Mathematical Reasoning for Elementary Teachers, Media Update

<ol> <li><strong>Thinking Critically</strong> <ul> <li>1.1 An Introduction to Problem Solving</li> <li>1.2 Polya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core State Standards for Mathematics</li> <li>1.3 More Problem-Solving Strategies</li> <li>1.4 Algebra as a Problem-Solving Strategy</li> <li>1.5 Additional Problem-Solving Strategies</li> <li>1.6 Reasoning Mathematically</li> </ul></li> <li><strong>Sets and Whole Numbers</strong> <ul> <li>2.1 Sets and Operations on Sets</li> <li>2.2 Sets, Counting, and the Whole Numbers</li> <li>2.3 Addition and Subtraction of Whole Numbers</li> <li>2.4 Multiplication and Division of Whole Numbers</li> </ul></li> <li><strong>Numeration and Computation</strong> <ul> <li>3.1 Numeration Systems Past and Present</li> <li>3.2 Algorithms for Addition and Subtraction of Whole Numbers</li> <li>3.3 Algorithms for Multiplication and Division of Whole Numbers</li> <li>3.4 Mental Arithmetic and Estimation</li> <li>3.5 Nondecimal Positional Systems</li> </ul></li> <li><strong>Number Theory</strong> <ul> <li>4.1 Divisibility of Natural Numbers</li> <li>4.2 Tests for Divisibility</li> <li>4.3 Greatest Common Divisors and Least Common Multiples</li> </ul></li> <li><strong>Integers</strong> <ul> <li>5.1 Representation of Integers</li> <li>5.2 Addition and Subtraction of Integers</li> <li>5.3 Multiplication and Division of Integers</li> </ul></li> <li><strong>Fractions and Rational Numbers</strong> <ul> <li>6.1 The Basic Concepts of Fractions and Rational Numbers</li> <li>6.2 Addition and Subtraction of Fractions</li> <li>6.3 Multiplication and Division of Fractions</li> <li>6.4 The Rational Number System</li> </ul></li> <li><strong>Decimals, Real Numbers, and Proportional Reasoning</strong> <ul> <li>7.1 Decimals and Real Numbers</li> <li>7.2 Computations with Decimals</li> <li>7.3 Proportional Reasoning</li> <li>7.4 Percent</li> </ul></li> <li><strong>Algebraic Reasoning, Graphing, and Connections with Geometry</strong> <ul> <li>8.1 Variables, Algebraic Expressions, and Functions</li> <li>8.2 Graphing Points, Lines, and Elementary Functions</li> <li>8.3 Connections between Algebra and Geometry</li> </ul></li> <li><strong>Geometric Figures</strong> <ul> <li>9.1 Figures in the Plane</li> <li>9.2 Curves and Polygons in the Plane</li> <li>9.3 Figures in Space</li> </ul></li> <li><strong>Measurement: Length, Area, and Volume</strong> <ul> <li>10.1 The Measurement Process</li> <li>10.2 Area and Perimeter</li> <li>10.3 The Pythagorean Theorem</li> <li>10.4 Volume</li> <li>10.5 Surface Area</li> </ul></li> <li><strong>Transformations, Symmetries, and Tilings</strong> <ul> <li>11.1 Rigid Motions and Similarity Transformations</li> <li>11.2 Patterns and Symmetries</li> <li>11.3 Tilings and Escher-like Designs</li> </ul></li> <li><strong>Congruence, Constructions, and Similarity</strong> <ul> <li>12.1 Congruent Triangles</li> <li>12.2 Constructing Geometric Figures</li> <li>12.3 Similar Triangles</li> </ul></li> <li><strong>Statistics: The Interpretation of Data</strong> <ul> <li>13.1 Organizing and Representing Data</li> <li>13.2 Measuring the Center and Variation of Data</li> <li>13.3 Statistical Inference</li> </ul></li> <li><strong>Probability</strong> <ul> <li>14.1 The Basics of Probability</li> <li>14.2 Applications of Counting Principles to Probability</li> <li>14.3 Permutations and Combinations</li> <li>14.4 Odds, Expected Values, Geometric Probability, and Simulations</li> </ul></li> </ol>