Tuesday, March 10, 2015

3/10 Pi Day (approximately)

Given when Math Club meets I could have done this lesson 4 days early or 3 days late. I chose the former because I've been super excited about attacking Pi head on and I didn't want the in class celebrations to steal any of my thunder.  I also tried a variety of strategies based on my previous sessions that I think worked out really well today.

So first of all, I had a parent volunteer helping out this time which is always super helpful especially when serving a messy treat and trying to do a relay activity that can potentially have multiple kids asking for the next piece simultaneously.

I started by serving pie, (never delay gratification - it just leads to begging). All the kids were surprisingly excited by super market apple pie and there was a lot more bang for the buck than any of my normal snacks. With my volunteer it was really fairly neat and all my worries about cleanup were fortunately not fulfilled.  Just for fun, I had everyone recite as many digits of pi as possible before being served in the line. Its fairly silly but this was also exciting for most of the kids.

We then took a small break while everyone was snacking to brainstorm about activities to run during math night at school which is coming up next month. It turns out pi muddles the brain and I mostly heard variations on "let's do a pie eating contest." So I'll give this a shot again next week and maybe exercise some fiat if I don't hear anything exciting. My main goal is to do something aimed at the 3rd and 4th grade with an eye on recruiting students for next year.

Next I had everyone tell me as many formulas using pi as they knew which produced all the usual suspects. After writing these down on the board I asked "So why is 2 * pi * r == circumference?" As expected there were not many ideas. The best idea was that as the diameter grew the circumference would obviously need to as well.  So I then talked a bit about approximating the circumference with regular polygons. See: http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html

Drawing on the board, I had the kids works out the hexagon case where pi is approximately 3.

We then talked briefly about area as well which required a little of the Pythagorean theorem to find the height of the triangle. Again I asked for answers as I drew the figures on the board. Hopefully, this discussion and the followup on how to continually divide the triangles into finer approximations was accessible to everyone. This could definitely have been expanded into a more student led activity but I would have needed most of the class time to do so.

With the conceptual work done, I moved onto a warm-up packet practicing applying the basic area, circumference etc. formulas. These were not meant to be tricky or fancy, but just to brush up basic skills for a few minutes prior to starting our real task.  Spontaneously the kids ran to the bucket of calculators that I did not even know were present in the classroom. This seemed reasonable for the problem set so I let it be. Interestingly, one kid was still confused on moving from diameter to radius so this was useful in flushing out some basic principles. I walked around and could see that almost everyone was making progress.

Finally we reached my main activity a math relay I took from here:

This worked really well engaging the kids. (And was only manageable with my extra helper) I had  a really high level of completion on the various stages and there was a quiet humming in the room as the various teams worked their way through the problems. I will definitely repeat some more game-like activities like this in the future.

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