Mathematical Reasoning for Elementary School Teachers

by Long, Calvin T.; Detemple, Duane W.

• ISBN13: 9780321043337
• ISBN10: 0321043332
• Edition: 2nd
• Format: Hardcover
• Copyright: 2001-01-01
• Publisher: Addison Wesley

Summary

Traditional skill and drill approach with activities for each chapter opener.

Table of Contents

Preface	ix
To the Student	xix
Thinking Critically	1	(77)
Some Surprising Tidbits	4	(7)
An Introduction to Problem Solving	11	(5)
Polya's Problem-Solving Principles	16	(11)
More Problem-Solving Strategies	27	(21)
Additional Problem-Solving Strategies	48	(10)
Problem Solving in the Real World	58	(20)
Summary	72	(2)
Review Exercises	74	(3)
Test	77	(1)
Sets, Whole Numbers, and Functions	78	(78)
Sets and Operations on Sets	80	(12)
Sets, Counting, and the Whole Numbers	92	(11)
Addition and Subtraction of Whole Numbers	103	(14)
Multiplication and Division of Whole Numbers	117	(19)
Functions	136	(20)
Summary	150	(3)
Review Exercises	153	(1)
Test	154	(2)
Numeration and Computation	156	(88)
Numeration Systems Past and Present	158	(18)
Nondecimal Positional Systems	176	(8)
Algorithms for Adding and Subtracting Whole Numbers	184	(15)
Algorithms for Multiplication and Division of Whole Numbers	199	(14)
Mental Arithmetic and Estimation	213	(12)
Getting the Most Out of Your Calculator	225	(19)
Summary	240	(1)
Review Exercises	241	(1)
Test	242	(2)
Number Theory	244	(56)
Divisibility of Natural Numbers	247	(14)
Tests for Divisibility	261	(9)
Greatest Common Divisors and Least Common Multiples	270	(13)
Clock Arithmetic	283	(17)
Summary	297	(1)
Review Exercises	298	(1)
Test	299	(1)
Integers	300	(51)
Representations of Integers	302	(11)
Addition and Subtraction of Integers	313	(21)
Multiplication and Division of Integers	334	(17)
Summary	346	(2)
Review Exercises	348	(2)
Test	350	(1)
Fractions and Rational Numbers	351	(61)
The Basic Concepts of Fractions and Rational Numbers	354	(17)
The Arithmetic of Rational Numbers	371	(19)
The Rational Number System	390	(22)
Summary	407	(2)
Review Exercises	409	(1)
Test	410	(2)
Decimals and Real Numbers	412	(65)
Decimals	415	(21)
Computations with Decimals	436	(13)
Ratio and Proportion	449	(11)
Percent	460	(17)
Summary	473	(1)
Review Exercises	474	(2)
Test	476	(1)
Statistics: The Interpretation of Data	477	(57)
The Graphical Representation of Data	479	(21)
Measures of Central Tendency and Variability	500	(18)
Statistical Inference	518	(16)
Summary	531	(1)
Review Exercises	532	(1)
Test	533	(1)
Probability	534	(58)
Empirical Probability	536	(14)
Principles of Counting	550	(17)
Theoretical Probability	567	(25)
Summary	588	(1)
Review Exercises	589	(2)
Test	591	(1)
Geometric Figures	592	(82)
Figures in the Plane	596	(20)
Curves and Polygons in the Plane	616	(21)
Figures in Space	637	(19)
Networks	656	(18)
Summary	668	(2)
Review Exercises	670	(2)
Test	672	(2)
Measurement	674	(74)
The Measurement Process	676	(16)
Area and Perimeter	692	(20)
The Pythagorean Theorem	712	(9)
Surface Area and Volume	721	(27)
Summary	742	(2)
Review Exercises	744	(1)
Test	745	(3)
Transformations, Symmetries, and Tilings	748	(62)
Rigid Motions and Similarity Transformations	751	(24)
Patterns and Symmetries	775	(14)
Tilings and Escher-like Designs	789	(21)
Summary	804	(2)
Review Exercises	806	(1)
Test	807	(3)
Congruence, Constructions, and Similarity	810	(60)
Congruent Triangles	812	(18)
Constructing Geometric Figures	830	(19)
Similar Triangles	849	(21)
Summary	865	(1)
Review Exercises	866	(2)
Test	868	(2)
Coordinate Geometry	870	(2)
The Cartesian Coordinate System	872	(13)
Lines and Their Graphs	885	(11)
Solving Geometric Problems Using Coordinates	906	(9)
Graphing Functions	915	(10)
Summary	925	(1)
Review Exercises	926	(2)
Test	928	(1)
Appendices
Appendix A Manipulatives in the Mathematics Classroom	929	(4)
Appendix B Spreadsheets	933	(6)
Appendix C Graphing Calculators	939	(4)
Appendix D A Brief Guide to The Geometer's Sketchpad	953
Answers to Selected Problems	A-1
Acknowledgments	A-57
Mathematical Lexicon	A-59
Index and Pronunciation Guide	A-61