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| Foundations For Learning Mathematics | |
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| Getting Started and Problem Solving | |
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| Pigs and Chickens | |
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| A Coin Problem | |
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| Patterns and Communication | |
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| Sequences and Patterns | |
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| Patterns in Multiplying by 11 | |
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| Pascal's Triangle | |
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| Communicating Patterns in a Magic Square | |
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| Reasoning and Proof | |
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| Does Your Answer Make Sense? | |
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| Inductive Thinking With Fractions | |
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| Deductive Reasoning and Venn Diagrams | |
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| Why is the Sum of Two Even Numbers an Even Number | |
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| Darts, Proof, and Communication | |
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| The Nine Dots Problem | |
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| How Many Games in the Tournament? | |
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| Representation and Connections | |
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| How Long Will it Take the Frog to Get Out of the Well? | |
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| How Many Pieces of Wire? | |
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| Looking Back on Chapter 1 | |
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| Summary | |
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| Review Exercises | |
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| Fundamental Concepts | |
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| Sets | |
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| Classifying Quadrilaterals | |
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| Describing Sets | |
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| How Many Subsets? | |
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| Translating Among Representations | |
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| Finding Information from Venn Diagrams | |
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| Algebraic Thinking | |
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| A Variable by Any Other Name is Still a Variable | |
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| Baby-sitting | |
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| Choosing Between Functions | |
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| Matching Graphs to Situations | |
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| Developing "Graph Sense." | |
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| Looking for Generalizations | |
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| How Many Dots? | |
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| Numeration | |
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| Relative Magnitude of Numbers | |
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| What if Our System was Based on One Hand? | |
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| How Well do you Understand Base Five? | |
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| Base Sixteen | |
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| Looking Back on Chapter 2 | |
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| Summary | |
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| Review Exercises | |
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| The Four Fundamental Operations Of Arithmetic | |
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| Understanding Addition | |
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| Pattern in the Addition Table | |
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| Mental Addition | |
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| Children's Strategirs for Adding Large Numbers | |
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| An Alternative Algorithm | |
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| Addition in Base Five | |
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| Children's Mistakes | |
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| What Was the Total Attendance? | |
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| Estimating by Making Compatible Numbers | |
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| Number Sense with Addition | |
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| Understanding Subtraction | |
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| Mental Subtraction | |
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| Children's Strategies for Subtraction with Large Numbers | |
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| An Alternative Algorithm | |
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| Children's Mistakes in Subtraction | |
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| Rough and Best Estimations with Subtraction | |
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| Number Sense with Subtraction | |
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| Understanding Multiplication | |
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| A Pattern in the Multiplication Table | |
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| Mental Multiplication | |
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| An Alternative Algorithm | |
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| Why Does the Trick for Multiplying by 11 Work? | |
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| Multiplication in Base Five | |
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| Children's Mistakes in Multiplication | |
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| Developing Estimation Strategies for Multiplication | |
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| Using Various Strategies in a Real-life Multiplication Situation | |
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| Number Sense with Multiplication | |
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| Understanding Division | |
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| Mental Division | |
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| Understanding Division Algorithms | |
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| The Scaffolding Algorithm | |
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| Children's Mistakes in Division | |
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| Estimates with Division | |
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| Number Sense with Division | |
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| Applying Models to a Real-life Situation | |
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| Operation Sense | |
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| Looking Back on Chapter 3 | |
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| Summary | |
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| Review Exercises | |
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| Number Theory | |
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| Divisibility and Related Concepts | |
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| Interesting Dates | |
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| Patterns in Odd and Even Numbers | |
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| Understanding Divisibility Relationships | |
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| Determining the Truth of an Inverse Statement | |
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| Understanding Why the Divisibility Rule for 3 Works | |
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| Divisibility by 4 and 8 | |
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| Creating a Divisibility Rule for 12 | |
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| Prime and Composite Numbers | |
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| The Sieve of Eratosthenes | |
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| Numbers with Personalities: Perfect and Other Numbers | |
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| Greatest Common Factor and Least Common Multiple | |
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| Cutting Squares Using Number Theory Concepts | |
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| Methods for Finding the GCF | |
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| Relationships Between the GCF and the LCM | |
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| Going Deeper into the GCF and LCM | |
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| Looking Back on Chapter 4 | |
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| Summary | |
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| Review Exercises | |
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| Extending The Number System | |
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| Integers | |
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| Subtraction with Integers | |
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| The Product of a Positive and a Negative Number | |
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| Fractions and Rational Numbers | |
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| Rational Number Contexts: What Does 3/4 Mean? | |
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| Wholes and Units: Sharing Brownies | |
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| Unitizing | |
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| Fund-Raising and Thermometers | |
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| Partitioning with Number Line Models | |
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| Partitioning with Area Models | |
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| Partitioning with Discrete Models | |
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| Determining an Appropriate Representation | |
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| Sharing Cooking | |
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| Ordering Rational Numbers | |
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| Estimating with Fractions | |
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| Understanding Operations with Fractions | |
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| Using Fraction Models to Understand Addition of Fractions | |
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| Connecting Improper Fractions and Mixed Numbers | |
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| Estimation and Mental Arithmetic: Sums and Differences of Fractions | |
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| Estimating sums and Differences with Fractions | |
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| Understanding Multiplication of Rational Numbers | |
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| Division of Rational Numbers | |
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| Estimating Products and Quotients | |
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| When Did He Run Out of Gas? | |
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| They've Lost Their Faculty! | |
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| Beyond Integers and Fractions: Decimals, Exponents, and Real Numbers | |
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| Base 10 Blocks and Decimals | |
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| When Two Decimals Are Equal | |
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| When is the Zero Necessary and When is it Optional? | |
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| Connecting Decimals and Fractions | |
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| Ordering Decimals | |
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| Rounding with Decimals | |
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| Decimals and Language | |
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| Decimal Sense: Grocery Store Estimates | |
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| Decimal Sense: How Much Will the Project Cost? | |
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| How Long Will She Run? | |
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| Exponents and Bacteria | |
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| Scientific Notation: How Far is a Light-Year? | |
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| Square Roots | |
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| Looking Back on Chapter 5 | |
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| Summary | |
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| Review Exercises | |
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| Proportional Reasoning | |
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| Ratio and Proportion | |
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| Unit Pricing--Is Bigger Always Cheaper? | |
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| How Many Trees Will be Saved? | |
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| How Much Money Will the Trip Cost? | |
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| Reinterpreting Old Problems | |
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| Using Estimation with Ratios | |
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| Comparing Rates | |
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| Is the School on Target? | |
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| Finding Information from Maps | |
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| From Raw Numbers to Rates | |
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| How Much Does That Extra Light Cost? | |
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| Percents | |
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| Who's the Better Free-Throw Shooter? | |
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| Understanding a Newspaper Article | |
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| Buying a House | |
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| Sale? | |
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| What is a Fair Reason? | |
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| How Much Money Did the Bookstore Pay for the Textbook? | |
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| The Copying Machine | |
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| 132% Increase | |
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| Saving for College | |
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| How Much Does that Credit Card Cost You? | |
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| Looking Back on Chapter 6 | |
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| Summary | |
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| Review Exercises | |
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| Uncertainty: Data And Chance | |
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| The Process of Collecting and Analyzing Data | |
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| What is Your Favorite Sport? | |
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| How Many Siblings do you Have? | |
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| Going Beyond a Computational Sense of Average | |
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| How Many Peanuts Can You Hold in One Hand? | |
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| How Long Does it Take Students to Finish the Final Exam? | |
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| Videocassette Recorders | |
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| Fatal Crashes | |
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| Hitting the Books | |
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| Going Beyond the Basics | |
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| How Many More Peanuts Can Adults Hold Than Children? | |
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| Scores on a TeSt | |
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| Which Battery do You Buy? | |
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| Understanding Standard Deviation | |
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| Analyzing Standardized Test Scores | |
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| How Long Should the Tire be Guaranteed? | |
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| Comparing Students in Three Countries | |
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| Grade Point Average | |
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| What Does Amy Need to Bring Her GPA up to 2.5? | |
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| Concepts Related to Chance | |
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| Probability of Having 2 Boys and 2 Girls | |
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| Probability of Having 3 Boys and 2 Girls | |
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| Probability of Having at Least 1 Girl | |
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| 50-50 Chance of Passing | |
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| What is the Probability of Rolling a 7? | |
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| What is the Probability of Rolling a 13 with 3 Dice? | |
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| "The Lady of the Tiger | |
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| Gumballs | |
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| Is this a Fair Game? | |
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| What about this Game? | |
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| Insurance Rates | |
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| Counting and Chance | |
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| How Many Ways to Take the Picture? | |
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| How Many Different Election Outcomes? | |
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| How Many Outcomes this Time? | |
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| Pick a Card, Any Card! | |
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| So You Think You're Going to Win the Lottery? | |
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| Looking Back on Chapter 7 | |
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| Summary | |
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| Review Exercises | |
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| Geometry As Shape | |
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| Basic Ideas and Building Blocks | |
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| Playing Tetris | |
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| Different Objects and Their Functions | |
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| Point, Line, and Plane | |
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| Measuring Angles | |
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| Two-Dimensional Figures | |
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| Recreating Shapes from Memory | |
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| All the Attributes | |
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| Classifying Figures | |
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| Investigations 8.2d Why Triangles are so Important | |
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| Classifying Triangles | |
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| Triangles and Venn Diagrams | |
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| Congruence with Triangles | |
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| Quadrilaterals and Attributes | |
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| Challenges | |
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| Relationships Among Quadrilaterals | |
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| Sum of Interior Angles of a Polygon | |
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| What are my Coordinates? | |
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| Understanding the Distance Formula | |
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| The Opposite Sides of a Parallelogram are Congruent | |
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| Midpoints of any Quadrilateral | |
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| Three-Dimensional Figures | |
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| What do you See? | |
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| Connecting Polygons to Polyhedra | |
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| Features of Three-Dimensional Objects | |
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| Prisms and Pyramids | |
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| Different Views of a Building | |
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| Isometric Drawings | |
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| Cross Sections | |
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| Nets | |
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| Looking Back on Chapter 8 | |
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| Summary | |
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| Review Exercises | |
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| Geometry As Transforming Shapes | |
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| Congruence Transformations | |