My math coach gave me this idea as we were planning my Circles unit. I think it went fairly well, so I’ll share it here. The idea is that we have, essentially, three basic objects that we’ve combined in different ways in geometry: circles, lines (including segments), and angles. So, as an opening activity to the unit, the task was this:
“Think of as many ways as possible to combine those three objects.”
First they brainstormed individually, as I reminded them that they can use multiple lines or angles or circles if they wanted. Then they went up to groups and made a master list per pair or group, eliminating ones that were “pretty much” the same. I gave them some vocabulary based on what I saw they drew, and they had to use that vocabulary to describe what each drawing had. Finally, they chose one example and created one neat, fully correct example, in color that we combined into class posters. (I approved what they chose, to ensure a variety of possible layouts.)
Between my two classes, they came up with almost every scenario I could think of that we would learn in the unit, with the exception of Tangent Line & Radius, which I drew and put in myself. Now they are hanging in the classroom, acting as a guide for our journey into circles.
James Cleveland-Tran
The Roots of the Equation 
Comments on: "Circles, Lines, and Angles" (4)
Love how this allows them to own their own discoveries throughout the unit!
Love this, maybe I’ll do it at the end, and see if we can get all, since I didn’t see until fair bit into the unit. Gonna blog on using constructions to guide study of circles…much more interesting that way. Cheers!
I’m interested in reading that. I was planning on ending with constructions (since we started with them, to go full circle), using what we learned in the circles unit to prove why they work. So I’d love to see what you write.
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