Description
Book SynopsisAbout our authors
Calvin Long received his B.S. in Mathematics from the University of Idaho. Following M.S. and Ph.D. degrees in Mathematics from the University of Oregon, he worked briefly as an analyst for the National Security Agency and then joined the faculty at Washington State University. His teaching ran the gamut from elementary algebra through graduate courses and included frequently teaching the content courses for prospective elementary school teachers.
His other professional activities include serving on numerous committees of the National Council of Teachers of Mathematics and the Mathematical Association of America, and holding various leadership positions in those organizations. Professor Long has also been heavily engaged in directing and instructing in-service workshops and institutes for teachers at all levels, has given more than 100 presentations at national and regional meetings of NCTM and its affiliated groups, and has present
Table of Contents
Table of Contents
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Thinking Critically
- 1.1 An Introduction to Problem Solving
- 1.2 Polya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core State Standards for Mathematics
- 1.3 More Problem-Solving Strategies
- 1.4 Algebra as a Problem-Solving Strategy
- 1.5 Additional Problem-Solving Strategies
- 1.6 Reasoning Mathematically
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Sets and Whole Numbers
- 2.1 Sets and Operations on Sets
- 2.2 Sets, Counting, and the Whole Numbers
- 2.3 Addition and Subtraction of Whole Numbers
- 2.4 Multiplication and Division of Whole Numbers
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Numeration and Computation
- 3.1 Numeration Systems Past and Present
- 3.2 Algorithms for Addition and Subtraction of Whole Numbers
- 3.3 Algorithms for Multiplication and Division of Whole Numbers
- 3.4 Mental Arithmetic and Estimation
- 3.5 Nondecimal Positional Systems
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Number Theory
- 4.1 Divisibility of Natural Numbers
- 4.2 Tests for Divisibility
- 4.3 Greatest Common Divisors and Least Common Multiples
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Integers
- 5.1 Representation of Integers
- 5.2 Addition and Subtraction of Integers
- 5.3 Multiplication and Division of Integers
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Fractions and Rational Numbers
- 6.1 The Basic Concepts of Fractions and Rational Numbers
- 6.2 Addition and Subtraction of Fractions
- 6.3 Multiplication and Division of Fractions
- 6.4 The Rational Number System
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Decimals, Real Numbers, and Proportional Reasoning
- 7.1 Decimals and Real Numbers
- 7.2 Computations with Decimals
- 7.3 Proportional Reasoning
- 7.4 Percent
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Algebraic Reasoning, Graphing, and Connections with Geometry
- 8.1 Variables, Algebraic Expressions, and Functions
- 8.2 Graphing Points, Lines, and Elementary Functions
- 8.3 Connections between Algebra and Geometry
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Geometric Figures
- 9.1 Figures in the Plane
- 9.2 Curves and Polygons in the Plane
- 9.3 Figures in Space
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Measurement: Length, Area, and Volume
- 10.1 The Measurement Process
- 10.2 Area and Perimeter
- 10.3 The Pythagorean Theorem
- 10.4 Volume
- 10.5 Surface Area
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Transformations, Symmetries, and Tilings
- 11.1 Rigid Motions and Similarity Transformations
- 11.2 Patterns and Symmetries
- 11.3 Tilings and Escher-like Designs
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Congruence, Constructions, and Similarity
- 12.1 Congruent Triangles
- 12.2 Constructing Geometric Figures
- 12.3 Similar Triangles
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Statistics: The Interpretation of Data
- 13.1 Organizing and Representing Data
- 13.2 Measuring the Center and Variation of Data
- 13.3 Statistical Inference
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Probability
- 14.1 The Basics of Probability
- 14.2 Applications of Counting Principles to Probability
- 14.3 Permutations and Combinations
- 14.4 Odds, Expected Values, Geometric Probability, and Simulations
