Course Modules

Unit 1: Area and Surface Area

Unit 1: Area and Surface Area Unit 1: Area and Surface Area

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Overview | Unit 1: Area and Surface Area Overview | Unit 1: Area and Surface Area 1

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1 Finding Area by Decomposing and Rearranging 1 Finding Area by Decomposing and Rearranging 2

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2 Reasoning to Find Area 2 Reasoning to Find Area 3

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3 Parallelograms 3 Parallelograms 4

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4 Bases and Heights of Parallelograms 4 Bases and Heights of Parallelograms 5

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6 From Parallelograms to Triangles 6 From Parallelograms to Triangles 7

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7 Area of Triangles | Formula for the Area of Triangles 7 Area of Triangles | Formula for the Area of Triangles 8

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9 Polygons 9 Polygons 10

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10 Polyhedra 10 Polyhedra 11

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12 More Nets, More Surface Area 12 More Nets, More Surface Area 13

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5 Area of Parallelograms 5 Area of Parallelograms 14

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14 Squares and Cubes | Surface Area of a Cube 14 Squares and Cubes | Surface Area of a Cube 15

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8 Formula for the Area of a Triangle I Bases and Heights of Triangles 8 Formula for the Area of a Triangle I Bases and Heights of Triangles 15

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11 Nets & Surface Area 11 Nets & Surface Area 16

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13 Distinguishing Between Surface Area and Volume 13 Distinguishing Between Surface Area and Volume 17

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Unit 2: Introducing Ratios

Unit 2: Introducing Ratios Unit 2: Introducing Ratios

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Overview | Unit 2: Introducing Ratios Overview | Unit 2: Introducing Ratios 1

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1 Introducing Ratios and Ratio Language | Representing Ratios with Diagrams 1 Introducing Ratios and Ratio Language | Representing Ratios with Diagrams 2

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2 Representing Ratios with Diagrams | Recipes 2 Representing Ratios with Diagrams | Recipes 3

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3 Recipes | Color Mixtures | Defining Equivalent Ratios 3 Recipes | Color Mixtures | Defining Equivalent Ratios 4

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4 Introducing Double Number Line Diagrams | Creating Double Number Line Diagrams 4 Introducing Double Number Line Diagrams | Creating Double Number Line Diagrams 5

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5 How Much for One? 5 How Much for One? 6

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6 Constant Speed | Comparing Situations by Examining Ratios 6 Constant Speed | Comparing Situations by Examining Ratios 7

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7 Representing Ratios with Tables | Navigating a Table of Equivalent Ratios 7 Representing Ratios with Tables | Navigating a Table of Equivalent Ratios 9

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8 Tables and Double Number Line Diagrams I Solving Equivalent Ratio Problems 8 Tables and Double Number Line Diagrams I Solving Equivalent Ratio Problems 10

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9 Part-Part-Whole Ratios 9 Part-Part-Whole Ratios 12

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10 Solving More Ratio Problems 10 Solving More Ratio Problems 14

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Unit 3: Unit Rates and Percentages

Unit 3: Unit Rates and Percentages Unit 3: Unit Rates and Percentages

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Overview | Unit 3: Unit Rates and Percentages Overview | Unit 3: Unit Rates and Percentages 1

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1 Anchoring Units of Measurement | Converting Units 1 Anchoring Units of Measurement | Converting Units 2

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2 Comparing Speeds and Prices 2 Comparing Speeds and Prices 3

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3 Interpreting Rates 3 Interpreting Rates 4

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4 Equivalent Ratios Have the Same Unit Rates 4 Equivalent Ratios Have the Same Unit Rates 5

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5 More about Constant Speed | Solving Rate Problems 5 More about Constant Speed | Solving Rate Problems 6

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6 What Are Percentages? 6 What Are Percentages? 7

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9 Benchmark Percentages 9 Benchmark Percentages 10

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11 Finding This Percent of That 11 Finding This Percent of That 12

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7 Percentages and Double Number Lines 7 Percentages and Double Number Lines 12

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8 Percentages and Tape Diagrams 8 Percentages and Tape Diagrams 13

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10 Solving Percentage Problems 10 Solving Percentage Problems 14

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12 Finding the Percentage 12 Finding the Percentage 15

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Unit 4: Scale Drawings

Unit 4: Scale Drawings Unit 4: Scale Drawings

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Overview | Unit 4: Scale Drawings Overview | Unit 4: Scale Drawings 1

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1 What are Scaled Copies? | Corresponding Parts and Scale Factors 1 What are Scaled Copies? | Corresponding Parts and Scale Factors 2

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2 Making Scaled Copies | Scaled Relationships 2 Making Scaled Copies | Scaled Relationships 3

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3 The Size of the Scale Factor 3 The Size of the Scale Factor 4

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4 Scaling and Area 4 Scaling and Area 5

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5 Scale Drawings |Scale Drawings and Maps 5 Scale Drawings |Scale Drawings and Maps 6

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6 Creating Scale Drawings | Changing Scales in Scale Drawings 6 Creating Scale Drawings | Changing Scales in Scale Drawings 7

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7 Scales without Units 7 Scales without Units 8

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8 Units in Scale Drawings 8 Units in Scale Drawings 9

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Unit 5: Dividing Fractions

Unit 5: Dividing Fractions Unit 5: Dividing Fractions

Page

Overview | Unit 5: Dividing Fractions Overview | Unit 5: Dividing Fractions 1

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1 Prime Factorization | Common Factors 1 Prime Factorization | Common Factors 2

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2 Common Multiples | Using Common Multiples and Common Factors 2 Common Multiples | Using Common Multiples and Common Factors 3

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3 Adding and Subtracting Unlike Denominators 3 Adding and Subtracting Unlike Denominators 4

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4 Size of Divisor and Size of Quotient 4 Size of Divisor and Size of Quotient 5

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5 Meanings of Division | Interpreting Division Situations 5 Meanings of Division | Interpreting Division Situations 6

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6 How Many Groups? (Part 1) | How Many Groups? (Part 2) 6 How Many Groups? (Part 1) | How Many Groups? (Part 2) 7

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7 Using Diagrams to Find the Number of Groups | What Fraction of a Group? 7 Using Diagrams to Find the Number of Groups | What Fraction of a Group? 8

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8 How Much in Each Group? (Part 1) I How Much in Each Group? (Part 2) 8 How Much in Each Group? (Part 1) I How Much in Each Group? (Part 2) 9

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9 Dividing by Unit and Non-Unit Fractions I Fractional Lengths 9 Dividing by Unit and Non-Unit Fractions I Fractional Lengths 10

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10 Rectangles with Fractional Side Lengths I Fractional Lengths in Triangles and Prisms 10 Rectangles with Fractional Side Lengths I Fractional Lengths in Triangles and Prisms 11

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11 Volume of Prisms 11 Volume of Prisms 12

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12 Solving Problems Involving Fractions 12 Solving Problems Involving Fractions 13

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Unit 6: Arithmetic and Base 10

Unit 6: Arithmetic and Base 10 Unit 6: Arithmetic and Base 10

Page

Overview | Unit 6: Arithmetic and Base 10 Overview | Unit 6: Arithmetic and Base 10 1

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1 Using Decimals in a Shopping Context 1 Using Decimals in a Shopping Context 2

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2 Adding and Subtracting Decimals with Many Non-Zero Digits 2 Adding and Subtracting Decimals with Many Non-Zero Digits 3

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3 Decimal Points in Products | Methods for Multiplying Decimals 3 Decimal Points in Products | Methods for Multiplying Decimals 4

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4 Using Diagrams to Represent Multiplication | Calculating Products of Decimals 4 Using Diagrams to Represent Multiplication | Calculating Products of Decimals 5

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5 Calculating Products of Decimals I Using the Partial Quotients Method 5 Calculating Products of Decimals I Using the Partial Quotients Method 6

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6 Using Long Division | Dividing Numbers That Result in Decimals 6 Using Long Division | Dividing Numbers That Result in Decimals 7

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7 Dividing Decimals by Whole Numbers | Dividing Decimals by Decimals 7 Dividing Decimals by Whole Numbers | Dividing Decimals by Decimals 8

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8 Using Operations on Decimals to Solve Problems 8 Using Operations on Decimals to Solve Problems 9

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Unit 7: Expressions and Equations

Unit 7: Expressions and Equations Unit 7: Expressions and Equations

Page

Overview | Unit 7: Expressions and Equations Overview | Unit 7: Expressions and Equations 1

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1 Tape Diagrams and Equations | Truth and Equations 1 Tape Diagrams and Equations | Truth and Equations 2

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2 Truths and Equations |Staying in Balance 2 Truths and Equations |Staying in Balance 3

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3 Practice Solving Equations and Representing Situations with Equations 3 Practice Solving Equations and Representing Situations with Equations 4

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4 A New Way to Interpret a/b | Revisit Percentages 4 A New Way to Interpret a/b | Revisit Percentages 5

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5 Write Expressions Where Letters Stand for Numbers I Meaning of Exponents 5 Write Expressions Where Letters Stand for Numbers I Meaning of Exponents 6

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6 Expressions with Exponents 6 Expressions with Exponents 7

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7 Evaluating Expressions with Exponents 7 Evaluating Expressions with Exponents 8

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8 Equivalent Exponential Expressions 8 Equivalent Exponential Expressions 9

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9 Order of Operations 9 Order of Operations 10

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10 Equal and Equivalent I The Distributive Property, Part 1 10 Equal and Equivalent I The Distributive Property, Part 1 11

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11 Distributive Property, Part 2 I Distributive Property, Part 3 11 Distributive Property, Part 2 I Distributive Property, Part 3 12

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12 Replacing Letters with Numbers 12 Replacing Letters with Numbers 13

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13 Two Related Quantities, Part 1 13 Two Related Quantities, Part 1 14

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14 Two Related Quantities, Part 2 14 Two Related Quantities, Part 2 15

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15 More Relationships 15 More Relationships 16

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Unit 8: Introducing Proportional Relationships

Unit 8: Introducing Proportional Relationships Unit 8: Introducing Proportional Relationships

Page

Overview | Unit 8: Introducing Proportional Relationships Overview | Unit 8: Introducing Proportional Relationships 1

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1 Introducing Proportional Relationships with Tables 1 Introducing Proportional Relationships with Tables 2

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2 More about Constant of Proportionality 2 More about Constant of Proportionality 3

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3 Proportional Relationships and Equations | Two Equations for Each Relationship 3 Proportional Relationships and Equations | Two Equations for Each Relationship 4

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4 Using Equations to Solve Problems 4 Using Equations to Solve Problems 5

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5 Comparing Relationships with Tables 5 Comparing Relationships with Tables 6

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6 Comparing Relationships with Equations 6 Comparing Relationships with Equations 7

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7 Solving Problems about Proportional Relationships I Introducing Graphs of Proportional Relationships 7 Solving Problems about Proportional Relationships I Introducing Graphs of Proportional Relationships 8

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8 Interpreting Graphs of Proportional Relationships 8 Interpreting Graphs of Proportional Relationships 9

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9 Using Graphs to Compare Relationships 9 Using Graphs to Compare Relationships 10

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10 Two Graphs for Each Relationship 10 Two Graphs for Each Relationship 11

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11 Understanding Proportional Relationships | Graphs of Proportional Relationships 11 Understanding Proportional Relationships | Graphs of Proportional Relationships 12

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12 Graphs of Proportional Relationships I Representing Proportional Relationships 12 Graphs of Proportional Relationships I Representing Proportional Relationships 13

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13 Representing Proportional Relationships I Comparing Proportional Relationships 13 Representing Proportional Relationships I Comparing Proportional Relationships 14

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Unit 9: Proportional Relationships and Percentages

Unit 9: Proportional Relationships and Percentages Unit 9: Proportional Relationships and Percentages

Page

Overview | Unit 9: Proportional Relationships and Percentages Overview | Unit 9: Proportional Relationships and Percentages 1

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1 Ratios and Rates With Fractions | Revisiting Proportional Relationships 1 Ratios and Rates With Fractions | Revisiting Proportional Relationships 2

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2 Half as Much Again 2 Half as Much Again 3

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3 Say It with Decimals 3 Say It with Decimals 4

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4 Increasing and Decreasing 4 Increasing and Decreasing 5

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5 One Hundred Percent 5 One Hundred Percent 6

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6 Percent Increase and Decrease with Equations 6 Percent Increase and Decrease with Equations 7

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7 Investing with Interest 7 Investing with Interest 8

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8 Tax and Tip 8 Tax and Tip 9

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9 Percentage Contexts 9 Percentage Contexts 10

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10 Finding the Percentage 10 Finding the Percentage 11

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11 Measurement Error I Percent Error 11 Measurement Error I Percent Error 12

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Unit 10: Rational Numbers

Unit 10: Rational Numbers Unit 10: Rational Numbers

Page

Overview | Unit 10: Rational Numbers Overview | Unit 10: Rational Numbers 1

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1 Positive and Negative Numbers 1 Positive and Negative Numbers 2

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2 Points on the Number Line | Comparing Positive and Negative Numbers 2 Points on the Number Line | Comparing Positive and Negative Numbers 3

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3 Ordering Rational Numbers | Using Negative Numbers to Make Sense of Contexts 3 Ordering Rational Numbers | Using Negative Numbers to Make Sense of Contexts 4

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4 Absolute Value of Numbers | Comparing Numbers and Distance from Zero 4 Absolute Value of Numbers | Comparing Numbers and Distance from Zero 5

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5 Temperature Changes | Elevation Changes 5 Temperature Changes | Elevation Changes 6

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6 Debts and Money 6 Debts and Money 7

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7 Representing Subtraction 7 Representing Subtraction 8

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8 Solve Problems by Adding and Subtracting 8 Solve Problems by Adding and Subtracting 9

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9 Writing and Graphing Inequalities 9 Writing and Graphing Inequalities 10

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10 Solutions of Inequalities 10 Solutions of Inequalities 11

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11 Interpreting Inequalities 11 Interpreting Inequalities 12

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12 Points on the Coordinate Plane | Constructing the Coordinate Plane 12 Points on the Coordinate Plane | Constructing the Coordinate Plane 13

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13 Interpreting Points on the Coordinate Plane 13 Interpreting Points on the Coordinate Plane 14

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14 Distances on a Coordinate Plane 14 Distances on a Coordinate Plane 15

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15 Shapes on the Coordinate Plane 15 Shapes on the Coordinate Plane 16

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Unit 11: Rational Number Arithmetic

Unit 11: Rational Number Arithmetic Unit 11: Rational Number Arithmetic

Page

Overview | Unit 11: Rational Number Arithmetic Overview | Unit 11: Rational Number Arithmetic 1

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1 Changing Temperatures | Changing Elevation 1 Changing Temperatures | Changing Elevation 2

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2 Money and Debts | Subtracting Rational Numbers 2 Money and Debts | Subtracting Rational Numbers 3

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3 Adding and Subtracting to Solve Problems 3 Adding and Subtracting to Solve Problems 4

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4 Position, Speed, and Direction | Multiplying Rational Numbers | Multiply! 4 Position, Speed, and Direction | Multiplying Rational Numbers | Multiply! 5

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5 Dividing Rational Numbers 5 Dividing Rational Numbers 6

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6 Negative Rates 6 Negative Rates 7

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7 Expressions with Rational Numbers | Solving Problems with Rational Numbers 7 Expressions with Rational Numbers | Solving Problems with Rational Numbers 8

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8 Solving Equations with Rational Numbers | Representing Contexts with Equations 8 Solving Equations with Rational Numbers | Representing Contexts with Equations 9

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Unit 12: Data Sets and Distributions

Unit 12: Data Sets and Distributions Unit 12: Data Sets and Distributions

Page

Overview | Unit 12: Data Sets and Distributions Overview | Unit 12: Data Sets and Distributions 1

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1 Got Data? | Statistical Questions 1 Got Data? | Statistical Questions 2

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2 Representing Data Graphically 2 Representing Data Graphically 3

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3 Dot Plots | Using Dot Plots to Answer Statistical Questions 3 Dot Plots | Using Dot Plots to Answer Statistical Questions 4

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4 Histograms | Using Histograms to Answer Statistical Questions 4 Histograms | Using Histograms to Answer Statistical Questions 5

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5 Using Histograms to Answer Statistical Questions I Describing Distributions on Histograms 5 Using Histograms to Answer Statistical Questions I Describing Distributions on Histograms 6

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6 Interpreting the Mean as Fair Share | Finding and Interpreting the Mean as the Balance Point 6 Interpreting the Mean as Fair Share | Finding and Interpreting the Mean as the Balance Point 7

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7 The Median of a Data Set 7 The Median of a Data Set 8

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8 Comparing Mean and Median 8 Comparing Mean and Median 9

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9 Quartiles | Box Plots 9 Quartiles | Box Plots 10

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Unit 13: Putting It All Together

Unit 13: Putting It All Together Unit 13: Putting It All Together

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Overview | Unit 13: Putting It All Together Overview | Unit 13: Putting It All Together 1

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13.1| Fermi Problems 13.1| Fermi Problems 2

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13.2| If Our Class Were the World 13.2| If Our Class Were the World 3

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13.3| Rectangle Madness 13.3| Rectangle Madness 4

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13.4| How Do We Choose? 13.4| How Do We Choose? 5

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13.5| More than Two Choices 13.5| More than Two Choices 6

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13.6| Picking Representatives 13.6| Picking Representatives 7

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