"Includes connections to Common Core Standards."--Cover. Includes bibliographical references (page 225) and index.
Contents:
1. Background -- Visualization in Math -- Focusing on the Important Math -- Building Mathematical Communication -- 2. Grades K--2 -- Counting up by 1s -- Counting Back by 1s -- Counting up by 2s -- Counting Back by 2s -- Counting up by 5s -- Counting Back by 5s -- Counting up by 10s -- Counting Back by 10s -- Comparing Numbers by Matching -- Benchmark Numbers: All About 5 -- Benchmark Numbers: All About 10 -- Ordinal Numbers -- Addition as Combining -- Addition to Describe Part-Part-Whole Situations -- Adding 0 and Adding 1 -- Addition: Commutativity -- Addition: Changing Addends, But Not the Sum -- Adding or Subtracting 10 -- Subtraction as Taking Away -- Subtraction to Compare -- Relating Addition and Subtraction -- Naming Two-Digit Numbers -- Naming Three-Digit Numbers -- Place Value: Grouping in Tens -- Place Value: Positions -- Comparing Sizes of Numbers -- Fractions: Halves -- Fractions: Quarters -- Measurement: meaning the Length. Contents note continued: Measurement: Effect of Unit Size -- Measurement: Standard Units of Length -- 2-D Shapes Versus 3-D Shapes -- Comparing 2-D Shapes -- Comparing 3-D Shapes -- Composing Shapes -- Shape Puzzles -- 3. Grades 3--5 -- Multiplication: Equal Groups -- Multiplication: Commutativity -- Multiplication: The Distributive Principle -- Multiplication: 2-Digit by 2-Digit -- Division as Equal Groups or Sharing -- Division: Remainders -- Rounding Numbers -- Place Value: Multiplying and Dividing by Powers of 10 -- Place Value: Renaming Numbers -- Factors: What They Are -- Factors Come in Pairs -- Fractions: Representing -- Fractions: Equivalence -- Fractions: Comparing -- Fractions: Mixed Number/Improper Fraction Relationship -- Fractions: Common Denominators -- Adding Fractions -- Multiplying Fractions -- Fractions: Multiplying as Resizing -- Fractions as Division -- Decimals: Relating Hundredths to Tenths -- Decimals: Equivalence -- Decimals: Adding and Subtracting. Contents note continued: Measurement: Time Intervals -- Measurement: Area of Rectangles -- Perimeter versus Area -- Measurement Conversions -- Graphs with Scales -- Coordinate Grids -- Classification of Shapes -- Parallel and Perpendicular Lines -- Lines of Symmetry -- Patterns versus Non-patterns -- Algebraic Thinking: Growing Additively -- Algebraic Thinking: Shrinking Additively -- Algebraic Thinking: Growing Multiplicatively -- 4. Grades 6--8 -- Common Factors -- Common Multiples -- Square Roots -- Fraction Division -- Ratios: Multiple Ratios Describe Any Situation -- Equivalent Ratios -- Equivalent Rates -- Solving Rate Problems -- Describing Percent -- Uses of Integers -- The Zero Principle -- Subtraction of Integers as a Directed Distance -- Multiplication and Division of Integers -- Area of a Parallelogram -- Area of a Triangle -- The Pythagorean Theorem -- Pi -- How Measurements Are and Are Not Related -- Mean -- Variability -- Sampling -- Probability: What It Means. Contents note continued: Unpredictability -- Rotations, Reflections, and Translations -- Scale Drawings -- Dilatations -- Angles with Parallel Lines -- Equivalent Expressions -- Equation as a Balance -- Different Types of Equations -- What Is Linear? -- Role of the Slope in the Equation of a Line -- Systems of Equations -- Function Rules.
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