The Math Teacher's Book of Lists

ISBN-13: 9780787973988 / Angielski / Miękka / 2005 / 436 str.

Judith A. Muschla; Gary Robert Muschla

Opis

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. money3/4coins 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.

Spis treści

Section One: Numbers: Theory and Operation.

List 1, The Real Numbers.

List 2, Classification of Real Numbers.

List 3, Cardinal and Ordinal Numbers.

List 4, Prime Numbers.

List 5, Types of Prime Numbers.

List 6, Composite Numbers.

List 7, Perfect Squares and Cubes.

List 8, Abundant, Deficient, and Perfect Numbers.

List 9, Amicable Numbers.

List 10, Some Lesser–Known Types of Numbers.

List 11, Multiplication Table.

List 12, Rules for Finding Divisibility.

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

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

List 15, Types of Fractions.

List 16, Rules for Simplifying Fractions.

List 17, Rules for Operations with Fractions.

List 18, Rules for Operations with Mixed Numbers.

List 19, Place Value Chart.

List 20, Types of Decimals.

List 21, Rules for Operations with Decimals.

List 22, Rules for Changing Decimals to Fractions.

List 23, Rules for Changing Fractions to Decimals.

List 24, Rules for Changing Decimals to Percents.

List 25, Rules for Changing Percents to Decimals.

List 26, Rules for Changing Fractions to Percents.

List 27, Rules for Changing Percents to Fractions.

List 28, Percent Equivalents.

List 29, Rules for Solving Proportions.

List 30, Rules for Finding Percents of Numbers.

List 31, Rules for Finding Percent and the Base.

List 32, Rules for Operations with Integers.

List 33, Properties of Integers.

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

List 35, Rules for Rounding Numbers.

List 36, Rules for Finding Prime Factorizations.

List 37, Scientific Notation.

List 38, Bases.

List 39, Big Numbers.

List 40, Mathematical Signs and Symbols.

Section Two: Measurement.

List 41, Things That Measure.

List 42, The Origin of Measurements.

List 43, Obsolete Units of Measure.

List 44, Measurement Abbreviations.

List 45, The English System of Weights and Measures.

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

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

List 48, Units of the Metric System.

List 49, Metric Standards.

List 50, Metric Prefixes.

List 51, Weights and Measures in the Metric System.

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

List 53, Rules for Adding Units of Measurement.

List 54, Rules for Subtracting Units of Measurement.

List 55, Rules for Multiplying Units of Measurement.

List 56, Rules for Dividing Units of Measurement.

List 57, English–Metric Equivalents.

List 58, Metric–English Equivalents.

List 59, Conversion Factors for Length.

List 60, Conversion Factors for Area.

List 61, Conversion Factors for Volume.

List 62, Conversion Factors for Liquid Capacity.

List 63, Conversion Factors for Dry Capacity.

List 64, Conversion Factors for Mass (Weight).

List 65, Measures of Force and Pressure.

List 66, Measurement of Time.

List 67, Temperature Formulas.

List 68, Getting a Feel for Temperature.

List 69, The Richter Scale.

List 70, Wind Speed.

List 71, The Saffir–Simpson Hurricane Scale.

List 72, The Fujita Scale of Tornado Intensity.

List 73, Computer Memory.

List 74, Paper Measures or Paper Weights.

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

Section Three: Geometry.

List 76, Undefined Terms of Geometry.

List 77, Euclid’s Axioms and Postulates.

List 78, Lines and Planes.

List 79, Steps for Naming an Angle.

List 80, Measuring Angles.

List 81, Drawing Angles.

List 82, Types of Angles and the Facts.

List 83, Facts About Pairs of Angles.

List 84, Angles Formed by a Transversal.

List 85, Principles of Parallel Lines.

List 86, Principles of Perpendicular Lines.

List 87, Types of Polygons.

List 88, Regular Polygons: Terms and Formulas.

List 89, Principles of Regular Polygons.

List 90, Shapes of Numbers.

List 91, Figurate Number Formulas.

List 92, Polyominoes.

List 93, Pentominoes and Hexominoes.

List 94, Basic Figures in Geometry.

List 95, Tangram Facts and Figures.

List 96, Triangle Terms.

List 97, Classifying Triangles.

List 98, Principles of Triangles.

List 99, Concurrent Segments of Triangles.

List 100, Special Right Triangles.

List 101, Pythagorean Triples.

List 102, Proving Triangles Congruent.

List 103, Properties of Similar Triangles.

List 104, Proving Triangles Similar.

List 105, Ratio and Proportion.

List 106, Deriving Proportions.

List 107, Principles Relating to Parallel and Proportional Lines.

List 108, Pascal’s Triangle.

List 109, The Harmonic Triangle.

List 110, Types of Quadrilaterals.

List 111, Properties of Special Quadrilaterals.

List 112, Classification of Quadrilaterals.

List 113, Proofs for Quadrilaterals.

List 114, Tessellations.

List 115, Circles.

List 116, Special Circles.

List 117, Circles: Line and Segment Principles.

List 118, Circles: Arcs and Angles.

List 119, Principles of Arcs and Angles.

List 120, Solids.

List 121, Platonic Solids.

List 122, Classifications of Solids.

List 123, Patterns of a Painted Cube.

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

List 125, Types of Symmetry.

List 126, Types of Transformations.

List 127, Transformation Matrices.

List 128, Fractal Facts.

List 129, Formulas for Perimeter and Circumference.

List 130, Area Formulas for Basic Figures.

List 131, More Formulas for Area.

List 132, Formulas for Surface Area.

List 133, Formulas for Finding Volume.

Section Four: Algebra.

List 134, How to Express Operations Algebraically.

List 135, Algebraic Grouping Symbols.

List 136, Properties of Real Numbers.

List 137, Summary of Properties of Sets of Numbers.

List 138, Relating Operations on the Real Numbers.

List 139, Axioms of Equality.

List 140, Axioms of Order.

List 141, Properties of Equality.

List 142, Properties of Inequalities.0

List 143, Powers of Real Numbers.

List 144, Rules for Exponents.

List 145, Order of Operations.

List 146, How to Construct a Number Line.

List 147, Steps for Graphing on a Number Line.

List 148, The Absolute Facts on Absolute Value.

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

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

List 151, Polynomials.

List 152, Multiplication with Monomials and Polynomials.

List 153, Guidelines for Factoring Polynomials of Degree 2.

List 154, Common Factoring Formulas.

List 155, Characteristics of the Coordinate Plane.

List 156, Plotting Points on the Coordinate Plane.

List 157, Common Forms of Linear Equations.

List 158, Formulas and the Coordinate Plane.

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

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

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

List 162, Types of Functions.

List 163, Direct Facts on Variation.

List 164, Functional Facts About Functions.

List 165, Square Roots.

List 166, Nth Roots.

List 167, Powers and Roots.

List 168, Conditions for Simplifying Radical Expressions.

List 169, Steps for Solving a Quadratic Equation.

List 170, Imaginary Numbers and Their Powers.

List 171, Discriminant and Coefficients.

List 172, Quadratic Functions.

List 173, Graph of a Circle.

List 174, Graph of an Ellipse.

List 175, Graph of a Parabola.

List 176, Graph of a Hyperbola.

List 177, Properties of Complex Numbers.

List 178, Operations with Complex Numbers.

List 179, Conjugate Complex Numbers.

List 180, Vectors.

List 181, Matrices.

List 182, Types of Matrices.

Section Five: Trigonometry and Calculus.

List 183, Right Triangle Definitions of Trigonometric Functions.

List 184, Trigonometric Functions of Complementary Angles.

List 185, How to Express Angles in Circular Measure.

List 186, Circular Function Definition of Trigonometric Functions.

List 187, Trigonometric Functions of Quadrantal Angles.

List 188, The Quadrant Signs of the Functions.

List 189, Variations of Trigonometric Functions.

List 190, Trigonometric Functions of Some Special Angles.

List 191, Fundamental Periods of Trigonometric Functions.

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

List 193, Graphs of the Trigonometric Functions.

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

List 195, Basic Trigonometric Identities.

List 196, Angle–Sum and Angle–Difference Formulas.

List 197, Double–Angle Formulas and Half–Angle Formulas.

List 198, Multiple–Angle Formulas, Product Formulas, and Sum and Difference Formulas.

List 199, Reduction Formulas.

List 200, General Guidelines for Proving Identities.

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

List 202, Trigonometric Identities and Oblique Triangles.

List 203, Inverse Trigonometric Functions.

List 204, Vertical and Horizontal Line Tests.

List 205, Relations Between Inverse Trigonometric Functions.

List 206, Graphs of the Inverse Trigonometric Functions.

List 207, Limits.

List 208, Operations with Limits.

List 209, Continuity.

List 210, Properties of Continuous Functions.

List 211, Differential Rules.

List 212, Higher–Order Derivatives.

List 213, Curve Drawing: Application of Higher–Order Derivatives.

List 214, Notation for Antiderivatives.

List 215, Integration Rules.

List 216, Definite Integrals.

List 217, Derivatives and Integrals of Trigonometric Functions.

List 218, Exponential Functions.

List 219, Natural Logarithmic Functions.

Section Six: Math in Other Areas.

List 220, Descriptive Statistics.

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

List 222, Topics in Discrete Math.

List 223, Permutations.

List 224, Combinations.

List 225, Probability and Odds.

List 226, Odds in Poker.

List 227, Odds in Dice.

List 228, The Chances Are.

List 229, Ways People Are Paid.

List 230, Deductions.

List 231, How to Write and Endorse a Check.

List 232, How to Complete a Check Register.

List 233, How to Balance a Checkbook.

List 234, Loans and Interest.

List 235, Steps to Making a Budget.

List 236, Items on Sale.

List 237, How Much to Tip.

List 238, Stock Market Words.

List 239, Reading a Financial Page.

List 240, How to Read a Food Label.

List 241, Cholesterol Content of Popular Foods.

List 242, A Basic Low–Fat Meal Plan.

List 243, Fat and Food.

List 244, Physical Activities and Burning Calories.

List 245, Finding Your Exercise Heart Rate.

List 246, The Numbers in Popular Sports.

List 247, Finding Statistics in Baseball.

List 248, Geometry and Nature.

List 249, Your Weight on Other Planets.

List 250, Some Mathematical Facts About Space.

List 251, Conservation Facts.

List 252, Some Helpful Formulas.

Section Seven: Potpourri.

List 253, The History of Mathematics.

List 254, Famous Mathematicians Through History.

List 255, Mathematical Quotations.

List 256, Careers in Math.

List 257, World Firsts.

List 258, Tricky Math Problems.

List 259, Mathematical Palindromes.

List 260, Roman Numerals.

List 261, Numbers and Symbolism.

List 262, A Number of Coincidences.

List 263, Math and Superstition.

List 264, Mathematical Idioms.

List 265, Numbers in Names and Events.

List 266, Math Words Used Every Day.

List 267, Numbers and Language.

List 268, The Greek Alphabet.8

Section Eight: Special Reference Lists for Students.

List 269, The Math Student’s Responsibilities.

List 270, Overcoming Math Anxiety.

List 271, Strategies for Taking Math Tests.

List 272, Steps for Solving Word Problems.

List 273, Problem–Solving Strategies for Middle School Students.

List 274, Problem–Solving Strategies for the Upper Grades.

List 275, Characteristics of Good Problem Solvers.

List 276, Steps for Writing Word Problems.

List 277, Math Journal Guidelines for Students.

List 278, Math Web Sites for Students.

Section Nine: Lists for Teachers’ Reference.

List 279, The Math Teacher’s Responsibilities.

List 280, Upgrading Your Mathematics Curriculum.

List 281, Materials Every Math Classroom Should Have.

List 282, Expanding the Horizons of Your Math Classes.

List 283, The Math Teacher’s Management Strategies.

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

List 285, How to Manage a Cooperative Math Class.

List 286, Student Guidelines for Working in Groups.

List 287, Steps for Conducting Effective Conferences with Students.

List 288, Steps to Help Students Develop Problem–Solving Skills.

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

List 290, Sources of Problems–of–the–Day.

List 291, The Use of Portfolios in Your Classes.

List 292, Helping Students Prepare for Math Tests.

List 293, Math Bulletin Board Ideas.

List 294, Topics for Possible Math Projects.0

List 295, How to Start a Math Magazine.

List 296, How to Start a Math Club.

List 297, Ideas for Math Field Trips.

List 298, Possible Guest Speakers for Your Math Classes.

List 299, Steps for Maintaining Positive Relations with Parents.

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

List 301, Back–to–School–Night Checklist.

List 302, Steps for Conducting Effective Parent–Teacher Conferences.

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

List 304, Professional Math Organizations.

List 305, Math Web Sites for Teachers.

List 306, A Self–Appraisal for Math Teachers.

Section Ten: Reproducible Teaching Aids.

Number Lines.

Rulers I.

Rulers II.

Protractors.

Squares.

Graphs for Trigonometric Functions.

1–Inch Grid.

1⁄2–Inch Grid.

1–cm Grid.

Isometric Dot Paper.

Square Grid Dot Paper.

Decimal Squares.

Fraction Strips.

Fraction Circles.

Algebra Tiles.

Tangram.

Patterns for Pattern Blocks.

Patterns for Cuisenaire Rods.

Net for Rectangular Prism.

Net for Pyramid.

Net for Cone.

Net for Tetrahedron.

Net for Hexahedron (Cube).

Net for Octahedron.

Net for Dodecahedron.

Net for Icosahedron.

Blank Checks.

Blank Check Register.

O autorze

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.

Blurb

The Math Teacher′s Book of Lists Second Edition, Grades 5–12

This second edition of the bestselling resource for mathematics teachers is a time–saving reference with 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 on 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. money—coins 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 TEACHING AIDS contains an assortment of helpful reproducibles including number lines, fraction strips, algebra tiles, and various nets for making 3–D geometric shapes.

The Math Teacher′s Book of Lists will save you time and help you instill in your students a genuine appreciation for the world of mathematics.

"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