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 Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/
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