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Overview | Who's Who | Credits | Video Index | Reading List | Support Materials
Session 1: What Is a Number System?
Part A: A Simpler Number System
Addition in Units Digit Arithmetic | Inverse, Identity, and Closure | Multiplication in Units Digit Arithmetic | Multiplicative Inverse and Identity
Part B: Compaing Number Systems
Part C: Building the Number Line
Homework
Notes:
Part A Notes Part B Notes
Solutions:
Part A Solutions Part B Solutions Part C Solutions Homework Solutions
Video
Session 2: Number Sets, Infinity, and Zero
Part A: Number Sets
Relating Number Sets | Operations
Part B: The Size of Infinity
Part C: Examining Zero
The Behavior of Zero | Positional Number Systems | Exploring Zero and Infinity on a Graph
Part A Notes Part B Notes Part C Notes
Session 3: Place Value
Part A: Base Two Numbers
From Base Ten to Base Two | From Base Two to Base Ten | Base Two Numbers in Computing
Part B: Exponents and Logarithms
Operations with Exponents | Scientific Notation | Logarithms
Part C: Place-Value Representation in Base Ten and Base Four
Examining Base Four | Operations in Base Four
Part B Notes Part C Notes
Session 4: Meanings and Models for Operations
Part A: Meanings and Relationships of the Operations
Addition | Subtraction | Multiplication | Division
Part B: Area Models for Multiplication and Division
Multiplication with Manipulatives | Multiplication Model | Division with Manipulatives | Division Model
Part C: Colored-Chip Models
Session 5: Divisibility Tests and Factors
Part A: Alpha Math
Part B: Developing Testing Rules
Developing Testing Rules | Divisibility Tests for 2,5, and 10 | Divisibility Tests for 3 and 9 | More Tests | Divisibility Test for 11
Part C: Factors
Part A Notes Part B Notes Part C Notes Homework Notes
Session 6: Number Theory
Part A: Models for Multiples and Factors
The Venn Diagram Model | Finding Prime Factors | The Area Model
Part B: Looking for Prime Numbers
Locating Prime Numbers | Necessary and Sufficient conditions | Is This Number Prime
Part A Notes
Part A Solutions Part B Solutions Homework Solutions
Session 7: Fractions and Decimals
Part A: Fractions to Decimals
Terminating Decimals | Repeating Decimals | Repeating Decimal Rings
Part B: Decimals to Fractions
Part C: Ordering Fractions
Session 8: Rational Numbers and Proportional Reasoning
Part A: Interpreting Fractions, Units, and Unitizing
Interpretation of Fractions | Units and Unitizing
Part B: Fractions with Cuisenaire Rods
Representing Fractions With Rods | Other Denominators | Modeling Oerations | Try It Yourself
Part C: Absolute and Relative Reasoning
Session 9: Fractions, Percents, and Ratios
Part A: Models for the Multiplication and Division of Fractions
Area Model for Multiplication | Try It Yourself | Area Model for Division | The Common Denominator Model for Division | Translating the Process to Decimals
Part B: Decimals and Percents
Percent as Proportion | Percents as Fractions and Decimals | Percents Models
Part C: Fibonacci Numbers
The Fibonacci Sequence | Ratios of Fibonacci Numbers | The Golden Mean and the Golden Rectangle
Part A Solutions Part B Solutions Part C Solutions
Session 10: Classroom Case Studies
Grades K-2
Part A: Observing a Case Study
Part B: Reasoning About Number and Operations
Part C: Problems that Illustrate Reasoning About Number and Operations
Grades 3-5
Part C: Problems That Illustrate Reasoning About Number and Operations
Grades 6-8
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