Contents
Lesson 1: Size of Divisor and Size of Quotient
1.1: Number Talk: Size of Dividend and Divisor
1.2: All Stacked Up
1.3: All in Order
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Lesson 1 Summary
Lesson 1 Practice Problems
Lesson 2: Meanings of Division
2.1: A Division Expression
2.2: Bags of Almonds
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2.3: Homemade Jams
Lesson 2 Summary
Lesson 2 Practice Problems
Lesson 3: How Many Groups?
3.1: How Many of These in That?
3.2: Representing Groups of Fractions with Tape Diagrams
3.3: Finding Number of Groups
Lesson 3 Summary
Lesson 3 Practice Problems
Lesson 4: What Fraction of a Group?
4.1: Estimating a Fraction of a Number
4.2: Fractions of Ropes
4.3: Fractional Batches of Ice Cream
Lesson 4 Summary
Lesson 4 Practice Problems
Lesson 5: How Much in Each Group? (Part 1)
5.1: Inventing a Situation
5.2: How Much in One Batch?
5.3: One Container and One Section of Highway
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Lesson 5 Summary
Lesson 5 Practice Problems
Lesson 6: How Much in Each Group? (Part 2)
6.1: Number Talk: Greater Than 1 or Less Than 1?
6.2: Two Water Containers
6.3: Amount in One Group
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6.4: Inventing Another Situation
Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Finding an Algorithm for Dividing Fractions
7.1: Multiplying Fractions
7.2: Dividing by Non-unit Fractions
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7.3: Dividing a Fraction by a Fraction
Lesson 7 Summary
Glossary
Lesson 7 Practice Problems
Lesson 8: Ratios and Rates With Fractions
8.1: Number Talk: Dividing by Half as Much
8.2: Using an Algorithm to Divide Fractions
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8.3: A Train is Traveling at . . .
8.4: Comparing Running Speeds
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Lesson 8 Summary
Glossary
Lesson 8 Practice Problems
Lesson 9: Fractional Lengths
9.1: Number Talk: Multiplication Strategies
9.2: Info Gap: How Many Would It Take?
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9.3: How Many Times as Tall or as Far?
9.4: Comparing Paper Rolls
Lesson 9 Summary
Lesson 9 Practice Problems
Lesson 10: Rectangles and Triangles with Fractional Lengths
10.1: Areas of Squares
10.2: How Many Would it Take? (Part 2)
10.3: Bases and Heights of Triangles
Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Volume of Prisms
11.1: A Box of Cubes
11.2: Volumes of Cubes and Prisms
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11.3: Cubes with Fractional Edge Lengths
11.4: Fish Tank and Baking Pan
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Lesson 11 Summary
Lesson 11 Practice Problems
Lesson 12: Solving Problems Involving Fractions
12.1: Operations with Fractions
12.2: Situations with \frac34 and \frac12
12.3: Pairs of Problems
12.4: Baking Cookies
Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Using Decimals in a Shopping Context
13.1: Snacks from the Concession Stand
13.2: Planning a Dinner Party
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Lesson 13 Summary
Lesson 13 Practice Problems
Lesson 14: Using Diagrams to Represent Addition and Subtraction
14.1: Do the Zeros Matter?
14.2: Finding Sums in Different Ways
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14.3: Subtracting Decimals of Different Lengths
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Lesson 14 Summary
Lesson 14 Practice Problems
Lesson 15: Adding and Subtracting Decimals
15.1: The Cost of a Photo Print
15.2: Calculating Sums
15.3: Decimals All Around
15.4: Missing Numbers
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Lesson 15 Summary
Lesson 15 Practice Problems
Lesson 16: Methods for Multiplying Decimals
16.1: Multiplying by 10
16.2: Fractionally Speaking: Multiples of Powers of Ten
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16.3: Using Properties to Reason about Multiplication
16.4: Connecting Area Diagrams to Calculations with Decimals
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Lesson 16 Summary
Lesson 16 Practice Problems
Lesson 17: Calculating Products of Decimals
17.1: Number Talk: Twenty Times a Number
17.2: Using the Partial Products Method
17.3: Calculating Products of Decimals
17.4: Practicing Multiplication of Decimals
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Lesson 17 Summary
Lesson 17 Practice Problems
Lesson 18: Using Long Division
18.1: Using Base-Ten Diagrams to Calculate Quotients
18.2: Using the Partial Quotients Method to Calculate Quotients
18.3: Lin Uses Long Division
18.4: Dividing Whole Numbers
Lesson 18 Summary
Glossary
Lesson 18 Practice Problems
Lesson 19: Dividing Numbers that Result in Decimals
19.1: Keep Dividing
19.2: Using Long Division to Calculate Quotients
19.3: Using Diagrams to Represent Division
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Lesson 19 Summary
Lesson 19 Practice Problems
Lesson 20: Dividing Decimals by Decimals
20.1: Number Talk: Dividing by 4
20.2: Dividends and Divisors
20.3: Placing Decimal Points in Quotients
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20.4: Practicing Division with Decimals
Lesson 20 Summary
Lesson 20 Practice Problems
Lesson 21: Using Operations on Decimals to Solve Problems
21.1: Close Estimates
21.2: Applying Division with Decimals
21.3: Distance between Hurdles
21.4: Examining a Tennis Court
Lesson 21 Summary
Lesson 21 Practice Problems
Lesson 22: Fitting Boxes into Boxes
22.1: Determining Shipping Costs (Part 1)
22.2: Determining Shipping Costs (Part 2)
22.3: Determining Shipping Costs (Part 3)
Lesson 23: Making and Measuring Boxes
23.1: Folding Paper Boxes
23.2: Sizing Up Paper Boxes
Learning Targets
Lesson 1: Size of Divisor and Size of Quotient
Lesson 2: Meanings of Division
Lesson 3: How Many Groups?
Lesson 4: What Fraction of a Group?
Lesson 5: How Much in Each Group? (Part 1)
Lesson 6: How Much in Each Group? (Part 2)
Lesson 7: Finding an Algorithm for Dividing Fractions
Lesson 8: Ratios and Rates With Fractions
Lesson 9: Fractional Lengths
Lesson 10: Rectangles and Triangles with Fractional Lengths
Lesson 11: Volume of Prisms
Lesson 12: Solving Problems Involving Fractions
Lesson 13: Using Decimals in a Shopping Context
Lesson 14: Using Diagrams to Represent Addition and Subtraction
Lesson 15: Adding and Subtracting Decimals
Lesson 16: Methods for Multiplying Decimals
Lesson 17: Calculating Products of Decimals
Lesson 18: Using Long Division
Lesson 19: Dividing Numbers that Result in Decimals
Lesson 20: Dividing Decimals by Decimals
Lesson 21: Using Operations on Decimals to Solve Problems
Lesson 22: Fitting Boxes into Boxes
Lesson 23: Making and Measuring Boxes
Lesson 1: Tape Diagrams and Equations
1.1: Which Diagram is Which?
1.2: Match Equations and Tape Diagrams
1.3: Draw Diagrams for Equations
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Lesson 1 Summary
Lesson 1 Practice Problems
Lesson 2: Truth and Equations
2.1: Three Letters
2.2: Storytime
2.3: Using Structure to Find Solutions
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Lesson 2 Summary
Glossary
Lesson 2 Practice Problems
Lesson 3: Staying in Balance
3.1: Hanging Around
3.2: Match Equations and Hangers
3.3: Connecting Diagrams to Equations and Solutions
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Lesson 3 Summary
Lesson 3 Practice Problems
Lesson 4: Practice Solving Equations and Representing Situations with Equations
4.1: Number Talk: Subtracting From Five
4.2: Row Game: Solving Equations Practice
4.3: Choosing Equations to Match Situations
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Lesson 4 Summary
Lesson 4 Practice Problems
Lesson 5: A New Way to Interpret a over b
5.1: Recalling Ways of Solving
5.2: Interpreting \frac{a}{b}
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5.3: Storytime Again
Lesson 5 Summary
Lesson 5 Practice Problems
Lesson 6: Write Expressions Where Letters Stand for Numbers
6.1: Algebra Talk: When x is 6
6.2: Lemonade Sales and Heights
6.3: Building Expressions
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Lesson 6 Summary
Lesson 6 Practice Problems
Lesson 7: Revisit Percentages
7.1: Number Talk: Percentages
7.2: Representing a Percentage Problem with an Equation
7.3: Puppies Grow Up, Revisited
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Lesson 7 Summary
Lesson 7 Practice Problems
Lesson 8: Equal and Equivalent
8.1: Algebra Talk: Solving Equations by Seeing Structure
8.2: Using Diagrams to Show That Expressions are Equivalent
8.3: Identifying Equivalent Expressions
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Lesson 8 Summary
Glossary
Lesson 8 Practice Problems
Lesson 9: The Distributive Property, Part 1
9.1: Number Talk: Ways to Multiply
9.2: Ways to Represent Area of a Rectangle
9.3: Distributive Practice
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Lesson 9 Summary
Glossary
Lesson 9 Practice Problems
Lesson 10: The Distributive Property, Part 2
10.1: Possible Areas
10.2: Partitioned Rectangles When Lengths are Unknown
10.3: Areas of Partitioned Rectangles
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Lesson 10 Summary
Lesson 10 Practice Problems
Lesson 11: Squares and Cubes
11.1: Perfect Squares
11.2: Building with 32 Cubes
11.3: Perfect Cubes
11.4: Introducing Exponents
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Lesson 11 Summary
Glossary
Lesson 11 Practice Problems
Lesson 12: Surface Area of a Cube
12.1: Exponent Review
12.2: The Net of a Cube
12.3: Every Cube in the Whole World
Lesson 12 Summary
Lesson 12 Practice Problems
Lesson 13: Meaning of Exponents
13.1: Notice and Wonder: Dots and Lines
13.2: The Genie’s Offer
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13.3: Make 81
Lesson 13 Summary
Lesson 13 Practice Problems
Lesson 14: Expressions with Exponents
14.1: Which One Doesn’t Belong: Twos
14.2: Is the Equation True?
14.3: What’s Your Reason?
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Lesson 14 Summary
Lesson 14 Practice Problems
Lesson 15: Evaluating Expressions with Exponents
15.1: Revisiting the Cube
15.2: Calculating Surface Area
15.3: Row Game: Expression Explosion
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Lesson 15 Summary
Lesson 15 Practice Problems
Lesson 16: Equivalent Exponential Expressions
16.1: Up or Down?
16.2: What's the Value?
16.3: Exponent Experimentation
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Lesson 16 Summary
Lesson 16 Practice Problems
Lesson 17: Two Related Quantities, Part 1
17.1: Which One Would You Choose?
17.2: Painting the Set
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Lesson 17 Summary
Glossary
Lesson 17 Practice Problems
Lesson 18: Two Related Quantities, Part 2
18.1: Walking to the Library
18.2: The Walk-a-thon
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Lesson 18 Summary
Glossary
Lesson 18 Practice Problems
Lesson 19: Tables, Equations, and Graphs, Oh My!
19.1: Matching Equations and Tables
19.2: Getting to Know an Equation
19.3: Sharing Your Equation with Others
Learning Targets
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
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: Squares and Cubes
Lesson 12: Surface Area of a Cube
Lesson 13: Meaning of Exponents
Lesson 14: Expressions with Exponents
Lesson 15: Evaluating Expressions with Exponents
Lesson 16: Equivalent Exponential Expressions
Lesson 17: Two Related Quantities, Part 1
Lesson 18: Two Related Quantities, Part 2
Lesson 19: Tables, Equations, and Graphs, Oh My!
Glossary
Attributions
Image Attributions
Notes
Notes
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