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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 | |