Math Forum - Suzanne Alejandre: Algebraic Factoring

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Suzanne Alejandre's

Understanding Algebraic Factoring

Vocabulary, Objectives, Materials

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Students sometimes think algebra and geometry are two static, unrelated subjects that were "invented" by some historical figure and appear in books but have no redeeming value or purpose.
One way to make these topics more meaningful and less mysterious is to look at the words themselves.

algebra
'ilm algebra wa'lmugabalah (Arabic)
The science of redintegration and equation = The reunion of broken parts.
redintegration = The process of making whole again OR restoring to a perfect state.
geometry
geo (Greek) = earth
metron (Greek) = measure
The measurement of the earth.
factor
factere(Latin) = to do or make
One of two or more numbers that when multiplied together produce a given product.
While working through algebraic factoring it is helpful to remember that all you are doing is working with breaking up and putting back together squares and rectangles!

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Objective:
To show the geometric basis of algebraic factoring.
Materials:

One set of algebra tiles which includes:
15 - 1 unit by 1 unit squares
10 - 1 unit by "x" unit rectangles
3 - "x" unit by "x" unit squares

Procedure:

Introduce (or review) the notations used for multiplication.

3 X 3
3 . 3
(3)(3)
and show these ideas using an array of the 1X1 unit squares.

Use the notation

(3)(3)

so that when the transition is made from numerals to algebraic expressions the notation will be the same.

If you think it is necessary, repeat this idea with several whole numbers until you think the students have the concept of how multiplication can be shown geometrically (using squares) as well as numerically.