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

ISBN-13: 9781118710104 / Angielski / Miękka / 2015 / 312 str.

Gary Robert Muschla

Opis

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.

Spis treści

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

O autorze

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.

Blurb

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.