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