Reading expertise, strengthen implementation, and improve student outcomes.

“Teachers love the ease of implementing the program, and students have fun while learning. Growth is evident in our data, and we have the support of Amplify experts who are available to answer questions and provide top-notch professional development.”

Bridget Vaughan, District K–8 Coordinator of ELA and Literacy

Quincy Public Schools, Massachusetts

A circular flow chart titled

A true Science of Reading early literacy suite for Grades K–5

Amplify has combined the critical elements of a Science of Reading system: assessment, core curriculum, personalized learning, and intervention. Based on 20 years of experience with the Science of Reading, this complete system saves you time and aligns your literacy practices.

  • Assess with mCLASS®: A universal and dyslexia screener, powered by DIBELS 8th Edition
  • Instruct with Amplify CKLA: Core curriculum to build foundational skills and knowledge
  • Practice with Boost Reading™: Personalized learning program to extend and reinforce core
  • Intervene with mCLASS Intervention: Staff-led Tier 2 and 3 intervention for intensive support
“There were other programs that claimed to be [based on the] Science of Reading, but no other vendor provided the suite of products together. We did not want to be picking from here, picking from there. [Amplify’s literacy suite] met our needs, because it aligned and provided us the best suite of products, hands down.”

Nicole Peterson, Principal, Midway Middle School

Sampson County Schools, North Carolina

Language Studio: Multilingual and English language learner support

Language Studio is Amplify CKLA’s dedicated K–5 program for multilingual and English language learners. Through daily 30-minute lessons, it strengthens reading, writing, speaking, and listening skills while reinforcing core instruction. This tailored support empowers students to confidently access grade-level content as they develop academic English.

A young girl immerses herself in the science of reading at a classroom desk, surrounded by peers and diverse educational materials.

Explore more programs in Amplify’s literacy and biliteracy suite.

All of the programs in our literacy suite and our biliteracy suite are designed to support and complement each other. Learn more about our related programs:

The power of productive struggle in K–5 math

A cartoon pizza cut into slices with a serving spatula in the center, flanked by colorful shapes and a cartoon animal on the right—an engaging way to spark curiosity about procedural fluency and fluency in math.

Struggling is not necessarily fun. It can be uncomfortable and frustrating. It can even feel like a great reason to give up.

But struggling and learning often go hand in hand. The key is for that struggle to be productive—for it to feel like something you worked through until you were successful, providing the confidence you need to tackle the next hard task.

That’s especially true—and essential—in math learning.

The key is productive struggle: the kind of effort that stretches students’ thinking without shutting them down. When designed intentionally, math activities for elementary students can challenge learners while still supporting confidence, curiosity, and persistence.

Here’s more about how productive struggle helps math students succeed.

What is productive struggle?

Productive struggle refers to students grappling with challenging problems that are not immediately solvable, but still within reach. It’s the space where students test ideas, make mistakes, revise strategies, and slowly build understanding.

Research shows that productive struggle helps learners move beyond surface-level memorization and toward deeper, more durable learning.

Rather than being told exactly what to do, students are encouraged to reason, explain, and persevere.

This doesn’t mean leaving students to flounder. Productive struggle requires clear goals, thoughtful scaffolds, and meaningful tasks so students know what they’re working toward and believe they can get there.

The role of growth mindset in math learning

Productive struggle is closely tied to another key idea: growth mindset.

A growth mindset is the belief that ability comes not from innate, baked-in talent, but through effort, strategies, and learning from mistakes. In the math classroom, this mindset helps students see challenges not as threats, but as opportunities.

When teachers communicate high expectations and normalize mistakes as part of learning, students are more willing to take risks. They begin to stop saying, “I can’t do this math problem,” and start saying, “I’m not there yet.”

This shift matters, especially in elementary grades. Students who develop a growth mindset early may be better equipped to avoid math anxiety and to handle increasingly complex math concepts, because they’ve learned that struggle is not a sign of failure, but part of the process.

Why struggle feels risky—and why it’s worth it

Supporting productive struggle can feel risky for teachers. Classrooms are busy. Time is limited. And no one wants students to feel frustrated or discouraged.

But avoiding struggle altogether creates its own problems. When math activities are too procedural or overly scaffolded, students may complete tasks without truly understanding them. Over time, students may come to believe that math is about following steps rather than making sense of ideas.

By contrast, well-designed struggle builds investment. Students engage more deeply when they’re asked to think, explain, and choose strategies. They develop problem-solving skills, perseverance, confidence, and a stronger sense of ownership over their learning.

What productive struggle looks like in practice

In classrooms that support productive struggle, students are actively involved, even when tasks are challenging. You might hear students explaining their reasoning, comparing strategies, or revising their thinking after a mistake.

Effective math activities for elementary students include:

  • Multiple entry points so all learners can begin.
  • Opportunities for students to explain why their strategy works.
  • Support for more than one correct approach.
  • Clear expectations paired with flexible pathways.

Even in kindergarten math activities, productive struggle for the youngest learners might look like counting, sorting, or representing numbers in different ways, paired with questions that prompt reasoning rather than quick answers.

Students need tasks that are mathematically meaningful, paired with structures that help them persist: opportunities to talk, visual representations, strategic questioning, and time to reflect.

In this way, struggle builds math muscle. Productive struggle helps students feel on top of their math game—and ready to learn more.

The next chapter in the Science of Reading

Introducing Amplify CKLA 3rd Edition, a K–5 core literacy program within Amplify’s literacy suite. For more than a decade, Amplify CKLA has transformed classrooms nationwide with its intentional knowledge building and systematic skills instruction. Available for the 2025–2026 school year, the 3rd Edition builds on this successful foundation to better support all students in becoming confident readers, writers, and thinkers. Together, let’s write the next chapter in the Science of Reading.

An astronaut floats in space near the Moon, with a speech bubble displaying

Amplify CKLA serves

150,000+

Classrooms

4,000,000+

Students

50

U.S. States and D.C.

Our approach

Improve outcomes with a program built on a decade of research, and that meets the strongest ESSA Tier I criteria.

Diagram illustrating the Simple View of Reading model, depicting language comprehension and word recognition pathways converging into skilled reading, with processes becoming increasingly strategic and automatic—a foundational concept in literacy curriculum for elementary education.

Grounded in the Science of Reading

As the original Science of Reading program, Amplify CKLA puts research into action with explicit, systematic foundational skills instruction and a proven knowledge-building sequence. In collaboration with education experts and practitioners, we provide powerful resources that deliver real results.

Background knowledge drives results

Amplify CKLA follows the Core Knowledge Sequence, a content-specific, cumulative, and coherent approach to knowledge building. This approach improves reading scores and closes achievement gaps by establishing a robust knowledge base that strengthens comprehension.

In Amplify CKLA 3rd Edition, we’ve enriched our Knowledge Sequence with a wider range of perspectives and high-quality texts in new and enhanced units.

An infographic showing the steps to pronounce

Build foundational skills for long-term success.

Students progress from simple to complex skill development starting with phonological and phonemic awareness. Instruction in Grades K–2 explicitly teaches the 150 spellings for the 44 sounds of English, following an intentional progression to ensure student success.

In our 3rd Edition, we’ve added dedicated Grades 3–5 foundational skills instruction that can either support core lessons or function as an intervention, based on student needs.

Daily writing deepens learning.

Grounded in the Science of Writing—the research on how kids learn to write—instruction is explicit, daily, and woven into the curriculum’s rich content. It covers both transcription (handwriting and spelling) and composition (organizing ideas into narratives) with high-impact activities like sentence-level combining and expanding, and pre-writing exercises. Writing and reading instruction are integrated so students simultaneously strengthen their communication skills, comprehension, and confidence.

A child in a green shirt smiles while writing in a notebook at a classroom desk, engaged in their k–5 literacy curriculum, with another student visible in the background.
An open laptop displaying a children's story titled

High-quality, diverse texts

Amplify CKLA students are immersed in a variety of texts—complex read-alouds, decodable chapter books, trade books, and content-rich readers—that reflect varied experiences and connect to learning goals.

Readers are 100% decodable for Grades K–2, empowering students to directly apply what they’ve learned. Novel Study units for Grades 3–5 offer a mix of contemporary and classic literature, and Culminating Research Units in every grade include a set of authentic texts and trade books.

Reach all learners with differentiated support.

Scaffolds and challenges, developed in collaboration with education experts, make content available to every student—including multilingual and English learners. With strategies embedded right in the curriculum, teachers can deliver in-the-moment, individualized instruction to meet all student needs.

For a dedicated English language development program aligned to Amplify CKLA, explore Language Studio.

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What’s included

The comprehensive resources in Amplify CKLA 3rd Edition support effective literacy instruction in every classroom.

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Various educational materials, including textbooks, workbooks, a picture book, documents, and a laptop displaying a slide titled

Easy-to-use teacher materials

Amplify CKLA teachers are empowered to deliver effective instruction with the following print and digital resources:

  • Teacher Guides (K–5)
  • Assessment Guides (K–5)
  • Authentic texts and trade books (K–5)
  • Knowledge Image Cards (K–2)
  • Knowledge Flip Books (K–2, digital)
  • Ready-made and customizable Presentation Screens (K–5, digital)
  • Remediation and intervention resources (K–5)
  • On-demand professional development (K–5, digital)

Immersive Amplify CKLA student resources

Amplify CKLA students stay engaged with the following print and digital resources:

  • Decodable readers (K–2)
  • Student Readers and novels (3–5)
  • Student Activity Books (K–5)
  • Poet’s Journal and Writer’s Journal (3–5)
  • eReaders (K–5, digital)
  • Sound Library featuring articulation videos and songs (K–2, digital)
  • Assignable Practice Games (K–5)
An open laptop displaying a poem and a person, alongside two educational booklets and a green butterfly, depicts the essence of a rich core knowledge language arts curriculum. The background includes simple graphic elements enhancing the scene.
A collection of six book covers including

Rich literary experiences

All of the high-quality, diverse texts in Amplify CKLA connect to the curriculum, fostering your students’ curiosity and helping them learn to read with confidence.

  • Trade Book Collections (K–5) inspire student research in each grade’s Culminating Research Unit.
  • Classic and contemporary literature (3–5) delight students in Novel Study Units.
  • Increasingly complex Student Readers (K–5) develop students’ literacy across grades.

Hands-on phonics materials

Multisensory phonics and foundational skills resources engage students with fun, varied approaches that promote mastery and build independence.

  • Chaining Folders and Small Letter Cards (K)
  • Read-Aloud Big Books (K–1)
  • Large Letter Cards (K–2)
  • Sound Cards (K–2)
  • Image Cards (K–3)
  • Blending Picture Cards (K)
  • Consonant and Vowel Code Posters and Spelling Cards (1–2)
  • Sound Library (K–2, digital)
Image includes various vowel sounds and combinations on flashcards and worksheets, along with a playful illustrated mammal, all part of a comprehensive literacy curriculum for elementary students.

All-in-one digital platform

Our comprehensive platform simplifies your day-to-day tasks and makes it easier to plan and deliver lessons.

  • Ready-made and customizable Presentation Screens
  • Auto-scored digital assessments
  • Standards-based reporting
  • Assignable Practice Games
  • Sound Library
  • eReaders

Professional Development

Move beyond traditional program training with Amplify’s digital PD Library, designed to fully support your shift to the Science of Reading and Amplify CKLA. Deepen your understanding with:

  • Program and planning resources
  • Model lesson videos from real classrooms
  • Guidance on using Amplify’s literacy suite to provide multi-tiered support
Two women are seated at a table with papers and a laptop. One woman is working on the literacy curriculum for elementary grades, while the other is smiling.
“Teachers love the ease of implementing the program, and students have fun while learning. Growth is evident in our data, and we have the support of Amplify experts who are available to answer questions and provide top-notch professional development.”

Bridget Vaughan, District K–8 Coordinator of ELA and Literacy

Quincy Public Schools, Massachusetts

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A true Science of Reading early literacy suite for Grades K–5

Amplify has combined the critical elements of a Science of Reading system: assessment, core curriculum, personalized learning, and intervention. Based on 20 years of experience with the Science of Reading, this complete system saves you time and aligns your literacy practices.

  • Assess with mCLASS®: A universal and dyslexia screener, powered by DIBELS 8th Edition
  • Instruct with Amplify CKLA: Core curriculum to build foundational skills and knowledge
  • Practice with Boost Reading™: Personalized learning program to extend and reinforce core
  • Intervene with mCLASS Intervention: Staff-led Tier 2 and 3 intervention for intensive support
“There were other programs that claimed to be [based on the] Science of Reading, but no other vendor provided the suite of products together. We did not want to be picking from here, picking from there. [Amplify’s literacy suite] met our needs, because it aligned and provided us the best suite of products, hands down.”

Nicole Peterson, Principal, Midway Middle School

Sampson County Schools, North Carolina

Language Studio: Multilingual and English language learner support

Language Studio is Amplify CKLA’s dedicated K–5 program for multilingual and English language learners. Through daily 30-minute lessons, it strengthens reading, writing, speaking, and listening skills while reinforcing core instruction. This tailored support empowers students to confidently access grade-level content as they develop academic English.

A young girl immerses herself in the science of reading at a classroom desk, surrounded by peers and diverse educational materials.

Explore more programs in Amplify’s literacy and biliteracy suite.

All of the programs in our literacy suite and our biliteracy suite are designed to support and complement each other. Learn more about our related programs:

Math that motivates your K–5 students

As a K–5 teacher, your day is a constant balance of subjects, personalities, and priorities. With so many different dynamics and responsibilities, math class shouldn’t be another struggle to muscle through!

That’s why we’ve compiled a wealth of resources and activities to help you engage students; meet instructional goals; and encourage fluency, number sense, and discussion in your classroom. 

Three children paint the walls of a room; one holds a paper with the fraction 2/3, while math symbols and a tree appear in the background.
A booklet titled "The Power of Fluency: Cultivating Flexible, Confident Problem-Solvers" with an illustrated cover and an open page showing text and graphics about classroom fluency.

The power of fluency

Teachers work to achieve so many outcomes during their math block. While balancing multiple priorities, it’s important to remember that procedural fluency remains integral to student learning. Access this guide to unpack the power of fluency and find free math fluency practice to use in your next lesson.

10 low-prep, high-impact math activities that get to some serious math

Envision your classroom engaged in a difficult math task—all students are participating, leveraging different scaffolds that you intentionally prepared ahead of time. Engagement is high, and students are both challenged and motivated. Make this a reality in your school with our free activities designed to encourage productive struggle while reaching all learners.

A teacher holds a clipboard while a student points at a chalkboard labeled "Guinea Pig," "Millipede," and "Goldfish" in a classroom setting.
A presentation slide titled "Three Practices to Support Problem-Based Learning" features students and teachers engaged in classroom activities and math instruction.

Three practices to support problem-based learning

As educators, we want all students to develop a rich and deep understanding of the math they experience in our classrooms. A problem-based learning approach supports this by centering problem-solving in ways that build lifelong mathematical proficiency. Read this guide for practical tips on introducing problem-based learning and deeper conceptual understanding into your math classroom.

Best practices from real educators like you

Learn tried and true strategies for leveling up math instruction from Beyond My Years podcast guests like Amplify’s own Dan Meyer, teacher and My Kindergarten Math Workbook author Keri Brown, educator and speaker Mike Flynn, teacher and I Hate Math author Ian Brown, and more!

More free resources for K–5 educators

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K–5 Insider

Sign up for our monthly email to get new K–5 content and activities directly in your inbox.

sign up 

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K–5 instructional routine cards

Find easy-to-implement routines to keep students interacting and engaged with a lesson.

Download

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Math that motivates: Success stories

See how real teachers and students are unlocking new levels of engagement and comprehension, proving that everyone can be a math person.

LEARN MORE 

Ready to make every student a math person?

Connect with a product expert today.

FAQ for K–5 educators

Procedural fluency is the ability to use procedures flexibly, accurately, and efficiently to solve problems. Procedural fluency goes beyond memorization—students develop fluency when they understand number relationships and can choose from multiple strategies based on the numbers involved.

Students who understand why procedures work feel confident tackling challenging problems. When students can choose strategies that make sense to them, rather than relying on rote memorization, they develop agency and see themselves as capable mathematical thinkers.

Understanding how numbers connect helps students develop flexible thinking and multiple solution strategies. Timed tests often prioritize speed over understanding, which can create math anxiety and discourage the productive struggle that deepens learning.

Teachers can achieve this balance by using a predictable routine: warm-ups for fluency practice, a core problem-solving activity during which students explore multiple strategies, and structured discussion to connect different approaches. This structure ensures both skill-building and mathematical discourse happen daily.

Synthesizing learning means bringing the lesson together by highlighting the key mathematical idea that students have just explored. After students share strategies, the teacher helps them make connections between different approaches and names the big takeaway, often through a brief summary or exit ticket.

The Five Practices for Orchestrating Productive Mathematical Discussions are: 1) Anticipating student strategies before the lesson, 2) monitoring student work during the activity, 3) selecting specific students to share, 4) sequencing presentations in a purposeful order, and 5) connecting different strategies to the mathematical goal.

Productive struggle is when students grapple with challenging problems that require genuine thinking, but that remain accessible with appropriate support. It’s essential for deeper understanding, because it compels students to think critically, test strategies, and build perseverance, moving beyond surface-level memorization.

They can celebrate mistakes as learning opportunities and emphasize that understanding develops through effort and persistence. They can also create a safe classroom environment in which all students feel comfortable sharing their developing ideas and foster structured discussions during which multiple strategies are valued, helping students see that there’s more than one right way to think mathematically.

These are problems accessible to all students (that’s the low floor) but open enough to challenge advanced thinkers (that’s the high ceiling). Tasks like these allow multiple entry points and solution strategies, making them ideal for generating rich classroom discussion in which every student can participate meaningfully.

Such routines build number sense and fluency while making discussions predictable and low stakes. These brief, structured activities (5–10 minutes) activate prior knowledge, help students see number relationships, and give everyone practice explaining their thinking—all without requiring extensive preparation or materials.

They can do so by maintaining meaningful objectives while providing varied supports—ensuring that students understand what’s being asked, offering manipulatives and visual tools, allowing partner discussion before whole-class sharing, asking guiding questions without giving away the answer, and strategically grouping students. The goal is supporting access to challenging work, not making it easier.

Powerful, personalized reading instruction that engages students and saves teachers time

Boost Reading is our personalized reading program for grades K–5. Its captivating storylines engage students in powerful reading instruction and practice. Whether students are learning to read fluently or sharpening their comprehension skills, Boost Reading accelerates their growth while freeing educators up to work with small groups or individual students.

We’ve aligned Boost Reading to the Arkansas English Language Arts standards: Boost Reading Skill Games and Texts: Alignment to Arkansas English Language Arts Standards

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Science of Reading-based support for every student

Students come to school with a range of abilities and achieve mastery at different rates. Providing each learner with the specific support they need to progress can be challenging. Enter Boost Reading’s personalized reading literacy program.

“Your team has taken a weight off my shoulders and I am so grateful and can’t thank you enough! My biggest concern during this time was how can I keep pushing my readers at their level—and giving them what they need—and Boost Reading solved that.”

Jeanine

2nd-grade teacher, Chicago, IL

“This program is extremely engaging and interactive for each student. They begged to get on Boost Reading and they cried when it was time to log off! This program is a great addition to our curriculum.”

Brittany

2nd grade teacher, Utah

“My students love the program, and they don’t even realize they are learning some tough concepts. Their reading scores are improving even since the beginning of the year.”

Amber

Junior High ELA teacher, California

Our approach

Leveraging compelling storytelling and the latest research, Boost Reading helps students achieve true mastery of the concepts they need to become strong, life long readers. See the research behind the program.

More than a digital worksheet

Built on the Science of Reading, Boost Reading offers a fresh, modern program that builds on student strengths while adapting to their needs.

Boost Reading - reading curriculum how it works image
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A program students love

Boost Reading offers an out-of-this world learning experience for students. The program’s age-appropriate narratives create a learning experience that leaps off the screen.

The right experience for every student

The program meets all students where they are with powerful individualized instruction and practice, enabling student growth at all reading levels.

Teacher assisting young students with an online reading program using laptops and headphones in a classroom.
An infographic showing that 31% of students were on track in reading before the mCLASS with Boost Reading program, which increased to 48% after, highlighting an improvement in reading skills.

Proven results

Boost Reading works. Efficacy studies show significant growth for students using Boost Reading. In as little as 30 minutes a week, Boost Reading accelerates growth for all students and helps multilingual learners close the gap with their peers. Learn more here.

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Comprehension processes: The missing link in reading comprehension

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Program highlights

Illustration showing a phonics lesson progression in a K–5 literacy resource: starting with vc, cvc words and blends, moving to early decoding with listed letters. Each step connected by arrows in

Full adaptivity

Students of Boost Reading use digital texts that adapt to their needs via an adaptive algorithm that unlocks each book at the exact right point in a reader’s development.

Personalized instruction

Boost Reading adapts to each reader’s unique needs across 13 skill areas, sending students on their own personalized reading journey. The programs offer both remediation and enrichment through a comprehensive range of instruction—from foundational skills to comprehension to close reading.

Two young girls, smiling and looking at a tablet together in a colorful classroom, engaged in an online reading program.
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Engagement engineering

Using the science behind engagement and motivation, Boost Reading is built to deliver compelling narrative experiences that speak to students’ stories of growth and development. This personal connection allows students to directly map their progress in the storyline to their reading effort and growth, helping them understand the value of effort and practice.

Based on the Science of Reading

Boost Reading is built on the latest research in the Science of Reading. It provides the explicit, systematic foundational skills essential for every student—and it goes beyond. It’s the only program that focuses on the things our brain does while we’re reading that allow us to make sense of text—also known as comprehension processes. Learn more about comprehension processes on Science of Reading: The Podcast.

Diagram illustrating the Science of Reading, depicting components of skilled reading in a flowchart. This connects language, vocabulary, sentences, reasoning, and mental model with increasingly automated word, sound, and letter processing
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Instruction based on student data

Boost Reading features an automatic placement tool that requires no prior assessment. The program is able to pinpoint the most effective starting point for each student and provide them an engaging reading program personalized for their exact individual needs. The program also integrates directly with Amplify’s mCLASS® with DIBELS® 8th Edition assessment as well as other third party assessments.

Reports at every level

Boost Reading provides actionable insights into students’ reading development across 13 literacy skill domains. The program creates reports for classroom teachers, literacy specialists, principals and district leaders, and even parents and caregivers at home.

Screenshot of an online reading program dashboard, showing student reading metrics and instructional recommendations.

Explore more Science of Reading-based programs.

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

Achieve next-level literacy growth with a cohesive Science of Reading suite.

The Science of Reading programs in Amplify’s early literacy suite empower you to meet the dynamic needs of every student learning to read. Discover the programs that best fit your literacy priorities and how they work together for a seamless teaching and learning environment.

“There were other programs that claimed to be Science of Reading, but no other vendor provided the suite of products together. So from our perspective, [Amplify’s literacy suite] met our needs because it aligned and provided us the best suite of products. Hands down. We couldn’t find anybody else who touched that.”

Nicole Peterson, Director, PreK–8 Education

Sampson County Schools, North Carolina

A true Science of Reading early literacy suite for grades K–5

Amplify has combined the critical elements of a Science of Reading system of assessment, core curriculum, personalized learning, and intervention. Based on 20 years of experience with the Science of Reading, this complete system saves you time and aligns your literacy practices.

  • Assess with mCLASS®: A universal and dyslexia screener, powered by DIBELS® 8th Edition
  • Instruct with Amplify Core Knowledge Language Arts (CKLA)®: Core curriculum to build foundational skills and knowledge
  • Support with Boost Reading: Student-led digital intervention to extend and reinforce core instruction
  • Intervene with mCLASS Intervention: Staff-led Tier 2 and 3 intervention for intensive support
  • Science of Reading professional development: Amplify training, events, and podcasts to strengthen instruction

mCLASS assessment

Powered by DIBELS 8th Edition, mCLASS is a universal and dyslexia screener, plus a progress monitoring tool, all in one. With this comprehensive tool, you have precise one-minute measures delivered one-on-one that give you the data you can trust to make informed instructional decisions.

Amplify CKLA core curriculum

mCLASS data informs instructional needs and identifies whole-class and small-group areas of focus.

mCLASS can replace Amplify CKLA’s benchmark assessments in K–2 and can identify appropriate Amplify CKLA instruction for small groups.

Boost Reading digital intervention

Boost Reading and mCLASS integrate to provide adaptive, student-led practice in targeted skill areas. 

mCLASS data automatically places students at the appropriate Boost Reading starting point.

You can track student progress with side-by-side mCLASS and Boost Reading growth data.

mCLASS Intervention

mCLASS assessment identifies risk early on and places students in and out of mCLASS Intervention groups.

mCLASS progress monitoring data creates intervention groups and daily lesson plans for 10-day cycles.

Amplify CKLA core curriculum

Amplify Core Knowledge Language Arts (CKLA) provides explicit, systematic foundational skills instruction combined with intentional knowledge building. Rich content spans topics in history, science, literature, and the arts to build deep background knowledge.

mCLASS assessment

Amplify CKLA instructs in the same critical literacy skills measured by mCLASS, aligning your assessment and core curriculum.

mCLASS can replace Amplify CKLA’s benchmark assessments in K–2 and can identify appropriate Amplify CKLA instruction for small groups.

Boost Reading digital intervention

Boost Reading reinforces skills through a shared scope and sequence with Amplify CKLA.

Instruction adjusts, providing differentiated skill development where needed and advancing students to the next level.

Dynamic growth reporting offers insight into how Amplify CKLA skills are developing over time.

mCLASS Intervention

mCLASS Intervention allows you to support Tier 1 instruction to get at-risk readers on track.

mCLASS Intervention lesson plans extend skills learned in Amplify CKLA curriculum.

Phonological awareness and phonics focus complements Amplify CKLA’s Skills Strand.

Boost Reading digital intervention

Boost Reading is a digital intervention program that adapts to every learner, reinforcing core instruction while providing support for remediation and intervention. The program delivers differentiated, student-led practice and clear growth reporting data, helping you understand how students are progressing at a glance.

mCLASS assessment

Boost Reading and mCLASS integrate to provide adaptive, student-led practice in targeted skill areas.

mCLASS data automatically places students at the appropriate Boost Reading starting point.

You can track student progress with side-by-side mCLASS and Boost Reading growth data.

Amplify CKLA core curriculum

Boost Reading reinforces skills through a shared scope and sequence with Amplify CKLA.

Instruction adjusts, providing differentiated skill development where needed and advancing students to the next level.

Advanced growth reporting offers insight into how Amplify CKLA skills are developing over time.

mCLASS Intervention

Boost Reading and mCLASS Intervention provide a complete system for intervention support.

Use mCLASS Intervention for staff-led small groups and Boost Reading for student-led digital intervention.

Together, they provide continuous intervention support across all tiers.

mCLASS Intervention

mCLASS Intervention is a Tier 2 and 3 targeted, staff-led intervention program made easy with automatic data-driven grouping and sequenced explicit, systematic skills lesson plans to support at-risk students.

mCLASS assessment

mCLASS assessment identifies risk early on and places students in and out of mCLASS intervention groups.

mCLASS benchmark and progress monitoring data creates groups and daily lesson plans for 10-day cycles.

Amplify CKLA core curriculum

mCLASS Intervention allows you to support Tier 1 instruction to get at-risk readers on track.

mCLASS Intervention lesson plans extend skills learned in Amplify CKLA instruction.

Phonological awareness and phonics focus complements Amplify CKLA’s Skills Strand.

Boost Reading digital intervention

Boost Reading and mCLASS Intervention provide a complete system for intervention support.

Use mCLASS Intervention for staff-led small groups and Boost Reading for student-led digital intervention.

Together, they provide continuous intervention support across all tiers.

A 20% boost in literacy rates:

Our Science of Reading programs are helping Aldine Independent School District in Texas rewrite its literacy narrative.

Read more

The cohesive early literacy system teachers and students deserve

Support your MTSS and RTI models

A strong Multi-Tiered System of Supports (MTSS) enables you to make data-based decisions and confidently meet every student’s needs. Our integrated early literacy suite includes universal and dyslexia screening, core curriculum, personalized learning, intervention, and ongoing professional development.

Each program in the suite is directly aligned to the Response to Intervention (RTI) model of tiered instruction.

Aligned resources that do away with piecemealing

A literacy ecosystem built on the same Science of Reading principles and pedagogical foundation ensures that students experience a cohesive and reinforced literacy journey. Our programs allow you to support all students without cobbling together additional resources to fill in the gaps.

They follow an explicit and systematic structure, build knowledge, and assess and instruct on all of the foundational skills essential to literacy development.

The data you need to make informed decisions

Our universal and dyslexia screening data is predictive and reliable, and it’s aligned to the entire instructional system. It enables you to make informed decisions for whole-group, small-group, and individual instruction, as well as resource allocation at the school and district level.

Amplify’s early literacy programs support you wherever you are in the Science of Reading journey. Download our Science of Reading roadmap to help you determine where to start.

Download now

Our early literacy programs in action

Case study: Aldine Independent School District, Texas

Implementing Amplify CKLA core curriculum, Boost Reading personalized learning, and mCLASS assessment boosted reading proficiency from 30% to 50%

Read more

Case study: Allen Parish School District, Louisiana

After just one year of integrating mCLASS assessment and Amplify CKLA core curriculum, Grade 1 student reading proficiency rose from 58% to 80% across eleven Title 1 schools

Read more

Case study: West Jefferson Hills School District, Pennsylvania

Students reached the 98th percentile among their peers nationwide after implementing Amplify CKLA core curriculum, Boost Reading personalized learning, and mCLASS assessment. The shift not only inspired students in their literacy journey, but also made teachers feel more confident in teaching literacy.

Read more

Science of Reading resources

Successfully adopting new Science of Reading literacy programs will change lives. We provide extensive resources, professional learning, and complementary events and webinars so you can begin using your new programs with fidelity.

Science of Reading essentials

Champion research-based literacy programs in your classroom with our extensive Science of Reading resources.

Science of Writing: A Primer

Unlock writing mastery! Explore our new primer on literacy research and the Science of Writing.

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Cultivate lifelong learning

Gain useful knowledge with our top-rated podcast.

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Staff development services

Invest in a professional development plan.

“[We wanted] something that moved kids beyond the traditional low-level type of thinking about literacy, reading, and engaging with text. The choice of Amplify became clear for our district. The tremendous professional support from Amplify, matched with the commitment of our people. We’re finally seeing something different, and the results are encouraging.”

Matthew Patterson, Ph.D., Assistant Superintendent

West Jefferson Hills School District , Pennsylvania

Passion for reading in Sampson County, NC

Mia and Grade 2 teacher Jenny Denning explored the power of the Amplify early literacy suite together.

Inspiring confidence in Tennessee

Kaleb and Assistant Principal Casey Price tackled reading from the ground up with Amplify’s early literacy programs.

Welcome to Amplify Science 6–8!

Amplify Science is an engaging core curriculum designed for three-dimensional, phenomena-based learning.

With Amplify Science, Oregon students don’t just passively learn about science concepts. Instead, they take on the role of scientists and engineers to actively investigate and figure out real-world phenomena. They do this through a blend of cohesive and compelling storylines, hands-on investigations, collaborative discussions, literacy-rich activities, and interactive digital tools.

Two students, one black and one asian, smiling and studying together at a laptop in a classroom with other students in background.

Publisher presentation

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Aerial view of the lawrence hall of science at the university of california, berkeley, showcasing the building and surrounding trees with a foggy city backdrop.

Proven to work

A pdf cover from wested titled "learning and literacy development together: initial results from a curriculum study," featuring an adult helping children with schoolwork in a classroom.

WestEd Randomized
Control Trial for Grade 1

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Pdf cover titled "curriculum materials designed for the next generation science standards: initial results from gold standard research trials", published by wested.

WestEd Randomized
Control Trial for Grade 7

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Amplify Science NE
Grades K–5

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Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers
do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS, and support students in mastering the Oregon Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Assorted office and household items displayed on a white background, including rubber bands, binder clips, cardboard, and sports balls.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Amplify Science Classroom Slides

Full coverage of the Oregon Science Standards

Amplify Science was designed from the ground up to meet the Next Generation Science Standards (NGSS). As such, it aligns to the Oregon Science Standards, which were also borne out of the NGSS.

The guidance below is meant to provide support for integrating additional activities that support full coverage of Oregon’s standards. Organized by grade level, each section below will outline:

  • Additional activities that support 100% alignment to the Oregon Science Standards.
  • The standard being addressed with the activities.
  • The recommended placement of the activities within a specific Amplify Science unit.
  • PDFs of any accompanying materials that are necessary to implement the activities.

Activity Title: Meet a Scientist Who Changed How We Think About Brain Cells

About this activity: In this activity, students read a short article about a scientist who studied the nervous system.

Recommended placement: Metabolism unit, Lesson 3.2

Materials:

Instructions: Download the PDF “Meet a Scientist Who Changed How We Think About Brain Cells” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies Underwater Currents

About this activity: In this activity, students read a short article about a scientist who studies ocean currents.

Recommended placement: Oceans, Atmosphere, and Climate unit, Lesson 2.1

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies Underwater Currents” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies How the Environment Affects Our Traits

About this activity: In this activity, students read two short articles, one about current research on genes and proteins, and one about a scientist who is studying how the environment can affect our traits.

Recommended placement: Traits and Reproduction unit, Lesson 2.4

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies How the Environment Affects Our Traits” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Who Becomes a Space Scientist?

About this activity: In this activity, Students read a short article about a scientist who studies space.

Recommended placement: Geology on Mars unit, Lesson 3.1

Materials:

Instructions: Download the PDF “Who Becomes a Space Scientist?” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies How Plants Find Water Underground

About this activity: In this activity, students read a short article about a scientist who studies how plants’ roots get water.

Recommended placement: Matter and Energy in Ecosystems unit, Lesson 1.6

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies How Plants Find Water Underground” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Bringing Back the Buffalo

About this activity: In this activity, students change one competing population to try to decrease the other in the Sim, and read a short article about a scientist who studies buffalo.

Recommended placement: Populations and Resources unit, Lesson 3.2

Materials:

Instructions: Download the PDF “Bringing Back the Buffalo” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Rereading “A Continental Puzzle”

About this activity: In this activity, students reread “A Continental Puzzle” and think about how patterns were helpful to Wegener’s work.

Recommended placement: Plate Motion unit, Lesson 3.2

Materials:

Instructions: Direct students back to “A Continental Puzzle” above and remind students of the Active Reading guidelines. Before students re-read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies Variation in Monkey Populations

About this activity: In this activity, students read a short article about a scientist who studies variation of traits in monkey populations.

Recommended placement: Natural Selection unit, Lesson 1.6

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies Variation in Monkey Populations” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Extinctions and Human Impacts

About this activity: The purpose of this lesson is for students to see how increases in human population and consumption of natural resources can negatively impact Earth’s systems.

Recommended placement: Natural Selection unit, Lesson 4.5

Materials:

Instructions: Download the PDF “Extinctions and Human Impacts” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Steno and the Shark

About this activity: In this activity, students read a short article about Nicolas Steno, a scientist from the 1600s whose studies of fossilized sharks’ teeth embedded in rock layers laid the foundation for the modern understanding of stratigraphy.

Recommended placement: Evolutionary History unit, Lesson 2.4

Materials:

Instructions: Download the PDF “Steno and the Shark” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Scale in the Solar System

About this activity: In this activity, students read and annotate the articles “Scale in the Solar System” and “The Solar System Is Huge.”

Recommended placement: Earth, Moon, and Sun unit, Lesson 1.2

Materials:

Instructions: Download the PDF “Scale in the Solar System” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free TG!

Three laptop screens displaying educational content on earth's energy system, including diagrams and text annotations.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

At your request, we did not include our materials kits with our submissions samples. However, we did provide grade-specific lists of all materials included in each kit, which you can also find with the links below.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t.or68sci@tryamplify.net
  • Enter the password: Science5OR
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: s.or68sci@tryamplify.net
  • Enter the password: Science5OR
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

Resources to support your review

New Mexico Educators: Welcome to Amplify Science 6–8!

Amplify Science is an engaging core curriculum designed for three-dimensional, phenomena-based learning that is rated ‘all green’ on EdReports.  

With Amplify Science, New Mexico students don’t just passively learn about science concepts. Instead, they take on the role of scientists and engineers to actively investigate and figure out real-world phenomena. They do this through a blend of cohesive and compelling storylines, hands-on investigations, collaborative discussions, literacy-rich activities, and interactive digital tools.

Students conduct science experiments using lab equipment, flashlights, and prisms. The EdReports logo and "Review Year 2020" are also shown.

Amplify Science Success Story

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Aerial view of the lawrence hall of science at the university of california, berkeley, showcasing the building and surrounding trees with a foggy city backdrop.

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS and support students in mastering the New Mexico STEM Ready! Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3-D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

Amplify Science Flextension

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Middle School Materials Kit List 

Assorted office and household items displayed on a white background, including rubber bands, binder clips, cardboard, and sports balls.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Amplify Science Student Investigation Notebooks

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Amplify Science Classroom Slides

Full coverage of NGSS and New Mexico STEM Ready! Science Standards

Amplify Science was designed from the ground up to meet the Next Generation Science Standards (NGSS). As such, it aligns to the New Mexico Science Standards, which were also borne out of the NGSS.

K-8 NGSS Correlation by Dimension

K-8 NM STEM Ready! Standards Correlation

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free Teacher Guide!

A laptop screen displays a simulation of energy arrows entering and exiting Earth's system, flanked by diagrams explaining water flow and an energy token model.
  • Teacher Reference Guide: Unlike a typical Teacher Guide that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

Materials Kit List

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t20.sci6-8@tryamplify.net
  • Enter the password: AmplifyNumber1
  • Click on Science in Your Programs
  • Click on the Program drop-down menu and select your desired domain
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: s20.sci6-8@tryamplify.net
  • Enter the password: AmplifyNumber1
  • Click Science in Your Programs
  • Click on the Program drop-down menu and select your desired domain
  • Select any unit title.

Additional resources to support your review

Welcome to Amplify Science 6–8!

Amplify Science is an engaging core curriculum designed for three-dimensional, phenomena-based learning.

With Amplify Science, Detroit students don’t just passively learn about science concepts. Instead, they take on the role of scientists and engineers to actively investigate and figure out real-world phenomena. They do this through a blend of cohesive and compelling storylines, hands-on investigations, collaborative discussions, literacy-rich activities, and interactive digital tools.

What is Amplify Science?

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true three-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.

Proven to work

WestEd Randomized
Control Trial for Grade 1

Read More

WestEd Randomized
Control Trial for Grade 7

Read More

Amplify Science NE
Grades K–5

Read More

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers
do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the Next Generation Science Standards (NGSS) and support students in mastering the Pennsylvania Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock-full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Assorted office and household items displayed on a white background, including rubber bands, binder clips, cardboard, and sports balls.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Amplify Science Classroom Slides

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free TG!

Three laptop screens displaying educational content on earth's energy system, including diagrams and text annotations.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

At your request, we did not include our materials kits with our submissions samples. However, we did provide grade-specific lists of all materials included in each kit, which you can also find with the links below.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t1.dps68sci@demo.tryamplify.net
  • Enter the password: Amplify1-dps68sci
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Spanish-language support

Amplify Science is committed to providing support to meet the needs of all learners, including multiple access points for Spanish-speaking students. Developed in conjunction with Spanish-language experts and classroom teachers, several components are available in Spanish across the Amplify Science curriculum.

Spanish-language materials include:

COMPONENTTEACHER/STUDENT
Student Investigation NotebooksStudent
Science articlesStudent
Video TranscriptsStudent
Digital simulation translation keysStudent
Printed classroom materials
Unit and chapter questions, key concepts, vocabulary cards, etc.
Teacher
CopymastersTeacher
AssessmentsTeacher
Digital student experience license
This license gives students access to the student resources in Spanish, including instructional text, articles, and assessments. Teachers can control student access to Spanish-language content through the digital Teacher’s Guide.
Teacher
Spanish teacher support license
This license includes teacher talk, projections, downloadable PDFs of all print resources, and video transcripts and closed captioning in Spanish.
Teacher

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: s1.dpsscience@demo.tryamplify.net
  • Enter the password: Amplify1-dpsscience
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

Resources to support your review

What’s New for Amplify Science 6–8!

Denver Public Schools (DPS), check out what’s new from Amplify Science 6-8!  The first part of this site will take you through the updates that have been made to Amplify Science. The second will be a refresher of Amplify Science for any new users in DPS. With Amplify Science, DPS students don’t just passively learn about science concepts. Instead, they take on the role of scientists and engineers to actively investigate and figure out real-world phenomena. With culturally sustaining pedagogy, Amplify Science strives to make sure every student feels included in the science classroom.

Two students collaborating on a project using a laptop in a classroom filled with other students working in the background.

Update: The Digital Experience

The digital experience allows students to engage with digital lessons and provides teachers with everything they need in one place—ready-to-use slides-based lessons, seamlessly integrated teacher prompts and guidance, robust PD resources, and more. It’s now easier and more engaging than ever to plan lessons, present digital content, and review student work. To learn more, click here.

Update: The PD Library

All professional development (PD) content is consolidated into the PD Library, a one-stop hub for all your self-paced PD needs. As a result, the “Professional Learning Resources” tile will no longer be available on the main Amplify Science Program Hub page. The rest of the non-PD content in the Program Hub will remain as is, including the on-demand resources.

Update: Educator & Student Home expansion

Educator and Student Home landing pages will now be available for all Amplify Science users. This Home page provides a central location to access all Amplify programs in one place and a customized stream based on your activity.

Your Amplify Science grades 6–8 students will no longer access My Work for assignments, scores, and teacher feedback. Instead, they’ll find it all on Student Home, the page they already land on when logging in to Amplify Science.

Keep in mind: Amplify Science middle school teachers will continue to have access to Classwork.

Update: Caregiver Hub

Throughout the school year, teachers can share the Amplify Science Caregiver Hub with students’ families. This site provides curriculum details, an overview of what caregivers can expect throughout the school year, and resources they can use with students at home.

What is Amplify Science?

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true three-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Aerial view of the lawrence hall of science at the university of california, berkeley, showcasing the building and surrounding trees with a foggy city backdrop.

Proven to work

WestEd Randomized
Control Trial for Grade 1

Read More

WestEd Randomized
Control Trial for Grade 7

Read More

Amplify Science NE
Grades K–5

Read More

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers
do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the Next Generation Science Standards (NGSS) and support students in mastering the Pennsylvania Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

DPS Scope and Sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Un gráfico que muestra los cursos de ciencias para los grados 6 a 8. Cada grado tiene una lista de clases categorizadas como Launch, GROW y GOAT, con el título de cada curso y la duración en minutos o días.

Program components

Available digitally and in print, our unit-specific reference guides are chock-full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Assorted office and household items displayed on a white background, including rubber bands, binder clips, cardboard, and sports balls.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Amplify Science Classroom Slides

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides, Student Investigation Notebooks, and sets of Student Books for each grade level.

A note about the Teacher Reference Guides:

It’s important that you see the full breadth and depth of our instruction. For that reason, we provide a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free Teacher’s Guide!

Three laptop screens displaying educational content on earth's energy system, including diagrams and text annotations.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

At your request, we did not include our materials kits with our submissions samples. However, we did provide grade-specific lists of all materials included in each kit, which you can also find with the links below.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t1.dps68sci@demo.tryamplify.net
  • Enter the password: Amplify1-dps68sci
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Spanish-language support

Amplify Science is committed to providing support to meet the needs of all learners, including multiple access points for Spanish-speaking students. Developed in conjunction with Spanish-language experts and classroom teachers, several components are available in Spanish across the Amplify Science curriculum.

Spanish-language materials include:

COMPONENTTEACHER/STUDENT
Student Investigation NotebooksStudent
Science articlesStudent
Video TranscriptsStudent
Digital simulation translation keysStudent
Printed classroom materials
Unit and chapter questions, key concepts, vocabulary cards, etc.
Teacher
CopymastersTeacher
AssessmentsTeacher
Digital student experience license
This license gives students access to the student resources in Spanish, including instructional text, articles, and assessments. Teachers can control student access to Spanish-language content through the digital Teacher’s Guide.
Teacher
Spanish teacher support license
This license includes teacher talk, projections, downloadable PDFs of all print resources, and video transcripts and closed captioning in Spanish.
Teacher

Resources to support your review

Contact Us

If you have any further questions as your review Amplify Science, please contact:

Senior Account Executive

719-964-4501

mlammers@amplify.com

Welcome to Amplify Science Pennsylvania
(6–8)!

Amplify Science is an engaging core curriculum designed for three-dimensional, phenomena-based learning.

With Amplify Science, Pennsylvania students shift from learning about to figuring out science, through authentic three-dimensional (3D) learning and phenomena-based exploration. In each unit, students take on the role of a scientist or engineer to investigate a real-world problem. This prepares them to become critical thinkers who can solve problems in their communities and beyond.

Two students sit at a classroom table, smiling and working together on a laptop and worksheet, guided by Pennsylvania teachers, with other students in the background.

What is Amplify Science Pennsylvania?

Customized lessons for Pennsylvania

Amplify Science Pennsylvania (6–8) combines our nationally recognized, proven curriculum with custom lessons specifically designed to ensure that you are meeting Pennsylvania’s STEELS standards.

A digital dashboard displays six science lesson tiles, featuring "Designing for Energy Sustainability" in the lower right corner, and supports three-dimensional learning inspired by Amplify Science and PA STEELS standards.

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach, in which students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true three-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Aerial view of the lawrence hall of science at the university of california, berkeley, showcasing the building and surrounding trees with a foggy city backdrop.

Proven to work

A pdf cover from wested titled "learning and literacy development together: initial results from a curriculum study," featuring an adult helping children with schoolwork in a classroom.

WestEd Randomized
Control Trial for Grade 1

Read More

Pdf cover titled "curriculum materials designed for the next generation science standards: initial results from gold standard research trials", published by wested.

WestEd Randomized
Control Trial for Grade 7

Read More

A teacher and students engage in a science activity around a table. The text promotes the Amplify Science K–8 curriculum, highlighting its focus on hands-on learning and real-world problem-solving.

Amplify Science Pennsylvania NE
Grades K–5

Read More

Instructional model

The Amplify Science Pennsylvania program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science Pennsylvania has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing on searching for evidence related to their investigation and on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers
do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

Our cyclical lesson design ensures that students receive multiple exposures to concepts through a variety of modalities. As they progress through the lessons within a unit, students build and deepen their understanding, increasing their ability to develop and refine complex explanations of the unit’s phenomenon.

It’s this proven program structure and lesson design that enables Amplify Science Pennsylvania to address 100% of the Next Generation Science Standards (NGSS), and support students in mastering the Pennsylvania Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science Pennsylvania. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multimodal instruction offers more opportunities for students to construct meaning, and practice and apply concepts, than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science Pennsylvania, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4–5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put all the materials back with ease.

Assorted office and household items displayed on a white background, including rubber bands, binder clips, cardboard, and sports balls.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

Amplify Science Classroom Slides

Explore your print samples

With your Amplify Science Pennsylvania print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we’ve provided a copy of each of our unit-specific Teacher Reference Guides.

Teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free Teacher’s Guide!

Three laptop screens displaying educational content on earth's energy system, including diagrams and text annotations.
  • Teacher Reference Guide: Unlike a typical Teacher Guide that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science Pennsylvania, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science Pennsylvania materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials. We give teachers enough materials to support 200 student uses.
  • Are more manageable. Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of four to five students.
  • Include supportive videos. Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

Within each kit, we provide grade-specific lists of all materials included, which you can also find using the links below.

Spanish-language support

Amplify Science Pennsylvania is committed to providing support to meet the needs of all learners, including multiple access points for Spanish-speaking students. Developed in conjunction with Spanish-language experts and classroom teachers, several components are available in Spanish across the Amplify Science Pennsylvania curriculum.

Spanish-language materials include:

COMPONENT TEACHER/STUDENT
Student Investigation Notebooks Student
Science articles Student
Video transcripts Student
Digital simulation translation keys Student
Printed classroom materials
Unit and chapter questions, key concepts, vocabulary cards, etc.
Teacher
Copymasters Teacher
Assessments Teacher
Digital student experience license
This license gives students access to the student resources in Spanish, including instructional text, articles, and assessments. Teachers can control student access to Spanish-language content through the digital Teacher’s Guide.
Teacher
Spanish teacher support license
This license includes teacher talk, projections, downloadable PDFs of all print resources, and video transcripts and closed captioning in Spanish.
Teacher

Resources to support your review

Contact us

Support is always available. Our team is dedicated to helping you every step of the way.

Contact your dedicated Pennsylvania representative here.

A woman with long brown hair and glasses wearing a light blue sweater, smiling at the camera against a gray background.

Julie Couch

District Enrollment
<1800 students

A woman with long blonde hair and blue eyes is smiling at the camera, wearing a black top, in a well-lit indoor setting.

Jen Mee

Western PA

A smiling person with shoulder-length gray hair, wearing a peach-colored scarf and a gray sweater, stands against a plain white background. This image captures the essence of Pennsylvania teachers who are dedicated to enriching Science programs for elementary students.

Monica Vincent

Southeast PA

A man with curly brown hair and a beard, smiling broadly, wearing a suit, dress shirt, and floral tie, standing outdoors with trees and grass in the background.

Keenan Zambelli

Northeast & Central PA

Publisher presentation

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Amplify Science and Lawrence Hall of Science

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

DO

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

TALK

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

READ

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

WRITE

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

VISUALIZE

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS, and support students in mastering the Oregon Science Standards.

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.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3-D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Amplify Science California supports 3-D learning with more materials than any other program.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

A laptop displays a PowerPoint presentation in presenter view, with slides about observing objects in plastic containers and related sensory instructions.

Full coverage of the Oregon Science Standards

Amplify Science was designed from the ground up to meet the Next Generation Science Standards (NGSS). As such, it aligns to the Oregon Science Standards, which were also borne out of the NGSS.

The guidance below is meant to provide support for integrating additional activities that support full coverage of Oregon’s standards. Organized by grade level, each section below will outline:

  • Additional activities that support 100% alignment to the Oregon Science Standards.
  • The standard being addressed with the activities.
  • The recommended placement of the activities within a specific Amplify Science unit.
  • PDFs of any accompanying materials that are necessary to implement the activities.

Activity Title: Meet a Scientist Who Changed How We Think About Brain Cells

About this activity: In this activity, students read a short article about a scientist who studied the nervous system.

Recommended placement: Metabolism unit, Lesson 3.2

Materials:

Instructions: Download the PDF “Meet a Scientist Who Changed How We Think About Brain Cells” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies Underwater Currents

About this activity: In this activity, students read a short article about a scientist who studies ocean currents.

Recommended placement: Oceans, Atmosphere, and Climate unit, Lesson 2.1

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies Underwater Currents” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies How the Environment Affects Our Traits

About this activity: In this activity, students read two short articles, one about current research on genes and proteins, and one about a scientist who is studying how the environment can affect our traits.

Recommended placement: Traits and Reproduction unit, Lesson 2.4

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies How the Environment Affects Our Traits” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Who Becomes a Space Scientist?

About this activity: In this activity, Students read a short article about a scientist who studies space.

Recommended placement: Geology on Mars unit, Lesson 3.1

Materials:

Instructions: Download the PDF “Who Becomes a Space Scientist?” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies How Plants Find Water Underground

About this activity: In this activity, students read a short article about a scientist who studies how plants’ roots get water.

Recommended placement: Matter and Energy in Ecosystems unit, Lesson 1.6

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies How Plants Find Water Underground” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Bringing Back the Buffalo

About this activity: In this activity, students change one competing population to try to decrease the other in the Sim, and read a short article about a scientist who studies buffalo.

Recommended placement: Populations and Resources unit, Lesson 3.2

Materials:

Instructions: Download the PDF “Bringing Back the Buffalo” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Rereading “A Continental Puzzle”

About this activity: In this activity, students reread “A Continental Puzzle” and think about how patterns were helpful to Wegener’s work.

Recommended placement: Plate Motion unit, Lesson 3.2

Materials:

Instructions: Direct students back to “A Continental Puzzle” above and remind students of the Active Reading guidelines. Before students re-read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Meet a Scientist Who Studies Variation in Monkey Populations

About this activity: In this activity, students read a short article about a scientist who studies variation of traits in monkey populations.

Recommended placement: Natural Selection unit, Lesson 1.6

Materials:

Instructions: Download the PDF “Meet a Scientist Who Studies Variation in Monkey Populations” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Extinctions and Human Impacts

About this activity: The purpose of this lesson is for students to see how increases in human population and consumption of natural resources can negatively impact Earth’s systems.

Recommended placement: Natural Selection unit, Lesson 4.5

Materials:

Instructions: Download the PDF “Extinctions and Human Impacts” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Steno and the Shark

About this activity: In this activity, students read a short article about Nicolas Steno, a scientist from the 1600s whose studies of fossilized sharks’ teeth embedded in rock layers laid the foundation for the modern understanding of stratigraphy.

Recommended placement: Evolutionary History unit, Lesson 2.4

Materials:

Instructions: Download the PDF “Steno and the Shark” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Activity Title: Scale in the Solar System

About this activity: In this activity, students read and annotate the articles “Scale in the Solar System” and “The Solar System Is Huge.”

Recommended placement: Earth, Moon, and Sun unit, Lesson 1.2

Materials:

Instructions: Download the PDF “Scale in the Solar System” above and remind students of the Active Reading guidelines. Before students read the article, invite them to share prior experiences. Then have students complete the copymaster above.

Explore your print samples

Amplify Science physical samples can be found at the Hamersley Library at Western Oregon University. There you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free TG!

A laptop screen shows an energy simulation, with surrounding text and diagrams explaining the Earth's system and energy flow.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

At your request, we did not include our materials kits with our submissions samples. However, we did provide grade-specific lists of all materials included in each kit, which you can also find with the links below.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below.
  • Select Log in with Amplify.
  • Enter the teacher username and password found on your unique login flyer enclosed in your physical sample box.
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below.
  • Select Log in with Amplify.
  • Enter the student username and password found on your unique login flyer enclosed in your physical sample box.
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

Resources to support your review

Oregon standards correlation for grades 6–8

QCD Science Adoption Criteria 2022 for grades 6-8

QCD IMET Citation guidance for grades 6-8

Oregon Science IMET for grades 6-8 (Excel download)

Oregon QCD-IMET Citation guidance for grades 6-8

Research behind Amplify Science

Phenomena in grades 6–8

Program structure for grades 6–8

Active Reading in grades 6–8

Engineering in Amplify Science

Approaches to assessment in grades 6–8

What is Amplify Caminos?

Amplify Caminos is a core Spanish language arts program for grades K–5 that delivers:

  • Authentic instruction built from the ground up for the Spanish language.
  • A unique research-based approach truly built on the Science of Reading.
  • A combination of explicit foundational skills with meaningful knowledge-building.
  • Embedded support and differentiation that gets all students reading grade-level texts together.
  • Opportunities for students to see the strengths and experiences that all people share while also celebrating each others’ unique identities and experiences.
A diagram showing two strands labeled Language Comprehension and Word Recognition, intertwining into fluent reading, with examples of educational materials on both sides.

How does Amplify Caminos work?

Grades K–2: Dedicated knowledge-building and explicit skills instruction
Every day, students in Grades K–2 complete one full lesson that builds foundational reading skills in the Amplify Caminos Lectoescritura strand, as well as one full lesson that builds background knowledge in the Amplify Caminos Conocimiento strand. Through learning in each of these strands, students develop the early literacy skills necessary to help them become confident readers and build the context to understand what they’re reading.

Grades 3–5: Integrated instruction
In Grades 3–5, the Amplify Caminos Lectoescritura and Conocimiento strands are integrated in one set of instructional materials. Lessons begin to combine skills and knowledge with increasingly complex texts, close reading, and a greater writing emphasis. Students can then use their skills to go on their own independent reading adventures.

What makes Amplify Caminos different?

Built on the Science of Reading

Built out of the latest research in the Science of Reading, Amplify Caminos delivers explicit instruction in both foundational literacy skills (systematic phonics, decoding, and fluency) and background knowledge in grades K–2 with an integrated approach to explicit instruction in grades 3–5.

Explicit systematic skills instruction

The skills instruction in Amplify Caminos was distinctly developed with the Spanish language in mind. Its foundational lessons are specific to the language, rather than a direct translation from Amplify CKLA’s English skills instruction.

Reading instruction begins with the vowels first, then the most common consonants, and finally the least common consonants. Students will blend and segment sounds to form syllables, and syllables to form words.

Although Spanish has a highly predictable orthography, there are a few silent letters (h is always silent, u is silent after g or q), as well as letters that can make different sounds, depending on the letters that follow them. For that reason, syllables with these letters are taught somewhat later in the progression. The same is true for syllables with infrequently occurring consonants, such as z, k, x, and w.

Coherent knowledge instruction

While students are learning how to read, the Conocimiento strand gives them authentic and engaging reasons to read.

Amplify Caminos uses spiral learning to reinforce every student’s ability to develop skills like reading, writing, speaking, and listening in Spanish that can be transferred to English. As students engage with their lessons, they explore the similarities and differences in grammar, vocabulary, writing, and language use between Spanish and English. This bridge helps students learning two languages to strengthen their knowledge in both.

Through cross-curricular content, students explore units that relate to storytelling, science, and the history of our world in a holistic and thoughtful way. With these units, you’ll bring the world to your students, showing them how reading can become an exciting, rewarding, and useful part of their lives.

Embedded differentiation for all learners

Amplify Caminos provides built-in differentiation strategies and supports in every lesson.

  • Apoyo a la enseñanza y desafío: Support and Challenge suggestions in every lesson provide assistance or opportunities for more advanced work toward the goal of the lesson.
  • Notas culturales: These point-of-use notes provide additional information about the traditions, foods, holidays, word variations, and more from across the Spanish-speaking world.
  • Apoyo adicional: Every lesson in the Lectoescritura (Skills) Strand provides additional support activities suggested to reinforce foundational skills instruction. These activities can be given to any student who requires extra help, including students with special needs.

Commitment to equity

Illustration of two astronauts in space, a woman singing, a person sketching outdoors, a hot air balloon, and a landscape, all connected by flowing musical notes.

We believe we have a responsibility to provide literacy instruction that gives every student an equal opportunity to succeed and even excel. Amplify Caminos builds students’ knowledge about the world, helping them see people who resemble them and their familiar situations or experiences while also exposing them to people whose appearances, lives, beliefs, and backgrounds differ from their own.

In addition to teaching all students to crack the written code (which is vital for equity), the Amplify Caminos program helps students celebrate their own unique identities and experiences while also seeing the strengths and experiences we all share.

Amplify Caminos includes both transadaptations and authentic texts written by Latin American and Spanish authors. Authentic literature exposes students to a variety of text types and perspectives to deepen their knowledge of fascinating topics in social studies, science, literature, and the arts. Authentic texts support text-to-self, text-to-world, and text-to-text connections for readers.

Amplify Caminos Authentic Literature

Amplify Caminos is built on the conviction that equitable instruction is vital to an effective program. Decodable Student Readers celebrate students’ diverse experiences and feature individuals with a broad range of identity factors, including socio-economic status, age, ability, race, ethnicity, country of origin, and more.

Amplify Caminos Student Readers

How does Amplify Caminos integrate with the other parts of the literacy system?

Amplify Caminos + mCLASS® Lectura

Achieve complete parity between English and Spanish assessments with mCLASS Lectura for K–6. mCLASS Lectura allows teachers to connect with their Spanish-speaking students face-to-face, one-on-one, and in the language most comfortable to them. The result? Valid and reliable student data reports
available in both English and Spanish, enabling teachers to pinpoint where their Spanish-speaking or emergent bilingual students really are in their skill development and what instruction to prioritize.

Amplify Caminos + Boost Reading

Boost Reading is an engaging, adaptive digital program that extends the learning in Amplify Caminos. Boost Reading offers support to a large sub-group of English learners (ELs) through Spanish voice-over. Spanish voiceover instructions are available in vocabulary and sentence-level comprehension games so ELs can build their vocabulary, language, and critical comprehension skills before moving into analyzing complex texts

Language selection screen with options for English and Spanish, a cartoon girl waving and saying "¡Hola!", and sidebar menu items: Journal, Practice, and Settings.

Check out these additional resources

Caminos review resources:

Demo access

Ready to explore on your own? Follow the instructions linked below to access your demo accounts for Caminos and mCLASS Lectura.

Caminos login instructions

mCLASS Lectura login instructions

What is Amplify Caminos?

Amplify Caminos is a core Spanish language arts program for grades TK–5 that delivers:

  • Authentic instruction built from the ground up for the Spanish language.
  • A unique research-based approach truly built on the Science of Reading.
  • A combination of explicit foundational skills with meaningful knowledge-building.
  • Embedded support and differentiation that gets all students reading grade-level texts together.
  • Opportunities for students to see the strengths and experiences that all people share while also celebrating each others’ unique identities and experiences.
Illustration depicting the flow of genetic information, represented by ribbons transitioning from dna to rna, connected to various educational images and diagrams.

How does Amplify Caminos work?

Grades K–2: Dedicated knowledge-building and explicit skills instruction
Every day, students in Grades K–2 complete one full lesson that builds foundational reading skills in the Amplify Caminos Lectoescritura strand, as well as one full lesson that builds background knowledge in the Amplify Caminos Conocimiento strand. Through learning in each of these strands, students develop the early literacy skills necessary to help them become confident readers and build the context to understand what they’re reading.

Grades 3–5: Integrated instruction
In Grades 3–5, the Amplify Caminos Lectoescritura and Conocimiento strands are integrated in one set of instructional materials. Lessons begin to combine skills and knowledge with increasingly complex texts, close reading, and a greater writing emphasis. Students can then use their skills to go on their own independent reading adventures.

What makes Amplify Caminos different?

Built on the Science of Reading

Built out of the latest research in the Science of Reading, Amplify Caminos delivers explicit instruction in both foundational literacy skills (systematic phonics, decoding, and fluency) and background knowledge in grades K–2 with an integrated approach to explicit instruction in grades 3–5.

Explicit systematic skills instruction

The skills instruction in Amplify Caminos was distinctly developed with the Spanish language in mind. Its foundational lessons are specific to the language, rather than a direct translation from Amplify CKLA’s English skills instruction.

Reading instruction begins with the vowels first, then the most common consonants, and finally the least common consonants. Students will blend and segment sounds to form syllables, and syllables to form words.

Although Spanish has a highly predictable orthography, there are a few silent letters (h is always silent, u is silent after g or q), as well as letters that can make different sounds, depending on the letters that follow them. For that reason, syllables with these letters are taught somewhat later in the progression. The same is true for syllables with infrequently occurring consonants, such as z, k, x, and w.

Coherent knowledge instruction

While students are learning how to read, the Conocimiento strand gives them authentic and engaging reasons to read.

Amplify Caminos uses spiral learning to reinforce every student’s ability to develop skills like reading, writing, speaking, and listening in Spanish that can be transferred to English. As students engage with their lessons, they explore the similarities and differences in grammar, vocabulary, writing, and language use between Spanish and English. This bridge helps students learning two languages to strengthen their knowledge in both.

Through cross-curricular content, students explore units that relate to storytelling, science, and the history of our world in a holistic and thoughtful way. With these units, you’ll bring the world to your students, showing them how reading can become an exciting, rewarding, and useful part of their lives.

A collage of illustrated book covers, including themes of Don Quixote, space exploration, and anthropomorphic animals in various scenarios, all enriched with Spanish language elements.

Embedded differentiation for all learners

Amplify Caminos provides built-in differentiation strategies and supports in every lesson.

  • Apoyo a la enseñanza y desafío: Support and Challenge suggestions in every lesson provide assistance or opportunities for more advanced work toward the goal of the lesson.
  • Notas culturales: These point-of-use notes provide additional information about the traditions, foods, holidays, word variations, and more from across the Spanish-speaking world.
  • Apoyo adicional: Every lesson in the Lectoescritura (Skills) Strand provides additional support activities suggested to reinforce foundational skills instruction. These activities can be given to any student who requires extra help, including students with special needs.

Commitment to equity

Illustration of diverse people engaged in different activities: a black woman listening to music, two astronauts in space, and a man reading a book by a plant.

We believe we have a responsibility to provide literacy instruction that gives every student an equal opportunity to succeed and even excel. Amplify Caminos builds students’ knowledge about the world, helping them see people who resemble them and their familiar situations or experiences while also exposing them to people whose appearances, lives, beliefs, and backgrounds differ from their own.

In addition to teaching all students to crack the written code (which is vital for fairness), the Amplify Caminos program helps students celebrate their own unique identities and experiences while also seeing the strengths and experiences we all share.

Amplify Caminos includes both transadaptations and authentic texts written by Latin American and Spanish authors. Authentic literature exposes students to a variety of text types and perspectives to deepen their knowledge of fascinating topics in social studies, science, literature, and the arts. Authentic texts support text-to-self, text-to-world, and text-to-text connections for readers.

Three children's book covers in Spanish are shown: "La Flor de Oro," "El conejo en la Luna," and "El secreto de las hormigas," each featuring illustrated artwork.

Amplify Caminos is built on the conviction that fairness in instruction is vital to an effective program. Decodable Student Readers celebrate students’ varied experiences and feature individuals with a broad range of identity factors, including socio-economic status, age, ability, race, ethnicity, country of origin, and more.

Five illustrated Spanish children's books are arranged together, featuring colorful covers with diverse characters and animals, including a llama, a cactus, and children.

How does Amplify Caminos integrate with the other parts of the literacy system?

Amplify Caminos + mCLASS® Lectura

Achieve complete parity between English and Spanish assessments with mCLASS Lectura for K–6. mCLASS Lectura allows teachers to connect with their Spanish-speaking students face-to-face, one-on-one, and in the language most comfortable to them. The result? Valid and reliable student data reports
available in both English and Spanish, enabling teachers to pinpoint where their Spanish-speaking or emergent bilingual students really are in their skill development and what instruction to prioritize.

Reading assessment validated for benchmark, progress monitoring, and dyslexia screening

Amplify Caminos + Amplify Reading

Amplify Reading is an engaging, adaptive digital program that extends the learning in Amplify Caminos. Amplify Reading offers support to a large sub-group of English learners (ELs) through Spanish voice-over. Spanish voiceover instructions are available in vocabulary and sentence-level comprehension games so ELs can build their vocabulary, language, and critical comprehension skills before moving into analyzing complex texts

Spanish Support

Check out these additional resources

Caminos review resources:

What is Amplify Science?

The Lawrence Hall of Science

Developed by the science education experts at UC Berkeley’s Lawrence Hall of Science and the digital learning team at Amplify, our program features:

  • phenomena-based approach where students construct a complex understanding of each unit’s anchor phenomenon.
  • A blend of cohesive storylines, hands-on investigations, rich discussions, literacy-rich activities, and digital tools.
  • Carefully crafted units, chapters, lessons, and activities designed to deliver true 3-dimensional learning.
  • An instructional design that supports all learners in accessing all standards.
Aerial view of the lawrence hall of science at the university of california, berkeley, showcasing the building and surrounding trees with a foggy city backdrop.

Proven to work

A pdf cover from wested titled "learning and literacy development together: initial results from a curriculum study," featuring an adult helping children with schoolwork in a classroom.

WestEd Randomized
Control Trial for Grade 1

Read More

Pdf cover titled "curriculum materials designed for the next generation science standards: initial results from gold standard research trials", published by wested.

WestEd Randomized
Control Trial for Grade 7

Read More

A teacher and students engage in a science activity around a table. The text promotes the Amplify Science K–8 curriculum, highlighting its focus on hands-on learning and real-world problem-solving.

Amplify Science NE
Grades K–5

Read More

Instructional model

The Amplify Science program is rooted in the proven, research-based pedagogy of Do, Talk, Read, Write, Visualize. Here’s how each element works:

Do

First-hand investigations are an important part of any science classroom, and Amplify Science has students getting hands-on in every unit—from building models of protein molecules to experimenting with electrical systems.

Talk

Student-to-student discourse and full-class discussions are an integral part of the program. Students are provided with numerous opportunities to engage in meaningful oral scientific argumentation, all while fostering a collaborative classroom environment.

Read

Students read scientific articles, focusing their reading activities on searching for evidence related to their investigation and, importantly, on asking and recording questions as they read through fascinating texts on 21st-century topics.

Write

Following real-world practices, students write scientific arguments based on evidence they’ve collected, making clear their reasoning about how a given piece of evidence connects to one of several claims.

Visualize

By manipulating digital simulations and using modeling tools to craft visualizations of their thinking— just as real scientists and engineers do—students take their learning far beyond the confines of what they can physically see in the classroom in an exciting and authentic way.

Program structure

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

It’s this proven program structure and lesson design that enables Amplify Science to address 100% of the NGSS, and support students in mastering the Utah Science Standards.

Flowchart depicting a critical thinking process with four circular nodes connected by arrows, each node representing a step: posing a real-world problem, exploring evidence, elaborating concepts, and evaluating claims.

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 serves a unique instructional purpose.

In grades 6–8:

  • One unit is a launch unit.
  • Three units are core units.
  • Two units are engineering internships.

Launch units are the first units taught in each year of Amplify Science. The goal of the Launch unit is to introduce students to norms, routines, and practices that will be built on throughout the year, including argumentation, active reading, and using the program’s technology. For example, rather than taking the time to explain the process of active reading in every unit in a given year, it is explained thoroughly in the Launch unit, thereby preparing students to read actively in all subsequent units.

Core units establish the context of the unit by introducing students to a real-world problem. As students move through lessons in a Core unit, they figure out the unit’s anchoring phenomenon, gain an understanding of the unit’s disciplinary core ideas and science and engineering practices, and make linkages across topics through the crosscutting concepts. Each Core unit culminates with a Science Seminar and final writing activity.

Engineering Internship units invite students to design solutions for real-world problems as interns for a fictional company called Futura. Students figure out how to help those in need, from tsunami victims in Sri Lanka to premature babies, through the application of engineering practices. In the process, they apply and deepen their learning from Core units.

Unit sequence

Our lessons follow a structure that is grounded in regular routines while still being flexible enough to allow for a variety of learning experiences.

In fact, our multi-modal instruction offers more opportunities for students to construct meaning, and practice and apply concepts than any other program. What’s more, our modular design means our units can be flexibly arranged to support your instructional goals.

Three columns listing education curriculum topics for grades 6, 7, and 8, focusing on science themes such as microbiomes, mars geology, and harnessing human energy.

Program components

Available digitally and in print, our unit-specific reference guides are chock full of helpful resources, including scientific background knowledge, planning information and resources, color-coded 3D Statements, detailed lesson plans, tips for delivering instruction, and differentiation strategies.

Amplify Science TG

Hands-on learning is an essential part of Amplify Science, and is integrated into every unit. Students actively participate in science, playing the roles of scientists and engineers as they gather evidence, think critically, solve problems, and develop and defend claims about the world around them. Every unit includes hands-on investigations that are critical to achieving the unit’s learning goals.

A young person wearing gloves looks through a microscope at a table with laboratory supplies, including bottles, slides, and a tray, against a plain blue background.

More hands-on with Flextensions:
Hands-on Flextensions are additional, optional investigations that are included at logical points in the learning progression and give students an opportunity to dig deeper if time permits. These activities offer teachers flexibility to choose to dedicate more time to hands-on learning. Materials referenced in Hands-on Flextension activities will either be included in the unit kit or are easily sourced. Supporting resources such as student worksheets will be included as downloadable PDF files.

Our kits include enough materials to support 200 student uses. In other words, teachers can easily support all five periods and small groups of 4-5 students each. Plus, our unit-specific kits mean teachers just grab the tub they need and then put it all back with ease.

Our digital Simulations and Practice Tools are powerful resources for exploration, data collection, and student collaboration. They allow students the ability to explore scientific concepts that might otherwise be invisible or impossible to see with the naked eye.

Available for every unit, our Student Investigation Notebooks contain instructions for activities and space for students to record data and observations, reflect on ideas from texts and investigations, and construct explanations and arguments.

In grades 6–8, one copy of the Student Investigation Notebook is included in each unit’s materials kit for use as a blackline master. Each notebook is also available as a downloadable PDF on the Unit Guide page of the digital Teacher’s Guide.

Two booklets titled "El clima cambiante de la Tierra: la desaparición del hielo" and "Earth’s Changing Climate: Vanishing Ice" with landscape illustrations on the covers.

These customizable PowerPoints are available for every lesson of the program and make delivering instruction a snap with visual prompts, colorful activity instructions, investigation set-up videos and animations, and suggested teacher talk in the notes section of each slide.

A laptop displays a PowerPoint presentation in presenter view, with slides about observing objects in plastic containers and related sensory instructions.

Explore your print samples

With your Amplify Science print samples, you’ll find unit-specific Teacher’s References Guides and Student Investigation Notebooks for each grade level.

A note about the Teacher’s Reference Guides:

It’s important that your committee sees the full breadth and depth of our instruction. For that reason, we provided a copy of each of our unit-specific Teacher Reference Guides.

Rest assured that teachers do not use these robust reference guides for day-to-day teaching. For that, we have a hands-free TG!

Three laptop screens displaying educational content on earth's energy system, including diagrams and text annotations.
  • Teacher Reference Guide: Unlike a typical TG that requires a series of supplemental books to support it, our encyclopedic reference guide is chock-full of everything a teacher needs to fully implement our program and the NGSS.
  • Ready-to-Teach Lesson Slides: For daily instruction, teachers need their hands free. That’s why we created ready-to-teach lesson slides for every single lesson. What’s more, they are editable and include suggested teacher talk and point-of-use differentiation and other instructional tips. Click to learn more.

A note about the Materials Kits:

Hands-on learning is at the heart of Amplify Science, and is integrated into every unit. In order to make hands-on learning more manageable for busy teachers, Amplify Science materials are organized into unit-specific kits.

Stacked storage bins with labels, arranged neatly; caption notes they are a sample and may not reflect actual quantities or sizes.

Our unit-specific kits:

  • Include more materials — We give teachers enough materials to support 200 student uses.
  • Are more manageable — Unlike other programs that require large groups of students to share limited sets of materials, our kits include enough to support small groups of 4–5 students.
  • Include supportive videos — Each hands-on activity provides clear instructions for the teacher, with more complex activities supported by video demonstrations and illustrations.

At your request, we did not include our materials kits with our submissions samples. However, we did provide grade-specific lists of all materials included in each kit, which you can also find with the links below.

Access your digital samples

Explore as a teacher

Follow these instructions to explore the Amplify Science digital platform as a teacher.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: t.msscienceut@tryamplify.net
  • Enter the password: AmplifyNumber1
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

To help familiarize yourself with navigating the digital platform, watch the below navigational video.

Explore as a student

Follow these instructions to explore the Amplify Science digital platform as a student.

  • Click the Access Amplify Science Platform button below and bookmark it.
  • Select Log in with Amplify.
  • Enter the username: s.msscienceut@tryamplify.net
  • Enter the password: AmplifyNumber1
  • Click the Science icon.
  • Click on the Grade Menu in the top center of the screen and select any grade.
  • Select any unit.

Resources to support your review

Grade K

Unit 1: Math Is…

Lesson 1-2: Math is Exploring and ThinkingConnecting Cubes

Unit 4: Sort, Classify and Count Objects

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

Unit 5: 2-Dimensional Shapes

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

Unit 6: Understand Addition

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

Unit 7: Understand Subtraction

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

Unit 8: Addition and Subtraction Strategies

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

Unit 13: Analyze, Compare and Compose Shapes

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

Unit 14: Compare Measurable Attributes

Lesson 14-1: Describe Attributes of ObjectsAnother Shape

Grade 1

Unit 2: Number Patterns

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

Unit 3: Place Value

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

Unit 4: Addition within 20: Facts and Strategies

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

Unit 5: Subtraction within 20: Facts and Strategies

Lesson 5-1: Relate Counting to SubtractionPacking a Picnic

Unit 7: Meanings of Addition

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

Unit 8: Meanings of Subtraction

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

Unit 13: Equal Shares

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

Grade 2

Unit 2: Place Value to 1,000

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

Unit 3: Patterns within Numbers

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

Unit 4: Meanings of Addition and Subtraction

Lesson 4-7: Represent and Solve Compare ProblemsAwesome Aquariums

Unit 5: Strategies to Add Fluently Within 100

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

Unit 7: Measure and Compare Lengths

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

Unit 8: Measurement, Time and Money

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

Unit 9: Strategies to Add 3-Digit Numbers

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

Unit 11: Data Analysis

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

Grade 3

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

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

Unit 3: Multiplication and Division

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

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

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

Unit 6: Connect Area and Multiplication

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

Unit 7: Fractions

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

Unit 9: Use Multiplication to Divide

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

Unit 12: Measurement and Data

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

Unit 13: Describe and Analyze 2-Dimensional Shapes

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

Grade 4

Unit 4: Multiplication as Comparison

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

Unit 5: Numbers and Number Patterns

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

Unit 6: Multiplication Strategies with Multi-Digit Numbers

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

Unit 9: Addition and Subtractions Meanings and Strategies with Fractions

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

Unit 10: Addition and Subtraction Strategies with Mixed Numbers

Lesson 10-1: Understand Decomposing Mixed NumbersMath Pizzeria

Unit 11: Multiply Fractions by Whole Numbers

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

Unit 12: Decimal Fractions

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

Grade 5

Unit 2: Volume

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

Unit 3: Place Value and Number Relationships

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

Unit 5: Multiply Multi-Digit Whole Numbers

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

Unit 6: Multiply Decimals

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

Unit 7: Divide Whole Numbers

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

Unit 8: Divide Decimals

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

Unit 10: Multiply Fractions

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

Unit 13: Geometry

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

Grade 6

Module 1: Ratios and Rates

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

Module 2: Fractions, Decimals, and Percents

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

Module 3: Compute with Multi-Digit Numbers and Fractions

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

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

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

Module 5: Numerical and Algebraic Expressions

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

Module 6: Relationships in Geometry

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

Module 7: Relationships Between Two Variables

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

Module 8: Area

Module 9: Volume and Surface Area

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

Module 10: Statistical Measures and Displays

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

Grade 7

Module 1: Proportional Relationships

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

Module 2: Solve Percent Problems

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

Module 3: Operations with Integers

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

Module 4: Operations with Rational Numbers

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

Module 5: Simplify Algebraic Expressions

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

Module 6: Write and Solve Equations

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

Module 7: Write and Solve Inequalities

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

Module 8: Geometric Figures

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

Module 9: Measure Figures

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

Module 10: Probability

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

Module 11: Sampling and Statistics

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

Grade 8

Module 1: Exponents and Scientific Notation

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

Module 2: Real Numbers

Lesson 2: RootsUnit 8
Lesson 4: Root Down

Module 3: Solve Equations with Variables on Each Side

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

Module 4: Linear Relationships and Slope

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

Module 5: Functions

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

Module 6: Systems of Linear Equations

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

Module 7: Triangles and the Pythagorean Theorem

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

Module 8: Transformations

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

Module 9: Congruence and Similarity

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

Module 10: Volume

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

Module 11: Scatter Plots and Two-Way Tables

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

Disclaimer

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

What is Amplify Caminos?

Amplify Caminos is a core Spanish language arts program for grades TK–5 that delivers:

  • Authentic instruction built from the ground up for the Spanish language.
  • A unique research-based approach truly built on the Science of Reading.
  • A combination of explicit foundational skills with meaningful knowledge-building.
  • Embedded support and differentiation that gets all students reading grade-level texts together.
  • Opportunities for students to see the strengths and experiences that all people share while also celebrating each others’ unique identities and experiences.
Infographic illustrating reading development as two strands—language comprehension and word recognition—that intertwine to form skilled reading, progressing from basic to advanced abilities.

How does Amplify Caminos work?

Grades K–2: Dedicated knowledge-building and explicit skills instruction
Every day, students in Grades K–2 complete one full lesson that builds foundational reading skills in the Amplify Caminos Lectoescritura strand, as well as one full lesson that builds background knowledge in the Amplify Caminos Conocimiento strand. Through learning in each of these strands, students develop the early literacy skills necessary to help them become confident readers and build the context to understand what they’re reading.

Grades 3–5: Integrated instruction
In Grades 3–5, the Amplify Caminos Lectoescritura and Conocimiento strands are integrated in one set of instructional materials. Lessons begin to combine skills and knowledge with increasingly complex texts, close reading, and a greater writing emphasis. Students can then use their skills to go on their own independent reading adventures.

What makes Amplify Caminos different?

Built on the Science of Reading

Built out of the latest research in the Science of Reading, Amplify Caminos delivers explicit instruction in both foundational literacy skills (systematic phonics, decoding, and fluency) and background knowledge in grades K–2 with an integrated approach to explicit instruction in grades 3–5.

Explicit systematic skills instruction

The skills instruction in Amplify Caminos was distinctly developed with the Spanish language in mind. Its foundational lessons are specific to the language, rather than a direct translation from Amplify CKLA’s English skills instruction.

Reading instruction begins with the vowels first, then the most common consonants, and finally the least common consonants. Students will blend and segment sounds to form syllables, and syllables to form words.

Although Spanish has a highly predictable orthography, there are a few silent letters (h is always silent, u is silent after g or q), as well as letters that can make different sounds, depending on the letters that follow them. For that reason, syllables with these letters are taught somewhat later in the progression. The same is true for syllables with infrequently occurring consonants, such as z, k, x, and w.

Coherent knowledge instruction

While students are learning how to read, the Conocimiento strand gives them authentic and engaging reasons to read.

Amplify Caminos uses spiral learning to reinforce every student’s ability to develop skills like reading, writing, speaking, and listening in Spanish that can be transferred to English. As students engage with their lessons, they explore the similarities and differences in grammar, vocabulary, writing, and language use between Spanish and English. This bridge helps students learning two languages to strengthen their knowledge in both.

Through cross-curricular content, students explore units that relate to storytelling, science, and the history of our world in a holistic and thoughtful way. With these units, you’ll bring the world to your students, showing them how reading can become an exciting, rewarding, and useful part of their lives.

A collage of illustrated children's book pages in Spanish, featuring a knight, animals, and a group of children, with one page showing Spanish text.

Embedded differentiation for all learners

Amplify Caminos provides built-in differentiation strategies and supports in every lesson.

  • Apoyo a la enseñanza y desafío: Support and Challenge suggestions in every lesson provide assistance or opportunities for more advanced work toward the goal of the lesson.
  • Notas culturales: These point-of-use notes provide additional information about the traditions, foods, holidays, word variations, and more from across the Spanish-speaking world.
  • Apoyo adicional: Every lesson in the Lectoescritura (Skills) Strand provides additional support activities suggested to reinforce foundational skills instruction. These activities can be given to any student who requires extra help, including students with special needs.

Commitment to equity

Illustration of two astronauts in space, a woman singing, a child drawing, and people in a hot air balloon with a colorful, imaginative background.

We believe we have a responsibility to provide literacy instruction that gives every student an equal opportunity to succeed and even excel. Amplify Caminos builds students’ knowledge about the world, helping them see people who resemble them and their familiar situations or experiences while also exposing them to people whose appearances, lives, beliefs, and backgrounds differ from their own.

In addition to teaching all students to crack the written code (which is vital for equity), the Amplify Caminos program helps students celebrate their own unique identities and experiences while also seeing the strengths and experiences we all share.

Amplify Caminos includes both transadaptations and authentic texts written by Latin American and Spanish authors. Authentic literature exposes students to a variety of text types and perspectives to deepen their knowledge of fascinating topics in social studies, science, literature, and the arts. Authentic texts support text-to-self, text-to-world, and text-to-text connections for readers.

Three children's book covers in Spanish are shown: "La Flor de Oro," "El conejo en la Luna," and "El secreto de las hormigas," each with colorful illustrations.
  • Amplify Caminos is built on the conviction that equitable instruction is vital to an effective program. Decodable Student Readers celebrate students’ diverse experiences and feature individuals with a broad range of identity factors, including socio-economic status, age, ability, race, ethnicity, country of origin, and more.
Five colorful children's books in Spanish are displayed, featuring illustrated covers with diverse characters, a llama, and a giant cactus.

How does Amplify Caminos integrate with the other parts of the literacy system?

Amplify Caminos + mCLASS® Lectura

Achieve complete parity between English and Spanish assessments with mCLASS Lectura for K–6. mCLASS Lectura allows teachers to connect with their Spanish-speaking students face-to-face, one-on-one, and in the language most comfortable to them. The result? Valid and reliable student data reports
available in both English and Spanish, enabling teachers to pinpoint where their Spanish-speaking or emergent bilingual students really are in their skill development and what instruction to prioritize.

A laptop screen displays a slide titled "Lectura data-driven instructional cycle" with sections for Assessment, Reporting, and Instruction, each showing a sample screenshot.

Amplify Caminos + Amplify Reading

Amplify Reading is an engaging, adaptive digital program that extends the learning in Amplify Caminos. Amplify Reading offers support to a large sub-group of English learners (ELs) through Spanish voice-over. Spanish voiceover instructions are available in vocabulary and sentence-level comprehension games so ELs can build their vocabulary, language, and critical comprehension skills before moving into analyzing complex texts

A language selection screen with options for English and Spanish, featuring a waving girl saying "¡Hola!" in a speech bubble.

Sample materials

Demo access

A laptop screen displays the Amplify login page with options to log in using Google, Clever, Amplify, scan QR code, or use district SSO.

Follow the instructions below to access your demo account.

  • Click the CKLA and Caminos Demo button below.
  • Select Log in with Amplify.
  • To explore as a teacher, enter this username: t1.westadackla@demo.tryamplify.net
  • To explore as a student, enter this username: s1.westadackla@demo.tryamplify.net
  • Enter the password: Amplify1-westadackla
  • Click the Programs and apps menu
  • Select CKLA Teacher Resource Site
  • Select the desire grade level
  • Use the toggle to switch between English (CKLA) and Spanish (Caminos) resources.

Note: Your demo account access expires on January 19, 2023.

CKLA and Caminos Demo

Check out these additional resources

Caminos review resources:

The next chapter in the Science of Reading

Introducing Amplify CKLA 3rd Edition, a K–5 core literacy program within Amplify’s literacy suite. For more than a decade, Amplify CKLA has transformed classrooms nationwide with its intentional knowledge building and systematic skills instruction. Available for the 2025–2026 school year, the 3rd Edition builds on this successful foundation to better support all students in becoming confident readers, writers, and thinkers. Together, let’s write the next chapter in the Science of Reading.

An astronaut floats in space near the Moon, with a speech bubble displaying

Amplify CKLA serves

150,000+

Classrooms

4,000,000+

Students

50

U.S. States and D.C.

Our approach

Improve outcomes with a program built on a decade of research, and that meets the strongest ESSA Tier I criteria.

Diagram illustrating the Simple View of Reading model, depicting language comprehension and word recognition pathways converging into skilled reading, with processes becoming increasingly strategic and automatic—a foundational concept in literacy curriculum for elementary education.

Grounded in the Science of Reading

As the original Science of Reading program, Amplify CKLA puts research into action with explicit, systematic foundational skills instruction and a proven knowledge-building sequence. In collaboration with education experts and practitioners, we provide powerful resources that deliver real results.

Background knowledge drives results

Amplify CKLA follows the Core Knowledge Sequence, a content-specific, cumulative, and coherent approach to knowledge building. This approach improves reading scores and closes achievement gaps by establishing a robust knowledge base that strengthens comprehension.

In Amplify CKLA 3rd Edition, we’ve enriched our Knowledge Sequence with a wider range of perspectives and high-quality texts in new and enhanced units.

An infographic showing the steps to pronounce

Build foundational skills for long-term success.

Students progress from simple to complex skill development starting with phonological and phonemic awareness. Instruction in Grades K–2 explicitly teaches the 150 spellings for the 44 sounds of English, following an intentional progression to ensure student success.

In our 3rd Edition, we’ve added dedicated Grades 3–5 foundational skills instruction that can either support core lessons or function as an intervention, based on student needs.

Daily writing deepens learning.

Grounded in the Science of Writing—the research on how kids learn to write—instruction is explicit, daily, and woven into the curriculum’s rich content. It covers both transcription (handwriting and spelling) and composition (organizing ideas into narratives) with high-impact activities like sentence-level combining and expanding, and pre-writing exercises. Writing and reading instruction are integrated so students simultaneously strengthen their communication skills, comprehension, and confidence.

A child in a green shirt smiles while writing in a notebook at a classroom desk, engaged in their k–5 literacy curriculum, with another student visible in the background.
An open laptop displaying a children's story titled

High-quality, diverse texts

Amplify CKLA students are immersed in a variety of texts—complex read-alouds, decodable chapter books, trade books, and content-rich readers—that reflect varied experiences and connect to learning goals.

Readers are 100% decodable for Grades K–2, empowering students to directly apply what they’ve learned. Novel Study units for Grades 3–5 offer a mix of contemporary and classic literature, and Culminating Research Units in every grade include a set of authentic texts and trade books.

Reach all learners with differentiated support.

Scaffolds and challenges, developed in collaboration with education experts, make content available to every student—including multilingual and English learners. With strategies embedded right in the curriculum, teachers can deliver in-the-moment, individualized instruction to meet all student needs.

For a dedicated English language development program aligned to Amplify CKLA, explore Language Studio.

Children sit on the floor in a classroom, some raising their hands, smiling and engaged. The lively atmosphere reflects the effectiveness of the k–5 literacy curriculum being implemented.

What’s included

The comprehensive resources in Amplify CKLA 3rd Edition support effective literacy instruction in every classroom.

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Easy-to-use teacher materials

Amplify CKLA teachers are empowered to deliver effective instruction with the following print and digital resources:

  • Teacher Guides (K–5)
  • Assessment Guides (K–5)
  • Authentic texts and trade books (K–5)
  • Knowledge Image Cards (K–2)
  • Knowledge Flip Books (K–2, digital)
  • Ready-made and customizable Presentation Screens (K–5, digital)
  • Remediation and intervention resources (K–5)
  • On-demand professional development (K–5, digital)

Immersive Amplify CKLA student resources

Amplify CKLA students stay engaged with the following print and digital resources:

  • Decodable readers (K–2)
  • Student Readers and novels (3–5)
  • Student Activity Books (K–5)
  • Poet’s Journal and Writer’s Journal (3–5)
  • eReaders (K–5, digital)
  • Sound Library featuring articulation videos and songs (K–2, digital)
  • Assignable Practice Games (K–5)
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Rich literary experiences

All of the high-quality, diverse texts in Amplify CKLA connect to the curriculum, fostering your students’ curiosity and helping them learn to read with confidence.

  • Trade Book Collections (K–5) inspire student research in each grade’s Culminating Research Unit.
  • Classic and contemporary literature (3–5) delight students in Novel Study Units.
  • Increasingly complex Student Readers (K–5) develop students’ literacy across grades.

Hands-on phonics materials

Multisensory phonics and foundational skills resources engage students with fun, varied approaches that promote mastery and build independence.

  • Chaining Folders and Small Letter Cards (K)
  • Read-Aloud Big Books (K–1)
  • Large Letter Cards (K–2)
  • Sound Cards (K–2)
  • Image Cards (K–3)
  • Blending Picture Cards (K)
  • Consonant and Vowel Code Posters and Spelling Cards (1–2)
  • Sound Library (K–2, digital)
Image includes various vowel sounds and combinations on flashcards and worksheets, along with a playful illustrated mammal, all part of a comprehensive literacy curriculum for elementary students.

All-in-one digital platform

Our comprehensive platform simplifies your day-to-day tasks and makes it easier to plan and deliver lessons.

  • Ready-made and customizable Presentation Screens
  • Auto-scored digital assessments
  • Standards-based reporting
  • Assignable Practice Games
  • Sound Library
  • eReaders

Professional Development

Move beyond traditional program training with Amplify’s digital PD Library, designed to fully support your shift to the Science of Reading and Amplify CKLA. Deepen your understanding with:

  • Program and planning resources
  • Model lesson videos from real classrooms
  • Guidance on using Amplify’s literacy suite to provide multi-tiered support
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Ready to continue your learning journey?

We also offer live, tailored professional learning sessions by expert partners to expand your Science of Reading expertise, strengthen implementation, and improve student outcomes.

“Teachers love the ease of implementing the program, and students have fun while learning. Growth is evident in our data, and we have the support of Amplify experts who are available to answer questions and provide top-notch professional development.”

Bridget Vaughan, District K–8 Coordinator of ELA and Literacy

Quincy Public Schools, Massachusetts

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A true Science of Reading early literacy suite for Grades K–5

Amplify has combined the critical elements of a Science of Reading system: assessment, core curriculum, personalized learning, and intervention. Based on 20 years of experience with the Science of Reading, this complete system saves you time and aligns your literacy practices.

  • Assess with mCLASS®: A universal and dyslexia screener, powered by DIBELS 8th Edition
  • Instruct with Amplify CKLA: Core curriculum to build foundational skills and knowledge
  • Practice with Boost Reading™: Personalized learning program to extend and reinforce core
  • Intervene with mCLASS Intervention: Staff-led Tier 2 and 3 intervention for intensive support
“There were other programs that claimed to be [based on the] Science of Reading, but no other vendor provided the suite of products together. We did not want to be picking from here, picking from there. [Amplify’s literacy suite] met our needs, because it aligned and provided us the best suite of products, hands down.”

Nicole Peterson, Principal, Midway Middle School

Sampson County Schools, North Carolina

Language Studio: Multilingual and English language learner support

Language Studio is Amplify CKLA’s dedicated K–5 program for multilingual and English language learners. Through daily 30-minute lessons, it strengthens reading, writing, speaking, and listening skills while reinforcing core instruction. This tailored support empowers students to confidently access grade-level content as they develop academic English.

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Explore more programs in Amplify’s literacy and biliteracy suite.

All of the programs in our literacy suite and our biliteracy suite are designed to support and complement each other. Learn more about our related programs:

5 ways to shift from balanced literacy to the Science of Reading

The Science of Reading is a big deal. We’re serious when we say that literacy instruction based on the Science of Reading can change lives, and we’re not the only ones.

Our friends at the Reading League say that instruction based on the Science of Reading “will elevate and transform every community, every nation, through the power of literacy.”

So it stands to reason that shifting to a Science of Reading curriculum is a pretty big deal, too. It’s not a light lift or a quick fix, and that makes total sense.

That’s why we want to help you make the shift. And actually, shifts.

Any big change is best done gradually. That’s why we’ve identified five key shifts in reading instruction that will set you on the path to transforming your classroom(s)—and your students’ futures.

The science of teaching reading

But first, a quick refresher.

As you likely know, the Science of Reading refers to the pedagogy and practices proven by extensive research to effectively teach children how to read. Learning to read is not innate and must be taught—and evidence from numerous studies tells us how.

This is where a Science of Reading-based approach differs fundamentally from a balanced literacy approach.

Balanced literacy can have several meanings, but generally it refers to instruction that focuses on a combination of shared reading, guided reading, and independent reading, with foundational skills typically not emphasized and rarely taught systematically.

While researchers are always learning new things and updating their understanding about literacy instruction, we do now know more than ever about how the brain learns to read and what methods are most effective in teaching reading. The conclusion? With explicit, systematic instruction, the vast majority of students can learn to read at or near grade level. That instruction must include phonics, phonemic awareness, fluencyvocabulary, and comprehension, with an emphasis on background knowledge. There is a lot of information to learn. What’s the best way to funnel it into daily classroom instruction? The answer is gradually.

Five incremental shifts from balanced literacy to the Science of Reading

Let’s explore the changes you can make today as you explore and implement true Science of Reading instruction.

  1. Use decodable readers, not leveled readers. Decodable readers—simple books that focus on the letter-sound correspondences that students have learned—support students in developing their phonics knowledge, rather than guessing or using picture cues. They support the systematic approach to instruction aligned with the Science of Reading, and they can even replace a workshop model with guided reading and leveled readers or predictable text.
  2. Provide all students with dedicated, systematic phonics instruction, not mini-lessons or isolated phonics instruction. Effective phonics instruction—for every student—takes time and is deliberately sequenced. (At least 60 minutes a day is required for solid, systematic foundational skills development.) Phonics instruction should also be part of a comprehensive Science of Reading approach to literacy instruction (as part of your core curriculum) versus taught as part of a disconnected program.
  3. Help students with phonics-based scaffolds, not three-cueing or word guessing. This is the part where learning to decode actually rewires students’ brains for reading. It requires that you provide scaffolds and ask students to practice sounding it out rather than responding to context clues. Spend your time on this approach, rather than on reading predictable books that make it easy for kids to spot and memorize patterns.
  4. To build comprehension skills, develop students’ knowledge. The Science of Reading shows that literacy skills grow best on a foundation of knowledge. In other words, the more you know, the easier and faster you can understand texts you encounter in the world. Spend two or three weeks on focused literary, social studies, and science topics. The topics should build on each other and deepen understanding and vocabulary. This approach can replace studying disconnected topics and practicing comprehension skills (exercises where students find the main idea or determine the author’s purpose) without attention to background knowledge.
  5. Follow a clear instructional path, not a choose-your-own-adventure model. The Science of Reading supports a path over patchwork approach. A cohesive curriculum with explicit guidance is the most beneficial—yet overlooked—element of teaching reading effectively. It can replace an approach with multiple instructional pathways and moving parts, and it gives every student the support they need now without waiting for intervention.

Learn more

Landing page for ebook

Science of Reading webinars 

Science of Reading microsite

Science of Reading: The Podcast

The power of data-driven instruction for reading success

Words tell stories—and so do numbers. Even though reading can take us to magical places and spark immeasurable wonder, it’s data that can best guide literacy instruction (and instructors) toward delivering reading success.

Amplify’s Executive Director of Learning Science Danielle Damico, Ph.D., notes in this webinar that educators and districts can, understandably, get stuck in out-of-date beliefs. One common one is that reading is a natural process, the product of variables we can’t change in schools. But data shows the opposite—and provides immense opportunity.

Data is at the heart of what we now call the Science of Reading—a term for the decades of data now available on how kids learn to read and write, and how to best teach them. In making the shift to instruction grounded in the Science of Reading, educators can make effective use of this data to change not only literacy practices, but lives.

If you’ve been following the Science of Reading movement, you likely know the power of making that shift. But whether you’ve been following it for years or are just learning about it, there are some questions you’ll need to explore. What data do you need to make your case to your school or district? And what data will help you monitor implementation—and future success?

Using data to make your case for the Science of Reading

When making the shift to instruction grounded in the Science of Reading, you need to build buy-in among key stakeholders. Your most powerful tool in this endeavor? Data.

If your screening data shows that 20% or more of your students require intervention, it’s time to make the shift. That key performance metric is sometimes all you need, but other indicators can include high error rates among students reading decodable words, fluency below grade-level, words-per-minute scores, or struggles in identifying base words with a prefix or suffix.

Your teaching materials are also a source of data. When you conduct an audit of their content and approach, do you notice—for example—a lack of direct connection between phonics lessons and texts? Emphasis on visual strategies for decoding? Few decodable texts in the first place? These clues (or even red flags) could point to materials that are not grounded in the explicit, systematic instruction recommended by the Science of Reading.

The same may be true of your shared or inherited instructional practices. Is reading typically taught through isolated topics or generic skills (like “find the main idea”) that are disconnected from knowledge domains? Those approaches to reading could contribute to low performance data—and could help you make your case as you champion a shift to data-driven instruction.

What does data-driven instruction look like—in implementation and beyond?

Science-based reading instruction reduces the need for intervention and allows students to move forward as capable, confident readers. Once you’ve begun to implement data-driven instruction, you’ll need to collect key information to make sure you get—and stay—on the right track for all of your students.

Among the eight core principles of the Science of Reading, universal screening and progress monitoring are two that are absolutely necessary to ensure that all students receive the right instruction. It’s also important that your universal screener measures phonemic awareness, phonics, fluency, vocabulary, and comprehension.

It’s important to monitor improvement in foundational literacy skills and decline in the number of students requiring literacy intervention as well. Collecting qualitative insights regarding classroom practices and tracking their alignment with Science of Reading principles forms a crucial part of the data landscape during this instructional shift.

And finally, as Danielle Damico notes, implementation data can help you:

  • Confirm that your program has indeed been implemented.
  • Ensure that student learning is meeting key goals.
  • Distinguish between an ineffective program and an effective program not being implemented as designed.
  • Determine opportunities for professional development and coaching.

To take a deeper dive into all the data that can help you champion, navigate, and succeed in this shift, download our ebook The Story That Data Tells: Using Data to Chart Your Course With the Science of Reading and explore our webinar What Does Data Tell Us? Building Buy-In and Determining Areas of Need With Data.

Season 10, Episode 14

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

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

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

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Season 10, Episode 14

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

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

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

To view this protected page, enter the password below:



Season 1, Episode 7

Teaching takes joy, starring Rebecka Peterson

Today on Beyond My Years, host Ana Torres delves into the wisdom offered by Rebecka Peterson, 2023’s National Teacher of the Year (NTOY) and an educator whose journey began much like Ana’s: as a young immigrant to the United States. Rebecka shares all that she has come to love and appreciate about the K–12 environment after a tough transition from teaching college-level courses. She also reveals her most important lesson learned: Teach humans over content. Rebecka talks about her “One Good Thing” blog, where she documented daily positives in her classroom that transformed her perspective on teaching. She shares personal experiences of feeling like an outsider and how those experiences drive her to create an environment of belonging for her students. Rebecka stresses the significance of building authentic relationships with students, as well as the impact of mentors in education. Taking all those lessons back to the classroom, Eric and Ana discuss strategies like “rebellious joy” that seem essential to sustaining a long career in education.

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Meet Our Guest(s):

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Rebecka Peterson

Recognized as the 2023 National Teacher of the Year, Rebecka Peterson is a math teacher who loves stories. Rebecka has been teaching for 16 years, the last 12 of which at Union High School in Tulsa, Oklahoma. She believes that when we learn each other’s stories, we carry a piece of each other with us, enabling us to authentically advocate for our students, teachers, and communities.

In the midst of a challenging first year of teaching, Rebecka joined other educators in a daily practice of noting “one good thing” in her classroom. Together they found inspiration by embracing the motto: “Every day may not be good, but there is one good thing in every day.” This shift in perspective transformed her work. Rebecka now collaborates with fellow educators, emphasizing the importance of cultivating “intentional joy” as a means of sustaining oneself in the difficult but beautiful profession of teaching.

Meet our host, Ana Torres.

Ana has been an educator for 30 years, working in both the K–8 and higher education sectors. She served as an administrator and instructor at various public and private colleges and universities and as a bilingual and dual language teacher, dual language math and reading interventionist, dual language instructional coach, assistant principal, and principal in K–8 schools. Ana is currently the Senior Biliteracy and Multilingual Product Specialist on Amplify’s product specialist team, and delivers literacy and biliteracy presentations across the nation. Ana’s passion and advocacy for biliteracy and multiculturalism has led her to educate leaders, teachers, and parents about the positive impact of bilingualism and biliteracy in our world.

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Meet our Classroom Insider, Eric Cross.

Eric Cross is a middle school science teacher who hopes to someday be a lifelong educator, like the guests on Beyond My Years! In each episode, Eric connects with host Ana Torres to discuss her guests’ best insights gleaned from their long and rewarding careers in the classroom. Then, Eric talks about bringing some of their wisdom into his current classroom and busy life.

Quotes

“There were moments that I was missing because I wasn’t making space for them to land.”

—Rebecka Peterson

“This was like training my brain to become a good noticer and to take delight in my students’ quirks, and their genius, and their goofiness, as well as their beauty.”

—Rebecka Peterson

“It takes a lot of courage to stand in the present. It is mindfulness. It is joy.”

—Rebecka Peterson

“This is our profession. I think we reclaim it, and we reclaim it with a sense of joy. We reclaim it by saying, ‘This is hard work. And this is really beautiful work. I am exhausted, and I am exhilarated. Yes, I’m ready to go home, and you better believe I’m going to be here tomorrow, ready to give my whole heart and soul and mind again.’”

—Rebecka Peterson

“I thought…I had to earn my seat at the table. I don’t want any kid to ever think they have to earn their spot. I want them to know they are in, exactly as they are. There is no need to perform. They are loved on their good days, their hard days, whether they make the “A” or not—they are in. And more than that, they are celebrated.”

—Rebecka Peterson

“Physicists have found that particles at the subatomic level move when they’re seen, so that bearing witness to them changes the trajectory of the particle. And I just think, on my good days, that’s what I do, right? When I see, I can change a trajectory. I think that’s our superpower as teachers…we see the invisible.”

—Rebecka Peterson

“When you build that currency in students, they will jump—literally, jump. They will do anything for you. It’s not a magic wand. No. It takes time. Seeing them, acknowledging them, and believing in them.”

—Ana Torres

“I hope that the way I love is so radical that it changes the way my students love themselves and love each other. … I hope with all my heart that is true. But even if it doesn’t, it changes something in me. I am better because of this profession and because of my students.”

—Rebecka Peterson

“That’s how we build our joy, how we build our resiliency—when we do the work together.”

—Rebecka Peterson