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

Homework

Notes:

Part A Notes
Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Homework

Notes:

Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Addition | Subtraction | Multiplication | Division

Homework

Notes:

Part A Notes
Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Homework

Notes:

Part A Notes
Part B Notes
Part C Notes
Homework Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Homework

Notes:

Part A Notes

Solutions:

Part A Solutions
Part B Solutions
Homework Solutions

Video

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

Homework

Notes:

Part A Notes
Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Homework

Notes:

Part A Notes
Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions
Homework Solutions

Video

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

Homework

Notes:

Part B Notes
Part C Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions

Video

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

Homework

Notes:

Part A Notes
Part B Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions

Video

Grades 3-5

Part A: Observing a Case Study

Part B: Reasoning About Number and Operations

Part C: Problems That Illustrate Reasoning About Number and Operations

Homework

Notes:

Part A Notes
Part B Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions

Video

Grades 6-8

Part A: Observing a Case Study

Part B: Reasoning About Number and Operations

Part C: Problems That Illustrate Reasoning About Number and Operations

Homework

Notes:

Part A Notes
Part B Notes

Solutions:

Part A Solutions
Part B Solutions
Part C Solutions

Video