About This Book v
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
