Open Up Resources Math Curriculum For Grade 6, Grade 7 And Grade 8

Open Up Resources
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.

6th Grade

• Unit 6.1: Area and Surface Area

  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

• 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
  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

7th Grade

• Grade 7 Unit 1: Scale Drawings

  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
  

• Grade 7 Unit 2: Introducing Proportional Relationships

  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
  

• Grade 7 Unit 3: Measuring Circles

  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
  

• Grade 7 Unit 4: Proportional Relationships and Percentages

  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
  

• Grade 7 Unit 5: Rational Number Arithmetic

  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
  

• Grade 7 Unit 6: Expressions, Equations, and Inequalities

  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)
  

• Grade 7 Unit 7: Angles, Triangles, and Prisms

  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
  

• Grade 7 Unit 8: Probability and Sampling

  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

• Grade 7 Unit 9: Putting It All Together

  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
  

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
  

  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
  

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

  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
  

• 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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