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Open Up Resources Curriculum for Grade 6, Grade 7, and Grade 8. Illustrative Math Questions and Answers.
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Open Up Resources Grade 6 | Open Up Resources Grade 7 | Open Up Resources Grade 8 |
The Open Up Resources Math curriculum, authored by Illustrative Mathematics is a free math curriculum for Grade 6, Grade 7, and Grade 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.
Reasoning to Find Area
Lesson 1: Tiling the Plane
Lesson 2: Finding Area by Decomposing and Rearranging
Lesson 3: Reasoning to Find Area
Parallelograms
Lesson 4: Parallelograms
Lesson 5: Bases and Heights of Parallelograms
Lesson 6: Area of Parallelograms
Triangles
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
Polygons
Lesson 11: Polygons
Surface Area
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
Squares and Cubes
Lesson 17: Squares and Cubes
Lesson 18: Surface Area of a Cube
Let’s Put it to Work
Lesson 19: Designing a Tent
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
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
Lesson 15: Finding This Percent of That
Lesson 16: Finding the Percentage
Let’s Put it to Work
Lesson 17: Painting a Room
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
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
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
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
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
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
Scaled Copies
Lesson 1: What are Scaled Copies?
Lesson 2: Corresponding Parts and Scale Factors
Lesson 3: Making Scaled Copies
Lesson 4: Scaled Relationships
Lesson 5: The Size of the Scale Factor
Lesson 6: Scaling and Area
Scale Drawings
Lesson 7: Scale Drawings
Lesson 8: Scale Drawings and Maps
Lesson 9: Creating Scale Drawings
Lesson 10: Changing Scales in Scale Drawings
Lesson 11: Scales without Units
Lesson 12: Units in Scale Drawings
Let’s Put It to Work
Lesson 13: Draw It to Scale
Representing Proportional Relationships with Tables
Lesson 1: One of These Things Is Not Like the Others
Lesson 2: Introducing Proportional Relationships with Tables
Lesson 3: More about Constant of Proportionality
Representing Proportional Relationships with Equations
Lesson 4: Proportional Relationships and Equations
Lesson 5: Two Equations for Each Relationship
Lesson 6: Using Equations to Solve Problems
Comparing Proportional and Nonproportional Relationships
Lesson 7: Comparing Relationships with Tables
Lesson 8: Comparing Relationships with Equations
Lesson 9: Solving Problems about Proportional Relationships
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
Let’s Put it to Work
Lesson 14: Four Representations
Lesson 15: Using Water Efficiently
Circumference of a Circle
Lesson 1: How Well Can You Measure?
Lesson 2: Exploring Circles
Lesson 3: Exploring Circumference
Lesson 4: Applying Circumference
Lesson 5: Circumference and Wheels
Area of a Circle
Lesson 6: Estimating Areas
Lesson 7: Exploring the Area of a Circle
Lesson 8: Relating Area to Circumference
Lesson 9: Applying Area of Circles
Let’s Put it to Work
Lesson 10: Distinguishing Circumference and Area
Lesson 11: Stained-Glass Windows
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
Lesson 5: Say It with Decimals
Percent Increase and Decrease
Lesson 6: Increasing and Decreasing
Lesson 7: One Hundred Percent
Lesson 8: Percent Increase and Decrease with Equations
Lesson 9: More and Less than 1%
Applying Percentages
Lesson 10: Tax and Tip
Lesson 11: Percentage Contexts
Lesson 12: Finding the Percentage
Lesson 13: Measurement Error
Lesson 14: Percent Error
Lesson 15: Error Intervals
Let’s Put it to Work
Lesson 16: Posing Percentage Problems
Interpreting Negative Numbers
Lesson 1: Interpreting Negative Numbers
Adding and Subtracting Rational Numbers
Lesson 2: Changing Temperatures
Lesson 3: Changing Elevation
Lesson 4: Money and Debts
Lesson 5: Representing Subtraction
Lesson 6: Subtracting Rational Numbers
Lesson 7: Adding and Subtracting to Solve Problems
Multiplying and Dividing Rational Numbers
Lesson 8: Position, Speed, and Direction
Lesson 9: Multiplying Rational Numbers
Lesson 10: Multiply!
Lesson 11: Dividing Rational Numbers
Lesson 12: Negative Rates
Four Operations with Rational Numbers
Lesson 13: Expressions with Rational Numbers
Lesson 14: Solving Problems with Rational Numbers
Solving Equations When There Are Negative Numbers
Lesson 15: Solving Equations with Rational Numbers
Lesson 16: Representing Contexts with Equations
Let’s Put it to Work
Lesson 17: The Stock Market
Representing Situations of the Form px + q = r and p(x + q) = r
Lesson 1: Relationships between Quantities
Lesson 2: Reasoning about Contexts with Tape Diagrams (Part 1)
Lesson 3: Reasoning about Contexts with Tape Diagrams (Part 2)
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
Lesson 6: Distinguishing between Two Types of Situations
Solving Equations of the Form px + q = r and p(x + q) = r and Problems That Lead to Those Equations
Lesson 7: Reasoning about Solving Equations (Part 1)
Lesson 8: Reasoning about Solving Equations (Part 2)
Lesson 9: Dealing with Negative Numbers
Lesson 10: Different Options for Solving One Equation
Lesson 11: Using Equations to Solve Problems
Lesson 12: Solving Problems about Percent Increase or Decrease
Inequalities
Lesson 13: Reintroducing Inequalities
Lesson 14: Finding Solutions to Inequalities in Context
Lesson 15: Efficiently Solving Inequalities
Lesson 16: Interpreting Inequalities
Lesson 17: Modeling with Inequalities
Writing Equivalent Expressions
Lesson 18: Subtraction in Equivalent Expressions
Lesson 19: Expanding and Factoring
Lesson 20: Combining Like Terms (Part 1)
Lesson 21: Combining Like Terms (Part 2)
Lesson 22: Combining Like Terms (Part 3)
Angle Relationships
Lesson 1: Relationships of Angles
Lesson 2: Adjacent Angles
Lesson 3: Nonadjacent Angles
Lesson 4: Solving for Unknown Angles
Lesson 5: Using Equations to Solve for Unknown Angles
Drawing Polygons with Given Conditions
Lesson 6: Building Polygons (Part 1)
Lesson 7: Building Polygons (Part 2)
Lesson 8: Triangles with 3 Common Measures
Lesson 9: Drawing Triangles (Part 1)
Lesson 10: Drawing Triangles (Part 2)
Solid Geometry
Lesson 11: Slicing Solids
Lesson 12: Volume of Right Prisms
Lesson 13: Decomposing Bases for Area
Lesson 14: Surface Area of Right Prisms
Lesson 15: Distinguishing Volume and Surface Area
Lesson 16: Applying Volume and Surface Area
Let’s Put It to Work
Lesson 17: Building Prisms
Probabilities of Single Step Events
Lesson 1: Mystery Bags
Lesson 2: Chance Experiments
Lesson 3: What Are Probabilities?
Lesson 4: Estimating Probabilities Through Repeated Experiments
Lesson 5: More Estimating Probabilities
Lesson 6: Estimating Probabilities Using Simulation
Probabilities of Multi-step Events
Lesson 7: Simulating Multi-step Experiments
Lesson 8: Keeping Track of All Possible Outcomes
Lesson 9: Multi-step Experiments
Lesson 10: Designing Simulations
Sampling
Lesson 11: Comparing Groups
Lesson 12: Larger Populations
Lesson 13: What Makes a Good Sample?
Lesson 14: Sampling in a Fair Way
Using Samples
Lesson 15: Estimating Population Measures of Center
Lesson 16: Estimating Population Proportions
Lesson 17: More about Sampling Variability
Lesson 18: Comparing Populations Using Samples
Lesson 19: Comparing Populations With Friends
Let’s Put it to Work
Lesson 18: Memory Test
Running a Restaurant
Lesson 1: Planning Recipes
Lesson 2: Costs of Running a Restaurant
Lesson 3: More Costs of Running a Restaurant
Lesson 4: Restaurant Floor Plan
Making Connections
Lesson 5: How Crowded Is this Neighborhood?
Lesson 6: Fermi Problems
Lesson 7: More Expressions and Equations
Lesson 8: Measurement Error (Part 1)
Lesson 9: Measurement Error (Part 2)
Designing a Course
Lesson 10: Measuring Long Distances Over Uneven Terrain
Lesson 11: Building a Trundle Wheel
Lesson 12: Using a Trundle Wheel to Measure Distances
Lesson 13: Designing a 5K Course
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
Congruence
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
Dilations
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
Similarity
Lesson 6: Similarity
Lesson 7: Similar Polygons
Lesson 8: Similar Triangles
Lesson 9: Side Length Quotients in Similar Triangles
Slope
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
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
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
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 . . .
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
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?
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
Putting It All Together
Lesson 1: What Influences Temperature?
Lesson 2: Tessellations of the Plane
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