Contents
Lesson 1: Lots of Flags
1.1: Scaled or Not?
1.2: Flags Are Many Sizes
1.3: What Percentage Is the Union?
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Lesson 1 Summary
Glossary
Lesson 1 Practice Problems
Lesson 2: Ratios and Rates With Fractions
2.1: Number Talk: Division
2.2: A Train is Traveling at . . .
2.3: Comparing Running Speeds
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2.4: Scaling the Mona Lisa
Lesson 2 Summary
Glossary
Lesson 2 Practice Problems
Lesson 3: Revisiting Proportional Relationships
3.1: Recipe Ratios
3.2: The Price of Rope
3.3: Swimming, Manufacturing, and Painting
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3.4: Finishing the Race and More Orange Juice
Lesson 3 Summary
Lesson 3 Practice Problems
Lesson 4: Half as Much Again
4.1: Notice and Wonder: Tape Diagrams
4.2: Walking Half as Much Again
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4.3: More and Less
4.4: Card Sort: Representations of Proportional Relationships
Lesson 4 Summary
Glossary
Lesson 4 Practice Problems
Lesson 5: Say It with Decimals
5.1: Notice and Wonder: Fractions to Decimals
5.2: Repeating Decimals
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5.3: More and Less with Decimals
5.4: Card Sort: More Representations
Lesson 5 Summary
Glossary
Lesson 5 Practice Problems
Lesson 6: Increasing and Decreasing
6.1: Improving Their Game
6.2: More Cereal and a Discounted Shirt
6.3: Using Tape Diagrams
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6.4: Agree or Disagree: Percentages
Lesson 6 Summary
Glossary
Lesson 6 Practice Problems
Lesson 7: One Hundred Percent
7.1: Notice and Wonder: Double Number Line
7.2: Double Number Lines
7.3: Representing More Juice
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7.4: Protecting the Green Sea Turtle
Lesson 7 Summary
Lesson 7 Practice Problems
Lesson 8: Percent Increase and Decrease with Equations
8.1: Number Talk: From 100 to 106
8.2: Interest and Depreciation
8.3: Matching Equations
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8.4: Representing Percent Increase and Decrease: Equations
Lesson 8 Summary
Lesson 8 Practice Problems
Lesson 9: More and Less than 1%
9.1: Number Talk: What Percentage?
9.2: Waiting Tables
9.3: Fractions of a Percent
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9.4: Population Growth
Lesson 9 Summary
Lesson 9 Practice Problems
Lesson 10: Tax and Tip
10.1: Notice and Wonder: The Price of Sunglasses
10.2: Shopping in Two Different Cities
10.3: Shopping in a Third City
10.4: Dining at a Restaurant
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Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Percentage Contexts
11.1: Leaving a Tip
11.2: A Car Dealership
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11.3: Commission at a Gym
11.4: Card Sort: Percentage Situations
Lesson 11 Summary
Lesson 11 Practice Problems
Lesson 12: Finding the Percentage
12.1: Tax, Tip, and Discount
12.2: What Is the Percentage?
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12.3: Info Gap: Sporting Goods
Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Measurement Error
13.1: Measuring to the Nearest
13.2: Measuring a Soccer Field
13.3: Measuring Your Classroom
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Lesson 13 Summary
Glossary
Lesson 13 Practice Problems
Lesson 14: Percent Error
14.1: Number Talk: Estimating a Percentage of a Number
14.2: Plants, Bicycles, and Crowds
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14.3: Measuring in the Heat
Lesson 14 Summary
Glossary
Lesson 14 Practice Problems
Lesson 15: Error Intervals
15.1: A Lot of Iron Ore
15.2: Saw Mill
15.3: Info Gap: Quality Control
Lesson 15 Summary
Lesson 15 Practice Problems
Lesson 16: Posing Percentage Problems
16.1: Sorting the News
16.2: Investigating
16.3: Displaying the News
Lesson 16 Summary
Learning Targets
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
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%
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
Lesson 16: Posing Percentage Problems
Lesson 1: Interpreting Negative Numbers
1.1: Using the Thermometer
1.2: Fractions of a Degree
1.3: Seagulls Soar, Sharks Swim
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1.4: Card Sort: Rational Numbers
Lesson 1 Summary
Glossary
Lesson 1 Practice Problems
Lesson 2: Changing Temperatures
2.1: Which One Doesn’t Belong: Arrows
2.2: Warmer and Colder
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2.3: Winter Temperatures
Lesson 2 Summary
Lesson 2 Practice Problems
Lesson 3: Changing Elevation
3.1: That's the Opposite
3.2: Cliffs and Caves
3.3: Adding Rational Numbers
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3.4: School Supply Number Line
Lesson 3 Summary
Lesson 3 Practice Problems
Lesson 4: Money and Debts
4.1: Concert Tickets
4.2: Cafeteria Food Debt
4.3: Bank Statement
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Lesson 4 Summary
Glossary
Lesson 4 Practice Problems
Lesson 5: Representing Subtraction
5.1: Equivalent Equations
5.2: Subtraction with Number Lines
5.3: We Can Add Instead
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Lesson 5 Summary
Lesson 5 Practice Problems
Lesson 6: Subtracting Rational Numbers
6.1: Number Talk: Missing Addend
6.2: Expressions with Altitude
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6.3: Does the Order Matter?
Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Adding and Subtracting to Solve Problems
7.1: Positive or Negative?
7.2: Phone Inventory
7.3: Solar Power
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7.4: Differences and Distances
Lesson 7 Summary
Lesson 7 Practice Problems
Lesson 8: Position, Speed, and Direction
8.1: Distance, Rate, Time
8.2: Going Left, Going Right
8.3: Velocity
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Lesson 8 Summary
Lesson 8 Practice Problems
Lesson 9: Multiplying Rational Numbers
9.1: Before and After
9.2: Backwards in Time
9.3: Cruising
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9.4: Rational Numbers Multiplication Grid
Lesson 9 Summary
Lesson 9 Practice Problems
Lesson 10: Multiply!
10.1: Which One Doesn’t Belong: Expressions
10.2: Card Sort: Matching Expressions
10.3: Row Game: Multiplying Rational Numbers
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Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Dividing Rational Numbers
11.1: Tell Me Your Sign
11.2: Multiplication and Division
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11.3: Drilling Down
Lesson 11 Summary
Glossary
Lesson 11 Practice Problems
Lesson 12: Negative Rates
12.1: Grapes per Minute
12.2: Water Level in the Aquarium
12.3: Up and Down with the Piccards
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Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Expressions with Rational Numbers
13.1: True or False: Rational Numbers
13.2: Card Sort: The Same But Different
13.3: Near and Far From Zero
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13.4: Seagulls and Sharks Again
Lesson 13 Summary
Glossary
Lesson 13 Practice Problems
Lesson 14: Solving Problems with Rational Numbers
14.1: Which One Doesn’t Belong: Equations
14.2: Draining and Filling a Tank
14.3: Buying and Selling Power
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Lesson 14 Summary
Lesson 14 Practice Problems
Lesson 15: Solving Equations with Rational Numbers
15.1: Number Talk: Opposites and Reciprocals
15.2: Match Solutions
15.3: Trip to the Mountains
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15.4: Card Sort: Matching Inverses
Lesson 15 Summary
Glossary
Lesson 15 Practice Problems
Lesson 16: Representing Contexts with Equations
16.1: Don't Solve It
16.2: Warmer or Colder than Before?
16.3: Animals Changing Altitudes
16.4: Equations Tell a Story
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Lesson 16 Summary
Lesson 16 Practice Problems
Lesson 17: The Stock Market
17.1: Revisiting Interest and Depreciation
17.2: Gains and Losses
17.3: What is a Stock Portfolio?
17.4: Your Own Stock Portfolio
Learning Targets
Lesson 1: Interpreting Negative 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
Lesson 8: Position, Speed, and Direction
Lesson 9: Multiplying Rational Numbers
Lesson 10: Multiply!
Lesson 11: Dividing Rational Numbers
Lesson 12: Negative Rates
Lesson 13: Expressions with Rational Numbers
Lesson 14: Solving Problems with Rational Numbers
Lesson 15: Solving Equations with Rational Numbers
Lesson 16: Representing Contexts with Equations
Lesson 17: The Stock Market
Lesson 1: Relationships between Quantities
1.1: Pricing Theater Popcorn
1.2: Entrance Fees
1.3: Making Toast
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Lesson 1 Summary
Lesson 1 Practice Problems
Lesson 2: Reasoning about Contexts with Tape Diagrams
2.1: Notice and Wonder: Remembering Tape Diagrams
2.2: Every Picture Tells a Story
2.3: Every Story Needs a Picture
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Lesson 2 Summary
Lesson 2 Practice Problems
Lesson 3: Reasoning about Equations with Tape Diagrams
3.1: Find Equivalent Expressions
3.2: Matching Equations to Tape Diagrams
3.3: Drawing Tape Diagrams to Represent Equations
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Lesson 3 Summary
Glossary
Lesson 3 Practice Problems
Lesson 4: Reasoning about Equations and Tape Diagrams (Part 1)
4.1: Algebra Talk: Seeing Structure
4.2: Situations and Diagrams
4.3: Situations, Diagrams, and Equations
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Lesson 4 Summary
Lesson 4 Practice Problems
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
5.1: Algebra Talk: Seeing Structure
5.2: More Situations and Diagrams
5.3: More Situations, Diagrams, and Equations
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Lesson 5 Summary
Lesson 5 Practice Problems
Lesson 6: Distinguishing between Two Types of Situations
6.1: Which One Doesn’t Belong: Seeing Structure
6.2: Card Sort: Categories of Equations
6.3: Even More Situations, Diagrams, and Equations
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Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Reasoning about Solving Equations (Part 1)
7.1: Hanger Diagrams
7.2: Hanger and Equation Matching
7.3: Use Hangers to Understand Equation Solving
Lesson 7 Summary
Lesson 7 Practice Problems
Lesson 8: Reasoning about Solving Equations (Part 2)
8.1: Equivalent to 2(x+3)
8.2: Either Or
8.3: Use Hangers to Understand Equation Solving, Again
Lesson 8 Summary
Lesson 8 Practice Problems
Lesson 9: Dealing with Negative Numbers
9.1: Which One Doesn’t Belong: Rational Number Arithmetic
9.2: Old and New Ways to Solve
9.3: Keeping It True
Lesson 9 Summary
Lesson 9 Practice Problems
Lesson 10: Different Options for Solving One Equation
10.1: Algebra Talk: Solve Each Equation
10.2: Analyzing Solution Methods
10.3: Solution Pathways
Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Using Equations to Solve Problems
11.1: Remember Tape Diagrams
11.2: At the Fair
11.3: Running Around
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Lesson 11 Summary
Lesson 11 Practice Problems
Lesson 12: Solving Problems about Percent Increase or Decrease
12.1: 20% Off
12.2: Walking More Each Day
12.3: A Sale on Shoes
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Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Reintroducing Inequalities
13.1: Greater Than One
13.2: The Roller Coaster
13.3: Is the Inequality True or False?
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Lesson 13 Summary
Lesson 13 Practice Problems
Lesson 14: Finding Solutions to Inequalities in Context
14.1: Solutions to Equations and Solutions to Inequalities
14.2: Earning Money for Soccer Stuff
14.3: Granola Bars and Savings
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Lesson 14 Summary
Glossary
Lesson 14 Practice Problems
Lesson 15: Efficiently Solving Inequalities
15.1: Lots of Negatives
15.2: Inequalities with Tables
15.3: Which Side are the Solutions?
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Lesson 15 Summary
Lesson 15 Practice Problems
Lesson 16: Interpreting Inequalities
16.1: Solve Some Inequalities!
16.2: Club Activities Matching
16.3: Club Activities Display
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Lesson 16 Summary
Lesson 16 Practice Problems
Lesson 17: Modeling with Inequalities
17.1: Possible Values
17.2: Elevator
17.3: Info Gap: Giving Advice
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Lesson 17 Summary
Lesson 17 Practice Problems
Lesson 18: Subtraction in Equivalent Expressions
18.1: Number Talk: Additive Inverses
18.2: A Helpful Observation
18.3: Organizing Work
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Lesson 18 Summary
Glossary
Lesson 18 Practice Problems
Lesson 19: Expanding and Factoring
19.1: Number Talk: Parentheses
19.2: Factoring and Expanding with Negative Numbers
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Lesson 19 Summary
Glossary
Lesson 19 Practice Problems
Lesson 20: Combining Like Terms (Part 1)
20.1: Why is it True?
20.2: A’s and B’s
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20.3: Making Sides Equal
Lesson 20 Summary
Lesson 20 Practice Problems
Lesson 21: Combining Like Terms (Part 2)
21.1: True or False?
21.2: Seeing it Differently
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21.3: Grouping Differently
Lesson 21 Summary
Lesson 21 Practice Problems
Lesson 22: Combining Like Terms (Part 3)
22.1: Are They Equal?
22.2: X’s and Y’s
22.3: Seeing Structure and Factoring
Lesson 22 Summary
Lesson 22 Practice Problems
Lesson 23: Applications of Expressions
23.1: Algebra Talk: Equivalent to 0.75t-21
23.2: Two Ways to Calculate
23.3: Which Way?
Learning Targets
Lesson 1: Relationships between Quantities
Lesson 2: Reasoning about Contexts with Tape Diagrams
Lesson 3: Reasoning about Equations with Tape Diagrams
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
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
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
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)
Lesson 23: Applications of Expressions
Glossary
Attributions
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Notes
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