Mathematics for elementary teachers

Cover Page......Page 1
Title Page......Page 7
Copyright Page......Page 8
About the Authors......Page 9
About the Cover......Page 10
Brief Contents......Page 11
Contents......Page 12
Preface......Page 15
Acknowledgments......Page 25
1 Introduction to Problem Solving......Page 29
1.1 The Problem Solving Process and Strategies......Page 31
1.2 Three Additional Strategies......Page 48
2 Sets, Whole Numbers, and Numeration......Page 71
2.1 Sets as a Basis for Whole Numbers......Page 73
2.2 Whole Numbers and Numeration......Page 87
2.3 The Hindu-Arabic System......Page 98
2.4 Relations and Functions......Page 110
3 Whole Numbers: Operations and Properties......Page 135
3.1 Addition and Subtraction......Page 137
3.2 Multiplication and Division......Page 151
3.3 Ordering and Exponents......Page 168
4 Whole Number Computation—Mental, Electronic, and Written......Page 183
4.1 Mental Math, Estimation, and Calculators......Page 185
4.2 Written Algorithms for Whole-Number Operations......Page 199
4.3 Algorithms in Other Bases......Page 220
5 Number Theory......Page 231
5.1 Primes, Composites, and Tests for Divisibility......Page 233
5.2 Counting Factors, Greatest Common Factor, and Least Common Multiple......Page 247
6 Fractions......Page 265
6.1 The Sets of Fractions......Page 267
6.2 Fractions: Addition and Subtraction......Page 283
6.3 Fractions: Multiplication and Division......Page 294
7 Decimals, Ratio, Proportion, and Percent......Page 313
7.1 Decimals......Page 315
7.2 Operations with Decimals......Page 325
7.3 Ratios and Proportion......Page 338
7.4 Percent......Page 348
8 Integers......Page 369
8.1 Addition and Subtraction......Page 371
8.2 Multiplication, Division, and Order......Page 385
9 Rational Numbers, Real Numbers, and Algebra......Page 407
9.1 The Rational Numbers......Page 409
9.2 The Real Numbers......Page 427
9.3 Functions and Their Graphs......Page 445
10 Statistics......Page 467
10.1 Organizing and Picturing Information......Page 469
10.2 Misleading Graphs and Statistics......Page 492
10.3 Analyzing Data......Page 512
11 Probability......Page 541
11.1 Probability and Simple Experiments......Page 543
11.2 Probability and Complex Experiments......Page 560
11.3 Additional Counting Techniques......Page 577
11.4 Simulation, Expected Value, Odds, and Conditional Probability......Page 588
12 Geometric Shapes......Page 609
12.1 Recognizing Geometric Shapes......Page 611
12.2 Analyzing Shapes......Page 628
12.3 Properties of Geometric Shapes: Lines and Angles......Page 643
12.4 Regular Polygons and Tessellations......Page 656
12.5 Describing Three-Dimensional Shapes......Page 668
13 Measurement......Page 693
13.1 Measurement with Nonstandard and Standard Units......Page 695
13.2 Length and Area......Page 714
13.3 Surface Area......Page 735
13.4 Volume......Page 745
14 Geometry Using Triangle Congruence and Similarity......Page 767
14.1 Congruence of Triangles......Page 769
14.2 Similarity of Triangles......Page 780
14.3 Basic Euclidean Constructions......Page 793
14.4 Additional Euclidean Constructions......Page 805
14.5 Geometric Problem Solving Using Triangle Congruence and Similarity......Page 818
15 Geometry Using Coordinates......Page 835
15.1 Distance and Slope in the Coordinate Plane......Page 837
15.2 Equations and Coordinates......Page 850
15.3 Geometric Problem Solving Using Coordinates......Page 862
16 Geometry Using Transformations......Page 877
16.1 Transformations......Page 879
16.2 Congruence and Similarity Using Transformations......Page 903
16.3 Geometric Problem Solving Using Transformations......Page 921
Epilogue: An Eclectic Approach to Geometry......Page 937
Topic 1. Elementary Logic......Page 940
Topic 2. Clock Arithmetic: A Mathematical System......Page 951
Answers to Exercise/Problem Sets—Part A, Chapter Tests, and Topics......Page 957
Photograph Credits......Page 1051
Index......Page 1053