Table of Contents

Section One: Numbers: Theory and Operation

List 1, The Real Numbers 2

List 2, Classification of Real Numbers 3

List 3, Cardinal and Ordinal Numbers 4

List 4, Prime Numbers 5

List 5, Types of Prime Numbers 6

List 6, Composite Numbers 8

List 7, Perfect Squares and Cubes 9

List 8, Abundant, Deficient, and Perfect Numbers 10

List 9, Amicable Numbers 12

List 10, Some Lesser-Known Types of Numbers 13

List 11, Multiplication Table 15

List 12, Rules for Finding Divisibility 16

List 13, Rules for Finding the Greatest Common Factor (GCF) 17

List 14, Rules for Finding the Least Common Multiple (LCM) 18

List 15, Types of Fractions 19

List 16, Rules for Simplifying Fractions 20

List 17, Rules for Operations with Fractions 21

List 18, Rules for Operations with Mixed Numbers 23

List 19, Place Value Chart 25

List 20, Types of Decimals 26

List 21, Rules for Operations with Decimals 27

List 22, Rules for Changing Decimals to Fractions 29

List 23, Rules for Changing Fractions to Decimals 31

List 24, Rules for Changing Decimals to Percents 32

List 25, Rules for Changing Percents to Decimals 33

List 26, Rules for Changing Fractions to Percents 34

List 27, Rules for Changing Percents to Fractions 35

List 28, Percent Equivalents 36

List 29, Rules for Solving Proportions 37

List 30, Rules for Finding Percents of Numbers 38

List 31, Rules for Finding Percent and the Base 39

List 32, Rules for Operations with Integers 40

List 33, Properties of Integers 42

List 34, Rules for Finding the Average (Mean) 43

List 35, Rules for Rounding Numbers 44

List 36, Rules for Finding Prime Factorizations 45

List 37, Scientific Notation 46

List 38, Bases 47

List 39, Big Numbers 48

List 40, Mathematical Signs and Symbols 49

Section Two: Measurement

List 41, Things That Measure 52

List 42, The Origin of Measurements 54

List 43, Obsolete Units of Measure 55

List 44, Measurement Abbreviations 56

List 45, The English System of Weights and Measures 58

List 46, Rules for Converting Units in the English System 62

List 47, U.S. and British Units of Measurement 63

List 48, Units of the Metric System 64

List 49, Metric Standards 65

List 50, Metric Prefixes 67

List 51, Weights and Measures in the Metric System 68

List 52, Converting One Unit to Another in the Metric System 69

List 53, Rules for Adding Units of Measurement 70

List 54, Rules for Subtracting Units of Measurement 70

List 55, Rules for Multiplying Units of Measurement 71

List 56, Rules for Dividing Units of Measurement 71

List 57, English–Metric Equivalents 72

List 58, Metric–English Equivalents 74

List 59, Conversion Factors for Length 75

List 60, Conversion Factors for Area 76

List 61, Conversion Factors for Volume 76

List 62, Conversion Factors for Liquid Capacity 77

List 63, Conversion Factors for Dry Capacity 77

List 64, Conversion Factors for Mass (Weight) 78

List 65, Measures of Force and Pressure 79

List 66, Measurement of Time 80

List 67, Temperature Formulas 81

List 68, Getting a Feel for Temperature 82

List 69, The Richter Scale 83

List 70, Wind Speed 84

List 71, The Saffir-Simpson Hurricane Scale 85

List 72, The Fujita Scale of Tornado Intensity 86

List 73, Computer Memory 87

List 74, Paper Measures or Paper Weights 88

List 75, U.S. Money: Coins and Bills 89

Section Three: Geometry

List 76, Undefined Terms of Geometry 91

List 77, Euclid’s Axioms and Postulates 92

List 78, Lines and Planes 93

List 79, Steps for Naming an Angle 94

List 80, Measuring Angles 95

List 81, Drawing Angles 96

List 82, Types of Angles and the Facts 97

List 83, Facts About Pairs of Angles 98

List 84, Angles Formed by a Transversal 99

List 85, Principles of Parallel Lines 100

List 86, Principles of Perpendicular Lines 101

List 87, Types of Polygons 101

List 88, Regular Polygons: Terms and Formulas 102

List 89, Principles of Regular Polygons 103

List 90, Shapes of Numbers 104

List 91, Figurate Number Formulas 106

List 92, Polyominoes 106

List 93, Pentominoes and Hexominoes 107

List 94, Basic Figures in Geometry 108

List 95, Tangram Facts and Figures 110

List 96, Triangle Terms 112

List 97, Classifying Triangles 113

List 98, Principles of Triangles 114

List 99, Concurrent Segments of Triangles 115

List 100, Special Right Triangles 116

List 101, Pythagorean Triples 117

List 102, Proving Triangles Congruent 118

List 103, Properties of Similar Triangles 118

List 104, Proving Triangles Similar 119

List 105, Ratio and Proportion 120

List 106, Deriving Proportions 121

List 107, Principles Relating to Parallel and Proportional Lines 122

List 108, Pascal’s Triangle 123

List 109, The Harmonic Triangle 124

List 110, Types of Quadrilaterals 125

List 111, Properties of Special Quadrilaterals 126

List 112, Classification of Quadrilaterals 127

List 113, Proofs for Quadrilaterals 128

List 114, Tessellations 129

List 115, Circles 130

List 116, Special Circles 131

List 117, Circles: Line and Segment Principles 132

List 118, Circles: Arcs and Angles 134

List 119, Principles of Arcs and Angles 135

List 120, Solids 137

List 121, Platonic Solids 139

List 122, Classifications of Solids 140

List 123, Patterns of a Painted Cube 141

List 124, Scale Factors for Similar and Plane Figures and Solids 142

List 125, Types of Symmetry 143

List 126, Types of Transformations 144

List 127, Transformation Matrices 145

List 128, Fractal Facts 146

List 129, Formulas for Perimeter and Circumference 147

List 130, Area Formulas for Basic Figures 148

List 131, More Formulas for Area 149

List 132, Formulas for Surface Area 151

List 133, Formulas for Finding Volume 152

Section Four: Algebra

List 134, How to Express Operations Algebraically 154

List 135, Algebraic Grouping Symbols 154

List 136, Properties of Real Numbers 155

List 137, Summary of Properties of Sets of Numbers 156

List 138, Relating Operations on the Real Numbers 157

List 139, Axioms of Equality 158

List 140, Axioms of Order 158

List 141, Properties of Equality 159

List 142, Properties of Inequalities 160

List 143, Powers of Real Numbers 161

List 144, Rules for Exponents 162

List 145, Order of Operations 162

List 146, How to Construct a Number Line 163

List 147, Steps for Graphing on a Number Line 164

List 148, The Absolute Facts on Absolute Value 165

List 149, Steps to Solve an Equation in One Variable 166

List 150, Steps to Solve an Inequality in One Variable 167

List 151, Polynomials 168

List 152, Multiplication with Monomials and Polynomials 169

List 153, Guidelines for Factoring Polynomials of Degree 2 170

List 154, Common Factoring Formulas 171

List 155, Characteristics of the Coordinate Plane 172

List 156, Plotting Points on the Coordinate Plane 173

List 157, Common Forms of Linear Equations 174

List 158, Formulas and the Coordinate Plane 175

List 159, Graphing Linear Equations in Two Variables on the Coordinate Plane 176

List 160, Graphing a Linear Inequality in Two Variables on the Coordinate Plane 177

List 161, Steps to Solve a System of Linear Equations in Two Variables 178

List 162, Types of Functions 180

List 163, Direct Facts on Variation 182

List 164, Functional Facts About Functions 183

List 165, Square Roots 184

List 166, Nth Roots 185

List 167, Powers and Roots 186

List 168, Conditions for Simplifying Radical Expressions 187

List 169, Steps for Solving a Quadratic Equation 188

List 170, Imaginary Numbers and Their Powers 190

List 171, Discriminant and Coefficients 191

List 172, Quadratic Functions 191

List 173, Graph of a Circle 192

List 174, Graph of an Ellipse 193

List 175, Graph of a Parabola 194

List 176, Graph of a Hyperbola 196

List 177, Properties of Complex Numbers 198

List 178, Operations with Complex Numbers 199

List 179, Conjugate Complex Numbers 199

List 180, Vectors 200

List 181, Matrices 202

List 182, Types of Matrices 204

Section Five: Trigonometry and Calculus

List 183, Right Triangle Definitions of Trigonometric Functions 206

List 184, Trigonometric Functions of Complementary Angles 207

List 185, How to Express Angles in Circular Measure 208

List 186, Circular Function Definition of Trigonometric Functions 209

List 187, Trigonometric Functions of Quadrantal Angles 210

List 188, The Quadrant Signs of the Functions 211

List 189, Variations of Trigonometric Functions 212

List 190, Trigonometric Functions of Some Special Angles 213

List 191, Fundamental Periods of Trigonometric Functions 214

List 192, Trigonometric Functions: Their Domains, Ranges, and Periods 215

List 193, Graphs of the Trigonometric Functions 216

List 194, General Trigonometric Functions: Their Periods and Amplitudes 217

List 195, Basic Trigonometric Identities 218

List 196, Angle-Sum and Angle-Difference Formulas 219

List 197, Double-Angle Formulas and Half-Angle Formulas 220

List 198, Multiple-Angle Formulas, Product Formulas, and Sum and Difference Formulas 221

List 199, Reduction Formulas 222

List 200, General Guidelines for Proving Identities 223

List 201, The Trigonometric Functions in Terms of One Another 224

List 202, Trigonometric Identities and Oblique Triangles 225

List 203, Inverse Trigonometric Functions 227

List 204, Vertical and Horizontal Line Tests 227

List 205, Relations Between Inverse Trigonometric Functions 228

List 206, Graphs of the Inverse Trigonometric Functions 229

List 207, Limits 230

List 208, Operations with Limits 231

List 209, Continuity 232

List 210, Properties of Continuous Functions 232

List 211, Differential Rules 233

List 212, Higher-Order Derivatives 234

List 213, Curve Drawing: Application of Higher-Order Derivatives 235

List 214, Notation for Antiderivatives 236

List 215, Integration Rules 236

List 216, Definite Integrals 237

List 217, Derivatives and Integrals of Trigonometric Functions 238

List 218, Exponential Functions 239

List 219, Natural Logarithmic Functions 240

Section Six: Math in Other Areas

List 220, Descriptive Statistics 242

List 221, Types of Graphs, Displays, and Tables 243

List 222, Topics in Discrete Math 244

List 223, Permutations 245

List 224, Combinations 247

List 225, Probability and Odds 248

List 226, Odds in Poker 250

List 227, Odds in Dice 251

List 228, The Chances Are 252

List 229, Ways People Are Paid 253

List 230, Deductions 254

List 231, How to Write and Endorse a Check 255

List 232, How to Complete a Check Register 257

List 233, How to Balance a Checkbook 259

List 234, Loans and Interest 261

List 235, Steps to Making a Budget 262

List 236, Items on Sale 263

List 237, How Much to Tip 265

List 238, Stock Market Words 266

List 239, Reading a Financial Page 269

List 240, How to Read a Food Label 271

List 241, Cholesterol Content of Popular Foods 273

List 242, A Basic Low-Fat Meal Plan 277

List 243, Fat and Food 278

List 244, Physical Activities and Burning Calories 280

List 245, Finding Your Exercise Heart Rate 281

List 246, The Numbers in Popular Sports 282

List 247, Finding Statistics in Baseball 287

List 248, Geometry and Nature 290

List 249, Your Weight on Other Planets 291

List 250, Some Mathematical Facts About Space 292

List 251, Conservation Facts 294

List 252, Some Helpful Formulas 295

Section Seven: Potpourri

List 253, The History of Mathematics 299

List 254, Famous Mathematicians Through History 301

List 255, Mathematical Quotations 307

List 256, Careers in Math 308

List 257, World Firsts 309

List 258, Tricky Math Problems 311

List 259, Mathematical Palindromes 313

List 260, Roman Numerals 314

List 261, Numbers and Symbolism 316

List 262, A Number of Coincidences 318

List 263, Math and Superstition 320

List 264, Mathematical Idioms 321

List 265, Numbers in Names and Events 323

List 266, Math Words Used Every Day 326

List 267, Numbers and Language 327

List 268, The Greek Alphabet 328

Section Eight: Special Reference Lists for Students

List 269, The Math Student’s Responsibilities 330

List 270, Overcoming Math Anxiety 331

List 271, Strategies for Taking Math Tests 332

List 272, Steps for Solving Word Problems 334

List 273, Problem-Solving Strategies for Middle School Students 335

List 274, Problem-Solving Strategies for the Upper Grades 336

List 275, Characteristics of Good Problem Solvers 337

List 276, Steps for Writing Word Problems 338

List 277, Math Journal Guidelines for Students 340

List 278, Math Web Sites for Students 341

Section Nine: Lists for Teachers’ Reference

List 279, The Math Teacher’s Responsibilities 343

List 280, Upgrading Your Mathematics Curriculum 344

List 281, Materials Every Math Classroom Should Have 346

List 282, Expanding the Horizons of Your Math Classes 347

List 283, The Math Teacher’s Management Strategies 348

List 284, Managing a Successful Math Class: Student Problems and Solutions 349

List 285, How to Manage a Cooperative Math Class 351

List 286, Student Guidelines for Working in Groups 352

List 287, Steps for Conducting Effective Conferences with Students 353

List 288, Steps to Help Students Develop Problem-Solving Skills 354

List 289, A Teacher’s Plan for Writing Word Problems 355

List 290, Sources of Problems-of-the-Day 356

List 291, The Use of Portfolios in Your Classes 357

List 292, Helping Students Prepare for Math Tests 358

List 293, Math Bulletin Board Ideas 359

List 294, Topics for Possible Math Projects 360

List 295, How to Start a Math Magazine 362

List 296, How to Start a Math Club 363

List 297, Ideas for Math Field Trips 364

List 298, Possible Guest Speakers for Your Math Classes 365

List 299, Steps for Maintaining Positive Relations with Parents 366

List 300, How Parents Can Help Their Children Learn Math 367

List 301, Back-to-School-Night Checklist 368

List 302, Steps for Conducting Effective Parent-Teacher Conferences 370

List 303, How to Have a Parents’ Math Night 371

List 304, Professional Math Organizations 373

List 305, Math Web Sites for Teachers 375

List 306, A Self-Appraisal for Math Teachers 376

Section Ten: Reproducible Teaching Aids

Number Lines 378

Rulers I 379

Rulers II 380

Protractors 381

Squares 382

Graphs for Trigonometric Functions 383

1-Inch Grid 384

1⁄2-Inch Grid 385

1-cm Grid 386

Isometric Dot Paper 387

Square Grid Dot Paper 388

Decimal Squares 389

Fraction Strips 390

Fraction Circles 391

Algebra Tiles 392

Tangram 393

Patterns for Pattern Blocks 394

Patterns for Cuisenaire ® Rods 395

Net for Rectangular Prism 396

Net for Pyramid 397

Net for Cone 398

Net for Tetrahedron 399

Net for Hexahedron (Cube) 400

Net for Octahedron 401

Net for Dodecahedron 402

Net for Icosahedron 403

Blank Checks 404

Blank Check Register 405

About the Author

Judith A. Muschla has taught mathematics in South River, New Jersey, for over twenty-five years.

Gary Robert Muschla, prolific author and classroom teacher, has taught reading and writing for more than twenty-five years in Spotswood, New Jersey. This is the eighth math resource coauthored by Judith Muschla and Gary Muschla. Their earlier books include The Math Teacher's Book of Lists, First Edition; Hands-On Math Projects with Real-Life Applications; Math Starters; The Geometry Teacher's Activities Kit; Math Smart; Algebra Teacher's Activities Kit; and Math Games all published by Jossey-Bass Publishers.

Reviews

?Through its assortment of informative lists, this book provides a clear and concise approach to mathematics. A practical reference for teachers, it will enable students to master a variety of topics within the parameters of both course and national standards.?--Elizabeth Razzano, mathematics teacher, East Brunswick High School, East Brunswick, New Jersey