About This Course
This is a video instructional series on the pre-algebra
concepts of number and operations. It is intended for K-8 teachers, but is suitable
for college prep programs and adult learners. It is made up of 9 half-hour video
programs.
Free sign up may be required for first-time users.
To hear the sound and view video, you should have Windows Media Player, DSL, a cable
modem, or a LAN connection to a T1 line or greater, and have Javascript enabled.
You can download a free copy of the player from here:
Acknowledgements
Video for Learning Math: Number and Operations and
the individual program descriptions are provided courtesty of Annenberg/CPB.
This site is not affiliated with nor endorsed by
Annenberg/CPB |
Lessons
(Select One)
- 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. Use a number line to classify the numbers we use, and examine how
the numbers and operations relate to one another.
- 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. Consider the magnitude of these infinite sets and discover that infinity comes
in more than one size. Examine place value and the significance of zero in a place value
system.
- 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. Examine the use of scientific notation to represent numbers with very large or
very small magnitude. Interpret whole numbers, common fractions, and decimals in base
four.
- 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. Examine which fractions
terminate and which repeat as decimals, and why all rational numbers must fall into one of
these categories. Explore methods to convert decimals to fractions and vice versa. Use
benchmarks and intuitive methods to order fractions.
- 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.
Explore ways to represent proportional relationships and the resulting operations with
ratios. Examine how ratios can represent either part-part or part-whole comparisons,
depending on how you define the unit, and explore how this affects their behavior in
computations.
- 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. Examine
benchmarks for understanding percents, especially percents less than 10 and greater than
100. Consider ways to use an elastic model, an area model, and other models to discuss
percents. Explore some ratios that occur in nature.
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