Illustrative Mathematics Curriculum for Grade 6, Grade 7, and Grade 8

Questions, answers, and resources for the Open Up Resources curriculum authored by Illustrative Mathematics are listed below. Click on the buttons to see a list of lessons in each unit and links to questions, answers, and explanatory videos for each lesson.

Grade 6

Unit 6.1: Area and Surface Area
- Lesson 1: Tiling the Plane
- Lesson 2: Finding Area by Decomposing and Rearranging
- Lesson 3: Reasoning to Find Area
- Lesson 4: Parallelograms
- Lesson 5: Bases and Heights of Parallelograms
- Lesson 6: Area of Parallelograms
- Lesson 7: From Parallelograms to Triangles
- Lesson 8: Area of Triangles
- Lesson 9: Formula for the Area of a Triangle
- Lesson 10: Bases and Heights of Triangles
- Lesson 11: Polygons
- Lesson 12: What is Surface Area?
- Lesson 13: Polyhedra
- Lesson 14: Nets and Surface Area
- Lesson 15: More Nets, More Surface Area
- Lesson 16: Distinguishing Between Surface Area and Volume
- Lesson 17: Squares and Cubes
- Lesson 18: Surface Area of a Cube
- Lesson 19: Designing a Tent
Unit 6.2: Introducing Ratios
- Lesson 1: Introducing Ratios and Ratio Language
- Lesson 2: Representing Ratios with Diagrams
- Lesson 3: Recipes
- Lesson 4: Color Mixtures
- Lesson 5: Defining Equivalent Ratios
- Lesson 6: Introducing Double Number Line Diagrams
- Lesson 7: Creating Double Number Line Diagrams
- Lesson 8: How Much for One?
- Lesson 9: Constant Speed
- Lesson 10: Comparing Situations by Examining Ratios
- Lesson 11: Representing Ratios with Tables
- Lesson 12: Navigating a Table of Equivalent Ratios
- Lesson 13: Tables and Double Number Line Diagrams
- Lesson 14: Solving Equivalent Ratio Problems
- Lesson 15: Part-Part-Whole Ratios
- Lesson 16: Solving More Ratio Problems
- Lesson 17: A Fermi Problem
Unit 6.3: Unit Rates and Percentages
- Lesson 1: The Burj Khalifa
- Lesson 2: Anchoring Units of Measurement
- Lesson 3: Measuring with Different-Sized Units
- Lesson 4: Converting Units
- Lesson 5: Comparing Speeds and Prices
- Lesson 6: Interpreting Rates
- Lesson 7: Equivalent Ratios Have the Same Unit Rates
- Lesson 8: More About Constant Speed
- Lesson 9: Solving Rate Problems
- Lesson 10: What Are Percentages?
- Lesson 11: Percentages and Double Number Lines
- Lesson 12: Percentages and Tape Diagrams
- Lesson 13: Benchmark Percentages
- Lesson 14: Solving Percentage Problems
- Lesson 15: Finding This Percent of That
- Lesson 16: Finding the Percentage
- Lesson 17: Painting a Room
Unit 6.4: Dividing Fractions
- Lesson 1: Size of Divisor and Size of Quotient
- Lesson 2: Meanings of Division
- Lesson 3: Interpreting Division Situations
- Lesson 4: How Many Groups? (Part 1)
- Lesson 5: How Many Groups? (Part 2)
- Lesson 6: Using Diagrams to Find the Number of Groups
- 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)
- Lesson 10: Dividing by Unit and Non-Unit Fractions
- Lesson 11: Using an Algorithm to Divide Fractions
- Lesson 12: Fractional Lengths
- Lesson 13: Rectangles with Fractional Side Lengths
- Lesson 14: Fractional Lengths in Triangles and Prisms
- Lesson 15: Volume of Prisms
- Lesson 16: Solving Problems Involving Fractions
- Lesson 17: Fitting Boxes into Boxes
Unit 6.5: Arithmetic in Base Ten
- Lesson 1: Using Decimals in a Shopping Context
- Lesson 2: Using Diagrams to Represent Addition and Subtraction
- Lesson 3: Adding and Subtracting Decimals with Few Non-Zero Digits
- Lesson 4: Adding and Subtracting Decimals with Many Non-Zero Digits
- Lesson 5: Decimal Points in Products
- Lesson 6: Methods for Multiplying Decimals
- Lesson 7: Using Diagrams to Represent Multiplication
- Lesson 8: Calculating Products of Decimals
- Lesson 9: Using the Partial Quotients Method
- Lesson 10: Using Long Division
- Lesson 11: Dividing Numbers that Result in Decimals
- Lesson 12: Dividing Decimals by Whole Numbers
- Lesson 13: Dividing Decimals by Decimals
- Lesson 14: Using Operations on Decimals to Solve Problems
- Lesson 15: Making and Measuring Boxes
Unit 6.6 Expressions and Equations
- Lesson 1: Tape Diagrams and Equations
- Lesson 2: Truth and Equations
- Lesson 3: Staying in Balance
- Lesson 4: Practice Solving Equations and Representing Situations with Equations
- Lesson 5: A New Way to Interpret a over b
- Lesson 6: Write Expressions Where Letters Stand for Numbers
- Lesson 7: Revisit Percentages
- Lesson 8: Equal and Equivalent
- Lesson 9: The Distributive Property, Part 1
- Lesson 10: The Distributive Property, Part 2
- Lesson 11: The Distributive Property, Part 3
- Lesson 12: Meaning of Exponents
- Lesson 13: Expressions with Exponents
- Lesson 14: Evaluating Expressions with Exponents
- Lesson 15: Equivalent Exponential Expressions
- Lesson 16: Two Related Quantities, Part 1
- Lesson 17: Two Related Quantities, Part 2
- Lesson 18: More Relationships
Unit 6.7: Rational Numbers
- Lesson 1: Positive and Negative Numbers
- Lesson 2: Points on the Number Line
- Lesson 3: Comparing Positive and Negative Numbers
- Lesson 4: Ordering Rational Numbers
- Lesson 5: Using Negative Numbers to Make Sense of Contexts
- Lesson 6: Absolute Value of Numbers
- Lesson 7: Comparing Numbers and Distance from Zero
- Lesson 8: Writing and Graphing Inequalities
- Lesson 9: Solutions of Inequalities
- Lesson 10: Interpreting Inequalities
- Lesson 11: Points on the Coordinate Plane
- Lesson 12: Constructing the Coordinate Plane
- Lesson 13: Interpreting Points on a Coordinate Plane
- Lesson 14: Distances on a Coordinate Plane
- Lesson 15: Shapes on the Coordinate Plane
- Lesson 16: Common Factors
- Lesson 17: Common Multiples
- Lesson 18: Using Common Multiples and Common Factors
Unit 6.8: Data Sets and Distributions
- Lesson 1: Got Data?
- Lesson 2: Statistical Questions
- Lesson 3: Representing Data Graphically
- Lesson 4: Dot Plots
- Lesson 5: Using Dot Plots to Answer Statistical Questions
- Lesson 6: Histograms
- Lesson 7: Using Histograms to Answer Statistical Questions
- Lesson 8: Describing Distributions on Histograms
- Lesson 9: Interpreting the Mean as Fair Share
- Lesson 10: Finding and Interpreting the Mean as the Balance Point
- Lesson 11: Deviation from the Mean
- Lesson 12: Using Mean and MAD to Make Comparisons
- Lesson 13: The Median of a Data Set
- Lesson 14: Comparing Mean and Median
- Lesson 15: Quartiles and Interquartile Range
- Lesson 16: Box Plots
- Lesson 17: Using Box Plots
- Lesson 18: Using Data to Solve Problems
Unit 6.9: Putting It All Together
- Lesson 1: Fermi Problems
- Lesson 2: If Our Class Were the World
- Lesson 3: Rectangle Madness
- Lesson 4: How Do We Choose?
- Lesson 5: More than Two Choices
- Lesson 6: Picking Representatives

Check out our most popular games!

Fraction Concoction Game:
Master fractions in the lab: mix, add, and subtract beakers to create the perfect concoction!

Fact Family Game:
Complete fact families and master the link between addition & subtraction and multiplication & division.

Number Bond Garden:
Clear the board by matching number pairs that sum to ten in this garden-themed mental math puzzle.

Online Addition Subtraction Game:
Practice your addition and subtraction skills to help the penguin find its mummy.

Penguin Solitaire
Penguin Solitaire is a fun game that aims to move all cards to the foundations to build four full sequences. There are two versions here: Penguin (Tuxedo) and Penguin (Original).

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