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Open Up Resources Math Curriculum for Grade 6, Grade 7, and Grade 8

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The Open Up Resources math curriculum, authored by Illustrative Mathematics, is a free math curriculum for Grades 6-8. Math resources, questions, and answers for this curriculum 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
  • Unit 6.2: Introducing Ratios
      What Are Ratios?

    • Lesson 1: Introducing Ratios and Ratio Language
    • Lesson 2: Representing Ratios with Diagrams

    • Equivalent Ratios

    • Lesson 3: Recipes
    • Lesson 4: Color Mixtures
    • Lesson 5: Defining Equivalent Ratios

    • Representing 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

    • Solving Ratio and Rate Problems

    • 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

    • Part-Part-Whole Ratios

    • Lesson 15: Part-Part-Whole Ratios
    • Lesson 16: Solving More Ratio Problems

    • Let's Put it to Work

    • Lesson 17: A Fermi Problem
  • Unit 6.3: Unit Rates and Percentages
      The Burj Khalifa

    • Lesson 1: The Burj Khalifa

    • Unit Conversion

    • Lesson 2: Anchoring Units of Measurement
    • Lesson 3: Measuring with Different-Sized Units
    • Lesson 4: Converting Units

    • Rates

    • 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

    • Percentages

    • 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

    • Percentages

    • Lesson 15: Finding This Percent of That
    • Lesson 16: Finding the Percentage

    • Let's Put it to Work

    • Lesson 17: Painting a Room
  • Unit 6.4: Dividing Fractions
      Making Sense of Division

    • Lesson 1: Size of Divisor and Size of Quotient
    • Lesson 2: Meanings of Division
    • Lesson 3: Interpreting Division Situations

    • Meanings of Fraction Division

    • 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)

    • Algorithm for Fraction Division

    • Lesson 10: Dividing by Unit and Non-Unit Fractions
    • Lesson 11: Using an Algorithm to Divide Fractions

    • Fractions in Lengths, Areas, and Volumes

    • Lesson 12: Fractional Lengths
    • Lesson 13: Rectangles with Fractional Side Lengths
    • Lesson 14: Fractional Lengths in Triangles and Prisms
    • Lesson 15: Volume of Prisms

    • Let's Put it to Work

    • Lesson 16: Solving Problems Involving Fractions
    • Lesson 17: Fitting Boxes into Boxes
  • Unit 6.5: Arithmetic in Base Ten
      Warming Up to Decimals

    • Lesson 1: Using Decimals in a Shopping Context

    • Adding and Subtracting Decimals

    • 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

    • Multiplying Decimals

    • 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

    • Dividing 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

    • Let's Put it to Work

    • Lesson 14: Using Operations on Decimals to Solve Problems
    • Lesson 15: Making and Measuring Boxes
  • Unit 6.6 Expressions and Equations
      Equations in One Variable

    • 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

    • Equal and Equivalent

    • 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

    • Expressions with Exponents

    • Lesson 12: Meaning of Exponents
    • Lesson 13: Expressions with Exponents
    • Lesson 14: Evaluating Expressions with Exponents
    • Lesson 15: Equivalent Exponential Expressions

    • Relationships Between Quantities

    • Lesson 16: Two Related Quantities, Part 1
    • Lesson 17: Two Related Quantities, Part 2
    • Lesson 18: More Relationships
  • Unit 6.7: Rational Numbers
      Negative Numbers and Absolute Value

    • 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

    • Inequalities

    • Lesson 8: Writing and Graphing Inequalities
    • Lesson 9: Solutions of Inequalities
    • Lesson 10: Interpreting Inequalities

    • The Coordinate Plane

    • 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

    • Common Factors and Common Multiples

    • Lesson 16: Common Factors
    • Lesson 17: Common Multiples
    • Lesson 18: Using Common Multiples and Common Factors
  • Unit 6.8: Data Sets and Distributions
      Data, Variability, and Statistical Questions

    • Lesson 1: Got Data?
    • Lesson 2: Statistical Questions

    • Dot Plots and Histograms

    • 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

    • Mean and MAD

    • 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

    • Median and IQR

    • 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

    • Let's Put it to Work

    • Lesson 18: Using Data to Solve Problems
  • Unit 6.9: Putting It All Together
      Making Connections

    • 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





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