Mathematics for Elementary Teachers with Activities 5th Edition by Sybilla Beckmann ISBN 9780134392790 0134392795

Mathematics for Elementary Teachers with Activities 5th Edition by Sybilla Beckmann – Ebook PDF Instant Download/Delivery: 9780134392790 ,0134392795
Full download Mathematics for Elementary Teachers with Activities 5th Edition after payment

Product details:

ISBN 10: 0134392795
ISBN 13: 9780134392790
Author: Sybilla Beckmann

Mathematics for Elementary Teachers with Activities 5th Edition Table of contents:

1 Numbers and the Base-Ten System

1.1 The Counting Numbers

How Is It Different to View the Counting Numbers as a List and for Describing Set Size?

How Do Children Connect Counting to Cardinality?

What Are the Origins of the Base-Ten System for Representing Counting Numbers?

What Is Place Value in the Base-Ten System?

What Is Difficult about Counting Number Words?

Why Do We Need the Whole Numbers?

What Ideas Lead to Number Lines?

Section Summary and Study Items

Section 1.1 The Counting Numbers

Key Skills and Understandings

Practice Exercises for Section 1.1

Answers to Practice Exercises for Section 1.1

Problems for Section 1.1

1.2 Decimals and Negative Numbers

What Are the Origins of Decimals and Negative Numbers?

How Do Decimals Extend the Base-Ten System?

How Do Decimals as Lengths Develop into Decimals on Number Lines?

What Is Difficult about Decimal Words?

What Are Negative Numbers and Where Are They on Number Lines?

Can Decimals with Infinitely Many Nonzero Entries Be Located on Number Lines?

Section Summary and Study Items

Section 1.2 Decimals and Negative Numbers

Key Skills and Understandings

Practice Exercises for Section 1.2

Answers to Practice Exercises for Section 1.2

Problems for Section 1.2

1.3 Reasoning to Compare Numbers in Base Ten

How Can We Compare Nonnegative Numbers by Viewing Them as Amounts?

Why Can We Compare Numbers the Way We Do?

A Technical Exception to the Rule for Comparing Numbers in Base Ten 

How Can Number Lines Help Us to Compare Numbers?

How Can We Use Real-World Contexts to Compare Negative Numbers?

Section Summary and Study Items

Section 1.3 Reasoning to Compare Numbers in Base Ten

Key Skills and Understandings

Practice Exercises for Section 1.3

Answers to Practice Exercises for Section 1.3

Problems For Section 1.3

1.4 Reasoning about Rounding

How Can We Use Place Value Understanding to Round Numbers?

What Is the Significance of Rounding When Working with Numbers That Represent Actual Quantities?

Section Summary and Study Items

Section 1.4 Reasoning about Rounding

Key Skills and Understandings

Practice Exercises for Section 1.4

Answers to Practice Exercises for Section 1.4

Problems For Section 1.4

Chapter Summary

2 Fractions and Problem Solving

2.1 Solving Problems and Explaining Solutions

What Is the Role of Problem Solving?

The Process of Problem Solving

Polya’s Steps

Solving Problems for Yourself 

How Can We Use Strip Diagrams and Other Math Drawings?

Why Should We Explain Solutions?

How Are Explanations in Mathematics Different from Other Explanations? 

How Do We Write Good Mathematical Explanations? 

2.2 Defining and Reasoning About Fractions

How Do We Define Fractions?

Why Are Fractions Numbers?

What Do We Mean by Equal Parts?

How Can We Interpret Fractions as Lengths and as Numbers on Number Lines?

How Can We Interpret Improper Fractions?

Preview: Decimal Representations of Fractions

Practice Exercises for Section 2.2

Answers to Practice Exercises for Section 2.2

Problems for Section 2.2

2.3 Reasoning About Equivalent Fractions

Why Is Every Fraction Equal to Infinitely Many Other Fractions?

Why Use Equivalent Fractions?

How Can we Interpret Simplifying Fractions?

Section Summary and Study Items

Section 2.3 Reasoning About Equivalent Fractions

Key Skills and Understandings

Practice Exercises for Section 2.3

Answers to Practice Exercises for Section 2.3

Problems for Section 2.3

2.4 Reasoning to Compare Fractions

How Can We Use Decimals to Compare Fractions?

Why Can We Compare Fractions by Using Common Denominators?

Why Can We Compare Fractions by Cross-Multiplying?

Why Can We Compare Fractions by Using Common Numerators?

How Can We Reason About Benchmarks to Compare Fractions?

Section Summary and Study Items

Section 2.4 Reasoning to Compare Fractions

Key Skills and Understandings

Practice Exercises for Section 2.4

Answers to Practice Exercises for Section 2.4

Problems for Section 2.4

2.5 Reasoning About Percent

How Do We Define Percent?

How Can We Use Math Drawings to Reason About Percentages?

How Can We Organize Our Thinking About Basic Percent Problems?

Using Algebra to Solve Percent Problems 

How Can We Reason About Percent Tables to Solve Percent Problems?

How Can We Reason About Equivalent Fractions to Solve Percent Problems?

Section Summary and Study Items

Section 2.5 Reasoning About Percent

Key Skills and Understandings

Practice Exercises for Section 2.5

Answers to Practice Exercises for Section 2.5

Problems for Section 2.5

Chapter Summary

3 Addition and Subtraction

3.1 Interpretations of Addition and Subtraction

What Are the First Ways of Thinking About Addition and Subraction?

How Are Addition and Subtraction Related?

What Are the Different Types of Addition and Subtraction Word Problems?

What Are Add to and Take from Problems?

What Are Put Together/Take Apart Problems?

What Are Compare Problems?

How Can We Represent Problems with Equations and Math Drawings?

Why Can’t We Rely on Keywords Alone?

How Can We Represent Addition and Subtraction on Number Lines?

Section Summary and Study Items

Section 3.1 Interpretations of Addition and Subtraction

Key Skills and Understandings

Practice Exercises for Section 3.1

Answers to Practice Exercises for Section 3.1

Problems for Section 3.1

3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts

What Is the Role of Parentheses in Expressions with Three or More Terms?

Why Does the Associative Property of Addition Make Sense?

Why Does the Commutative Property of Addition Make Sense?

How Do We Interpret the Equal Sign Correctly?

What Are Children’s Learning Paths for Single-Digit Facts and How Do They Rely on Properties of Addition?

How Can Children Use The Commutative Property in Single-Digit Addition? 

How Can Children Use the Associative Property in Derived Fact Methods? 

How Is Viewing Subtraction Problems as Unknown Addend Problems Helpful for Children? 

What Are Some Special Strategies for Multidigit Addition and Subtraction?

Make-a-Round-Number Method 

Rounding and Compensating 

Subtraction Problems as Unknown Addend Problems 

How Can We Organize Strings of Equations So They Communicate Accurately?

Section Summary and Study Items

Section 3.2 The Commutative and Associative Properties of Addition, Mental Math, and Single-Digit Facts

Key Skills and Understandings

Practice Exercises for Section 3.2

Answers to Practice Exercises for Section 3.2

Problems for Section 3.2

3.3 Why the Standard Algorithms for Addition and Subtraction in Base Ten Work

What Is an Algorithm?

How Does the Addition Algorithm Develop?

How Do Math Drawings and Bundled Objects Support Understanding of the Addition Algorithm for Whole Numbers? 

How Does the Addition Algorithm for Decimals Develop? 

How Does the Subtraction Algorithm Develop?

How Do Math Drawings and Bundled Objects Support Understanding of the Subtraction Algorithm? 

How Does the Subtraction Algorithm for Decimals Develop? 

Section Summary and Study Items

Section 3.3 Why the Standard Algorithms for Addition and Subtraction in Base Ten Work

Key Skills and Understandings

Practice Exercises for Section 3.3

Answers to Practice Exercises for Section 3.3

Problems for Section 3.3

3.4 Reasoning About Fraction Addition and Subtraction

Why Do We Add and Subtract Fractions with Like Denominators the Way We Do?

Why Do We Add and Subtract Fractions with Unlike Denominators by Finding Common Denominators?

Why Can We Express Mixed Numbers as Improper Fractions?

Why Can We Write Finite Decimals as Fractions and How Does That Explain Decimal Names?

When Is Combining Not Adding?

Section Summary and Study Items

Section 3.4 Reasoning About Fraction Addition and Subtraction

Key Skills and Understandings

Practice Exercises for Section 3.4

Answers to Practice Exercises for Section 3.4

Problems for Section 3.4

3.5 Why We Add and Subtract with Negative Numbers the Way We Do

Why Does Adding a Number to Its Negative Result in Zero?

Why Does It Make Sense to Interpret A +(–B) as A – B?

Why Does It Make Sense to Interpret A–(–B) as A + B?

How Can We Extend Addition and Subtraction on Number Lines to Negative Numbers?

Section Summary and Study Items

Section 3.5 Why We Add and Subtract with Negative Numbers the Way We Do

Key Skills and Understandings

Practice Exercises for Section 3.5

Answers to Practice Exercises for Section 3.5

Problems for Section 3.5

Chapter Summary

4 Multiplication

4.1 Interpretations of Multiplication

How Can We Define Multiplication?

How Can We Tell If a Problem Is Solved by Multiplication?

Array Problems

Multiplicative Comparison Problems

Ordered Pair Problems

Section Summary and Study Items

Section 4.1 Interpretations of Multiplication

Key Skills and Understandings

Practice Exercises for Section 4.1

Answers to Practice Exercises for Section 4.1

Problems for Section 4.1

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

Why Does the Commutative Property of Multiplication Make Sense?

Why Can We Multiply to Find Areas of Rectangles?

How Can We Use Area to Explain the Commutative Property of Multiplication?

Why Can We Multiply to Find Volumes of Boxes?

Why Does the Associative Property of Multiplication Make Sense?

How Do the Associative and Commutative Properties of Multiplication Help Us Calculate Flexibly?

Section Summary and Study Items

Section 4.3 The Commutative and Associative Properties of Multiplication, Areas of Rectangles, and Volumes of Boxes

Key Skills and Understandings

Practice Exercises for Section 4.3

Answers to Practice Exercises for Section 4.3

Problems for Section 4.3

4.4 The Distributive Property

How Do We Interpret Expressions Involving Both Multiplication and Addition?

Why Does the Distributive Property Make Sense?

Variations on the Distributive Property

How Does the Distributive Property Help Us Calculate Flexibly?

Where Does FOIL Come From?

How Can We Extend the Distributive Property?

Section Summary and Study Items

Section 4.4 The Distributive Property

Key Skills and Understandings

Practice Exercises for Section 4.4

Answers to Practice Exercises for Section 4.4

Problems for Section 4.4

4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts

What Is a Learning Path for Single-Digit Multiplication Facts?

How Is Algebra Behind Flexible Calculation Strategies?

Section Summary and Study Items

Section 4.5 Properties of Arithmetic, Mental Math, and Single-Digit Multiplication Facts

Key Skills and Understandings

Practice Exercises for Section 4.5

Answers to Practice Exercises for Section 4.5

Problems for Section 4.5

4.6 Why the Standard Algorithm for Multiplying Whole Numbers Works

What Are Methods for Writing the Steps of the Standard Multiplication Algorithm?

How Can We Relate the Common and Partial-Products Written Methods for the Standard Algorithm?

Why Do We Place Extra Zeros on Some Lines When We Use the Common Method to Record the Steps of the Standard Algorithm?

Why Does the Standard Multiplication Algorithm Produce Correct Answers?

Section Summary and Study Items

Section 4.6 Why the Standard Algorithm for Multiplying Whole Numbers Works

Key Skills and Understandings

Practice Exercises for Section 4.6

Answers to Practice Exercises for Section 4.6

Problems for Section 4.6

Chapter Summary

5 Multiplication of Fractions, Decimals, and Negative Numbers

5.1 Making Sense of Fraction Multiplication

How Can We Extend Our Previous Understanding of Multiplication to Fractions?

What Is the Procedure for Multiplying Fractions?

Why Is the Procedure for Multiplying Fractions Valid?

Section Summary and Study Items

Section 5.1 Making Sense of Fraction Multiplication

Key Skills and Understandings

Practice Exercises for Section 5.1

Answers to Practice Exercises for Section 5.1

Problems for Section 5.1

5.2 Making Sense of Decimal Multiplication

What Is the Procedure for Multiplying Decimals?

How Can We Use Estimation to Determine Where the Decimal Point Goes?

Why Is the Rule for Placing the Decimal Point Valid?

Section Summary and Study Items

Section 5.2 Making Sense of Decimal Multiplication

Key Skills and Understandings

Practice Exercises for Section 5.2

Answers to Practice Exercises for Section 5.2

Problems for Section 5.2

5.3 Extending Multiplication to Negative Numbers

5.4 Powers and Scientific Notation

What Are Powers and Exponents?

What Is Scientific Notation?

Section Summary and Study Items

Section 5.4 Powers and Scientific Notation

Key Skills and Understandings

Practice Exercises for Section 5.4

Answers to Practice Exercises for Section 5.4

Problems for Section 5.4

Chapter Summary

6 Division

6.1 Interpretations of Division

How Can We Define Division?

The How-Many-Groups Interpretation 

The How-Many-Units-in-1-Group Interpretation 

How Can We Distinguish How-Many-Groups from How-Many-Units-in-1-Group Problems? 

How Can We Relate the How-Many-Groups and How-Many-Units-in-1-Group Inter­pretations? 

What Are Array, Area, and Other Division Word Problems?

Why Can’t We Divide by Zero?

How Do We Divide with Negative Numbers?

Section Summary and Study Items

Section 6.1 Interpretations of Division

Key Skills and Understandings

Practice Exercises for Section 6.1

Answers to Practice Exercises for Section 6.1

Problems for Section 6.1

6.2 Division and Fractions and Division with Remainder

How Can We Explain the Connection Between Fractions and Division?

How Are Exact Division and Division with Remainder Related?

How Can We Connect Whole-Number-with-Remainder Answers to Mixed Number Answers? 

Why Can We Use Division to Convert Improper Fractions to Mixed Numbers? 

Section Summary and Study Items

Section 6.2 Division and Fractions and Division with Remainder

Key Skills and Understandings

Practice Exercises for Section 6.2

Answers to Practice Exercises for Section 6.2

Problems for Section 6.2

6.3 Why Division Algorithms Work

How Can We Reason to Solve Division Problems?

Why Does the Scaffold Method of Division Work?

Using the Scaffold Method Flexibly 

Why Does the Common Method for Implementing the Standard Division Algorithm Work?

Why Do We Calculate Decimal Answers to Whole Number Division Problems the Way We Do?

Why Can We Express Fractions as Decimals?

How Can We Reason About Math Drawings to Express Fractions as Decimals?

What Are Issues to Consider when Dividing with Multidigit Divisors?

Section Summary and Study Items

Section 6.3 Why Division Algorithms Work

Key Skills and Understandings

Practice Exercises for Section 6.3

Answers to Practice Exercises for Section 6.3

Problems for Section 6.3

6.4 Fraction Division from the How-Many-Groups Perspective

How Can We Interpret Fraction Division as How-Many-Groups?

Why Can We Divide Fractions by Giving Them Common Denominators and Then Dividing the Numerators?

Why Can We Divide Fractions by Dividing the Numerators and the Denominators?

Section Summary and Study Items

Section 6.4 Fraction Division from the How-Many-Groups Perspective

Key Skills and Understandings

Practice Exercises for Section 6.4

Answers to Practice Exercises for Section 6.4

Problems for Section 6.4

6.5 Fraction Division from the How-Many-Units-in-1-Group Perspective

How Can We Interpret Fraction Division as How-Many-Units-in-1-Group?

How Does the “Invert and Multiply” or “Multiply by the Reciprocal” Procedure Work?

Why Is the “Invert and Multiply” Procedure Valid?

How Is Dividing by ½ Different from Dividing in ½?

How Can We Make Sense of Complex Fractions?

Section Summary and Study Items

Section 6.5 Fraction Division from the How-Many-Units-in-1-Group Perspective

Key Skills and Understandings

Practice Exercises for Section 6.5

Answers to Practice Exercises for Section 6.5

Problems for Section 6.5

6.6 Dividing Decimals

How Do the Two Interpretations of Division Extend to Decimals?

The How-Many-Groups Interpretation 

The How-Many-Units-in-1-Group Interpretation 

How Can We Use Multiplying and Dividing by the Same Power of 10 to Explain Why We Shift Decimal Points?

How Can We Use Dollars and Cents to Explain Why We Shift Decimal Points?

How Can We Change the Unit to Explain Why We Shift Decimal Points?

How Can We Use Estimation to Decide Where to Put the Decimal Point?

How Can We Divide Numbers in the Millions, Billions, and Trillions?

Section Summary and Study Items

Section 6.6 Dividing Decimals

Key Skills and Understandings

Practice Exercises for Section 6.6

Answers to Practice Exercises for Section 6.6

Problems for Section 6.6

Chapter Summary

7 Ratio and Proportional Relationships

7.1 Motivating and Defining Ratio and Proportional Relationships

How Can We Define Ratio from the Multiple-Batches Perspective?

How Can We Define Ratio from the Variable-Parts Perspective?

Are Part-to-Part Ratios Different from Part-to-Whole?

What Are Proportional Relationships and Proportions?

Section Summary and Study Items

Section 7.1 Motivating and Defining Ratio and Proportional Relationships

Key Skills and Understandings

Practice Exercises for Section 7.1

Answers to Practice Exercises for Section 7.1

Problems For Section 7.1

7.2 Solving Proportion Problems by Reasoning with Multiplication and Division

What Are Initial Ways of Reasoning with Tables, Number Lines, and Strip Diagrams to Solve Proportion Problems?

How Can We Reason about Multiplication and Division with Quantities to Solve Proportion Problems?

Variable-parts: Multiply 1 Part

Multiple-batches: Multiply 1 Batch

Multiple-batches: Multiply 1 Unit-rate-batch

Variable-parts: Multiply 1 Total Amount

Section Summary and Study Items

Section 7.2 Solving Proportion Problems by Reasoning with Multiplication and Division

Key Skills and Understandings

Practice Exercises for Section 7.2

Answers to Practice Exercises for Section 7.2

Problems For Section 7.2

7.3 The Values of a Ratio: Unit Rates and Multipliers

How Are Ratios Connected to Fractions

How Can We Interpret the Values of a Ratio as Unit Rates?

How Can We Interpret the Values of a Ratio as Multipliers that Compare Total Amounts?

What Is the Logic Behind Solving Proportions by Cross-Multiplying Fractions?

Section Summary and Study Items

Section 7.3 The Values of a Ratio: Unit Rates and Multipliers

Key Skills and Understandings

Practice Exercises for Section 7.3

Answers to Practice Exercises for Section 7.3

Problems For Section 7.3

7.4 Proportional Relationships

How Can We Find and Explain Equations for Proportional Relationships?

What Are Errors to Watch for in Formulating Equations?

How Do We Use Coordinate Planes?

How Are Graphs of Proportional Relationships Special?

How Are Equations, Graphs, and the Constant of Proportionality Related for Proportional Relationships?

How Can We Develop and Explain Equations for Lines Through the Origin?

Section Summary and Study Items

Section 7.4 Proportional Relationships

Key Skills and Understandings

Practice Exercises for Section 7.4

Answers to Practice Exercises for Section 7.4

Problems for Section 7.4

7.5 Proportional Relationships Versus Inversely Proportional Relationships

7.6 Percent Revisited: Percent Increase and Decrease

How Can We Reason to Calculate Percent Increase or Decrease?

How Can We Use the Definitions?

How Can We Reason with the Distributive Property?

How Can We Reason to Calculate Amounts When the Percent Increase or Decrease Is Given?

How Can We Use the Definitions of Percent Increase and Decrease?

How Can We Reason with the Distributive Property?

Why Is It Important to Attend to the Reference Amount?

Section Summary and Study Items

Section 7.6 Percent Revisited: Percent Increase and Decrease

Key Skills and Understandings

Practice Exercises for Section 7.6

Answers to Practice Exercises for Section 7.6

Problems For Section 7.6

Chapter Summary

8 Number Theory

8.1 Factors and Multiples

What Are Factors and Multiples?

How Do We Find All Factors?

Section Summary and Study Items

Section 8.1 Factors and Multiples

Key Skills and Understandings

Practice Exercises for Section 8.1

Answers to Practice Exercises for Section 8.1

Problems For Section 8.1

8.2 Even and Odd

8.3 Divisibility Tests

8.4 Prime Numbers

How Does the Sieve of Eratosthenes Make a List of Prime Numbers?

How Can We Determine If a Number Is Prime?

How Can We Factor Numbers into Products of Prime Numbers?

How Many Prime Numbers Are There?

Section Summary and Study Items

Section 8.4 Prime Numbers

Key Skills and Understandings

Practice Exercises for Section 8.4

Answers to Practice Exercises for Section 8.4

Problems For Section 8.4

8.5 Greatest Common Factor and Least Common Multiple

Definitions of GCF and LCM

What Are Methods for Finding GCFs and LCMs?

How Do We Use GCFs and LCMs with Fractions?

Section Summary and Study Items

Section 8.5 Greatest Common Factor and Least Common Multiple

Key Skills and Understandings

Practice Exercises for Section 8.5

Answers to Practice Exercises for Section 8.5

Problems For Section 8.5

8.6 Rational and Irrational Numbers

Why Do Decimal Representations of Fractions Eventually Repeat?

How Can We Use Math Drawings to See Decimal Representations of Fractions?

Can We Express Repeating and Terminating Decimals as Fractions?

What Is Another Method for Writing Repeating Decimals as Fractions?

Why Is 0.99999 . . . = 1?

Why Is the Square Root of 2 Irrational?

How Does Proof by Contradiction Work?

Section Summary and Study Items

Section 8.6 Rational and Irrational Numbers

Key Skills and Understandings

Practice Exercises for Section 8.6

Answers to Practice Exercise for Section 8.6

Problems For Section 8.6

Chapter Summary

9 Algebra

9.1 Numerical Expressions

How Can We Interpret and Evaluate Numerical Expressions?

How Can We Evaluate Expressions with Fractions?

Section Summary and Study Items

Section 9.1 Numerical Expressions

Key Skills and Understandings

Practice Exercises for Section 9.1

Answers to Practice Exercises for Section 9.1

Problems For Section 9.1

9.2 Expressions with Variables

What Are Variables?

How Do We Work with Expressions with Variables?

What Does It Mean to Evaluate Expressions with Variables?

What Are Equivalent Expressions?

Section Summary and Study Items

Section 9.2 Expressions with Variables

Key Skills and Understandings

Practice Exercises for Section 9.2

Answers to Practice Exercises for Section 9.2

Problems For Section 9.2

9.3 Equations

What Are Different Ways We Use Equations?

Some Equations Show Calculations

Some Equations Are Identities: They Are True for All Values of the Variables

Some Equations Relate Quantities That Vary Together

Some Equations Must Be Solved to Solve a Problem

What Are Solutions of Equations?

How Can We Solve Equations by Reasoning About Relationships?

What Is the Reasoning Behind the Methods We Use to Solve Equations in Algebra?

Section Summary and Study Items

Section 9.3 Equations

Key Skills and Understandings

Practice Exercises for Section 9.3

Answers to Practice Exercises for Section 9.3

Problems For Section 9.3

9.4 Solving Algebra Word Problems with Strip Diagrams and with Algebra

9.5 Sequences

How Can We Reason About Repeating Patterns?

How Can We Reason About Arithmetic Sequences?

How Can We Reason About Geometric Sequences?

Is a Sequence Determined by Its First Few Entries?

Section Summary and Study Items

Section 9.5 Sequences

Key Skills and Understandings

Practice Exercises for Section 9.5

Answers to Practice Exercises for Section 9.5

Problems For Section 9.5

9.6 Functions

How Can We Describe Functions with Words?

How Do Tables and Graphs Represent Functions?

How Do Expressions and Equations Represent Functions?

Section Summary and Study Items

Section 9.6 Functions

Key Skills and Understandings

Practice Exercises for Section 9.6

Answers to Practice Exercises for Section 9.6

Problems For Section 9.6

9.7 Linear and Other Relationships

Why Are Linear Relationships Characterized by Constant Rate of Change?

How Can We Develop and Explain Equations for Linear Relationships Using Constant Rate of Change?

What Kinds of Real-World Situations Do Linear Relationships Model?

How Do Linear Relationships Contrast with Other Relationships?

Inversely Proportional Relationships Versus Linear Relationships

Quadratic Functions

Exponential Functions

Functions Coordinate Values

How Can We Reason about the Structure of Quadratic Equations?

Section Summary and Study Items

Section 9.7 Linear and Other Relationship

Key Skills and Understandings

Practice Exercises for Section 9.7

Answers to Practice Exercises for Section 9.7

Problems For Section 9.7

Chapter Summary

10 Geometry

10.1 Lines and Angles

What Are Points, Lines, Line Segments, Rays, and Planes?

How Can We Define Angles?

How Do We Measure Angles and What Are Some Special Angles?

What Angle Relationships Do Configurations of Lines Produce?

How Are Angles Related When Two Lines Cross?

How Are Angles Related When a Line Crosses Two Parallel Lines?

How Are Angles Related When Three Lines Form a Triangle?

Section Summary and Study Items

Section 10.1 Lines and Angles

Key Skills and Understandings

Practice Exercises for Section 10.1

Answers to Practice Exercises for Section 10.1

Problems For Section 10.1

10.2 Angles and Phenomena in the World

How Can We Model with Angles and Sun Rays?

How Can We Model with Angles and Reflected Light?

Section Summary and Study Items

Section 10.2 Angles and Phenomena in the World

Key Skills and Understandings

Practice Exercises for Section 10.2

Answers to Practice Exercises for Section 10.2

Problems For Section 10.2

10.3 Circles and Spheres

What Are Mathematical Definitions of Circle and Sphere?

How Can Circles or Spheres Meet?

Section Summary and Study Items

Section 10.3 Circles and Spheres

Key Skills and Understandings

Practice Exercises for Section 10.3

Answers to Practice Exercises for Section 10.3

Problems For Section 10.3

10.4 Triangles, Quadrilaterals, and Other Polygons

What Are Quadrilaterals?

How Can We Use Short Lists of Properties to Define Special Quadrilaterals?

How Can We Classify Special Quadrilaterals in a Hierarchy?

What Are Triangles?

What Are Polygons?

How Can We Show Relationships with Venn Diagrams?

How Can We Construct Triangles and Quadrilaterals?

Section Summary and Study Items

Section 10.4 Triangles, Quadrilaterals, and Other Polygons

Key Skills and Understandings

Practice Exercises for Section 10.4

Answers to Practice Exercises for Section 10.4

Problems For Section 10.4

Chapter Summary

11 Measurement

11.1 Concepts of Measurement

Why Does Measurement Require Selecting a Measurable Attribute?

What Are the Order and Additive Structures of Measures?

Why Do We Need Units and How Do We Interpret the Meaning of Measurements?

How Do Measurement Concepts Underlie the Process of Measurement?

What Systems of Measurement Do We Use?

The U.S. Customary System

The Metric System

How Are the Metric and U.S. Customary Systems Related?

How Are Units of Length, Area, Volume, and Capacity Related?

How Do We Decide Which Unit to Use?

Section Summary and Study Items

Section 11.1 Concepts of Measurement

Key Skills and Understandings

Practice Exercises for Section 11.1

Answers to Practice Exercises for Section 11.1

Problems For Section 11.1

11.2 Length, Area, Volume, and Dimension

11.3 Error and Precision in Measurements

How Do We Interpret Reported Measurements?

How Do We Calculate with Measurements?

Section Summary and Study Items

Section 11.3 Error and Precision in Measurements

Key Skills and Understandings

Practice Exercises for Section 11.3

Answers to Practice Exercises for Section 11.3

Problems For Section 11.3

11.4 Converting from One Unit of Measurement to Another

How Can We Reason About Multiplication and Division to Convert Measurements?

Why Does Dimensional Analysis Work?

How Can We Reason to Convert Areas and Volumes?

Section Summary and Study Items

Section 11.4 Converting from One Unit of Measurement to Another

Key Skills and Understandings

Practice Exercises for Section 11.4

Answers to Practice Exercises for Section 11.4

Problems For Section 11.4

Chapter Summary

12 Area of Shapes

12.1 Areas of Rectangles Revisited

12.2 Moving and Additivity Principles About Area

12.3 Areas of Triangles

How Can We Use Moving and Additivity Principles to Determine Areas of Triangles?

What Are Base and Height for Triangles?

What Is a Formula for the Area of a Triangle?

Why Is the Area Formula for Triangles Valid?

Section Summary and Study Items

Section 12.3 Areas of Triangles

Key Skills and Understandings

Practice Exercises for Section 12.3

Answers to Practice Exercises for Section 12.3

Problems For Section 12.3

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

How Are the Circumference, Diameter, and Radius of Circles Related?

How Are the Area and Radius of Circles Related?

Section Summary and Study Items

Section 12.6 Area and Circumference of Circles and the Number Pi

Key Skills and Understandings

Practice Exercises for Section 12.6

Answers to Practice Exercises for Section 12.6

Problems For Section 12.6

12.7 Approximating Areas of Irregular Shapes

12.8 Contrasting and Relating the Perimeter and Area of Shapes

How Can We Determine Perimeters of Polygons?

How Is Perimeter Different from Area?

If We Know the Perimeter What Can We Say About the Area?

Section Summary and Study Items

Section 12.8 Contrasting and Relating the Perimeter and Area of Shapes

Key Skills and Understandings

Practice Exercises for Section 12.8

Answers to Practice Exercises for Section 12.8

Problems For Section 12.8

12.9 Using the Moving and Additivity Principles to Prove the Pythagorean Theorem

What Does the Pythagorean Theorem Tell Us?

Why Is the Pythagorean Theorem True?

What Is the Converse of the Pythagorean Theorem?

Section Summary and Study Items

Section 12.9 Using Moving and Additivity Principles to Prove the Pythagorean Theorem

Key Skills and Understandings

Practice Exercises for Section 12.9

Answers to Practice Exercises for Section 12.9

Problems For Section 12.9

Chapter Summary

13 Solid Shapes and Their Volume and Surface Area

13.1 Polyhedra and Other Solid Shapes

What Are Polyhedra?

What Are Prisms, Cylinders, Pyramids, and Cones?

What Is Special About the Platonic Solids?

Section Summary and Study Items

Section 13.1 Polyhedra and Other Solid Shapes

Key Skills and Understandings

Practice Exercises for Section 13.1

Answers to Practice Exercises for Section 13.1

Problems For Section 13.1

13.2 Patterns and Surface Area

13.3 Volumes of Solid Shapes

What Is Volume?

How Do the Moving and Additivity Principles Apply to Volumes?

How Does Cavalieri’s Principle About Shearing Apply to Volumes?

How Does the Volume Formula for Prisms and Cylinders Develop?

How Does the Volume Formula for Pyramids and Cones Develop?

How Does the Volume Formula for a Sphere Develop?

How Are Volume and Surface Area Different?

Section Summary and Study Items

Section 13.3 Volumes of Solid Shapes

Key Skills and Understandings

Practice Exercises for Section 13.3

Answers to Practice Exercises for Section 13.3

Problems For Section 13.3

13.4 Volume of Submersed Objects Versus Weight of Floating Objects

Chapter Summary

14 Geometry of Motion and Change

14.1 Reflections, Translations, and Rotations

What Are Reflections, Translations, Rotations, and Glide-Reflections?

What Is Special About Reflections, Translations, Rotations, and Glide-Reflections?

Section Summary and Study Items

Section 14.1 Reflections, Translations, and Rotations

Key Skills and Understandings

Practice Exercises for Section 14.1

Answers to Practice Exercises for Section 14.1

Problems For Section 14.1

14.2 Symmetry

What Is Symmetry?

Section Summary and Study Items

Section 14.2 Symmetry

Key Skills and Understandings

Practice Exercises for Section 14.2

Answers to Practice Exercises for Section 14.2

Problems For Section 14.2

14.3 Congruence

What Is Congruence?

What Are Criteria for Congruence?

The Side-Side-Side (SSS) Congruence Criterion

The Angle-Side-Angle (ASA) Congruence Criterion

The Side-Angle-Side (SAS) Congruence Criterion

What Conditions on Side Lengths and Angles Do Not Specify a Unique Triangle?

How Can We Apply Congruence to Explain Properties of Shapes?

Section Summary and Study Items

Section 14.3 Congruence

Key Skills and Understandings

Practice Exercises for Section 14.3

Answers to Practice Exercises for Section 14.3

Problems For Section 14.3

14.4 Constructions with Straightedge and Compass

How Can We Divide a Line Segment in Half and Construct a Perpendicular Line?

How Can We Divide an Angle in Half?

How Do Special Properties of Rhombuses Explain Why Constructions Work?

Section Summary and Study Items

Section 14.4 Constructions with Straightedge and Compass

Key Skills and Understandings

Practice Exercises for Section 14.4

Answers to Practice Exercises for Section 14.4

Problems For Section 14.4

14.5 Similarity

What Is Similarity Informally?

How Can We Use Scale Factors to Define Similarity?

How Can We Reason to Solve Problems About Similar Objects or Shapes?

Section Summary and Study Items

Section 14.5 Similarity

Key Skills and Understandings

Practice Exercises for Section 14.5

Answers to Practice Exercises for Section 14.5

Problems For Section 14.5

14.6 Dilations and Similarity

What Are Dilations?

What Properties Do Dilations Have?

How Can We Use Transformations to Discuss Similarity?

When Are Two Shapes Similar?

The Angle-Angle-Angle Criterion for Triangle Similarity

Applying the Angle-Angle-Angle Criterion with Parallel Lines

How Does the Angle-Angle-Angle Criterion Apply to Lines and Slope?

How Can We Use Similar Triangles to Determine Distances?

Finding Distances by “Sighting”

Finding Heights by Using Sun Rays and Shadows

Section Summary and Study Items

Section 14.6 Dilations and Similarity

Key Skills and Understandings

Practice Exercises for Section 14.6

Answers to Practice Exercises for Section 14.6

Problems For Section 14.6

14.7 Areas, Volumes, and Similarity

Chapter Summary

15 Statistics

15.1 Formulating Statistical Questions, Gathering Data, and Using Samples

What Are Statistical Questions?

What Data Do We Collect for Observational Studies and Experiments?

Observational Studies

Experiments

What Are Populations and Samples?

How Do We Use Random Samples to Predict Characteristics of a Full Population?

Random Samples

Predicting the Characteristics of a Full Population

Why Is Randomness Important?

Section Summary and Study Items

Section 15.1 Formulating Statistical Questions, Gathering Data, and Using Samples

Key Skills and Understandings

Practice Exercises for Section 15.1

Answers to Practice Problems for Section 15.1

Problems For Section 15.1

15.2 Displaying Data and Interpreting Data Displays

How Can We Display Categorical Data?

Real Graphs, Pictographs, and Bar Graphs

Pie Graphs

How Can We Display Numerical Data?

Dot Plots

Histograms

Stem-and-Leaf Plots

Line Graphs

Scatterplots

How Can We Create and Interpret Data Displays?

How Can Students Read Graphs at Different Levels?

Section Summary and Study Items

Section 15.2 Displaying Data and Interpreting Data Displays

Key Skills and Understandings

Practice Exercises for Section 15.2

Answers to Practice Exercises for Section 15.2

Problems For Section 15.2

15.3 The Center of Data: Mean, Median, and Mode

What Is the Mean and What Does It Tell Us?

The Mean as “Leveling Out”

The Mean as Balance Point

What Is The Median and What Does It Tell Us?

How Is the Median Different from the Mean?

What Are Common Errors with the Mean and the Median?

What Is the Mode?

Section Summary and Study Items

Section 15.3 The Center of Data: Mean, Median, and Mode

Key Skills and Understandings

Practice Exercises for Section 15.3

Answers to Practice Exercises for Section 15.3

Problems For Section 15.3

15.4 Summarizing, Describing, and Comparing Data Distributions

Why Do Data Distributions Have Different Shapes?

What Are Characteristics of Distributions Arising from Random Samples of a Population?

How Can We Summarize Distributions with the Median, Interquartile Range, and Box Plots?

Quartiles and Percentiles

The Interquartile Range as Measure of Variation

Box Plots

Percentiles Versus Percent Correct

How Can We Summarize Distributions with the Mean and the Mean Absolute Deviation (MAD)?

How Can We Use Measures of Center and Variation to Make Comparisons?

What Are Normal Curves and How Do They Apply to Standardized Test Results?

Section Summary and Study Items

Section 15.4 Summarizing, Describing, and Comparing Data Distributions

Key Skills and Understandings

Practice Exercises for Section 15.4

Answers to Practice Exercises for Section 15.4

Problems For Section 15.4

Chapter Summary

16 Probability

16.1 Basic Principles of Probability

What Are Principles That Underlie How We Determine Probabilities?

How Do We Develop and Use Uniform Probability Models?

Why Is the Probability of an Outcome a Unit Fraction?

Why Is the Probability of an Event the Fraction of Outcomes that Compose the Event?

How Is Empirical Probability Related to Theoretical Probability?

Section Summary and Study Items

Section 16.1 Basic Principles of Probability

Key Skills and Understandings

Practice Exercises for Section 16.1

Answers to Practice Exercises for Section 16.1

Problems For Section 16.1

16.2 Counting the Number of Outcomes

How Are Two-Stage Experiments Related to Ordered Pair Problems?

How Can We Count Outcomes of Multistage Experiments?

How Do We Count When There Are Dependent Outcomes?

Section Summary and Study Items

Section 16.2 Counting the Number of Outcomes

Key Skills and Understandings

Practice Exercises for Section 16.2

Answers to Practice Exercises for Section 16.2

Problems For Section 16.2

16.3 Calculating Probabilities of Compound Events

How Are Independent and Dependent Outcomes Different?

How Can We Calculate Probabilities of Compound Events?

What Is Expected Value?

Section Summary and Study Items

Section 16.3 Calculating Probabilities of Compound Events

Key Skills and Understandings

Practice Exercises for Section 16.3

Answers to Practice Exercises for Section 16.3

Problems For Section 16.3

16.4 Using Fraction Arithmetic to Calculate Probabilities

Why Can We Multiply Fractions to Calculate Probabilities?

Why Can We Use Fraction Multiplication and Addition to Calculate Probabilities?

The Surprising Case of Spot, the Drug-Sniffing Dog

Section Summary and Study Items

Section 16.4 Using Fraction Arithmetic to Calculate Probabilities

Key Skills and Understandings

Practice Exercises for Section 16.4

Answers to Practice Exercises for Section 16.4

Problems For Section 16.4

People also search for Mathematics for Elementary Teachers with Activities 5th Edition:

    
mathematics for elementary teachers with activities pdf
    
mathematics for elementary teachers with activities pdf free
    
mathematics for elementary teachers with activities 6th edition answer key
    
mathematics for elementary teachers and activities sybilla beckmann
    
mathematics for elementary teachers an activity approach

Tags: Sybilla Beckmann, Mathematics, Elementary Teachers, Activities