Mathematical Reasoning for Elementary Teachers

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

• ISBN13: 9780201785692
• ISBN10: 0201785692
• Edition: 3rd
• Format: Textbook Paperback
• Copyright: 2003-01-01
• Publisher: Addison Wesley

Summary

The fourth edition of Mathematical Reasoning has an increased focus on professional development and connecting the material from this class to the elementary and middle school classroom. The authors have provided more meaningful content and pedagogy to arm readers with all the tools that they will need to become excellent elementary or middle school teachers. Thinking Critically. Sets and Whole Numbers. Numeration and Computation. Number Theory. Integers. Fractions and Rational Numbers. Decimals and Real Numbers. Algebraic Reasoning and Representation. Statistics: The Interpretation of Data. Probability. Geometric Figures. Measurement. Transformations, Symmetries, and Tilings. Congruence, Constructions, and Similarities. For all readers interested in mathematical reasoning for elementary teachers.

Table of Contents

Preface	vii
To The Student	xix
Thinking Critically	1	(68)
Some Surprising Tidbits	4	(7)
An Introduction to Problem Solving	11	(5)
Polya's Problem-Solving Principles	16	(12)
More Problem-Solving Strategies	28	(22)
Additional Problem-Solving Strategies	50	(19)
Summary	63	(2)
Review Exercises	65	(2)
Test	67	(2)
Sets and Whole Numbers	69	(70)
Sets and Operations on Sets	72	(12)
Sets, Counting, and the Whole Numbers	84	(14)
Addition and Subtraction of Whole Numbers	98	(15)
Multiplication and Division of Whole Numbers	113	(26)
Summary	134	(2)
Review Exercises	136	(1)
Test	137	(2)
Numeration and Computation	139	(88)
Numeration Systems Past and Present	141	(14)
Nondecimal Positional Systems	155	(8)
Algorithms for Adding and Subtracting Whole Numbers	163	(16)
Algorithms for Multiplication and Division of Whole Numbers	179	(16)
Mental Arithmetic and Estimation	195	(13)
Getting the Most Out of Your Calculator	208	(19)
Summary	222	(2)
Review Exercises	224	(1)
Test	225	(2)
Number Theory	227	(54)
Divisibility of Natural Numbers	230	(16)
Tests for Divisibility	246	(9)
Greatest Common Divisors and Least Common Multiples	255	(14)
Codes and Credit Card Numbers: Connections to Number Theory	269	(12)
Summary	277	(1)
Review Exercises	278	(1)
Test	279	(2)
Integers	281	(62)
Representations of Integers	283	(11)
Addition and Subtraction of Integers	294	(22)
Multiplication and Division of Integers	316	(11)
Clock Arithmetic	327	(16)
Summary	337	(2)
Review Exercises	339	(2)
Test	341	(2)
Fractions and Rational Numbers	343	(64)
The Basic Concepts of Fractions and Rational Numbers	345	(19)
The Arithmetic of Rational Numbers	364	(22)
The Rational Number System	386	(21)
Summary	402	(2)
Review Exercises	404	(1)
Test	405	(2)
Decimals and Real Numbers	407	(66)
Decimals	410	(21)
Computations with Decimals	431	(14)
Ratio and Proportion	445	(11)
Percent	456	(17)
Summary	470	(1)
Review Exercises	471	(1)
Test	472	(1)
Algebraic Reasoning and Representation	473	(58)
Algebraic Expressions and Equations	477	(12)
Functions	489	(15)
Graphing Functions in the Cartesian Plane	504	(27)
Summary	526	(1)
Review Exercises	527	(2)
Test	529	(2)
Statistics: The Interpretation of Data	531	(62)
The Graphical Representation of Data	533	(24)
Measures of Central Tendency and Variability	557	(18)
Statistical Inference	575	(18)
Summary	589	(1)
Review Exercises	590	(1)
Test	591	(2)
Probability	593	(60)
Empirical Probability	595	(14)
Principles of Counting	609	(18)
Theoretical Probability	627	(26)
Summary	649	(2)
Review Exercises	651	(1)
Test	652	(1)
Geometric Figures	653	(88)
Figures in the Plane	657	(22)
Curves and Polygons in the Plane	679	(21)
Figures in Space	700	(20)
Networks	720	(21)
Summary	734	(2)
Review Exercises	736	(3)
Test	739	(2)
Measurement	741	(82)
The Measurement Process	743	(18)
Area and Perimeter	761	(22)
The Pythagorean Theorem	783	(10)
Surface Area and Volume	793	(30)
Summary	815	(2)
Review Exercises	817	(2)
Test	819	(4)
Transformations, Symmetries, and Tilings	823	(66)
Rigid Motions and Similarity Transformations	826	(25)
Patterns and Symmetries	851	(15)
Tilings and Escher-Like Designs	866	(23)
Summary	883	(2)
Review Exercises	885	(1)
Test	886	(3)
Congruence, Constructions, and Similarity	889
Congruent Triangles	891
Constructing Geometric Figures	911
Similar Triangles	931
Summary	948
Review Exercises	950
Test	952
Appendices
Appendix A Manipulatives in the Mathematics Classroom	955
Appendix B Spreadsheets	959
Appendix C Graphing Calculators	965
Appendix D A Brief Guide to The Geometer's Sketchpad	979
Appendix E Resoruces	990
Answers to Selected Problems	1	(56)
Acknowledgments	57	(2)
Mathematical Lexicon	59	(2)
Index and Pronunciation Guide	61