JUDITH A. MUSCHLA has over 25 years of experience as a mathematics educator in South River, New Jersey. She was a member of the New Jersey state Standards Review Panel for the Mathematics Curriculum Content Standards. GARY ROBERT MUSCHLA is a skilled teacher of middle school math, reading, and writing. He has co-authored several math activity books with Judith Muschla, including Algebra Teacher's Activities Kit, Hands-On Math Projects with Real Life Applications, and Math Starters. ERIN MUSCHLA-BERRY teaches mathematics at Monroe Township Middle School in Monroe, New Jersey. This is her eighth collaboration with Judith and Gary Muschla.

• About This Book vAbout the Authors viiAcknowledgments ixSECTION 1: STANDARDS AND ACTIVITIES FOR NUMBER AND QUANTITY 1The Real Number System 2N-RN.1 2Activity: Understanding Integer and Rational Exponents 2N-RN.2 3Activity: Finding the Values of Expressions  3N-RN.3 4Activity: Sums and Properties of Rational and Irrational Numbers 5Quantities  6N-Q.1 7Activity: A Recommendation for the Boss 7N-Q.2 8Activity: Defining Appropriate Quantities   8N-Q.3 10Activity: Determining Levels of Accuracy in Measurement 10The Complex Number System 11N-CN.1 11Activity: Classifying Complex Numbers  11N-CN.2 13Activity: Operations with Complex Numbers 13N-CN.7 14Activity: Matching Roots 14Reproducibles for Section 1: Number and QuantityN-RN.1: The Meaning of Rational Exponents 16N-RN.2: Equations and Their Values. 17N-RN.3: Proving the Sum of Two Rational Numbers Is Rational  18N-RN.3: Proving the Sum of Rational and Irrational Numbers Is Irrational  19N-Q.1: Guidelines for Choosing a Delivery Vehicle   20N-Q.2: Defining Appropriate Quantities for Problem Solving  21N-CN.1: Graphic Organizer for Complex Numbers  22N-CN.2: Complex Number Cards—Solutions and Problems  23N-CN.7: Quadratic Equations and Their Roots. 24SECTION 2: STANDARDS AND ACTIVITIES FOR ALGEBRA 25Seeing Structure in Expressions 26A-SSE.1   26Activity: Interpreting Expressions 26A-SSE.2   27Activity: Rewriting Expressions 28A-SSE.3   29Activity: Expressions and Equivalent Forms 29A-SSE.4   30Activity: Deriving a Formula 30Arithmetic with Polynomials and Rational Expressions   32A-APR.1   32Activity: Pick the Polynomial 32A-APR.2   33Activity: Solving a Division Puzzle 34A-APR.3   35Activity: Matching Functions, Graphs, and Zeroes of a Function 35A-APR.4   36Activity: Proving the Polynomial Identity   36A-APR.6   38Activity: Mistakes in Rational Expressions  38Creating Equations39A-CED.1   39Activity: Creating Equations and Inequalities 40A-CED.2   41Activity: Creating and Graphing Equations  41A-CED.3   43Activity: Pricing T-Shirts   43A-CED.4   44Activity: Rearranging Formulas and Equations 44Reasoning with Equations and Inequalities 45A-REI.1 45Activity: Organizing the Steps for Solving Equations 46A-REI.2 47Activity: Solving Equations 47A-REI.3 48Activity: What’s the Solution?   49A-REI.4 50Activity: Racing to Solve Quadratic Equations 50A-REI.5 51Activity: Solving a System of Equations 51A-REI.6 52Activity: Solving Systems in Many Ways   53A-REI.7 54Activity: Solving Systems of Equations  54A-REI.10   56Activity: Tracing Equations  56A-REI.11   57Activity: Selecting Pairs of Equations with the Same Solutions  57A-REI.12   58Activity: Identifying Solutions through Graphing 59Reproducibles for Section 2: AlgebraA-SSE.1: The Expressions Game 61A-SSE.2: Identifying and Rewriting Expressions 62A-SSE.3: Expressions and Equivalent Forms Cards 63A-SSE.4: Identifying Errors in a Derived Formula 64A-APR.1: Polynomial Cards 65A-APR.2: Polynomial Division Cards 66A-APR.3: Finding Your Match, I 67A-APR.3: Finding Your Match, II 68A-APR.6: Correcting Mistakes in Rational Expressions 69A-CED.1: Which One Does Not Belong?   70A-CED.2: Word Problems, Equations, and Graphs  71A-CED.3: T-Shirts for the Math Club 72A-CED.4: Formula and Equation Cards  73A-REI.1: Equation and Step Cards 74A-REI.2: Rational and Radical Equation Problem Cards 75A-REI.3: Equation and Inequality Cards  76A-REI.4: Quadratic Equations and Score Sheet 77A-REI.5: Steps for Solving a System of Equations 78A-REI.6: Task Cards for Solving Systems of Linear Equations   79A-REI.7: Task Cards for Equations and Solutions  80A-REI.10: Tracing Equations with Graphing Calculators 81A-REI.11: Equations and Solutions 82A-REI.12: Solving Inequalities and Systems of Inequalities by Graphing 83SECTION 3: STANDARDS AND ACTIVITIES FOR FUNCTIONS 84Interpreting Functions 85F-IF.1 85Activity: Identifying Functions   85F-IF.2 86Activity: Grouping Rules, Inputs, and Outputs 86F-IF.3 87Activity: Figurate Numbers 87F-IF.4 89Activity: Finding Similarities and Differences in Functions 90F-IF.5 92Activity: Recognizing Functions 92F-IF.6 93Activity: Matching Functions, Tables, and Average Rates of Change 93F-IF.7 95Activity: Making a Function Booklet 96F-IF.8 97Activity: Writing Functions in Equivalent Forms 97F-IF.9 99Activity: Comparing Functions   99Building Functions 100F-BF.1 101Activity: Writing Functions  101F-BF.2 102Activity: The Game of Arithmetic and Geometric Sequences   102F-BF.3 104Activity: Matching Functions with Their Graphs 104F-BF.4 105Activity: Finding the Inverse of a Function—Bingo   106Linear, Quadratic, and Exponential Models 107F-LE.1 107Activity: Modeling Linear and Exponential Functions 108F-LE.2 109Activity: Constructing Linear and Exponential Functions 110F-LE.3   111Activity: Analyzing Exponential and Polynomial Functions 111F-LE.4   112Activity: Logarithmic and Exponential Equations   112F-LE.5   113Activity: Interpreting Parameters of Functions 113Trigonometric Functions   115F-TF.1   115Activity: Understanding Radian Measure  115F-TF.2   116Activity: Trigonometric Functions and the Unit Circle  116F-TF.5   117Activity: Modeling Monthly Precipitation  117F-TF.8   119Activity: Proving and Applying the Pythagorean Identity 119Reproducibles for Section 3: FunctionsF-IF.2: Function Cards 121F-IF.4: Function Sets, I 122F-IF.4: Function Sets, II 123F-IF.6: Equations, Tables, and Average Rates of Change Cards, I 124F-IF.6: Equations, Tables, and Average Rates of Change Cards, II 125F-IF.7: A Function Booklet 126F-IF.9: Comparing Function Cards, I 127F-IF.9: Comparing Function Cards, II 128F-BF.2: Arithmetic and Geometric Sequence Game Cards 129F-BF.3: Graphs and Functions  130F-BF.4: Function Bingo Board  131F-BF.4: Functions for Bingo   132F-LE.1: Tables and Rates of Change 133F-LE.2: Information Cards for Linear and Exponential Functions 134F-LE.4: Logarithmic Equation, Exponential Equation, and Solution Cards  135F-TF.1: Drawing an Angle Whose Measure Is 1 Radian 136F-TF.2: Explaining Trigonometric Functions Using the Unit Circle 138F-TF.8: Proving the Pythagorean Identity  139F-TF.8: Angles and Their Quadrants 140SECTION 4: STANDARDS AND ACTIVITIES FOR GEOMETRY 141Congruence   142G-CO.1 142Activity: Drawing and Defining Figures  142G-CO.2 143Activity: Presenting a Mini-Lesson on Transformations 143G-CO.3 145Activity: Carrying a Figure onto Itself 145G-CO.4 146Activity: Identifying and Defining Transformations  146G-CO.5 147Activity: Drawing and Identifying Transformations  147G-CO.6 148Activity: Predicting the Effects of Transformations   149G-CO.7 149Activity: Identifying Congruent Triangles   150G-CO.8 151Activity: Congruence and Rigid Motions   151G-CO.9 152Activity: Proving Theorems about Lines and Angles 152G-CO.10   153Activity: Proofs about Triangles 153G-CO.11   154Activity: Proving Theorems about Parallelograms  154G-CO.12   156Activity: Constructing Geometric Figures  156G-CO.13   157Activity: Constructing Regular Polygons   157Similarity, Right Triangles, and Trigonometry  158G-SRT.1   158Activity: Dilating Lines and Line Segments  159G-SRT.2   160Activity: Identifying Similar Triangles. 160G-SRT.3   161Activity: Establishing the AA Criterion for Two Similar Triangles  161G-SRT.4   162Activity: Proving Theorems about Triangles  162G-SRT.5   164Activity: Reflecting on Congruence and Symmetry   164G-SRT.6   165Activity: Exploring the Ratios of Sides in a Right Triangle 165G-SRT.7  166Activity: Relating the Sine and Cosine of Complementary Angles 166G-SRT.8  167Activity: Problems, Questions, and Solutions 167Circles   168G-C.1   169Activity: Proving All Circles Are Similar   169G-C.2   169Activity: Eliminating Figures Based on What They Are Not   170G-C.3   171Activity: Working with Inscribed and Circumscribed Circles   171G-C.5   172Activity: Critiquing Derivations  172Expressing Geometric Properties with Equations 173G-GPE.1  173Activity: Working with Equations 174G-GPE.2  175Activity: Deriving the Equation of a Parabola 175G-GPE.4  176Activity: Proving Geometric Theorems with Coordinates 176G-GPE.5  177Activity: Slopes of Parallel and Perpendicular Lines  177G-GPE.6  178Activity: Partitioning Line Segments 179G-GPE.7  180Activity: Graphing and Finding Perimeters and Areas of Polygons 180Geometric Measurement and Dimension 181G-GMD.1 181Activity: Presenting a Mini-Lesson on Formulas   181G-GMD.3 183Activity: Using Volume Formulas to Solve Problems  183G-GMD.4 184Activity: Cross-Sections and Rotations   184Modeling with Geometry   185G-MG.1   185Activity: Using Properties of Geometric Shapes   186G-MG.2   187Activity: A Plan for Recreational Facilities  187G-MG.3   188Activity: Planning to Build a Garage 188Reproducibles for Section 4: GeometryG-CO.1: Instructions for Drawing Figures  190G-CO.2: Transformation Tasks   191G-CO.3: Polygons 192G-CO.4: Transformations 193G-CO.5: Figures and Transformations 194G-CO.6: Figures and Images 195G-CO.7: Triangles, Sides, and Angles 196G-CO.8: Identifying Congruent Triangles   197G-CO.9: Proof Prompts   198G-CO.10: Finding the Missing Steps in Proofs about Triangles 200G-CO.11: Steps for Proving Theorems about Parallelograms   203G-CO.12: Construction Task Cards 205G-CO.13: Inscribing Regular Polygons in Circles 206G-SRT.1: Exploring Dilations 207G-SRT.2: Determining if Triangles Are Similar 208G-SRT.3: Drawing Triangles Based on Angle Measures 209G-SRT.4: Proving the Triangle Proportionality Theorem 210G-SRT.4: Proving the Converse of the Triangle Proportionality Theorem   211G-SRT.4: Proving the Pythagorean Theorem by Using Similar Triangles  212G-SRT.6: Ratios of Sides in a Right Triangle 213G-SRT.8: Problems and Solutions 214G-C.1: Going ‘Round in Circles 216G-C.2: A Circle with Segments, Angles, and Triangles 217G-C.3: Inscribed and Circumscribed Circles 218G-C.5: Miguel’s Derivations 219G-GPE.1: Equations of a Circle 220G-GPE.2: Steps for Deriving the Equation of a Parabola 221G-GPE.4: Task Cards and Coordinates  223G-GPE.5: Using Slopes to Write Equations  224G-GPE.6: Endpoints and Ratios  226G-GPE.7: Graphs, Perimeters, and Areas of Polygons 227G-GMD.3: Finding Volume  228G-GMD.4: Statements for the Cross-Sections and Rotations Game 229G-MG.1: Using Properties of Geometric Shapes to Find Area   230G-MG.2: Township Facts 231G-MG.3: A Plot Plan 232SECTION 5: STANDARDS AND ACTIVITIES FOR STATISTICS AND PROBABILITY 233Interpreting Categorical and Quantitative Data  234S-ID.1   234Activity: Representing Data   234S-ID.2   235Activity: Comparing Two Different Data Sets 236S-ID.3   236Activity: Interpreting Data Sets  237S-ID.4   238Activity: Analyzing Test Scores 238S-ID.5   239Activity: Making and Interpreting Two-Way Frequency Tables   239S-ID.6   240Activity: Representing Data on a Scatter Plot 240S-ID.7   242Activity: Identifying Slopes and Y-Intercepts 242S-ID.8   243Activity: Computing and Interpreting the Correlation Coefficient 243S-ID.9   244Activity: Determining Correlation and Causation   244Making Inferences and Justifying Conclusions  246S-IC.1   246Activity: Random Samples and Inferences 246S-IC.2   247Activity: Simulations and Probability 248S-IC.3   249Activity: Surveys, Experiments, and Observational Studies  249S-IC.4   250Activity: Evaluating Sample Surveys and Simulations 250S-IC.5   252Activity: Comparing Two Treatments 252S-IC.6   253Activity: Evaluating Reports and Data   253Conditional Probability and the Rules of Probability 254S-CP.1   255Activity: Describing Events as Subsets 255S-CP.2   256Activity: Identifying Events 256S-CP.3   257Activity: Using Conditional Probability   258S-CP.4260Activity: Understanding Independence and Conditional Probability 260S-CP.5262Activity: Explaining Conditional Probability and Independence 262S-CP.6263Activity: Finding Conditional Probability  263S-CP.7264Activity: Using the Addition Rule  265Reproducibles for Section 5: Statistics and ProbabilityS-ID.2: Guidelines for Comparing Two Different Data Sets 267S-ID.4: Analysis Guidelines 268S-ID.5: Examples of Two-Way Frequency Tables 269S-ID.5: Survey Questions  270S-ID.7: Description, Data, Slope, and Y-Intercept Cards 271S-ID.9: Correlation and Causation Statements 272S-IC.1: Examples of Samples   273S-IC.3: Identifying Surveys, Experiments, and Observational Studies  274S-IC.4: A Sample Survey and Simulation Samples   275S-IC.5: Bean Plant Growth Chart  276S-IC.6: Beach Revenue Data 277S-CP.1: Subsets of a Sample Space 279S-CP.3: Independent and Dependent Events 280S-CP.4: Student Data on Exercising and Dieting  281S-CP.6: Considering Outcomes 282S-CP.7: Using the Addition Rule to Find Probabilities  283INDEX 285

JUDITH A. MUSCHLA has over 25 years of experience as a mathematics educator in South River, New Jersey. She was a member of the New Jersey state Standards Review Panel for the Mathematics Curriculum Content Standards. GARY ROBERT MUSCHLA is a skilled teacher of middle school math, reading, and writing. He has co-authored several math activity books with Judith Muschla, including Algebra Teacher's Activities Kit, Hands-On Math Projects with Real Life Applications, and Math Starters. ERIN MUSCHLA-BERRY teaches mathematics at Monroe Township Middle School in Monroe, New Jersey. This is her eighth collaboration with Judith and Gary Muschla.

• About This Book vAbout the Authors viiAcknowledgments ixSECTION 1: STANDARDS AND ACTIVITIES FOR NUMBER AND QUANTITY 1The Real Number System 2N-RN.1 2Activity: Understanding Integer and Rational Exponents 2N-RN.2 3Activity: Finding the Values of Expressions  3N-RN.3 4Activity: Sums and Properties of Rational and Irrational Numbers 5Quantities  6N-Q.1 7Activity: A Recommendation for the Boss 7N-Q.2 8Activity: Defining Appropriate Quantities   8N-Q.3 10Activity: Determining Levels of Accuracy in Measurement 10The Complex Number System 11N-CN.1 11Activity: Classifying Complex Numbers  11N-CN.2 13Activity: Operations with Complex Numbers 13N-CN.7 14Activity: Matching Roots 14Reproducibles for Section 1: Number and QuantityN-RN.1: The Meaning of Rational Exponents 16N-RN.2: Equations and Their Values. 17N-RN.3: Proving the Sum of Two Rational Numbers Is Rational  18N-RN.3: Proving the Sum of Rational and Irrational Numbers Is Irrational  19N-Q.1: Guidelines for Choosing a Delivery Vehicle   20N-Q.2: Defining Appropriate Quantities for Problem Solving  21N-CN.1: Graphic Organizer for Complex Numbers  22N-CN.2: Complex Number Cards—Solutions and Problems  23N-CN.7: Quadratic Equations and Their Roots. 24SECTION 2: STANDARDS AND ACTIVITIES FOR ALGEBRA 25Seeing Structure in Expressions 26A-SSE.1   26Activity: Interpreting Expressions 26A-SSE.2   27Activity: Rewriting Expressions 28A-SSE.3   29Activity: Expressions and Equivalent Forms 29A-SSE.4   30Activity: Deriving a Formula 30Arithmetic with Polynomials and Rational Expressions   32A-APR.1   32Activity: Pick the Polynomial 32A-APR.2   33Activity: Solving a Division Puzzle 34A-APR.3   35Activity: Matching Functions, Graphs, and Zeroes of a Function 35A-APR.4   36Activity: Proving the Polynomial Identity   36A-APR.6   38Activity: Mistakes in Rational Expressions  38Creating Equations39A-CED.1   39Activity: Creating Equations and Inequalities 40A-CED.2   41Activity: Creating and Graphing Equations  41A-CED.3   43Activity: Pricing T-Shirts   43A-CED.4   44Activity: Rearranging Formulas and Equations 44Reasoning with Equations and Inequalities 45A-REI.1 45Activity: Organizing the Steps for Solving Equations 46A-REI.2 47Activity: Solving Equations 47A-REI.3 48Activity: What’s the Solution?   49A-REI.4 50Activity: Racing to Solve Quadratic Equations 50A-REI.5 51Activity: Solving a System of Equations 51A-REI.6 52Activity: Solving Systems in Many Ways   53A-REI.7 54Activity: Solving Systems of Equations  54A-REI.10   56Activity: Tracing Equations  56A-REI.11   57Activity: Selecting Pairs of Equations with the Same Solutions  57A-REI.12   58Activity: Identifying Solutions through Graphing 59Reproducibles for Section 2: AlgebraA-SSE.1: The Expressions Game 61A-SSE.2: Identifying and Rewriting Expressions 62A-SSE.3: Expressions and Equivalent Forms Cards 63A-SSE.4: Identifying Errors in a Derived Formula 64A-APR.1: Polynomial Cards 65A-APR.2: Polynomial Division Cards 66A-APR.3: Finding Your Match, I 67A-APR.3: Finding Your Match, II 68A-APR.6: Correcting Mistakes in Rational Expressions 69A-CED.1: Which One Does Not Belong?   70A-CED.2: Word Problems, Equations, and Graphs  71A-CED.3: T-Shirts for the Math Club 72A-CED.4: Formula and Equation Cards  73A-REI.1: Equation and Step Cards 74A-REI.2: Rational and Radical Equation Problem Cards 75A-REI.3: Equation and Inequality Cards  76A-REI.4: Quadratic Equations and Score Sheet 77A-REI.5: Steps for Solving a System of Equations 78A-REI.6: Task Cards for Solving Systems of Linear Equations   79A-REI.7: Task Cards for Equations and Solutions  80A-REI.10: Tracing Equations with Graphing Calculators 81A-REI.11: Equations and Solutions 82A-REI.12: Solving Inequalities and Systems of Inequalities by Graphing 83SECTION 3: STANDARDS AND ACTIVITIES FOR FUNCTIONS 84Interpreting Functions 85F-IF.1 85Activity: Identifying Functions   85F-IF.2 86Activity: Grouping Rules, Inputs, and Outputs 86F-IF.3 87Activity: Figurate Numbers 87F-IF.4 89Activity: Finding Similarities and Differences in Functions 90F-IF.5 92Activity: Recognizing Functions 92F-IF.6 93Activity: Matching Functions, Tables, and Average Rates of Change 93F-IF.7 95Activity: Making a Function Booklet 96F-IF.8 97Activity: Writing Functions in Equivalent Forms 97F-IF.9 99Activity: Comparing Functions   99Building Functions 100F-BF.1 101Activity: Writing Functions  101F-BF.2 102Activity: The Game of Arithmetic and Geometric Sequences   102F-BF.3 104Activity: Matching Functions with Their Graphs 104F-BF.4 105Activity: Finding the Inverse of a Function—Bingo   106Linear, Quadratic, and Exponential Models 107F-LE.1 107Activity: Modeling Linear and Exponential Functions 108F-LE.2 109Activity: Constructing Linear and Exponential Functions 110F-LE.3   111Activity: Analyzing Exponential and Polynomial Functions 111F-LE.4   112Activity: Logarithmic and Exponential Equations   112F-LE.5   113Activity: Interpreting Parameters of Functions 113Trigonometric Functions   115F-TF.1   115Activity: Understanding Radian Measure  115F-TF.2   116Activity: Trigonometric Functions and the Unit Circle  116F-TF.5   117Activity: Modeling Monthly Precipitation  117F-TF.8   119Activity: Proving and Applying the Pythagorean Identity 119Reproducibles for Section 3: FunctionsF-IF.2: Function Cards 121F-IF.4: Function Sets, I 122F-IF.4: Function Sets, II 123F-IF.6: Equations, Tables, and Average Rates of Change Cards, I 124F-IF.6: Equations, Tables, and Average Rates of Change Cards, II 125F-IF.7: A Function Booklet 126F-IF.9: Comparing Function Cards, I 127F-IF.9: Comparing Function Cards, II 128F-BF.2: Arithmetic and Geometric Sequence Game Cards 129F-BF.3: Graphs and Functions  130F-BF.4: Function Bingo Board  131F-BF.4: Functions for Bingo   132F-LE.1: Tables and Rates of Change 133F-LE.2: Information Cards for Linear and Exponential Functions 134F-LE.4: Logarithmic Equation, Exponential Equation, and Solution Cards  135F-TF.1: Drawing an Angle Whose Measure Is 1 Radian 136F-TF.2: Explaining Trigonometric Functions Using the Unit Circle 138F-TF.8: Proving the Pythagorean Identity  139F-TF.8: Angles and Their Quadrants 140SECTION 4: STANDARDS AND ACTIVITIES FOR GEOMETRY 141Congruence   142G-CO.1 142Activity: Drawing and Defining Figures  142G-CO.2 143Activity: Presenting a Mini-Lesson on Transformations 143G-CO.3 145Activity: Carrying a Figure onto Itself 145G-CO.4 146Activity: Identifying and Defining Transformations  146G-CO.5 147Activity: Drawing and Identifying Transformations  147G-CO.6 148Activity: Predicting the Effects of Transformations   149G-CO.7 149Activity: Identifying Congruent Triangles   150G-CO.8 151Activity: Congruence and Rigid Motions   151G-CO.9 152Activity: Proving Theorems about Lines and Angles 152G-CO.10   153Activity: Proofs about Triangles 153G-CO.11   154Activity: Proving Theorems about Parallelograms  154G-CO.12   156Activity: Constructing Geometric Figures  156G-CO.13   157Activity: Constructing Regular Polygons   157Similarity, Right Triangles, and Trigonometry  158G-SRT.1   158Activity: Dilating Lines and Line Segments  159G-SRT.2   160Activity: Identifying Similar Triangles. 160G-SRT.3   161Activity: Establishing the AA Criterion for Two Similar Triangles  161G-SRT.4   162Activity: Proving Theorems about Triangles  162G-SRT.5   164Activity: Reflecting on Congruence and Symmetry   164G-SRT.6   165Activity: Exploring the Ratios of Sides in a Right Triangle 165G-SRT.7  166Activity: Relating the Sine and Cosine of Complementary Angles 166G-SRT.8  167Activity: Problems, Questions, and Solutions 167Circles   168G-C.1   169Activity: Proving All Circles Are Similar   169G-C.2   169Activity: Eliminating Figures Based on What They Are Not   170G-C.3   171Activity: Working with Inscribed and Circumscribed Circles   171G-C.5   172Activity: Critiquing Derivations  172Expressing Geometric Properties with Equations 173G-GPE.1  173Activity: Working with Equations 174G-GPE.2  175Activity: Deriving the Equation of a Parabola 175G-GPE.4  176Activity: Proving Geometric Theorems with Coordinates 176G-GPE.5  177Activity: Slopes of Parallel and Perpendicular Lines  177G-GPE.6  178Activity: Partitioning Line Segments 179G-GPE.7  180Activity: Graphing and Finding Perimeters and Areas of Polygons 180Geometric Measurement and Dimension 181G-GMD.1 181Activity: Presenting a Mini-Lesson on Formulas   181G-GMD.3 183Activity: Using Volume Formulas to Solve Problems  183G-GMD.4 184Activity: Cross-Sections and Rotations   184Modeling with Geometry   185G-MG.1   185Activity: Using Properties of Geometric Shapes   186G-MG.2   187Activity: A Plan for Recreational Facilities  187G-MG.3   188Activity: Planning to Build a Garage 188Reproducibles for Section 4: GeometryG-CO.1: Instructions for Drawing Figures  190G-CO.2: Transformation Tasks   191G-CO.3: Polygons 192G-CO.4: Transformations 193G-CO.5: Figures and Transformations 194G-CO.6: Figures and Images 195G-CO.7: Triangles, Sides, and Angles 196G-CO.8: Identifying Congruent Triangles   197G-CO.9: Proof Prompts   198G-CO.10: Finding the Missing Steps in Proofs about Triangles 200G-CO.11: Steps for Proving Theorems about Parallelograms   203G-CO.12: Construction Task Cards 205G-CO.13: Inscribing Regular Polygons in Circles 206G-SRT.1: Exploring Dilations 207G-SRT.2: Determining if Triangles Are Similar 208G-SRT.3: Drawing Triangles Based on Angle Measures 209G-SRT.4: Proving the Triangle Proportionality Theorem 210G-SRT.4: Proving the Converse of the Triangle Proportionality Theorem   211G-SRT.4: Proving the Pythagorean Theorem by Using Similar Triangles  212G-SRT.6: Ratios of Sides in a Right Triangle 213G-SRT.8: Problems and Solutions 214G-C.1: Going ‘Round in Circles 216G-C.2: A Circle with Segments, Angles, and Triangles 217G-C.3: Inscribed and Circumscribed Circles 218G-C.5: Miguel’s Derivations 219G-GPE.1: Equations of a Circle 220G-GPE.2: Steps for Deriving the Equation of a Parabola 221G-GPE.4: Task Cards and Coordinates  223G-GPE.5: Using Slopes to Write Equations  224G-GPE.6: Endpoints and Ratios  226G-GPE.7: Graphs, Perimeters, and Areas of Polygons 227G-GMD.3: Finding Volume  228G-GMD.4: Statements for the Cross-Sections and Rotations Game 229G-MG.1: Using Properties of Geometric Shapes to Find Area   230G-MG.2: Township Facts 231G-MG.3: A Plot Plan 232SECTION 5: STANDARDS AND ACTIVITIES FOR STATISTICS AND PROBABILITY 233Interpreting Categorical and Quantitative Data  234S-ID.1   234Activity: Representing Data   234S-ID.2   235Activity: Comparing Two Different Data Sets 236S-ID.3   236Activity: Interpreting Data Sets  237S-ID.4   238Activity: Analyzing Test Scores 238S-ID.5   239Activity: Making and Interpreting Two-Way Frequency Tables   239S-ID.6   240Activity: Representing Data on a Scatter Plot 240S-ID.7   242Activity: Identifying Slopes and Y-Intercepts 242S-ID.8   243Activity: Computing and Interpreting the Correlation Coefficient 243S-ID.9   244Activity: Determining Correlation and Causation   244Making Inferences and Justifying Conclusions  246S-IC.1   246Activity: Random Samples and Inferences 246S-IC.2   247Activity: Simulations and Probability 248S-IC.3   249Activity: Surveys, Experiments, and Observational Studies  249S-IC.4   250Activity: Evaluating Sample Surveys and Simulations 250S-IC.5   252Activity: Comparing Two Treatments 252S-IC.6   253Activity: Evaluating Reports and Data   253Conditional Probability and the Rules of Probability 254S-CP.1   255Activity: Describing Events as Subsets 255S-CP.2   256Activity: Identifying Events 256S-CP.3   257Activity: Using Conditional Probability   258S-CP.4260Activity: Understanding Independence and Conditional Probability 260S-CP.5262Activity: Explaining Conditional Probability and Independence 262S-CP.6263Activity: Finding Conditional Probability  263S-CP.7264Activity: Using the Addition Rule  265Reproducibles for Section 5: Statistics and ProbabilityS-ID.2: Guidelines for Comparing Two Different Data Sets 267S-ID.4: Analysis Guidelines 268S-ID.5: Examples of Two-Way Frequency Tables 269S-ID.5: Survey Questions  270S-ID.7: Description, Data, Slope, and Y-Intercept Cards 271S-ID.9: Correlation and Causation Statements 272S-IC.1: Examples of Samples   273S-IC.3: Identifying Surveys, Experiments, and Observational Studies  274S-IC.4: A Sample Survey and Simulation Samples   275S-IC.5: Bean Plant Growth Chart  276S-IC.6: Beach Revenue Data 277S-CP.1: Subsets of a Sample Space 279S-CP.3: Independent and Dependent Events 280S-CP.4: Student Data on Exercising and Dieting  281S-CP.6: Considering Outcomes 282S-CP.7: Using the Addition Rule to Find Probabilities  283INDEX 285

JUDITH A. MUSCHLA has over 25 years of experience as a mathematics educator in South River, New Jersey. She was a member of the New Jersey state Standards Review Panel for the Mathematics Curriculum Content Standards. GARY ROBERT MUSCHLA is a skilled teacher of middle school math, reading, and writing. He has co-authored several math activity books with Judith Muschla, including Algebra Teacher's Activities Kit, Hands-On Math Projects with Real Life Applications, and Math Starters. ERIN MUSCHLA-BERRY teaches mathematics at Monroe Township Middle School in Monroe, New Jersey. This is her eighth collaboration with Judith and Gary Muschla.

• About This Book vAbout the Authors viiAcknowledgments ixSECTION 1: STANDARDS AND ACTIVITIES FOR NUMBER AND QUANTITY 1The Real Number System 2N-RN.1 2Activity: Understanding Integer and Rational Exponents 2N-RN.2 3Activity: Finding the Values of Expressions  3N-RN.3 4Activity: Sums and Properties of Rational and Irrational Numbers 5Quantities  6N-Q.1 7Activity: A Recommendation for the Boss 7N-Q.2 8Activity: Defining Appropriate Quantities   8N-Q.3 10Activity: Determining Levels of Accuracy in Measurement 10The Complex Number System 11N-CN.1 11Activity: Classifying Complex Numbers  11N-CN.2 13Activity: Operations with Complex Numbers 13N-CN.7 14Activity: Matching Roots 14Reproducibles for Section 1: Number and QuantityN-RN.1: The Meaning of Rational Exponents 16N-RN.2: Equations and Their Values. 17N-RN.3: Proving the Sum of Two Rational Numbers Is Rational  18N-RN.3: Proving the Sum of Rational and Irrational Numbers Is Irrational  19N-Q.1: Guidelines for Choosing a Delivery Vehicle   20N-Q.2: Defining Appropriate Quantities for Problem Solving  21N-CN.1: Graphic Organizer for Complex Numbers  22N-CN.2: Complex Number Cards—Solutions and Problems  23N-CN.7: Quadratic Equations and Their Roots. 24SECTION 2: STANDARDS AND ACTIVITIES FOR ALGEBRA 25Seeing Structure in Expressions 26A-SSE.1   26Activity: Interpreting Expressions 26A-SSE.2   27Activity: Rewriting Expressions 28A-SSE.3   29Activity: Expressions and Equivalent Forms 29A-SSE.4   30Activity: Deriving a Formula 30Arithmetic with Polynomials and Rational Expressions   32A-APR.1   32Activity: Pick the Polynomial 32A-APR.2   33Activity: Solving a Division Puzzle 34A-APR.3   35Activity: Matching Functions, Graphs, and Zeroes of a Function 35A-APR.4   36Activity: Proving the Polynomial Identity   36A-APR.6   38Activity: Mistakes in Rational Expressions  38Creating Equations39A-CED.1   39Activity: Creating Equations and Inequalities 40A-CED.2   41Activity: Creating and Graphing Equations  41A-CED.3   43Activity: Pricing T-Shirts   43A-CED.4   44Activity: Rearranging Formulas and Equations 44Reasoning with Equations and Inequalities 45A-REI.1 45Activity: Organizing the Steps for Solving Equations 46A-REI.2 47Activity: Solving Equations 47A-REI.3 48Activity: What’s the Solution?   49A-REI.4 50Activity: Racing to Solve Quadratic Equations 50A-REI.5 51Activity: Solving a System of Equations 51A-REI.6 52Activity: Solving Systems in Many Ways   53A-REI.7 54Activity: Solving Systems of Equations  54A-REI.10   56Activity: Tracing Equations  56A-REI.11   57Activity: Selecting Pairs of Equations with the Same Solutions  57A-REI.12   58Activity: Identifying Solutions through Graphing 59Reproducibles for Section 2: AlgebraA-SSE.1: The Expressions Game 61A-SSE.2: Identifying and Rewriting Expressions 62A-SSE.3: Expressions and Equivalent Forms Cards 63A-SSE.4: Identifying Errors in a Derived Formula 64A-APR.1: Polynomial Cards 65A-APR.2: Polynomial Division Cards 66A-APR.3: Finding Your Match, I 67A-APR.3: Finding Your Match, II 68A-APR.6: Correcting Mistakes in Rational Expressions 69A-CED.1: Which One Does Not Belong?   70A-CED.2: Word Problems, Equations, and Graphs  71A-CED.3: T-Shirts for the Math Club 72A-CED.4: Formula and Equation Cards  73A-REI.1: Equation and Step Cards 74A-REI.2: Rational and Radical Equation Problem Cards 75A-REI.3: Equation and Inequality Cards  76A-REI.4: Quadratic Equations and Score Sheet 77A-REI.5: Steps for Solving a System of Equations 78A-REI.6: Task Cards for Solving Systems of Linear Equations   79A-REI.7: Task Cards for Equations and Solutions  80A-REI.10: Tracing Equations with Graphing Calculators 81A-REI.11: Equations and Solutions 82A-REI.12: Solving Inequalities and Systems of Inequalities by Graphing 83SECTION 3: STANDARDS AND ACTIVITIES FOR FUNCTIONS 84Interpreting Functions 85F-IF.1 85Activity: Identifying Functions   85F-IF.2 86Activity: Grouping Rules, Inputs, and Outputs 86F-IF.3 87Activity: Figurate Numbers 87F-IF.4 89Activity: Finding Similarities and Differences in Functions 90F-IF.5 92Activity: Recognizing Functions 92F-IF.6 93Activity: Matching Functions, Tables, and Average Rates of Change 93F-IF.7 95Activity: Making a Function Booklet 96F-IF.8 97Activity: Writing Functions in Equivalent Forms 97F-IF.9 99Activity: Comparing Functions   99Building Functions 100F-BF.1 101Activity: Writing Functions  101F-BF.2 102Activity: The Game of Arithmetic and Geometric Sequences   102F-BF.3 104Activity: Matching Functions with Their Graphs 104F-BF.4 105Activity: Finding the Inverse of a Function—Bingo   106Linear, Quadratic, and Exponential Models 107F-LE.1 107Activity: Modeling Linear and Exponential Functions 108F-LE.2 109Activity: Constructing Linear and Exponential Functions 110F-LE.3   111Activity: Analyzing Exponential and Polynomial Functions 111F-LE.4   112Activity: Logarithmic and Exponential Equations   112F-LE.5   113Activity: Interpreting Parameters of Functions 113Trigonometric Functions   115F-TF.1   115Activity: Understanding Radian Measure  115F-TF.2   116Activity: Trigonometric Functions and the Unit Circle  116F-TF.5   117Activity: Modeling Monthly Precipitation  117F-TF.8   119Activity: Proving and Applying the Pythagorean Identity 119Reproducibles for Section 3: FunctionsF-IF.2: Function Cards 121F-IF.4: Function Sets, I 122F-IF.4: Function Sets, II 123F-IF.6: Equations, Tables, and Average Rates of Change Cards, I 124F-IF.6: Equations, Tables, and Average Rates of Change Cards, II 125F-IF.7: A Function Booklet 126F-IF.9: Comparing Function Cards, I 127F-IF.9: Comparing Function Cards, II 128F-BF.2: Arithmetic and Geometric Sequence Game Cards 129F-BF.3: Graphs and Functions  130F-BF.4: Function Bingo Board  131F-BF.4: Functions for Bingo   132F-LE.1: Tables and Rates of Change 133F-LE.2: Information Cards for Linear and Exponential Functions 134F-LE.4: Logarithmic Equation, Exponential Equation, and Solution Cards  135F-TF.1: Drawing an Angle Whose Measure Is 1 Radian 136F-TF.2: Explaining Trigonometric Functions Using the Unit Circle 138F-TF.8: Proving the Pythagorean Identity  139F-TF.8: Angles and Their Quadrants 140SECTION 4: STANDARDS AND ACTIVITIES FOR GEOMETRY 141Congruence   142G-CO.1 142Activity: Drawing and Defining Figures  142G-CO.2 143Activity: Presenting a Mini-Lesson on Transformations 143G-CO.3 145Activity: Carrying a Figure onto Itself 145G-CO.4 146Activity: Identifying and Defining Transformations  146G-CO.5 147Activity: Drawing and Identifying Transformations  147G-CO.6 148Activity: Predicting the Effects of Transformations   149G-CO.7 149Activity: Identifying Congruent Triangles   150G-CO.8 151Activity: Congruence and Rigid Motions   151G-CO.9 152Activity: Proving Theorems about Lines and Angles 152G-CO.10   153Activity: Proofs about Triangles 153G-CO.11   154Activity: Proving Theorems about Parallelograms  154G-CO.12   156Activity: Constructing Geometric Figures  156G-CO.13   157Activity: Constructing Regular Polygons   157Similarity, Right Triangles, and Trigonometry  158G-SRT.1   158Activity: Dilating Lines and Line Segments  159G-SRT.2   160Activity: Identifying Similar Triangles. 160G-SRT.3   161Activity: Establishing the AA Criterion for Two Similar Triangles  161G-SRT.4   162Activity: Proving Theorems about Triangles  162G-SRT.5   164Activity: Reflecting on Congruence and Symmetry   164G-SRT.6   165Activity: Exploring the Ratios of Sides in a Right Triangle 165G-SRT.7  166Activity: Relating the Sine and Cosine of Complementary Angles 166G-SRT.8  167Activity: Problems, Questions, and Solutions 167Circles   168G-C.1   169Activity: Proving All Circles Are Similar   169G-C.2   169Activity: Eliminating Figures Based on What They Are Not   170G-C.3   171Activity: Working with Inscribed and Circumscribed Circles   171G-C.5   172Activity: Critiquing Derivations  172Expressing Geometric Properties with Equations 173G-GPE.1  173Activity: Working with Equations 174G-GPE.2  175Activity: Deriving the Equation of a Parabola 175G-GPE.4  176Activity: Proving Geometric Theorems with Coordinates 176G-GPE.5  177Activity: Slopes of Parallel and Perpendicular Lines  177G-GPE.6  178Activity: Partitioning Line Segments 179G-GPE.7  180Activity: Graphing and Finding Perimeters and Areas of Polygons 180Geometric Measurement and Dimension 181G-GMD.1 181Activity: Presenting a Mini-Lesson on Formulas   181G-GMD.3 183Activity: Using Volume Formulas to Solve Problems  183G-GMD.4 184Activity: Cross-Sections and Rotations   184Modeling with Geometry   185G-MG.1   185Activity: Using Properties of Geometric Shapes   186G-MG.2   187Activity: A Plan for Recreational Facilities  187G-MG.3   188Activity: Planning to Build a Garage 188Reproducibles for Section 4: GeometryG-CO.1: Instructions for Drawing Figures  190G-CO.2: Transformation Tasks   191G-CO.3: Polygons 192G-CO.4: Transformations 193G-CO.5: Figures and Transformations 194G-CO.6: Figures and Images 195G-CO.7: Triangles, Sides, and Angles 196G-CO.8: Identifying Congruent Triangles   197G-CO.9: Proof Prompts   198G-CO.10: Finding the Missing Steps in Proofs about Triangles 200G-CO.11: Steps for Proving Theorems about Parallelograms   203G-CO.12: Construction Task Cards 205G-CO.13: Inscribing Regular Polygons in Circles 206G-SRT.1: Exploring Dilations 207G-SRT.2: Determining if Triangles Are Similar 208G-SRT.3: Drawing Triangles Based on Angle Measures 209G-SRT.4: Proving the Triangle Proportionality Theorem 210G-SRT.4: Proving the Converse of the Triangle Proportionality Theorem   211G-SRT.4: Proving the Pythagorean Theorem by Using Similar Triangles  212G-SRT.6: Ratios of Sides in a Right Triangle 213G-SRT.8: Problems and Solutions 214G-C.1: Going ‘Round in Circles 216G-C.2: A Circle with Segments, Angles, and Triangles 217G-C.3: Inscribed and Circumscribed Circles 218G-C.5: Miguel’s Derivations 219G-GPE.1: Equations of a Circle 220G-GPE.2: Steps for Deriving the Equation of a Parabola 221G-GPE.4: Task Cards and Coordinates  223G-GPE.5: Using Slopes to Write Equations  224G-GPE.6: Endpoints and Ratios  226G-GPE.7: Graphs, Perimeters, and Areas of Polygons 227G-GMD.3: Finding Volume  228G-GMD.4: Statements for the Cross-Sections and Rotations Game 229G-MG.1: Using Properties of Geometric Shapes to Find Area   230G-MG.2: Township Facts 231G-MG.3: A Plot Plan 232SECTION 5: STANDARDS AND ACTIVITIES FOR STATISTICS AND PROBABILITY 233Interpreting Categorical and Quantitative Data  234S-ID.1   234Activity: Representing Data   234S-ID.2   235Activity: Comparing Two Different Data Sets 236S-ID.3   236Activity: Interpreting Data Sets  237S-ID.4   238Activity: Analyzing Test Scores 238S-ID.5   239Activity: Making and Interpreting Two-Way Frequency Tables   239S-ID.6   240Activity: Representing Data on a Scatter Plot 240S-ID.7   242Activity: Identifying Slopes and Y-Intercepts 242S-ID.8   243Activity: Computing and Interpreting the Correlation Coefficient 243S-ID.9   244Activity: Determining Correlation and Causation   244Making Inferences and Justifying Conclusions  246S-IC.1   246Activity: Random Samples and Inferences 246S-IC.2   247Activity: Simulations and Probability 248S-IC.3   249Activity: Surveys, Experiments, and Observational Studies  249S-IC.4   250Activity: Evaluating Sample Surveys and Simulations 250S-IC.5   252Activity: Comparing Two Treatments 252S-IC.6   253Activity: Evaluating Reports and Data   253Conditional Probability and the Rules of Probability 254S-CP.1   255Activity: Describing Events as Subsets 255S-CP.2   256Activity: Identifying Events 256S-CP.3   257Activity: Using Conditional Probability   258S-CP.4260Activity: Understanding Independence and Conditional Probability 260S-CP.5262Activity: Explaining Conditional Probability and Independence 262S-CP.6263Activity: Finding Conditional Probability  263S-CP.7264Activity: Using the Addition Rule  265Reproducibles for Section 5: Statistics and ProbabilityS-ID.2: Guidelines for Comparing Two Different Data Sets 267S-ID.4: Analysis Guidelines 268S-ID.5: Examples of Two-Way Frequency Tables 269S-ID.5: Survey Questions  270S-ID.7: Description, Data, Slope, and Y-Intercept Cards 271S-ID.9: Correlation and Causation Statements 272S-IC.1: Examples of Samples   273S-IC.3: Identifying Surveys, Experiments, and Observational Studies  274S-IC.4: A Sample Survey and Simulation Samples   275S-IC.5: Bean Plant Growth Chart  276S-IC.6: Beach Revenue Data 277S-CP.1: Subsets of a Sample Space 279S-CP.3: Independent and Dependent Events 280S-CP.4: Student Data on Exercising and Dieting  281S-CP.6: Considering Outcomes 282S-CP.7: Using the Addition Rule to Find Probabilities  283INDEX 285