Contents
Lesson 1: Tiling the Plane
1.1: Which One Doesn’t Belong: Tilings
1.2: More Red, Green, or Blue?
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Lesson 1 Summary
Glossary
Lesson 1 Practice Problems
Lesson 2: Finding Area by Decomposing and Rearranging
2.1: What is Area?
2.2: Composing Shapes
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2.3: Tangram Triangles
Lesson 2 Summary
Glossary
Lesson 2 Practice Problems
Lesson 3: Reasoning to Find Area
3.1: Comparing Regions
3.2: On the Grid
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3.3: Off the Grid
Lesson 3 Summary
Lesson 3 Practice Problems
Lesson 4: Parallelograms
4.1: Features of a Parallelogram
4.2: Area of a Parallelogram
4.3: Lots of Parallelograms
Lesson 4 Summary
Glossary
Lesson 4 Practice Problems
Lesson 5: Areas of Parallelograms
5.1: A Parallelogram and Its Rectangles
5.2: Finding the Formula for Area of Parallelograms
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5.3: More Areas of Parallelograms
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Lesson 5 Summary
Glossary
Lesson 5 Practice Problems
Lesson 6: From Parallelograms to Triangles
6.1: Same Parallelograms, Different Bases
6.2: A Tale of Two Triangles (Part 1)
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6.3: A Tale of Two Triangles (Part 2)
Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Area of Triangles
7.1: Composing Parallelograms
7.2: More Triangles
7.3: Decomposing a Parallelogram
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Lesson 7 Summary
Lesson 7 Practice Problems
Lesson 8: Formula for the Area of a Triangle
8.1: Bases and Heights of a Triangle
8.2: Finding a Formula for Area of a Triangle
8.3: Applying the Formula for Area of Triangles
Lesson 8 Summary
Glossary
Lesson 8 Practice Problems
Lesson 9: Polygons
9.1: Which One Doesn’t Belong: Bases and Heights
9.2: What Are Polygons?
9.3: Quadrilateral Strategies
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9.4: Pinwheel
Lesson 9 Summary
Glossary
Lesson 9 Practice Problems
Lesson 10: What is Surface Area?
10.1: Covering the Cabinet (Part 1)
10.2: Covering the Cabinet (Part 2)
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10.3: Building with Snap Cubes
Lesson 10 Summary
Glossary
Lesson 10 Practice Problems
Lesson 11: Polyhedra and Nets
11.1: What are Polyhedra?
11.2: Prisms and Pyramids
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11.3: Using Nets to Find Surface Area
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Lesson 11 Summary
Glossary
Lesson 11 Practice Problems
Lesson 12: More Nets, More Surface Area
12.1: Notice and Wonder: Wrapping Paper
12.2: Building Prisms and Pyramids
12.3: Comparing Boxes
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Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Designing a Tent
13.1: Tent Design - Part 1
13.2: Tent Design - Part 2
Learning Targets
Lesson 1: Tiling the Plane
Lesson 2: Finding Area by Decomposing and Rearranging
Lesson 3: Reasoning to Find Area
Lesson 4: Parallelograms
Lesson 5: Areas of Parallelograms
Lesson 6: From Parallelograms to Triangles
Lesson 7: Area of Triangles
Lesson 8: Formula for the Area of a Triangle
Lesson 9: Polygons
Lesson 10: What is Surface Area?
Lesson 11: Polyhedra and Nets
Lesson 12: More Nets, More Surface Area
Lesson 13: Designing a Tent
Lesson 1: Representing Ratios with Diagrams
1.1: Number Talk: Dividing by 4 and Multiplying by \frac14
1.2: A Collection of Snap Cubes
1.3: Blue Paint and Art Paste
1.4: Card Sort: Spaghetti Sauce
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Lesson 1 Summary
Lesson 1 Practice Problems
Lesson 2: Mixtures
2.1: Flower Pattern
2.2: Powdered Drink Mix
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2.3: Batches of Cookies
Lesson 2 Summary
Glossary
Lesson 2 Practice Problems
Lesson 3: Defining Equivalent Ratios
3.1: Dots and Half Dots
3.2: Tuna Casserole
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3.3: What Are Equivalent Ratios?
Lesson 3 Summary
Glossary
Lesson 3 Practice Problems
Lesson 4: Introducing Double Number Line Diagrams
4.1: Number Talk: Adjusting Another Factor
4.2: Drink Mix on a Double Number Line
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4.3: Blue Paint on a Double Number Line
Lesson 4 Summary
Glossary
Lesson 4 Practice Problems
Lesson 5: Creating Double Number Line Diagrams
5.1: Ordering on a Number Line
5.2: Just a Little Green
5.3: Art Paste on a Double Number Line
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5.4: Revisiting Tuna Casserole
Lesson 5 Summary
Glossary
Lesson 5 Practice Problems
Lesson 6: Per Each
6.1: Number Talk: Dividing by Powers of 10
6.2: More Shopping
6.3: Moving 10 Meters
Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Comparing Situations by Examining Ratios
7.1: Treadmills
7.2: Concert Tickets
7.3: Sparkling Orange Juice
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Lesson 7 Summary
Glossary
Lesson 7 Practice Problems
Lesson 8: Representing Ratios with Tables
8.1: How Is It Growing?
8.2: A Huge Amount of Sparkling Orange Juice
8.3: Batches of Trail Mix
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Lesson 8 Summary
Glossary
Lesson 8 Practice Problems
Lesson 9: Navigating a Table of Equivalent Ratios
9.1: Number Talk: Multiplying by a Unit Fraction
9.2: Comparing Taco Prices
9.3: Hourly Wages
9.4: Zeno’s Memory Card
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Lesson 9 Summary
Lesson 9 Practice Problems
Lesson 10: Solving Equivalent Ratio Problems
10.1: What Do You Want to Know?
10.2: Info Gap: Hot Chocolate and Potatoes
10.3: Comparing Reading Rates
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Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Part-Part-Whole Ratios
11.1: True or False: Multiplying by a Unit Fraction
11.2: Cubes of Paint
11.3: Sneakers, Chicken, and Fruit Juice
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11.4: Invent Your Own Ratio Problem
Lesson 11 Summary
Glossary
Lesson 11 Practice Problems
Lesson 12: Solving More Ratio Problems
12.1: You Tell the Story
12.2: A Trip to the Aquarium
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12.3: Salad Dressing and Moving Boxes
Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: The Burj Khalifa
13.1: Estimating Height
13.2: Window Washing
13.3: Climbing the Burj Khalifa
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Lesson 13 Summary
Lesson 13 Practice Problems
Lesson 14: Measuring with Different-Sized Units
14.1: Width of a Paper
14.2: Measurement Stations
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Lesson 14 Summary
Lesson 14 Practice Problems
Lesson 15: Converting Units
15.1: Number Talk: Fractions of a Number
15.2: Road Trip
15.3: Veterinary Weights
15.4: Cooking with a Tablespoon
Lesson 15 Summary
Lesson 15 Practice Problems
Lesson 16: Comparing Speeds and Prices
16.1: Closest Quotient
16.2: More Treadmills
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16.3: The Best Deal on Beans
Lesson 16 Summary
Glossary
Lesson 16 Practice Problems
Lesson 17: Interpreting Rates
17.1: Something per Something
17.2: Cooking Oatmeal
17.3: Cheesecake, Milk, and Raffle Tickets
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Lesson 17 Summary
Glossary
Lesson 17 Practice Problems
Lesson 18: Equivalent Ratios Have the Same Unit Rates
18.1: Which One Doesn’t Belong: Comparing Speeds
18.2: Price of Burritos
18.3: Making Bracelets
18.4: How Much Applesauce?
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Lesson 18 Summary
Lesson 18 Practice Problems
Lesson 19: Solving Rate Problems
19.1: Grid of 100
19.2: Card Sort: Is it a Deal?
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19.3: The Fastest of All
Lesson 19 Summary
Lesson 19 Practice Problems
Lesson 20: Percentages and Double Number Lines
20.1: Fundraising Goal
20.2: Three-Day Biking Trip
20.3: Puppies Grow Up
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Lesson 20 Summary
Glossary
Lesson 20 Practice Problems
Lesson 21: Percentages and Tape Diagrams
21.1: Notice and Wonder: Tape Diagrams
21.2: Revisiting Jada's Puppy
21.3: 5 Dollars
21.4: Staying Hydrated
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Lesson 21 Summary
Lesson 21 Practice Problems
Lesson 22: Benchmark Percentages
22.1: What Percentage Is Shaded?
22.2: Liters, Meters, and Hours
22.3: Nine is . . .
22.4: Matching the Percentage
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Lesson 22 Summary
Lesson 22 Practice Problems
Lesson 23: Solving Percentage Problems
23.1: Number Talk: Decimals
23.2: Info Gap: Music Devices
23.3: Everything is On Sale
Lesson 23 Summary
Lesson 23 Practice Problems
Lesson 24: Finding the Percentage
24.1: True or False: Percentages
24.2: Jumping Rope
24.3: Restaurant Capacity
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Lesson 24 Summary
Lesson 24 Practice Problems
Lesson 25: A Fermi Problem
25.1: Fix It!
25.2: Who Was Fermi?
25.3: Researching Your Own Fermi Problem
Lesson 26: Painting a Room
26.1: Getting Ready to Paint
26.2: How Much It Costs to Paint
26.3: How Long It Takes to Paint
Learning Targets
Lesson 1: Representing Ratios with Diagrams
Lesson 2: Mixtures
Lesson 3: Defining Equivalent Ratios
Lesson 4: Introducing Double Number Line Diagrams
Lesson 5: Creating Double Number Line Diagrams
Lesson 6: Per Each
Lesson 7: Comparing Situations by Examining Ratios
Lesson 8: Representing Ratios with Tables
Lesson 9: Navigating a Table of Equivalent Ratios
Lesson 10: Solving Equivalent Ratio Problems
Lesson 11: Part-Part-Whole Ratios
Lesson 12: Solving More Ratio Problems
Lesson 13: The Burj Khalifa
Lesson 14: Measuring with Different-Sized Units
Lesson 15: Converting Units
Lesson 16: Comparing Speeds and Prices
Lesson 17: Interpreting Rates
Lesson 18: Equivalent Ratios Have the Same Unit Rates
Lesson 19: Solving Rate Problems
Lesson 20: Percentages and Double Number Lines
Lesson 21: Percentages and Tape Diagrams
Lesson 22: Benchmark Percentages
Lesson 23: Solving Percentage Problems
Lesson 24: Finding the Percentage
Lesson 25: A Fermi Problem
Lesson 26: Painting a Room
Glossary
Attributions
Image Attributions
Notes
Notes
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