Q&A #13682

Manipulatives for square roots

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From: Suzanne A. (for Teacher2Teacher Service)
Date: May 16, 2004 at 16:59:02
Subject: Re: Manipulatives for square roots

Hi Paul,

Please realize that I haven't actually tried this idea with students so if
I were doing it I probably wouldn't have "real" answers to your questions
until I tried it myself! I don't think I've ever thought up a lesson that
worked perfectly the first time. I've used the idea for students to think
about factors but I had never thought to try it to use with square roots of
numbers that aren't perfect squares. So, if/when you actually try this I'd
love to hear what happened!

>1) When you say draw a 4 by 6 and then say "draw a 2X2 and and 2X3, I am not
>sure how you are drawing them.  Are these drawn "by" each other or one
>horizontal, one vertical (like algebra tiles in GSP)?

I hadn't really thought about it. Does it matter? I guess I'm thinking that I
have 24 squares to work with and no matter where I put them on my paper, I'm
representing 24.

>2) I can hear a student asking "why did you draw a 2X2?  Why didn't you draw
>a 1X4?  Not sure how to respond to that.

If you have done some work before this exercise so that students understand
what a perfect square is, then they may realize that 2x2 is 4 and the sqrt of
4 is 2.

Actually, I wouldn't show the students what to do. I would challenge them.
Chances are that some students will draw one configuration while others
will draw another and still others will draw another. Talk about what the
different rectangles and/or squares represent. Once they see all the
different ways that the numbers can be visualized then you would want to give
them a challenge --- think of all the factors of the number. Is one of them a
square number? What's the other factor? .... you'd have to structure the
questions so that they can get to the point of connecting the visual example
with the square root notation.

 -Suzanne A., for the T2T service

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