Q&A #740

Activity to show (a+b)^2 = (a+b)(a+b)

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From: Gail (for Teacher2Teacher Service)
Date: Nov 03, 1998 at 18:37:27
Subject: Re: Activity to show (a+b)^2 = (a+b)(a+b)

I am an elementary teacher, but I wonder if you could use what we use to
demonstrate multiplication. It is similar to algeblocks, which show the
geometric model for agebraic equations. My students set up a multiplication
problem by building a rectangle that has sides the lengths of the two
factors. So, if you were finding 13 x 13, you would use unit blocks to build
a frame for a rectangle that had a ten and three ones vertically, and a ten
and three ones horizontally (this is hard to explain without pictures.

To build the rectangle, you just fill in the frame. The side that has a ten
by ten space would fit a hundred, and the part with a three ones by ten piece
would fit three tens (there are two of them.) The part that is left to fill
is the three ones by three ones part holds 9 ones.

If you built that, and pointed out that the sides were 4 + 9 (hence, 4 + 9
squared and were also 13, then (4 + 9)  (4 + 9) = 13 x 13.

-Gail, for the Teacher2Teacher service

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