# Mathematics for Elementary School Teachers

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• ISBN10:

## 0201699516

• Edition: 2nd
• Format: Hardcover
• Publisher: Pearson College Div
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### Summary

Future elementary and middle school teachers need a clear, coherent presentation of the mathematical concepts, procedures, and processes they will be called upon to teach. This text uniquely balances "what" they will teach (concepts and content) with "how" to teach (processes and communication). As a result, students using "Mathematics for Elementary School Teachers" leave the course knowing more than basic math skills; they develop a deep understanding of concepts that enables them to effectively teach others. This Fourth Edition features an increased focus on the ' big ideas' of mathematics, as well as the individual skills upon which those ideas are built.

Preface ix
 Viewing Mathematics
1(57)
 Mathematics as Communication
1(13)
 Communicating Mathematically
 Using Technology to Communicate Mathematically
 Mathematics as Reasoning
14(23)
 Types of Reasoning
 Inductive Reasoning and Patterns
 Deductive Reasoning
 Proportional Reasoning
 Spatial Reasoning
 Importance of Reasoning Processes
 Mathematics as Problem Solving
37(11)
 The Role of Problem Solving
 A Problem-Solving Model
 Problem-Solving Strategies
 Importance of Problem Solving
 A Connected, Balanced View of Mathematics
48(10)
 Importance of a Connected View of Mathematics
 Importance of a Balanced View of Mathematics
 Developing a Connected, Balanced View of Mathematics
 Chapter Summary
53(2)
 Chapter Review
55(3)
 Sets and Whole-Number Operations and Properties
58(64)
 Sets and Whole Numbers
59(14)
 Connecting Sets to Whole-Number Ideas
 Using Sets to Define Whole Numbers
 Using Sets to Compare and Order Whole Numbers
 Important Subsets of Whole Numbers
 Addition and Subtraction of Whole Numbers
73(15)
 Using Models and Sets to Define Addition
 Modeling Subtraction
 Multiplication and Division of Whole Numbers
88(15)
 Using Models and Sets to Define Multiplication
 Properties of Multiplication
 Modeling Division
 Using Multiplication to Define Division
 Comparing Division to Multiplication
 The Division Algorithm for Whole Numbers
 Numeration
103(19)
 Numeration Systems
 The Hindu-Arabic Place-Value Numeration System
 Other Early Numeration Systems
 Comparing Numeration Systems
 Chapter Summary
118(2)
 Chapter Review
120(2)
 Estimation and Computation
122(66)
 Strategies and Procedures for Mental Computation
123(12)
 When to Use Mental Computation
 Mental Computation Techniques
 Strategies and Procedures for Estimation
135(10)
 Computational Estimation Techniques
 Choosing an Estimation Technique
145(19)
 Developing Algorithms for Subtraction
 Calculator Techniques for Addition and Subtraction
 Algorithms for Multiplication and Division
164(24)
 Developing Algorithms for Multiplication
 Calculator Techniques for Multiplication
 Developing Algorithms for Division
 Using a Calculator to Evaluate Multiplication and Division Expressions
 Chapter Summary
184(2)
 Chapter Review
186(2)
 Number Theory
188(42)
 Factors and Divisibility
189(17)
 Connecting Factors and Multiples
 Defining Divisibility
 Techniques for Determining Divisibility
 Using Factors to Classify Natural Numbers
 Prime and Composite Numbers
206(24)
 Defining Prime and Composite Numbers
 Techniques for Finding Prime Numbers
 The Role of Prime Numbers in Mathematics
 Greatest Common Factor and Least Common Multiple
 Prime and Composite Numbers and Relationships
 Chapter Summary
227(1)
 Chapter Review
228(2)
 Understanding Integer Operations and Properties
230(46)
 Addition, Subtraction, and Order Properties of Integers
231(24)
 Integer Uses and Basic Ideas
 Modeling Integer Subtraction
 Applications of Integer Addition and Subtraction
 Comparing and Ordering Integers
 Multiplication, Division, and Other Properties of Integers
255(21)
 Modeling Integer Multiplication
 Applications of Integer Multiplication
 Properties of Integer Multiplication
 Explaining Integer Division
 More Properties of Integer Multiplication and Division
 Chapter Summary
273(1)
 Chapter Review
274(2)
 Rational Number Operations and Properties
276(68)
 Rational Number Ideas and Symbols
277(18)
 Modeling Rational Numbers
 Defining Rational Numbers
 Using Fractions to Represent Rational Numbers
 Properties of Fractions
 Using Decimals to Represent Rational Numbers
 Connecting Rational Numbers to Whole Numbers, Integers, and Other Numbers
295(11)
 Modeling Addition and Subtraction of Rational Numbers
 Adding and Subtracting Rational Numbers in Fraction Form
 Properties of Rational Number Addition and Subtraction
 Adding and Subtracting Rational Numbers in Decimal Form
 Estimation Strategies
 Multiplying Rational Numbers
306(13)
 Modeling Rational Number Multiplication
 Multiplying Rational Numbers in Fraction Form
 Properties of Rational Number Multiplication
 Multiplying Rational Numbers in Decimal Form
 Estimation Strategies
 Dividing, Comparing, and Ordering Rational Numbers
319(25)
 Modeling Rational Number Division
 Defining Rational Number Division
 Dividing Rational Numbers in Fraction Form
 Dividing Rational Numbers in Decimal Form
 Estimation Strategies
 Comparing Rational Numbers
 Other Characteristics of Rational Numbers
 Chapter Summary
339(3)
 Chapter Review
342(2)
 Proportional Reasoning
344(46)
 The Concept of Ratio
345(6)
 Meaning of Ratio
 Uses of Ratio
 Ratios in Decimal Form
 Proportional Variation and Solving Proportions
351(17)
 Recognizing Proportional Variation
 Characteristics of Quantities That Vary Proportionally
 Proportional Variation in Geometry
 Properties of Proportions
 Solving Proportional Problems
 Solving Percent Problems
368(22)
 Definition of Percent
 Connecting Percents, Ratios, and Decimals
 Types of Percent Problems
 Solving Percent Problems
 Percent Increase or Decrease
 Simple and Compound Interest
 Estimating the Percent of a Number
 Chapter Summary
386(1)
 Chapter Review
387(3)
 Analyzing Data
390(62)
 Types of Data Displays
391(18)
 Common Forms of Data Display
 Representing Frequency and Distribution of Data
 Representing Variation and Comparing Data
 Representing Part-to-Whole Relationships in Data
 Data Displays That Show Relationships
409(11)
 Displaying Two-Variable Data
 Scatterplots and Trend Lines
 Describing the Average and Spread of Data
420(13)
 Different Types of Averages
 Numerical Descriptions of the Spread and Distribution of Data
 Graphical Descriptions of the Spread and Distribution of Data
 Decision Making with Data
433(19)
 Evaluating Data Collection Procedures
 Making Valid Conclusions from Data
 Evaluating a Data-Based Conclusion
 Connecting Data Analysis and Problem Solving
 Chapter Summary
446(2)
 Chapter Review
448(4)
 Probability
452(50)
 Understanding Probability
453(11)
 Defining Probability
 Identifying Sample Spaces
 Connecting Probability to Models and Counting
464(9)
 Representing and Counting Experimental Outcomes
 Probabilities of Independent Events
 Conditional Probability
 Simulations
473(8)
 Approximating Probabilities with Simulations
 Creating Simulations with Technology
 Odds and Long-Term Behavior
481(6)
 Odds in Favor and Odds Against
 Expected Value
 Connecting Expected Value and Odds to Fairness
 Permutations and Combinations
487(15)
 Listing Permutations
 Solving Permutations Problems
 Counting Combinations
 Chapter Summary
497(2)
 Chapter Review
499(3)
 Introducing Geometry
502(82)
 Basic Ideas of Geometry
503(22)
 Seeing Geometry in the World
 Modeling and Defining Basic Geometric Ideas
 Solving Problems in Geometry
525(16)
 Point and Line Problems
 Segment, Angle, and Triangle Problems
541(14)
 Angles in Intersecting Lines
 Angles in Polygons
 Angles in Regular Polygons
 Angles in Circles
555(15)
 Congruent Triangles
 The Pythagorean Theorem
 Special Right Triangles
570(14)
 Chapter Summary
579(3)
 Chapter Review
582(2)
 Extending Geometry
584(62)
 Transformations
585(17)
 Translations, Rotations, and Reflections
 Connecting Transformations and Symmetry
 Transformations That Change Size
 Transformations That Change Both Size and Shape
 Geometric Patterns
602(14)
 Geometric Patterns and Tessellations Polygons That Tessellate
 Combinations of Regular Polygons That Tessellate
 Other Ways to Generate Tessellations
 Tessellations with Irregular or Curved Sides
 Special Polygons
616(10)
 Golden Triangles and Rectangles
 Star Polygons
 Star-Shaped Polygons
 Three-Dimensional Figures
626(20)
 The Regular Polyhedra
 Prisms and Pyramids
 Cylinders, Cones, and Spheres
 Symmetry in Three Dimensions
 Visualizing Three-Dimensional Figures
 Chapter Summary
642(2)
 Chapter Review
644(2)
 Measurement
646(56)
 The Concept of Measurement
647(12)
 The Measurement Process
 Types of Measures and Units Used
 Nonstandard Units of Measure
 Standard Units of Measure
 Measuring Time and Temperature
 Measuring the Perimeter and Area of Polygons
659(19)
 Perimeters of Common Polygons
 Areas of Common Polygons
 Circumference and Area of Circles
 Comparing Perimeters and Areas of Similar Polygons
 Measuring the Surface Area and Volume of Solids
678(24)
 Surface Areas of Solids
 Volumes of Solids
 Comparing Surface Areas and Volumes of Similar Solids
 Chapter Summary
697(2)
 Chapter Review
699(3)
 Exploring Ideas of Algebra and Coordinate Geometry
702(69)
 Variables, Expressions, and Equations
703(16)
 Understanding How Letters Are Used in Mathematics
 Understanding Numerical and Algebraic Expressions
 Understanding Equations
 Analyzing Different Types of Equations
 Solving Equations
719(17)
 Understanding the Meaning of a Solution to an Equation
 Developing Ways to Solve Linear and Quadratic Equations
 Exploring Graphs of Linear Equations
736(8)
 Developing Techniques for Graphing Linear Equations
 Understanding How Graphs and Equations Are Related
 Understanding How Slope Is Related to Horizontal and Vertical Lines
 Connecting Algebra and Geometry
744(27)
 Finding the Midpoint of a Line Segment
 Finding the Distance Between Two Points
 Finding the Equation of a Line
 Using Coordinate Geometry to Verify Geometric Conjectures
 Developing the Equation of a Circle
 Describing Transformations Using Coordinate Geometry
 Chapter Summary
767(2)
 Chapter Review
769(2)
Appendix A Graphing Calculator 771(11)
Appendix B Geometry Exploration Software 782(12)
Appendix C Glossary of Geometric Terms 794(3)
Appendix D Constructions 797(10)
References 807