Efnisyfirlit

• Title
• Copyright
• Contents
• Preface
• 1 Thinking Critically
  • 1.1 An Introduction to Problem Solving
  • 1.2 Pólya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common
    • Guess and Check
    • Make an Orderly List
    • Draw a Diagram
    • Pólya’s Problem-Solving Principles and the Standards for Mathematical Practice of the Common Core
  • 1.3 More Problem-Solving Strategies
    • Look for a Pattern
    • Make a Table
    • Use a Variable
    • Consider Special Cases
    • Pascal’s Triangle
  • 1.4 Algebra as a Problem-Solving Strategy
    • Use a Variable
    • Use Two Variables
  • 1.5 Additional Problem-Solving Strategies
    • Working Backward
    • Eliminate Possibilities
    • The Pigeonhole Principle
  • 1.6 Reasoning Mathematically
    • Inductive Reasoning
    • Representational Reasoning
    • Mathematical Statements
    • Deductive Reasoning
  • Chapter 1 Summary
  • Chapter 1 Review Exercises
• 2 Sets and Whole Numbers
  • 2.1 Sets and Operations on Sets
    • Venn Diagrams
    • Relationships and Operations on Sets
    • Using Sets for Problem Solving
  • 2.2 Sets, Counting, and the Whole Numbers
    • One-to-One Correspondence and Equivalent Sets
    • The Whole Numbers
    • Representingthe Whole Numbers Pictorially and with Manipulatives
    • Ordering the Whole Numbers
    • Problem Solving with Whole Numbers and Venn Diagrams
  • 2.3 Addition and Subtraction of Whole Numbers
    • The Set Model of Whole-Number Addition
    • The Measurement (Number-Line) Model of Addition
    • Properties of Whole-Number Addition
    • Subtraction of Whole Numbers
    • Take-Away Model
    • Missing-Addend Model
    • Comparison Model
    • Number-Line Model
  • 2.4 Multiplication and Division of Whole Numbers
    • Multiplication of Whole Numbers
    • Multiplication as Repeated Addition
    • The Array Model for Multiplication
    • The Rectangular Area Model for Multiplication
    • The Skip-CountModel for Multiplication
    • The Multiplication Tree Model
    • The Cartesian Product Model of Multiplication
    • Properties of Whole-Number Multiplication
    • Division of Whole Numbers
    • The Repeated-Subtraction Model of Division
    • The Partition Model of Division
    • The Missing-Factor Model of Division
    • Division by Zero Is Undefined
    • Division with Remainders
    • Why Does Quotient with Remainder (the Division Algorithm) Work?
    • Exponents and the Power Operation
  • Chapter 2 Summary
  • Chapter 2 Review Exercises
• 3 Numeration and Computation
  • 3.1 Numeration Systems Past and Present
    • The Egyptian System
    • The Roman System
    • The Babylonian System
    • The Mayan System
    • The Indo-Arabic System
    • Physical Models for Positional Systems
  • 3.2 Algorithms for Addition and Subtraction of Whole Numbers
    • The Addition Algorithm
    • The Subtraction Algorithm
  • 3.3 Algorithms for Multiplication and Division of Whole Numbers
    • Multiplication Algorithms
    • Division Algorithms
  • 3.4 Mental Arithmetic and Estimation
    • The One-Digit Facts
    • Easy Combinations
    • Adjustment
    • Working from Left to Right
    • Estimation
    • Front-End Method
    • Rounding
    • Approximating by Rounding
  • 3.5 Nondecimal Positional Systems
    • Base-Five and Base-Six Place Value Including Conversion to the Decimal System and Operations
    • Addition, Subtraction, and Multiplication in Base Six
  • Chapter 3 Summary
  • Chapter 3 Review Exercises
• 4 Number Theory
  • 4.1 Divisibility of Natural Numbers
    • Divides, Divisors, Factors, Multiples
    • Prime and Composite Numbers
    • The Divisors of a Natural Number
    • Two Questions about Primes
    • There Are Infinitely Many Primes
    • Determining Whether a Given Natural Number Is Prime
  • 4.2 Tests for Divisibility
    • Divisibility of Sums and Differences
    • Divisibility by 2, 5, and 10
    • Divisibilityby 4, 8, and Other Powers of 2
    • Divisibility by 3 and 9
    • Combining Divisibility Tests
    • Summary of Useful Divisibility Tests
    • Applications of Divisibility
    • Illustrating Factors and Divisibility with a Manipulative
  • 4.3 Greatest Common Divisors and Least Common Multiples
    • GCD Method 1: Greatest Common Divisors by Intersection of Sets
    • GCD Method 2:Greatest Common Divisor from Prime Factorizations
    • GCD Method 3: Greatest Common Divisor from the Euclidean Algorithm
    • An Application of the Greatest Common Factor
    • The Least Common Multiple
    • LCM Method 1: Least Common Multiples by Intersection of Sets
    • LCM Method 2: Least Common Multiples from Prime Factorizations
    • LCM Method 3:Least Common Multiples by Using the Euclidean Algorithm
    • An Application of the LCM
  • Chapter 4 Summary
  • Chapter 4 Review Exercises
• 5 Integers
  • 5.1 Representations of Integers
    • Absolute Value of an Integer
    • Criteria for the Representation of the Integers
    • Representing Integers with Colored Counters
    • The Addition-by-0 Property with Colored Counters
    • Taking Opposites with Colored Counters
    • Mail-Time Representations of Integers
    • Number-Line Representations of Integers
  • 5.2 Addition and Subtraction of Integers
    • Addition of Integers
    • Addition of Integers by Using Sets of Colored Counters
    • Addition of Integers by Using Mail-Time Stories
    • Addition of Integers by Usinga Number Line
    • Subtraction of Integers
    • Subtraction of Integers with Colored Counters
    • The Equivalence of Subtraction with Addition of the Opposite
    • Subtraction of Integers by Using Mail-Time Stories
    • Subtraction of Integers by Using the Number Line
    • Ordering the Set of Integers
  • 5.3 Multiplication and Division of Integers
    • Multiplication of Integers
    • Multiplication of Integers by Using Loops of Colored Counters
    • Multiplication of Integers by Using Mail-Time Stories
    • Multiplicationof Integers by Using a Number Line
    • Division of Integers
    • Multiplication and Division with Colored-Counter Arrays
  • Chapter 5 Summary
  • Chapter 5 Review Exercises
• 6 Fractions and Rational Numbers
  • 6.1 The Basic Concepts of Fractions and Rational Numbers
    • Fraction Models
    • Equivalent Fractions
    • Fractions in Simplest Form
    • Common Denominators
    • Rational Numbers
    • Ordering Fractions and Rational Numbers
  • 6.2 Addition and Subtraction of Fractions
    • Addition of Fractions
    • Proper Fractions and Mixed Numbers
    • Subtraction of Fractions
  • 6.3 Multiplication and Division of Fractions
    • Multiplication of a Fraction by an Integer
    • Multiplication of an Integer by a Fraction
    • Multiplication of a Fraction by a Fraction
    • Division of Fractions
    • Algorithms for Calculating the Division of Fractions
    • Reciprocals as Multiplicative Inverses in the Rational Numbers
  • 6.4 The Rational Number System
    • Properties of Addition and Subtraction
    • Properties of Multiplication and Division
    • Properties of the Order Relation
    • The Density Property of Rational Numbers
    • Computations with Rational Numbers
    • Estimations
    • Mental Arithmetic
  • Chapter 6 Summary
  • Chapter 6 Review Exercises
• 7 Decimals, Real Numbers, and Proportional Reasoning
  • 7.1 Decimals and Real Numbers
    • Representations of Decimals
    • Multiplying and Dividing Decimals by Powers of 10
    • Terminating Decimals as Fractions
    • Repeating Decimals and Rational Numbers
    • The Set of Real Numbers
    • Real Numbers and the Number Line
  • 7.2 Computations with Decimals
    • Rounding Decimals
    • Adding and Subtracting Decimals
    • Ordering Decimals and the Real Numbers
    • Multiplying Decimals
    • Dividing Decimals
  • 7.3 Proportional Reasoning
    • Ratio
    • Proportion
    • Applications of Proportional Reasoning
  • 7.4 Percent
    • Percent
    • Solving the Three Basic Types of Percent Problems
    • Percentage Increase and Decrease
    • Compound Interest
    • The Mathematics of Growth
  • Chapter 7 Summary
  • Chapter 7 Review Exercises
• 8 Algebraic Reasoning, Graphing, and Connections with Geometry
  • 8.1 Variables, Algebraic Expressions, and Functions
    • Variables
    • Algebraic Expressions
    • Solving Equations
    • Defining and Visualizing Functions
    • Describing and Visualizing Functions
  • 8.2 Graphing Points, Lines, and Elementary Functions
    • The Cartesian Coordinate Plane
    • The Distance Formula
    • Slope
    • Equations of Lines
    • Nonlinear Functions
  • 8.3 Connections between Algebra and Geometry
    • Parallel and Perpendicular Lines
    • Circles
  • Chapter 8 Summary
  • Chapter 8 Review Exercises
• 9 Geometric Figures
  • 9.1 Figures in the Plane
    • Points and Lines
    • Line Segments and the Distance between Points
    • Rays, Angles,and Angle Measure
    • Pairs of Angles and the Corresponding-Angles Theorem
    • The Measure of Angles in Triangles
    • Directed Angles
  • 9.2 Curves and Polygons in the Plane
    • Curves and Regions
    • Convex Curves and Figures
    • Polygonal Curves and Polygons
    • Triangles
    • Quadrilaterals
    • Regular Polygons
  • 9.3 Figures in Space
    • Planes and Lines in Space
    • Curves, Surfaces, and Solids
    • Polyhedra
    • Regular Polyhedra
    • Euler’s Formula for Polyhedra
    • Cones and Cylinders
  • Chapter 9 Summary
  • Chapter 9 Review Exercises
• 10 Measurement: Length, Area, and Volume
  • 10.1 The Measurement Process
    • The U.S. Customary, or “English,” System of Measures
    • Metric Units: The International System
    • Length
    • Area
    • Volume and Capacity
    • Weight and Mass
    • Temperature
    • Unit Analysis
  • 10.2 Area and Perimeter
    • Measurements in Nonstandard Units
    • The Congruence and Addition Properties of Area
    • Areas of Polygons: A Conceptual Understanding
    • Length of a Curve
    • The Area of a Circle
  • 10.3 The Pythagorean Theorem
    • Proving the Pythagorean Theorem
    • Applications of the Pythagorean Theorem
    • The Converse of the Pythagorean Theorem
  • 10.4 Volume
    • Volumes of Right Prisms and Right Cylinders
    • Volumes of Oblique Prisms and Cylinders
    • Volumes of Pyramids and Cones
    • Volume of a Sphere
  • 10.5 Surface Area
    • Surface Area of Right Prisms and Cylinders
    • Surface Area of Pyramids
    • Surface Area of Right Circular Cones
    • The Surface Area of a Sphere
    • Comparing Measurements of Similar Figures
  • Chapter 10 Summary
  • Chapter 10 Review Exercises
• 11 Transformations, Symmetries, and Tilings
  • 11.1 Rigid Motions and Similarity Transformations
    • The Four Basic Rigid Motions
    • Translations
    • Rotations
    • Reflections
    • Glide–Reflections
    • The Net Outcome of Two Successive Reflections
    • The Net Outcome of Three Successive Reflections
    • Classification of General Rigid Motions
    • Dilations and Similarity Motions
  • 11.2 Patterns and Symmetries
    • What Is Symmetry?
    • Reflection Symmetry
    • Rotation Symmetry
    • Point Symmetry
    • Periodic Patterns: Figures with Translation Symmetries
    • Border Patterns and Their Classification
    • Wallpaper Patterns
  • 11.3 Tilings and Escher-like Designs
    • Tiles and Tilings
    • Regular Tilings of the Plane
    • Semiregular Tilings of the Plane
    • Tilings with Irregular Polygons
    • Escher-like Designs
  • Chapter 11 Summary
  • Chapter 11 Review Exercises
• 12 Congruence, Constructions, and Similarity
  • 12.1 Congruent Triangles
    • Congruent Line Segments and Their Construction
    • Corresponding Parts and the Congruence of Triangles
    • The Side–Side–Side (SSS) Property
    • The Triangle Inequality
    • The Side–Angle–Side (SAS) Property
    • The Angle–Side–Angle (ASA) Property
    • The Angle–Angle–Side (AAS) Property
    • Are There SSA and AAA Congruence Properties?
  • 12.2 Constructing Geometric Figures
    • Constructing Parallel and Perpendicular Lines
    • Constructing the Midpoint and Perpendicular Bisector of a Line Segment
    • Constructing the Angle Bisector
    • Constructing Regular Polygons
    • Mira™ and Paper-Folding Constructions
    • Constructions with Geometry Software
  • 12.3 Similar Triangles
    • The Angle–Angle–Angle (AAA) and Angle–Angle (AA) Similarity Properties
    • The Side–Side–Side (SSS) Similarity Property
    • The Side–Angle–Side (SAS) Similarity Property
    • Geometric Problem Solving with Similar Triangles
  • Chapter 12 Summary
  • Chapter 12 Review Exercises
• 13 Statistics: The Interpretation of Data
  • 13.1 Organizing and Representing Data
    • Dot Plots
    • Stem-and-Leaf Plots
    • Histograms
    • Line Graphs
    • Bar Graphs
    • Pie Charts
    • Pictographs
    • Choosing Good Visualizations
  • 13.2 Measuring the Center and Variation of Data
    • Measures of Central Tendency
    • The Mean
    • The Median
    • The Mode
    • Measures of Variability
    • Box Plots
    • The Standard Deviation
  • 13.3 Statistical Inference
    • Populations and Samples
    • Population Means and Standard Deviations
    • Estimating Population Means and Standard Deviations
    • Distributions
    • z Scores and Percentiles
  • Chapter 13 Summary
  • Chapter 13 Review Exercises
• 14 Probability
  • 14.1 The Basics of Probability
    • The Sample Space, Events, and Probability Functions
    • Experimental Probability
    • Theoretical Probability
    • Mutually Exclusive Events
    • Complementary Events
  • 14.2 Applications of Counting Principles to Probability
    • The Addition Principle of Counting
    • Factorials and Rearrangements of Ordered Lists
    • The Multiplication Principle of Counting
    • Probability Trees
    • Conditional Probability
    • Independent Events
  • 14.3 Permutations and Combinations
    • Formulas for the Number of r-Permutations
    • Formulas for the Number of r-Combinations
    • Solving Problems with Permutations and Combinations
  • 14.4 Odds, Expected Values, Geometric Probability, and Simulations
    • Odds
    • Expected Value
    • Geometric Probability
    • Simulation
  • Chapter 14 Summary
  • Chapter 14 Review Exercises
• Answers to Odd-Numbered Problems
• Mathematical Lexicon
• Credits
• Index
  • A
  • B
  • C
  • D
  • E
  • F
  • G
  • H
  • I
  • J
  • K
  • L
  • M
  • N
  • O
  • P
  • Q
  • R
  • S
  • T
  • U
  • V
  • W
  • X
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  • Z

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