Episodes in this Series
- 101. Video 1. What Is a Number System?
- 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; a finite number system that follows some (but not all) of the same rules; using a number line to classify numbers and to examine how the numbers and operations relate to one another. 27 minutes.
- 102. Video 2. Number Sets, Infinity, and Zero
- The number line and the relationships among sets of numbers in the real number system; operations and properties that apply to each of the sets; the magnitude of these infinite sets; the various "sizes" of infinity; place value and the significance of 0 in a place value system. 27 minutes.
- 103. Video 3. Place Value
- Place value systems based on numbers other than 10; the base 2 numbers and their use in computers; exponents and logarithms; the use of scientific notation to represent very large or very small numbers; interpreting whole numbers, common fractions, and decimals in base 4. 27 minutes.
- 104. Video 4. Meanings and Models for Operations
- The operations of addition, subtraction, multiplication, and division and their relationships to whole numbers; area models for multiplication and division; using two-color chips to model operations with positive and negative numbers. 27 minutes.
- 105. Video 5. Divisibility Tests and Factors
- Alpha math problems and how they help with the conceptual understanding of operations; how and why various divisibility tests work; introduction to factors and multiples. 27 minutes.
- 106. Video 6. Number Theory
- Visual methods for finding least common multiples and greatest common factors, including Venn diagram models and area models; definition of prime numbers; locating prime numbers on a number grid and determining whether very large numbers are prime. 27 minutes.
- 107. Video 7. Fractions and Decimals
- Terminating and non-terminating decimals; predicting the number of decimal places in a terminating decimal and the period of a non-terminating decimal; which fractions terminate and which repeat as decimals—and why all rational numbers must fall into one of these categories; converting between decimals and fractions; using benchmarks and intuitive methods to order fractions. 27 minutes.
- 108. Video 8. Rational Numbers and Proportional Reasoning
- A model for computations with fractions; proportional reasoning and the difference between absolute and relative thinking; representing proportional relationships and the resulting operations with ratios; ratios as either part-part or part-whole comparisons and how the distinction affects their behavior in computations. 27 minutes.
- 109. Video 9. Fractions, Percents, and Ratios
- An area model for multiplication and division with fractions; operations with decimals; percents and the relationships among representations using fractions, decimals, and percents; benchmarks for understanding percents, especially those less than 10 or greater than 100; using an elastic model, an area model, and other models to discuss percents; some ratios that occur in nature. 27 minutes.
- 110. Video 10. Classroom Case Studies, K-2
- Teachers of grades K-2 who have participated in the course explain and illustrate how they have adapted their new knowledge to their own classrooms. 27 minutes.
- 111. Video 11. Classroom Case Studies, 3-5
- Teachers of grades 3-5 who have participated in the course explain and illustrate how they have adapted their new knowledge to their own classrooms. 27 minutes.
- 112. Video 12. Classroom Case Studies, 6-8
- Teachers of grades 6-8 who have participated in the course explain and illustrate how they have adapted their new knowledge to their own classrooms. 27 minutes.
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