Teacher2Teacher 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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