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• 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
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