Mathematics for Elementary and Middle School Teachers with Activities, 6th edition

Published by Pearson (21 October 2021) © 2022

  • Sybilla Beckmann

Paperback + Student Resources

ISBN-13: 9780136937562
Activity Manual for Mathematics for Elementary and Middle School Teachers with Activities
Published 2021

Title overview

Mathematics for Elementary and Middle School Teachers, 6th Edition fosters a deep understanding of mathematics that will help you become a more effective math teacher, and connects the foundations of K-8 mathematics to the "why" behind procedures and formulas. Known for her many contributions to mathematics education, Sybilla Beckmann helps future teachers explain why the standard procedures and formulas of elementary and middle school mathematics are valid, why nonstandard methods can also be valid, and more. Chapters are designed to help you understand how mathematical ideas develop across grade levels. The text also addresses the K-8 CCSS for Mathematical Content from a teacher's perspective.

Table of contents

Table of Contents

  • Preface
  • Solving Problems and Explaining Solutions
  1. Numbers and the Base-Ten System
    • 1.1 The Counting Numbers
    • 1.2 Decimals and Negative Numbers
    • 1.3 Reasoning to Compare Numbers in Base Ten
    • 1.4 Reasoning about Rounding
    • CHAPTER REVIEW PROBLEMS
  2. Fractions and Problem Solving
    • 2.1 Defining and Reasoning about Fractions
    • 2.2 Reasoning about Equivalent Fractions
    • 2.3 Reasoning to Compare Fractions
    • 2.4 Reasoning about Percent
    • CHAPTER REVIEW PROBLEMS
  3. Addition and Subtraction
    • 3.1 Interpretations of Addition and Subtraction
    • 3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts
    • 3.3 Why the Standard Algorithms for Addition and Subtraction in Base Ten Work
    • 3.4 Reasoning about Fraction Addition and Subtraction
    • 3.5 Why We Add and Subtract with Negative Numbers the Way We Do
    • CHAPTER REVIEW PROBLEMS
  4. Multiplication
    • 4.1 Interpretations of Multiplication
    • 4.2 Why Multiplying by 10 Is Special in Base Ten
    • 4.3 The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes
    • 4.4 The Distributive Property
    • 4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts
    • 4.6 Why the Standard Algorithm for Multiplying Whole Numbers Works
    • CHAPTER REVIEW PROBLEMS
  5. Multiplication of Fractions, Decimals, and Negative Numbers
    • 5.1 Making Sense of Fraction Multiplication
    • 5.2 Making Sense of Decimal Multiplication
    • 5.3 Extending Multiplication to Negative Numbers
    • 5.4 Powers and Scientific Notation
    • CHAPTER REVIEW PROBLEMS
  6. Division
    • 6.1 Interpretations of Division
    • 6.2 Division and Fractions and Division with Remainder
    • 6.3 Why Division Algorithms Work
    • 6.4 Fraction Division from the How-Many-Groups Perspective
    • 6.5 Fraction Division from the How-Many-Units-in-1-Group Perspective
    • 6.6 Dividing Decimals
    • CHAPTER REVIEW PROBLEMS
  7. Ratio and Proportional Relationships
    • 7.1 Motivating and Defining Ratio and Proportional Relationships
    • 7.2 Solving Proportion Problems by Reasoning with Multiplication and Division
    • 7.3 The Values of a Ratio: Unit Rates and Multipliers
    • 7.4 Proportional Relationships
    • 7.5 Proportional Relationships versus Inversely Proportional Relationships
    • 7.6 Percent Revisited: Percent Increase and Decrease
    • CHAPTER REVIEW PROBLEMS
  8. Number Theory
    • 8.1 Factors and Multiples
    • 8.2 Even and Odd
    • 8.3 Divisibility Tests
    • 8.4 Prime Numbers
    • 8.5 Greatest Common Factor and Least Common Multiple
    • 8.6 Rational and Irrational Numbers
    • CHAPTER REVIEW PROBLEMS
  9. Algebra
    • 9.1 Numerical Expressions
    • 9.2 Expressions with Variables
    • 9.3 Equations
    • 9.4 Solving Algebra Word Problems with Strip Diagrams and with Algebra
    • 9.5 Sequences
    • 9.6 Functions
    • 9.7 Linear and Other Relationships
    • CHAPTER REVIEW PROBLEMS
  10. Geometry
    • 10.1 Lines and Angles
    • 10.2 Angles and Phenomena in the World
    • 10.3 Circles and Spheres
    • 10.4 Triangles, Quadrilaterals, and Other Polygons
    • CHAPTER REVIEW PROBLEMS
  11. Measurement
    • 11.1 Concepts of Measurement
    • 11.2 Length, Area, Volume, and Dimension
    • 11.3 Error and Precision in Measurements
    • 11.4 Converting from One Unit of Measurement to Another
    • CHAPTER REVIEW PROBLEMS
  12. Area of Shapes
    • 12.1 Areas of Rectangles Revisited
    • 12.2 Moving and Additivity Principles About Area
    • 12.3 Areas of Triangles
    • 12.4 Areas of Parallelograms and Other Polygons
    • 12.5 Shearing: Changing Shapes Without Changing Area
    • 12.6 Area and Circumference of Circles and the Number Pi
    • 12.7 Approximating Areas of Irregular Shapes
    • 12.8 Contrasting and Relating the Perimeter and Area of Shapes
    • 12.9 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem
    • CHAPTER REVIEW PROBLEMS
  13. Solid Shapes and Their Volume and Surface Area
    • 13.1 Polyhedra and Other Solid Shapes
    • 13.2 Patterns and Surface Area
    • 13.3 Volumes of Solid Shapes
    • 13.4 Volume of Submersed Objects versus Weight of Floating Objects
    • CHAPTER REVIEW PROBLEMS
  14. Geometry of Motion and Change
    • 14.1 Reflections, Translations, and Rotations
    • 14.2 Symmetry
    • 14.3 Congruence
    • 14.4 Constructions with Straightedge and Compass
    • 14.5 Similarity
    • 14.6 Dilations and Similarity
    • 14.7 Areas, Volumes, and Similarity
    • CHAPTER REVIEW PROBLEMS
  15. Statistics
    • 15.1 Formulating Statistical Questions, Gathering Data, and Using Samples
    • 15.2 Displaying Data and Interpreting Data Displays
    • 15.3 The Center of Data: Mean, Median, and Mode
    • 15.4 Summarizing, Describing, and Comparing Data Distributions
    • CHAPTER REVIEW PROBLEMS
  16. Probability
    • 16.1 Basic Principles of Probability
    • 16.2 Counting the Number of Outcomes
    • 16.3 Calculating Probabilities of Compound Events
    • 16.4 Using Fraction Arithmetic to Calculate Probabilities
    • CHAPTER REVIEW PROBLEMS

Downloads

Bibliography

Index

Credits

MC1000005137

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