About the Authors vii

Acknowledgments ix

SECTION 1: STANDARDS AND ACTIVITIES FOR NUMBER AND QUANTITY 1

The Real Number System 2

N-RN.1 2

Activity: Understanding Integer and Rational Exponents 2

N-RN.2 3

Activity: Finding the Values of Expressions  3

N-RN.3 4

Activity: Sums and Properties of Rational and Irrational Numbers 5

Quantities  6

N-Q.1 7

Activity: A Recommendation for the Boss 7

N-Q.2 8

Activity: Defining Appropriate Quantities   8

N-Q.3 10

Activity: Determining Levels of Accuracy in Measurement 10

The Complex Number System 11

N-CN.1 11

Activity: Classifying Complex Numbers  11

N-CN.2 13

Activity: Operations with Complex Numbers 13

N-CN.7 14

Activity: Matching Roots 14

Reproducibles for Section 1: Number and Quantity

N-RN.1: The Meaning of Rational Exponents 16

N-RN.2: Equations and Their Values. 17

N-RN.3: Proving the Sum of Two Rational Numbers Is Rational  18

N-RN.3: Proving the Sum of Rational and Irrational Numbers Is Irrational  19

N-Q.1: Guidelines for Choosing a Delivery Vehicle   20

N-Q.2: Defining Appropriate Quantities for Problem Solving  21

N-CN.1: Graphic Organizer for Complex Numbers  22

N-CN.2: Complex Number Cards—Solutions and Problems  23

N-CN.7: Quadratic Equations and Their Roots. 24

SECTION 2: STANDARDS AND ACTIVITIES FOR ALGEBRA 25

Seeing Structure in Expressions 26

A-SSE.1   26

Activity: Interpreting Expressions 26

A-SSE.2   27

Activity: Rewriting Expressions 28

A-SSE.3   29

Activity: Expressions and Equivalent Forms 29

A-SSE.4   30

Activity: Deriving a Formula 30

Arithmetic with Polynomials and Rational Expressions   32

A-APR.1   32

Activity: Pick the Polynomial 32

A-APR.2   33

Activity: Solving a Division Puzzle 34

A-APR.3   35

Activity: Matching Functions, Graphs, and Zeroes of a Function 35

A-APR.4   36

Activity: Proving the Polynomial Identity   36

A-APR.6   38

Activity: Mistakes in Rational Expressions  38

Creating Equations39

A-CED.1   39

Activity: Creating Equations and Inequalities 40

A-CED.2   41

Activity: Creating and Graphing Equations  41

A-CED.3   43

Activity: Pricing T-Shirts   43

A-CED.4   44

Activity: Rearranging Formulas and Equations 44

Reasoning with Equations and Inequalities 45

A-REI.1 45

Activity: Organizing the Steps for Solving Equations 46

A-REI.2 47

Activity: Solving Equations 47

A-REI.3 48

Activity: What’s the Solution?   49

A-REI.4 50

Activity: Racing to Solve Quadratic Equations 50

A-REI.5 51

Activity: Solving a System of Equations 51

A-REI.6 52

Activity: Solving Systems in Many Ways   53

A-REI.7 54

Activity: Solving Systems of Equations  54

A-REI.10   56

Activity: Tracing Equations  56

A-REI.11   57

Activity: Selecting Pairs of Equations with the Same Solutions  57

A-REI.12   58

Activity: Identifying Solutions through Graphing 59

Reproducibles for Section 2: Algebra

A-SSE.1: The Expressions Game 61

A-SSE.2: Identifying and Rewriting Expressions 62

A-SSE.3: Expressions and Equivalent Forms Cards 63

A-SSE.4: Identifying Errors in a Derived Formula 64

A-APR.1: Polynomial Cards 65

A-APR.2: Polynomial Division Cards 66

A-APR.3: Finding Your Match, I 67

A-APR.3: Finding Your Match, II 68

A-APR.6: Correcting Mistakes in Rational Expressions 69

A-CED.1: Which One Does Not Belong?   70

A-CED.2: Word Problems, Equations, and Graphs  71

A-CED.3: T-Shirts for the Math Club 72

A-CED.4: Formula and Equation Cards  73

A-REI.1: Equation and Step Cards 74

A-REI.2: Rational and Radical Equation Problem Cards 75

A-REI.3: Equation and Inequality Cards  76

A-REI.4: Quadratic Equations and Score Sheet 77

A-REI.5: Steps for Solving a System of Equations 78

A-REI.6: Task Cards for Solving Systems of Linear Equations   79

A-REI.7: Task Cards for Equations and Solutions  80

A-REI.10: Tracing Equations with Graphing Calculators 81

A-REI.11: Equations and Solutions 82

A-REI.12: Solving Inequalities and Systems of Inequalities by Graphing 83

SECTION 3: STANDARDS AND ACTIVITIES FOR FUNCTIONS 84

Interpreting Functions 85

F-IF.1 85

Activity: Identifying Functions   85

F-IF.2 86

Activity: Grouping Rules, Inputs, and Outputs 86

F-IF.3 87

Activity: Figurate Numbers 87

F-IF.4 89

Activity: Finding Similarities and Differences in Functions 90

F-IF.5 92

Activity: Recognizing Functions 92

F-IF.6 93

Activity: Matching Functions, Tables, and Average Rates of Change 93

F-IF.7 95

Activity: Making a Function Booklet 96

F-IF.8 97

Activity: Writing Functions in Equivalent Forms 97

F-IF.9 99

Activity: Comparing Functions   99

Building Functions 100

F-BF.1 101

Activity: Writing Functions  101

F-BF.2 102

Activity: The Game of Arithmetic and Geometric Sequences   102

F-BF.3 104

Activity: Matching Functions with Their Graphs 104

F-BF.4 105

Activity: Finding the Inverse of a Function—Bingo   106

Linear, Quadratic, and Exponential Models 107

F-LE.1 107

Activity: Modeling Linear and Exponential Functions 108

F-LE.2 109

Activity: Constructing Linear and Exponential Functions 110

F-LE.3   111

Activity: Analyzing Exponential and Polynomial Functions 111

F-LE.4   112

Activity: Logarithmic and Exponential Equations   112

F-LE.5   113

Activity: Interpreting Parameters of Functions 113

Trigonometric Functions   115

F-TF.1   115

Activity: Understanding Radian Measure  115

F-TF.2   116

Activity: Trigonometric Functions and the Unit Circle  116

F-TF.5   117

Activity: Modeling Monthly Precipitation  117

F-TF.8   119

Activity: Proving and Applying the Pythagorean Identity 119

Reproducibles for Section 3: Functions

F-IF.2: Function Cards 121

F-IF.4: Function Sets, I 122

F-IF.4: Function Sets, II 123

F-IF.6: Equations, Tables, and Average Rates of Change Cards, I 124

F-IF.6: Equations, Tables, and Average Rates of Change Cards, II 125

F-IF.7: A Function Booklet 126

F-IF.9: Comparing Function Cards, I 127

F-IF.9: Comparing Function Cards, II 128

F-BF.2: Arithmetic and Geometric Sequence Game Cards 129

F-BF.3: Graphs and Functions  130

F-BF.4: Function Bingo Board  131

F-BF.4: Functions for Bingo   132

F-LE.1: Tables and Rates of Change 133

F-LE.2: Information Cards for Linear and Exponential Functions 134

F-LE.4: Logarithmic Equation, Exponential Equation, and Solution Cards  135

F-TF.1: Drawing an Angle Whose Measure Is 1 Radian 136

F-TF.2: Explaining Trigonometric Functions Using the Unit Circle 138

F-TF.8: Proving the Pythagorean Identity  139

F-TF.8: Angles and Their Quadrants 140

SECTION 4: STANDARDS AND ACTIVITIES FOR GEOMETRY 141

Congruence   142

G-CO.1 142

Activity: Drawing and Defining Figures  142

G-CO.2 143

Activity: Presenting a Mini-Lesson on Transformations 143

G-CO.3 145

Activity: Carrying a Figure onto Itself 145

G-CO.4 146

Activity: Identifying and Defining Transformations  146

G-CO.5 147

Activity: Drawing and Identifying Transformations  147

G-CO.6 148

Activity: Predicting the Effects of Transformations   149

G-CO.7 149

Activity: Identifying Congruent Triangles   150

G-CO.8 151

Activity: Congruence and Rigid Motions   151

G-CO.9 152

Activity: Proving Theorems about Lines and Angles 152

G-CO.10   153

Activity: Proofs about Triangles 153

G-CO.11   154

Activity: Proving Theorems about Parallelograms  154

G-CO.12   156

Activity: Constructing Geometric Figures  156

G-CO.13   157

Activity: Constructing Regular Polygons   157

Similarity, Right Triangles, and Trigonometry  158

G-SRT.1   158

Activity: Dilating Lines and Line Segments  159

G-SRT.2   160

Activity: Identifying Similar Triangles. 160

G-SRT.3   161

Activity: Establishing the AA Criterion for Two Similar Triangles  161

G-SRT.4   162

Activity: Proving Theorems about Triangles  162

G-SRT.5   164

Activity: Reflecting on Congruence and Symmetry   164

G-SRT.6   165

Activity: Exploring the Ratios of Sides in a Right Triangle 165

G-SRT.7  166

Activity: Relating the Sine and Cosine of Complementary Angles 166

G-SRT.8  167

Activity: Problems, Questions, and Solutions 167

Circles   168

G-C.1   169

Activity: Proving All Circles Are Similar   169

G-C.2   169

Activity: Eliminating Figures Based on What They Are Not   170

G-C.3   171

Activity: Working with Inscribed and Circumscribed Circles   171

G-C.5   172

Activity: Critiquing Derivations  172

Expressing Geometric Properties with Equations 173

G-GPE.1  173

Activity: Working with Equations 174

G-GPE.2  175

Activity: Deriving the Equation of a Parabola 175

G-GPE.4  176

Activity: Proving Geometric Theorems with Coordinates 176

G-GPE.5  177

Activity: Slopes of Parallel and Perpendicular Lines  177

G-GPE.6  178

Activity: Partitioning Line Segments 179

G-GPE.7  180

Activity: Graphing and Finding Perimeters and Areas of Polygons 180

Geometric Measurement and Dimension 181

G-GMD.1 181

Activity: Presenting a Mini-Lesson on Formulas   181

G-GMD.3 183

Activity: Using Volume Formulas to Solve Problems  183

G-GMD.4 184

Activity: Cross-Sections and Rotations   184

Modeling with Geometry   185

G-MG.1   185

Activity: Using Properties of Geometric Shapes   186

G-MG.2   187

Activity: A Plan for Recreational Facilities  187

G-MG.3   188

Activity: Planning to Build a Garage 188

Reproducibles for Section 4: Geometry

G-CO.1: Instructions for Drawing Figures  190

G-CO.2: Transformation Tasks   191

G-CO.3: Polygons 192

G-CO.4: Transformations 193

G-CO.5: Figures and Transformations 194

G-CO.6: Figures and Images 195

G-CO.7: Triangles, Sides, and Angles 196

G-CO.8: Identifying Congruent Triangles   197

G-CO.9: Proof Prompts   198

G-CO.10: Finding the Missing Steps in Proofs about Triangles 200

G-CO.11: Steps for Proving Theorems about Parallelograms   203

G-CO.12: Construction Task Cards 205

G-CO.13: Inscribing Regular Polygons in Circles 206

G-SRT.1: Exploring Dilations 207

G-SRT.2: Determining if Triangles Are Similar 208

G-SRT.3: Drawing Triangles Based on Angle Measures 209

G-SRT.4: Proving the Triangle Proportionality Theorem 210

G-SRT.4: Proving the Converse of the Triangle Proportionality Theorem   211

G-SRT.4: Proving the Pythagorean Theorem by Using Similar Triangles  212

G-SRT.6: Ratios of Sides in a Right Triangle 213

G-SRT.8: Problems and Solutions 214

G-C.1: Going ‘Round in Circles 216

G-C.2: A Circle with Segments, Angles, and Triangles 217

G-C.3: Inscribed and Circumscribed Circles 218

G-C.5: Miguel’s Derivations 219

G-GPE.1: Equations of a Circle 220

G-GPE.2: Steps for Deriving the Equation of a Parabola 221

G-GPE.4: Task Cards and Coordinates  223

G-GPE.5: Using Slopes to Write Equations  224

G-GPE.6: Endpoints and Ratios  226

G-GPE.7: Graphs, Perimeters, and Areas of Polygons 227

G-GMD.3: Finding Volume  228

G-GMD.4: Statements for the Cross-Sections and Rotations Game 229

G-MG.1: Using Properties of Geometric Shapes to Find Area   230

G-MG.2: Township Facts 231

G-MG.3: A Plot Plan 232

SECTION 5: STANDARDS AND ACTIVITIES FOR STATISTICS AND PROBABILITY 233

Interpreting Categorical and Quantitative Data  234

S-ID.1   234

Activity: Representing Data   234

S-ID.2   235

Activity: Comparing Two Different Data Sets 236

S-ID.3   236

Activity: Interpreting Data Sets  237

S-ID.4   238

Activity: Analyzing Test Scores 238

S-ID.5   239

Activity: Making and Interpreting Two-Way Frequency Tables   239

S-ID.6   240

Activity: Representing Data on a Scatter Plot 240

S-ID.7   242

Activity: Identifying Slopes and Y-Intercepts 242

S-ID.8   243

Activity: Computing and Interpreting the Correlation Coefficient 243

S-ID.9   244

Activity: Determining Correlation and Causation   244

Making Inferences and Justifying Conclusions  246

S-IC.1   246

Activity: Random Samples and Inferences 246

S-IC.2   247

Activity: Simulations and Probability 248

S-IC.3   249

Activity: Surveys, Experiments, and Observational Studies  249

S-IC.4   250

Activity: Evaluating Sample Surveys and Simulations 250

S-IC.5   252

Activity: Comparing Two Treatments 252

S-IC.6   253

Activity: Evaluating Reports and Data   253

Conditional Probability and the Rules of Probability 254

S-CP.1   255

Activity: Describing Events as Subsets 255

S-CP.2   256

Activity: Identifying Events 256

S-CP.3   257

Activity: Using Conditional Probability   258

S-CP.4260

Activity: Understanding Independence and Conditional Probability 260

S-CP.5262

Activity: Explaining Conditional Probability and Independence 262

S-CP.6263

Activity: Finding Conditional Probability  263

S-CP.7264

Activity: Using the Addition Rule  265

Reproducibles for Section 5: Statistics and Probability

S-ID.2: Guidelines for Comparing Two Different Data Sets 267

S-ID.4: Analysis Guidelines 268

S-ID.5: Examples of Two-Way Frequency Tables 269

S-ID.5: Survey Questions  270

S-ID.7: Description, Data, Slope, and Y-Intercept Cards 271

S-ID.9: Correlation and Causation Statements 272

S-IC.1: Examples of Samples   273

S-IC.3: Identifying Surveys, Experiments, and Observational Studies  274

S-IC.4: A Sample Survey and Simulation Samples   275

S-IC.5: Bean Plant Growth Chart  276

S-IC.6: Beach Revenue Data 277

S-CP.1: Subsets of a Sample Space 279

S-CP.3: Independent and Dependent Events 280

S-CP.4: Student Data on Exercising and Dieting  281

S-CP.6: Considering Outcomes 282

S-CP.7: Using the Addition Rule to Find Probabilities  283

INDEX 285