We have incorporated Shapedoku into this unit as well after reading Reinforcing Geometric Properties with Shapedoku Puzzles in the October 2013 Mathematics Teacher.įinally, we tried something different for conversation about angles in quadrilaterals. And you wouldn’t believe that I have actually had a conversation with my students about the word being dilate instead of dialate. She didn’t say about which line to reflect one of the triangles, but the line is drawn in the diagram. (Of course the response could use more attention to precision. This student suggested that ∆DJC~∆EJB because of a reflection and a dilation. I love that my students have embraced our inclusive definition of trapezoids, and I love that they feel confident enough in their understanding to include a parallelogram as the answer to a question about a trapezoid.įor the similar triangles and justification requested in parts (e) and (f), a few students justified the similarity of triangles using transformations. I have two favorite responses.įor the trapezoid requested in part (d), a few students listed a parallelogram. I can’t remember where I got the regular pentagon task, either, and my attempts at googling have failed. My students had been asking for more practice with proofs, and so I figured this was an opportunity to let them compare their work with the rest of the class. When I saw the student results (27 out of 30 correct), I had to think quickly about whether it was worth the time to go through the proof. But I like that it asks for both a calculation and a proof of why the triangle must be isosceles. I can’t remember where I got the next problem. I’m convinced that my students think differently than I do because of how they’ve learned geometry. We’ve asked “what do you see that’s not pictured?” We’ve learned geometry by drawing auxiliary lines. I think this has to do with look for and make use of structure. I went straight to a convex polygon first when I thought about it. I was surprised at how quickly my students thought to draw a concave polygon to explore this problem. What is the largest number of right angles an octagon can have? A search on NRICH for polygon angles turned up some out-of-the-ordinary tasks.Ī quadrilateral can have four right angles. I had heard of the NRICH site before but had not used it. We found several good tasks to use throughout our unit on polygons.
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