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.

6th Grade

7th Grade

8th Grade

  • Grade 8 Unit 1: Rigid Transformations and Congruence

    Rigid Transformations
    Lesson 1: Moving in the Plane
    Lesson 2: Naming the Moves
    Lesson 3: Grid Moves
    Lesson 4: Making the Moves
    Lesson 5: Coordinate Moves
    Lesson 6: Describing Transformations

    Properties of Rigid Transformations
    Lesson 7: No Bending or Stretching
    Lesson 8: Rotation Patterns
    Lesson 9: Moves in Parallel
    Lesson 10: Composing Figures

    Lesson 11: What Is the Same?
    Lesson 12: Congruent Polygons
    Lesson 13: Congruence

    Angles in a Triangle
    Lesson 14: Alternate Interior Angles
    Lesson 15: Adding the Angles in a Triangle
    Lesson 16: Parallel Lines and the Angles in a Triangle

    Let’s Put It to Work
    Lesson 17: Rotate and Tessellate

  • Grade 8 Unit 2: Dilations, Similarity, and Introducing Slope

    Lesson 1: Projecting and Scaling
    Lesson 2: Circular Grid
    Lesson 3: Dilations with no Grid
    Lesson 4: Dilations on a Square Grid
    Lesson 5: More Dilations

    Lesson 6: Similarity
    Lesson 7: Similar Polygons
    Lesson 8: Similar Triangles
    Lesson 9: Side Length Quotients in Similar Triangles

    Lesson 10: Meet Slope
    Lesson 11: Writing Equations for Lines
    Lesson 12: Using Equations for Lines

    Let’s Put It to Work
    Lesson 13: The Shadow Knows

  • Grade 8 Unit 3: Linear Relationships

    Proportional Relationships
    Lesson 1: Understanding Proportional Relationships
    Lesson 2: Graphs of Proportional Relationships
    Lesson 3: Representing Proportional Relationships
    Lesson 4: Comparing Proportional Relationships

    Representing Linear Relationships
    Lesson 5: Introduction to Linear Relationships
    Lesson 6: More Linear Relationships
    Lesson 7: Representations of Linear Relationships
    Lesson 8: Translating to y=mx+b

    Finding Slopes
    Lesson 9: Slopes Don’t Have to be Positive
    Lesson 10: Calculating Slope
    Lesson 11: Equations of All Kinds of Lines

    Linear Equations
    Lesson 12: Solutions to Linear Equations
    Lesson 13: More Solutions to Linear Equations

    Let’s Put It to Work
    Lesson 14: Using Linear Relations to Solve Problems

  • Grade 8 Unit 4: Linear Equations and Linear Systems

    Puzzle Problems
    Lesson 1: Number Puzzles

    Linear Equations in One Variable
    Lesson 2: Keeping the Equation Balanced
    Lesson 3: Balanced Moves
    Lesson 4: More Balanced Moves
    Lesson 5: Solving Any Linear Equation
    Lesson 6: Strategic Solving
    Lesson 7: All, Some, or No Solutions
    Lesson 8: How Many Solutions?
    Lesson 9: When Are They the Same?

    Systems of Linear Equations
    Lesson 10: On or Off the Line?
    Lesson 11: On Both of the Lines
    Lesson 12: Systems of Equations
    Lesson 13: Solving Systems of Equations
    Lesson 14: Solving More Systems
    Lesson 15: Writing Systems of Equations

    Let’s Put It to Work
    Lesson 16: Solving Problems with Systems of Equations

  • Grade 8 Unit 5: Functions and Volume

    Inputs and Outputs
    Lesson 1: Inputs and Outputs
    Lesson 2: Introduction to Functions

    Representing and Interpreting Functions
    Lesson 3: Equations for Functions
    Lesson 4: Tables, Equations, and Graphs of Functions
    Lesson 5: More Graphs of Functions
    Lesson 6: Even More Graphs of Functions
    Lesson 7: Connecting Representations of Functions

    Linear Functions and Rates of Change
    Lesson 8: Linear Functions
    Lesson 9: Linear Models
    Lesson 10: Piecewise Linear Functions

    Cylinders and Cones
    Lesson 11: Filling containers
    Lesson 12: How Much Will Fit?
    Lesson 13: The Volume of a Cylinder
    Lesson 14: Finding Cylinder Dimensions
    Lesson 15: The Volume of a Cone
    Lesson 16: Finding Cone Dimensions

    Dimensions and Spheres
    Lesson 17: Scaling One Dimension
    Lesson 18: Scaling Two Dimensions
    Lesson 19: Estimating a Hemisphere
    Lesson 20: The Volume of a Sphere
    Lesson 21: Cylinders, Cones, and Spheres

    Let’s Put It to Work
    Lesson 22: Volume As a Function of . . .

  • Grade 8 Unit 6: Associations in Data

    Does This Predict That?
    Lesson 1: Organizing Data
    Lesson 2: Plotting Data

    Associations in Numerical Data
    Lesson 3: What a Point in a Scatter Plot Means
    Lesson 4: Fitting a Line to Data
    Lesson 5: Describing Trends in Scatter Plots
    Lesson 6: The Slope of a Fitted Line
    Lesson 7: Observing More Patterns in Scatter Plots
    Lesson 8: Analyzing Bivariate Data

    Associations in Categorical Data
    Lesson 9: Looking for Associations
    Lesson 10: Using Data Displays to Find Associations

    Let’s Put It to Work
    Lesson 11: Gone In 30 Seconds

  • Grade 8 Unit 7: Exponents and Scientific Notation

    Exponent Review
    Lesson 1: Exponent Review

    Associations in Numerical Data
    Lesson 2: Multiplying Powers of Ten
    Lesson 3: Powers of Powers of 10
    Lesson 4: Dividing Powers of 10
    Lesson 5: Negative Exponents with Powers of 10
    Lesson 6: What about Other Bases?
    Lesson 7: Practice with Rational Bases
    Lesson 8: Combining Bases

    Scientific Notation
    Lesson 9: Describing Large and Small Numbers Using Powers of 10
    Lesson 10: Representing Large Numbers on the Number Line
    Lesson 11: Representing Small Numbers on the Number Line
    Lesson 12: Applications of Arithmetic with Powers of 10
    Lesson 13: Definition of Scientific Notation
    Lesson 14: Multiplying, Dividing, and Estimating with Scientific Notation
    Lesson 15: Adding and Subtracting with Scientific Notation

    Let’s Put It to Work
    Lesson 16: Is a Smartphone Smart Enough to Go to the Moon?

  • Grade 8 Unit 8: Pythagorean Theorem and Irrational Numbers

    The Size of Shapes
    Lesson 1: The Areas of Squares and Their Side Lengths

    Side Lengths and Areas of Squares
    Lesson 2: Side Lengths and Areas
    Lesson 3: Rational and Irrational Numbers
    Lesson 4: Square Roots on the Number Line
    Lesson 5: Reasoning About Square Roots

    The Pythagorean Theorem
    Lesson 6: Finding Side Lengths of Triangles
    Lesson 7: A Proof of the Pythagorean Theorem
    Lesson 8: Finding Unknown Side Lengths
    Lesson 9: The Converse
    Lesson 10: Applications of the Pythagorean Theorem
    Lesson 11: Finding Distances in the Coordinate Plane

    Side Lengths and Volumes of Cubes
    Lesson 12: Edge Lengths and Volumes
    Lesson 13: Cube Roots

    Decimal Representation of Rational and Irrational Numbers
    Lesson 14: Decimal Representations of Rational Numbers
    Lesson 15: Infinite Decimal Expansions

  • Grade 8 Unit 9: Putting It All Together

    Putting It All Together
    Lesson 1: What Influences Temperature?
    Lesson 2: Tessellations of the Plane

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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