In class we learned how to fold a piece of paper into a box. Easy, right? Well, not really,not if you are attempting to teach geometry at the same time. It started with the teacher asking us, as we sat with a 8.5 X 8.5 piece of paper in our hands..."What shape is it you are holding?"
Easy, we said... it's a square! "How do you know?" she asks. Well... we just know! "Wrong! Tell me why it is a square!"
We began to shout out all sorts of things: "because it is a quadilateral", "because it has 4 equal sides", "because it has all right angles", "because the opposite sides are all parallel", "because it has 4 vertices"
"Prove it to me!" shouted our teacher
Then geometry became hard!
We eventually learned that by folding and re-folding we were able to prove that we had a square and for someone like myself, who hasn't had a geometry lesson in over 25 years I actually caught on and could "SEE" it! This made me realize, once again, how hands on manipulatives helps the brain! Even a manipulative like a simple piece of paper that could later be turned into a box and where the teacher asked, "Prove to me the volume"
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