Preface 

ix  


1  (57) 

Mathematics as Communication 


1  (13) 

Views and Attitudes about Mathematics 



Communicating Mathematically 



Using Technology to Communicate Mathematically 




14  (23) 



Inductive Reasoning and Patterns 









Importance of Reasoning Processes 



Mathematics as Problem Solving 


37  (11) 

The Role of Problem Solving 





ProblemSolving 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 




53  (2) 


55  (3) 

Sets and WholeNumber Operations and Properties 


58  (64) 


59  (14) 

Connecting Sets to WholeNumber 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 



Basic Properties of Addition 





Using Addition to Define Subtraction 



Comparing Subtraction to Addition 



Multiplication and Division of Whole Numbers 


88  (15) 

Using Models and Sets to Define Multiplication 



Properties of Multiplication 





Using Multiplication to Define Division 



Comparing Division to Multiplication 



The Division Algorithm for Whole Numbers 




103  (19) 



The HinduArabic PlaceValue Numeration System 



Other Early Numeration Systems 



Comparing Numeration Systems 




118  (2) 


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 



Algorithms for Addition and Subtraction 


145  (19) 

Developing Algorithms for Addition 



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 




184  (2) 


186  (2) 


188  (42) 


189  (17) 

Connecting Factors and Multiples 





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 




227  (1) 


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 Addition 



Properties of Integer Addition 



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 




273  (1) 


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 





Using Decimals to Represent Rational Numbers 



Connecting Rational Numbers to Whole Numbers, Integers, and Other Numbers 



Adding and Subtracting Rational 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 





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 





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 





Comparing Rational Numbers 



Other Characteristics of Rational Numbers 




339  (3) 


342  (2) 


344  (46) 


345  (6) 







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 




368  (22) 



Connecting Percents, Ratios, and Decimals 



Types of Percent Problems 





Percent Increase or Decrease 



Simple and Compound Interest 



Estimating the Percent of a Number 




386  (1) 


387  (3) 


390  (62) 


391  (18) 

Common Forms of Data Display 



Representing Frequency and Distribution of Data 



Representing Variation and Comparing Data 



Representing ParttoWhole Relationships in Data 



Data Displays That Show Relationships 


409  (11) 

Displaying TwoVariable 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 



Additional Ways to Describe the Spread and Distribution of Data 



Decision Making with Data 


433  (19) 

Evaluating Data Collection Procedures 



Making Valid Conclusions from Data 



Misleading Conclusions from Graphs 



Evaluating a DataBased Conclusion 



Connecting Data Analysis and Problem Solving 




446  (2) 


448  (4) 


452  (50) 

Understanding Probability 


453  (11) 



Identifying Sample Spaces 



The Addition Property of Probability 



Connecting Probability to Models and Counting 


464  (9) 

Representing and Counting Experimental Outcomes 



Probabilities of Independent Events 






473  (8) 

Approximating Probabilities with Simulations 



Creating Simulations with Technology 



Odds and LongTerm Behavior 


481  (6) 

Odds in Favor and Odds Against 





Connecting Expected Value and Odds to Fairness 



Permutations and Combinations 


487  (15) 



Solving Permutations Problems 






497  (2) 


499  (3) 


502  (82) 


503  (22) 

Seeing Geometry in the World 



Modeling and Defining Basic Geometric Ideas 



Solving Problems in Geometry 


525  (16) 



Segment, Angle, and Triangle Problems 



Quadrilateral, Polygon, and Circle Problems 




541  (14) 

Angles in Intersecting Lines 





Angles in Regular Polygons 






555  (15) 







More about Quadrilaterals 


570  (14) 

Properties of Quadrilaterals 



Quadrilaterals and Geometric Constructions 



WhatIf Questions about Quadrilaterals 




579  (3) 


582  (2) 


584  (62) 


585  (17) 

Translations, Rotations, and Reflections 



Connecting Transformations and Symmetry 



Transformations That Change Size 



Transformations That Change Both Size and Shape 




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 




616  (10) 

Golden Triangles and Rectangles 







ThreeDimensional Figures 


626  (20) 





Cylinders, Cones, and Spheres 



Symmetry in Three Dimensions 



Visualizing ThreeDimensional Figures 




642  (2) 


644  (2) 


646  (56) 

The Concept of Measurement 


647  (12) 



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 





Circumference and Area of Circles 



Comparing Perimeters and Areas of Similar Polygons 



Measuring the Surface Area and Volume of Solids 


678  (24) 





Comparing Surface Areas and Volumes of Similar Solids 




697  (2) 


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 





Analyzing Different Types of 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 




767  (2) 


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  
Selected Answers 

1  (1) 
Index 

1  