From: Suzanne A. (for Teacher2Teacher Service)
Date: May 16, 2004 at 09:58:51
Subject: Re: Manipulatives for square roots

Hi Paul,

If you had the students think in terms of factors of the number and the
square or rectangle representations of them, I think you could get this
idea across. Let's see if I can make an example:

If we use 24, what are the ways that we can represent that number visually?

1 by 24   (if I could draw here I would use graph paper and show a
            one by twenty-four rectangle either horizontally or vertically)

2 by 12   (I would draw a 1x2 rectangle and a 1x12 rectangle)

3 by 8    (I would draw a 1x3 and a 2x4)

4 by 6    (I would draw a 2x2 and a 2x3)

At this point you might talk about why you stop here since you could
consider 6 by 4, 8 by 3, 12 by 2, and 24 by 1.

Now I would have the students think about which arrays are perfect
squares and which are not. In that way you are visually showing that
24 can be thought of as 2sqrt(6).

When I taught middle school I wrote these pages:

Understanding Factoring through Geometry
http://mathforum.org/alejandre/factor1.html

Understanding Algebraic Factoring
http://mathforum.org/alejandre/algfac.html

I found that if my students could visualize numbers by drawing them
on graph paper or using tiles or squares of paper, it helped a lot with
a variety of concepts.

I hope this made sense! If not, please feel free to reply and I'll draw
again, perhaps by making a web page or two.

Sincerely,
Suzanne

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