About the Authors vii

Acknowledgments ix

Preface xvii

**SECTION 1: RATIOS AND PROPORTIONAL RELATIONSHIPS 1**

Teaching Notes for the Activities of Section 1 2

1–1: (6.RP.1) Understanding Ratios 2

1–2: (6.RP.2) Unit Rates and Ratios 2

1–3: (6.RP.3) Equivalent Ratios and the Coordinate Plane 3

1–4: (6.RP.3) Finding the Percent of a Number and Finding the Whole 3

1–5: (7.RP.1) Finding Unit Rates 4

1–6: (7.RP.2) Graphing Proportional Relationships 4

1–7: (7.RP.2) Representing Proportional Relationships 5

1–8: (7.RP.3) Solving Word Problems Involving Percents 5

Reproducibles for Section 1 6

**SECTION 2: THE NUMBER SYSTEM AND NUMBER AND QUANTITY 19**

Teaching Notes for the Activities of Section 2 20

2–1: (6.NS.5) Representing Positive and Negative Numbers 20

2–2: (6.NS.6) Graphing Rational Numbers on a Number Line 20

2–3: (6.NS.6) Graphing Points in the Coordinate Plane 21

2–4: (6.NS.7) The Absolute Value and Order of Rational Numbers 22

2–5: (6.NS.8) Using the Coordinate Plane to Solve Problems 22

2–6: (7.NS.1) Using the Number Line to Add and Subtract Rational Numbers23

2–7: (7.NS.1) Using Properties to Add and Subtract Rational Numbers 24

2–8: (7.NS.2) Multiplying and Dividing Rational Numbers 25

2–9: (7.NS.2) Converting Rational Numbers to Decimals26

2–10: (7.NS.3) Solving Word Problems Involving Rational Numbers 27

2–11: (8.NS.1) Expressing Fractions as Repeating Decimals and Repeating Decimals as Fractions 27

2–12: (8.NS.2) Using Rational Approximations of Irrational Numbers 28

2–13: (N-RN.1) Using the Properties of Exponents29

2–14: (N-RN.2) Rewriting Expressions Involving Radicals and Rational Exponents 29

2–15: (N-RN.3) Sums and Products of Rational and Irrational Numbers 30

2–16: (N-Q.1) Interpreting and Using Units 31

2–17: (N-Q.2) Defining Appropriate Quantities 31

2–18: (N-Q.3) Choosing Appropriate Levels of Accuracy for Measurement 32

2–19: (N-CN.1) Writing Complex Numbers 33

2–20: (N-CN.2) Adding, Subtracting, and Multiplying Complex Numbers 34

2–21: (N-CN.7) Solving Quadratic Equations That Have Complex Solutions 34

Reproducibles for Section 2 35

**SECTION 3: BASIC EXPRESSIONS, EQUATIONS, AND INEQUALITIES 60**

Teaching Notes for the Activities of Section 3 61

3–1: (6.EE.1) Writing and Evaluating Numerical Expressions with Whole-Number Exponents 61

3–2: (6.EE.2) Writing and Reading Algebraic Expressions 62

3–3: (6.EE.2) Evaluating Algebraic Expressions 62

3–4: (6.EE.3) Applying Properties of Operations to Generate Equivalent Expressions 63

3–5: (6.EE.4) Identifying Equivalent Expressions 63

3–6: (6.EE.5) Identifying Solutions of Equations and Inequalities 64

3–7: (6.EE.6) Writing Expressions in Which Variables Represent Numbers 64

3–8: (6.EE.7) Writing and Solving Equations 65

3–9: (6.EE.8) Using Inequalities 65

3–10: (6.EE.9) Using Variables to Represent Two Quantities 66

3–11: (7.EE.1) Adding, Subtracting, Factoring, and Expanding Linear Expressions 67

3–12: (7.EE.2) Rewriting Expressions in Different Forms 67

3–13: (7.EE.3) Solving Multi-Step Problems 68

3–14: (7.EE.4) Solving Equations and Inequalities 68

3–15: (8.EE.1) Applying Properties of Integer Exponents 69

3–16: (8.EE.2) Using Square Roots and Cube Roots 69

3–17: (8.EE.3) Using Numbers Expressed in Scientific Notation 70

3–18: (8.EE.4) Operations with Scientific Notation 71

3–19: (8.EE.5) Graphing Proportional Relationships 71

3–20: (8.EE.6) Deriving the Equation y = mx 72

3–21: (8.EE.7) Identifying Equations That Have One Solution, No Solutions, or Infinitely Many Solutions 73

3–22: (8.EE.7) Solving Equations with Variables on Both Sides 73

3–23: (8.EE.8) Solving Systems of Linear Equations Algebraically 74

3–24: (8.EE.8) Solving Systems of Equations by Graphing 75

Reproducibles for Section 3 75

**SECTION 4: POLYNOMIAL, RATIONAL, EXPONENTIAL, AND RADICAL EXPRESSIONS, EQUATIONS, AND INEQUALITIES 103**

Teaching Notes for the Activities of Section 4 104

4–1: (A-SSE.1) Interpreting Expressions 104

4–2: (A-SSE.2) Using the Structure of an Expression to Identify Ways to Rewrite It 104

4–3: (A-SSE.3) Factoring Quadratic Expressions to Reveal Zeroes 105

4–4: (A-SSE.3) Completing the Square to Reveal Maximum or Minimum Values 106

4–5: (A-SSE.4) Finding Sums of Finite Geometric Series 106

4–6: (A-APR.1) Adding, Subtracting, and Multiplying Polynomials 107

4–7: (A-APR.2) Applying the Remainder Theorem 107

4–8: (A-APR.3) Using Zeroes to Construct a Rough Graph of a Polynomial Function 108

4–9: (A-APR.4) Proving Polynomial Identities 109

4–10: (A-APR.6) Rewriting Rational Expressions 110

4–11: (A-CED.1) Writing and Solving Equations and Inequalities in One Variable 111

4–12: (A-CED.2) Writing and Graphing Equations in Two Variables 111

4–13: (A-CED.3) Representing Constraints and Interpreting Solutions 112

4–14: (A-CED.4) Highlighting Quantities of Interest in Formulas 113

4–15: (A-REI.1) Justifying Solutions to Equations 113

4–16: (A-REI.2) Solving Rational and Radical Equations 114

4–17: (A-REI.3) Solving Multi-Step Linear Equations in One Variable 115

4–18: (A-REI.3) Solving Multi-Step Linear Inequalities in One Variable 115

4–19: (A-REI.4) Solving a Quadratic Equation by Completing the Square 116

4–20: (A-REI.4) Solving Quadratic Equations in a Variety of Ways 116

4–21: (A-REI.5) Solving Systems of Equations 117

4–22: (A-REI.6) Solving Systems of Linear Equations 118

4–23: (A.REI.7) Solving a System of a Linear and a Quadratic Equation 118

4–24: (A-REI.10) Relating Graphs to the Solutions of Equations 119

4–25: (A-REI.11) Using Graphs and Tables to Find Solutions to Systems of Equations 120

4–26: (A-REI.12) Solving Systems of Inequalities by Graphing 120

Reproducibles for Section 4 121

**SECTION 5: FUNCTIONS 155**

Teaching Notes for the Activities of Section 5 156

5–1: (8.F.1) Identifying Functions 156

5–2: (8.F.2) Comparing Functions 157

5–3: (8.F.3) Determining Whether Data Lies on a Line 157

5–4: (8.F.4) Finding the Slope and Y-Intercept of a Line 157

5–5: (8.F.5) Analyzing and Graphing Functions 158

5–6: (F-IF.1) Understanding Functions 159

5–7: (F-IF.2) Finding the Values of Functions 159

5–8: (F-IF.3) Defining Sequences Recursively 160

5–9: (F-IF.4) Identifying Key Features of Graphs 160

5–10: (F-IF.5) Relating the Domain of a Function to Its Graph or Description 161

5–11: (F-IF.6) Finding the Average Rate of Change over Specified Intervals 162

5–12: (F-IF.7) Graphing Linear and Quadratic Functions 162

5–13: (F-IF.7) Graphing Polynomial Functions 163

5–14: (F-IF.8) Rewriting Quadratic Equations 164

5–15: (F-IF.9) Comparing Properties of Functions 165

5–16: (F-BF.1) Writing Functions 165

5–17: (F-BF.2) Writing Arithmetic and Geometric Sequences 166

5–18: (F-BF.3) Transforming a Function 166

5–19: (F-BF.4) Finding the Inverses of Functions 167

5–20: (F-LE.1) Proving Linear Functions Grow by Equal Differences over Equal Intervals 168

5–21: (F-LE.1) Proving Exponential Functions Grow by Equal Factors over Equal Intervals 168

5–22: (F-LE.2) Constructing Linear and Exponential Functions 169

5–23: (F-LE.3) Observing the Behavior of Quantities That Increase Exponentially 170

5–24: (F-LE.4) Writing and Solving Exponential Equations 170

5–25: (F-LE.5) Interpreting Parameters in a Linear or Exponential Function 171

5–26: (F-TF.1) Using Radian and Degree Measures 172

5–27: (F-TF.2) Using the Unit Circle 172

5–28: (F-TF.5) Modeling Periodic Phenomena 173

5–29: (F-TF.8) Finding the Values of the Sine, Cosine, and Tangent Functions 174

Reproducibles for Section 5 175

**SECTION 6: STATISTICS AND PROBABILITY 221**

Teaching Notes for the Activities of Section 6 222

6–1: (6.SP.1) Identifying Statistical Questions 222

6–2: (6.SP.2) Describing Data Distributions 222

6–3: (6.SP.3) Finding the Mean, Median, Mode, and Range 223

6–4: (6.SP.4) Using Dot Plots to Display Data 224

6–5: (6.SP.4) Constructing a Box Plot 224

6–6: (6.SP.5) Summarizing and Describing Data 225

6–7: (7.SP.1) Drawing Inferences from Samples 227

6–8: (7.SP.2) Drawing Inferences about a Population Using Random Samples 227

6–9: (7.SP.3) Comparing Two Data Sets 228

6–10: (7.SP.4) Drawing Inferences about Populations 229

6–11: (7.SP.5) Understanding the Probability of Events 229

6–12: (7.SP.6) Probabilities and Predictions 230

6–13: (7.SP.7) Using Probability Models to Find Probabilities of Events 230

6–14: (7.SP.8) Understanding the Probability of Compound Events 231

6–15: (7.SP.8) Finding Probabilities of Compound Events Using Tables, Lists, and Tree Diagrams 232

6–16: (8.SP.1) Constructing and Interpreting Scatter Plots 233

6–17: (8.SP.2) Fitting Lines to Data 234

6–18: (8.SP.3) Using Equations of Linear Models234

6–19: (8.SP.4) Constructing and Interpreting Two-Way Tables 235

6–20: (S-ID.1) Representing Data with Plots on the Real Number Line 236

6–21: (S-ID.2) Comparing Two Data Sets 236

6–22: (S-ID.3) Interpreting Differences in Shape, Center, and Spread of Data Distributions 237

6–23: (S-ID.4) Recognizing Characteristics of Normal Distributions 238

6–24: (S-ID.5) Summarizing Categorical Data in Two-Way Frequency Tables 238

6–25: (S-ID.6) Finding the Equation of the Line of Best Fit 239

6–26: (S-ID.6) Using Linear and Quadratic Models 240

6–27: (S-ID.7) Interpreting the Slope and Y-Intercept of a Linear Model 241

6–28: (S-ID.8) Computing and Interpreting the Correlation Coefficient 241

6–29: (S-ID.9) Distinguishing between Correlation and Causation 242

6–30: (S-IC.1) Understanding the Terminology of Statistical Experiments 242

6–31: (S-IC.2) Evaluating Probability Models through Simulations 243

6–32: (S-IC.3) Recognizing Surveys, Experiments, and Observational Studies 244

6–33: (S-IC.4) Using Simulations with Random Sampling 244

6–34: (S-IC.5) Comparing Two Treatments Using Simulations 245

6–35: (S-IC.6) Evaluating Data in Reports 246

6–36: (S-CP.1) Describing Events as Subsets of a Sample Space 246

6–37: (S-CP.2) Identifying Independent Events 247

6–38: (S-CP.3) Interpreting Conditional Probability 247

6–39: (S-CP.4) Understanding Two-Way Frequency Tables 248

6–40: (S-CP.5) Exploring Concepts of Conditional Probability 249

6–41: (S-CP.6) Finding Conditional Probabilities as a Fraction of Outcomes 249

6–42: (S-CP.7) Applying the Addition Rule 250

Reproducibles for Section 6 250

INDEX 305