The Math Teacher's Book Of Lists

This is the second edition of the bestselling resource for mathematics teachers. This time-saving reference provides over 300 useful lists for developing instructional materials and planning lessons for middle school and secondary students. Some of the lists supply teacher background; others are to copy for student use, and many offer new twists to traditional classroom topics. For quick access and easy use, the lists are numbered consecutively, organized into sections focusing on the different areas of math, and printed in a large 8-1/2" x 11" lay-flat format for easy photocopying. Here's an overview of the ready-to-use lists you'll find in each section: I. NUMBERS: THEORY AND OPERATIONS presents 40 lists including classification of real numbers, types of fractions, types of decimals, rules for various operations, big numbers, and mathematical signs and symbols. II. MEASUREMENT contains over 30 lists including, things that measure, measurement abbreviations, the English and Metric Systems, and U.S. money¾coins and bills. III. GEOMETRY offers more than 50 lists covering topics such as lines and planes, types of polygons, types of quadrilaterals, circles, Pythagorean triples, and formulas for finding area and volume. IV. ALGEBRA gives you over 40 lists including how to express operations algebraically, powers and roots, common factoring formulas, quadratic functions, and types of matrices. V. TRIGONOMETRY AND CALCULUS provides more than 30 lists including the quadrant signs of the functions, reduction formulas, integration rules, and natural logarithmic functions. VI. MATH IN OTHER AREAS offers more than 30 lists that tie math to other content areas, such as descriptive statistics, probability and odds, numbers in popular sports, and some mathematical facts about space. VII. POTPOURRI features 16 lists that explore the various aspects of math including, famous mathematicians through history, world firsts, math and superstition, and the Greek alphabet. VIII. SPECIAL REFERENCE LISTS FOR STUDENTS provides 10 lists of interest to students such as overcoming math anxiety, steps for solving word problems, and math web sites for students. IX. LISTS FOR TEACHERS’ REFERENCE contains 25 lists such as how to manage a cooperative math class, sources of problems-of-the-day, how to have a parents’ math night, and math web sites for teachers. X. REPRODUCIBLE TECHING AIDS contains an assortment of helpful reproducibles including number lines, fraction strips, algebra tiles, and various nets for making 3-D geometric shapes.

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