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Day 21: Discussion of Solving Proportions with Angles

I tried something new yesterday. U2 WS1 had about 20 problems broken into 4 groups - all related to proportions. The first group was very straightforward - solve the proportion. The 2nd group were word problems related to percents, so students had to set up the proportion themselves. The third group were word problems related to angles, so again, students were changed with the setup. And the last group had pictures of circles divided into pieces. Some amount of the circle was shaded in and I asked students to work through the steps given (fraction, proportion, angle) to connect everything.

It was way too much work to go over through a traditional discussion, so I had each class group whiteboard the same 4 problems (one problem from each section). When they were done, I gave them about 10 minutes to walk around the room checking everyone else's boards and asking questions. After that I tried to answer any lingering questions they might have had.

It worked well in 2nd hour (I'm learning that most things work well in that class). 5th hour worked to the extent that students who were trying got something out of it, but that class is so frenzied, allowing them leeway to work in groups AND walk around class is like herding cats. 6th hour worked, but it took longer than expected, so we'll need a few minutes tomorrow to answer any questions.

Proportions are again something that students learned in prior math classes, but the skills I'm seeing reinforce my theory that even students who can follow the steps involved have no real idea what they're doing. My point is to hammer home the idea that angles are portions of circles in the hopes that these students will not use angle and segment measurements interchangeably.
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