Episode Guide

1. What Is a Number System?—Understand the nature of the real number system, the elements and operations that make up the system, and some of the rules that govern the operations. Examine a finite number system that follows some (but not all) of the same rules, and then compare this system to the real number system.

2. Number Sets, Infinity, and Zero—Continue examining the number line and the relationships among sets of numbers that make up the real number system. Explore which operations and properties hold true for each of the sets.

3. Place Value—Look at place value systems based on numbers other than 10. Examine the base two numbers and learn uses for base two numbers in computers. Explore exponents and relate them to logarithms.

4. Meanings and Models for Operations—Examine the operations of addition, subtraction, multiplication, and division and their relationships to whole numbers. Work with area models for multiplication and division. Explore the use of two-color chips to model operations with positive and negative numbers.

5. Divisibility Tests and Factors—Explore number theory topics. Analyze Alpha math problems and discuss how they help with the conceptual understanding of operations. Examine various divisibility tests to see how and why they work. Begin examining factors and multiples.

6. Number Theory—Examine visual methods for finding least common multiples and greatest common factors, including Venn diagram models and area models. Explore prime numbers. Learn to locate prime numbers on a number grid and to determine whether very large numbers are prime.

7. Fractions and Decimals—Extend your understanding of fractions and decimals. Examine terminating and non-terminating decimals. Explore ways to predict the number of decimal places in a terminating decimal and the period of a non-terminating decimal.

8. Rational Numbers and Proportional Reasoning—Begin examining rational numbers. Explore a model for computations with fractions. Analyze proportional reasoning and the difference between absolute and relative thinking.

9. Fractions, Percents, and Ratios—Continue exploring rational numbers, working with an area model for multiplication and division with fractions, and examining operations with decimals. Explore percents and the relationships among representations using fractions, decimals, and percents.

10. Classroom Case Studies, K-2—Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers (former course participants) who have adapted their new knowledge to their classrooms.

11. Classroom Case Studies, 3-5—Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants) who have adapted their new knowledge to their classrooms.

12. Classroom Case Studies, 6-8—Watch this program in the 10th session for grade 6-8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6-8 teachers (former course participants) who have adapted their new knowledge to their classrooms.