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