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# Mathematical Reasoning for Elementary Teachers

by ;
Edition:
3rd
ISBN13:

### 9780201785692

ISBN10:
0201785692
Format:
Textbook Paperback
Pub. Date:
1/1/2003
Publisher(s):

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## 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.

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)
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)
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
959
 Appendix C Graphing Calculators
965
 Appendix D A Brief Guide to The Geometer's Sketchpad
979
 Appendix E Resoruces
990