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Mathematical Reasoning for Elementary Teachers

by:
ISBN: 9780321013309 | 0321013301
Format: Paperback
Publisher: PRENTICE HALL PTR
Pub. Date: 1/1/1996

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SummaryTable of Contents
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.
... MORE
Prefacexi
To the Studentxxviii
Thinking Critically
1(76)
Some Surprising Tidbits
4(7)
An Introduction to Problem Solving
11(5)
Polya's Problem-Solving Principles
16(11)
More Problem-Solving Strategies
27(20)
Still More Problem-Solving Strategies
47(10)
Problem Solving in the Real World
57(20)
Chapter 1 Summary
70(2)
Chapter Review Exercises
72(3)
Chapter Test
75(2)
Sets, Whole Numbers, and Functions
77(81)
Sets and Operations on Sets
80(15)
Sets, Counting, and the Whole Numbers
95(12)
Addition and Subtraction of Whole Numbers
107(13)
Multiplication and Division of Whole Numbers
120(17)
Relations and Functions
137(21)
Chapter 2 Summary
153(2)
Chapter Review Exercises
155(1)
Chapter Test
156(2)
Numeration and Computation
158(88)
Numeration Systems Past and Present
160(15)
Nondecimal Positional Systems
175(8)
Algorithms for Adding and Subtracting Whole Numbers
183(16)
Algorithms for Multiplication and Division of Whole Numbers
199(15)
Mental Arithmetic and Estimation
214(13)
Getting the Most Out of Your Calculator
227(19)
Chapter 3 Summary
241(2)
Chapter Review Exercises
243(1)
Chapter Test
244(2)
Number Theory
246(66)
Divisibility of Natural Numbers
249(13)
Tests for Divisibility
262(9)
Greatest Common Divisors and Least Common Multiples
271(20)
Clock Arithmetic
291(21)
Chapter 4 Summary
309(1)
Chapter Review Exercises
310(1)
Chapter Test
311(1)
Integers
312(56)
Representations of Integers
314(10)
Addition and Subtraction of Integers
324(22)
Multiplication and Division of Integers
346(22)
Chapter 5 Summary
364(2)
Chapter Review Exercises
366(1)
Chapter Test
367(1)
Fractions and Rational Numbers
368(62)
The Basic Concepts of Fractions and Rational Numbers
370(17)
The Arithmetic of Rational Numbers
387(20)
The Rational Number System
407(23)
Chapter 6 Summary
425(2)
Chapter Review Exercises
427(1)
Chapter Test
428(2)
Decimals and Real Numbers
430(61)
Decimals
433(18)
Computations with Decimals
451(12)
Ratio and Proportion
463(11)
Percent
474(17)
Chapter 7 Summary
488(1)
Chapter Review Exercises
489(1)
Chapter Test
490(1)
Statistics: The Interpretation of Data
491(57)
The Graphical Representation of Data
493(22)
Measures of Central Tendency and Variability
515(16)
Statistical Inference
531(17)
Chapter 8 Summary
545(1)
Chapter Review Exercises
545(2)
Chapter Test
547(1)
Probability
548(57)
Empirical Probability
550(15)
Principles of Counting
565(17)
Theoretical Probability
582(23)
Chapter 9 Summary
601(2)
Chapter Review Exercises
603(1)
Chapter Test
604(1)
Geometric Figures
605(96)
Figures in the Plane
609(20)
Curves and Polygons in the Plane
629(21)
Tiling with Polygons
650(16)
Networks
666(11)
Figures in Space
677(24)
Chapter 10 Summary
695(1)
Chapter Review Exercises
696(3)
Chapter Test
699(2)
Congruence, Constructions, and Similarity
701(59)
Congruent Triangles
702(20)
Constructing Geometric Figures
722(19)
Similar Triangles
741(19)
Chapter II Summary
755(1)
Chapter Review Exercises
756(2)
Chapter Test
758(2)
Measurement
760(74)
The Measurement Process
762(14)
Area and Perimeter
776(21)
The Pythagorean Theorem
797(9)
Surface Area and Volume
806(28)
Chapter 12 Summary
828(1)
Chapter Review Exercises
829(2)
Chapter Test
831(3)
Geometric Transformations
834(63)
Rigid Motions
836(26)
Patterns and Symmetries
862(18)
Similarity Transformations
880(17)
Chapter 13 Summary
891(2)
Chapter Review Exercises
893(1)
Chapter Test
894(3)
Coordinate Geometry
897(65)
The Cartesian Coordinate System
899(15)
Lines and Their Graphs
914(20)
Solving Geometric Problems Using Coordinates
934(9)
Graphing Functions and Relations
943(19)
Chapter 14 Summary
957(2)
Chapter Review Exercises
959(2)
Chapter Test
961(1)
Appendix A Manipulatives in the Mathematics Classroom962(4)
Appendix B Logic and Mathematical Reasoning966(19)
Appendix C Logo: A Programming Language for Learning Mathematics985(17)
Appendix D A Brief Guide to The Geometer's Sketchpad1002
Answers to Selected ProblemsA-1
AcknowledgmentsA-91
LexiconA-93
Index and Pronunciation GuideA-95

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