## April 29, 2014

### Circle Graphs

Our state test is approaching and I'm trying to find ways to mix review in with new material. I only mentioned circles in my geometry class on pi day plus it never hurts to practice data analysis, hence circle graphs! As students walked in I had four questions up on the white boards that I had them walk around and answer  (number of siblings, favorite color, type of pets, number of times moved). They all found the mean, median, mode, range for the number of siblings then completed the following assignment.

In the past kids have immediately associated circle graphs with percents. Instead of discouraging that instinct I wanted to allow kids to find percents, then help them convert that to degrees to make a precise circle graph. Hence the empty third column. However, my students this year didn't even think of percents. So my vague step four was lost on them. When I asked them what they needed to make a precise graph they quickly came up with a protractor, so we set up proportions and skipped straight to the angle. The rest of it went fine.

So, knowing that, how would you rephrase step four? Any other ideas to make this better or more interesting?

1. Maybe I'm under-thinking things, but given the variety of approaches you've seen your students take, it strikes me that vague is kinda good here. I mean they find some method to use, you give 'em a little space to write down percents, proportions, whatevs and then they're good to go?

1. They didn't really think to use proportions on their own, but that's okay. Sometimes teasing the idea out of them (individually or as a class) is an important part of the process. If you think it's good then it's good :)

2. I also like the vagueness of step 4, along with the big hint in step 5 that the central angle has something to do with it.

I see two opportunities that could be exploited here:
In step 6, you just tell them the degree measure of the arc is the same as the central angle. It might be more fruitful to ask what they /think/ the degree measure of the arc should be, and justify why they think that.
You mention arc length in step 6 and have them calculate circumference in step 7. Depending on your learning goals, you might say something like 7b) Using all the information you have so far, what do you think is the length of each arc in centimeters?

1. Truth - I have no idea why we ever talk about arc length in degrees, it makes little sense to me. That's probably why I skipped to just telling them. Adjustment made.

In step 9 I asked them to find the arc length in centimeters. I wasn't sure how long this would take so I moved it to the end. I also wanted everything to fit on one page so I squished what should be 7b and 8b together. Maybe I'll change it to 7b: find the measure of ONE arc in centimeters. Then they don't spend forever finding all the arcs but have the experience.

Thanks for the feedback!