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Odyssey, Cobblestone Publishing, Inc.; ISSN 0163-0946
Background For Teachers:
Expanded notation is a method of writing numbers using the distributive property. Expanded notation begins as early as 1st grade. As students progress through school, expanded notation may be represented in different ways. In 4th grade, the number 4,376 may first be expanded to 4,000 + 300 + 70 + 6. By 5th grade, it may then be represented as (4 x 1,000) + (3 x 100) + (7 x 10) + (6 x 1). By 6th grade, students need to be able to write 4,376 as (4 x 10^3) + (3 x 10^2) + (7 x 10^1) + (6 x 10^0).
Scientific notation is a method of writing numbers that are very
large or very small with only a few symbols. Numbers in scientific
notation are written as a product of two factors. The first factor, also
known as a coefficient, is greater than or equal to 1, but less than
10. The second factor is a power of 10. For example, 7 x 10^11 is
scientific notation for 700,000,000,000.
Read to students the book If You Hopped Like a Frog. Point out to students some of the facts using very large numbers. For example, if you grew as fast in your first nine months as you did in the nine months before you were born, you would weigh more than 2,500,000 elephants. Write the number 2,500,000 on the board. Have students practice reading this number. Tell students that this number is written in standard notation. We will be learning about other ways to write very large numbers such as expanded notation and scientific notation.
(The activities listed below are intended to be taught sequentially. They will take several lessons/days to complete with students.)
Ma, Liping. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States.
This research investigates the importance of a profound understanding of fundamental mathematics on the part of the teacher. Teachers with this profound understanding incorporate the following four properties in their teaching and learning: connectedness, multiple perspectives, basic ideas, and longitudinal coherence.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
Teachers need many different kinds of mathematical knowledge. They must have a deep understanding of concepts, practices, principles, representations, and applications. They need knowledge about math as an entire domain, and they also need a thorough knowledge of the curriculum on their own grade level. Teachers must know how to convey mathematical ideas effectively in a coherent and connected manner.
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