Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12

Bring Common Core Math into high school with smart, engaging activities

Teaching Common Core Math Standards with Hands-On Activities, Grades 9-12 provides high school teachers with the kind of help they need to begin teaching the standards right away. This invaluable guide pairs each standard with one or more classroom-ready activities and suggestions for variations and extensions. Covering a range of abilities and learning styles, these activities bring the Common Core Math Standards to life as students gain fluency in math communication and develop the skillset they need to tackle successively more complex math courses in the coming years. Make math anxiety a thing of the past as you show your students how they use math every day of their lives, and give them the cognitive tools to approach any math problem with competence and confidence.

The Common Core Standards define the knowledge and skills students need to graduate high school fully prepared for college and careers. Meeting these standards positions American students more competitively in the global economy, and sets them on a track to achieve their dreams. This book shows you how to teach the math standards effectively, and facilitate a deeper understanding of math concepts and calculations.

• Help students apply their understanding of math concepts
• Teach essential abstract and critical thinking skills
• Demonstrate various problem-solving strategies
• Lay a foundation for success in higher mathematics

The rapid adoption of the Common Core Standards across the nation has left teachers scrambling for aligned lessons and activities. If you want to bring new ideas into the classroom today, look no further. Teaching Common Core Math Standards with Hands-On Activities is the high school math teacher's solution for smart, engaging Common Core math.

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

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.

Easy-to-use, engaging activities that enhance your curriculum and align with the Common Core

Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12 is a valuable resource for teachers who need to make the adjustment to the new standards right away. This book provides little- or no-prep activities specifically created to address Common Core math standards at the high school level. The easy-to-navigate design allows you to find what you need quickly, and thorough teacher's notes make implementation easy.

In this book, the Muschlas extend their popular Teaching the Common Core series to the higher grade levels with lessons that can be quickly adapted to suit your students' ability levels and learning styles. Students will build critical thinking skills, learn how to communicate math concepts, hone problem-solving abilities, and have fun while you prepare them to excel in higher education and in the workplace.

The activities in Teaching the Common Core Math Standards with Hands-On Activities, Grades 9-12 are designed to capture students' attention. Icons make it easy to identify lessons that involve collaborative learning or technology. Inside, you'll find reproducible resources, answer keys, and hints for instruction, giving you everything you need to ensure that every lesson runs smoothly and helps students master the Common Core Standards, beginning right away.