We’ve had two more math circle sessions, and I (at least) enjoyed both of them quite a bit.  The second session (which was really the first official session), I slightly repurposed an activity from “computer science unplugged”.  We took turns being, and then programming, “Drawbots”. Initially we started with blank paper, and had the drawbot face away from the whiteboard, and the programmers face toward the whiteboard (but sitting on their hands).  Then I drew various figures on the board, and the programmers described to the drawbots how to reproduce the figures using only words.
It was a hoot.  I started with simple drawings: a rectangle with an inset square with an inset circle, and similar arrangements.  Then (warning them I was doing to do something difficult), I drew two parallel wavy lines.  Hilarity and mayhem ensued.  One student was so frustrated, she started to cry. I assured them all that mistakes and frustration were the point of the exercise – that made her smile and she quickly recovered. (whew!)
Next I brought out some numbered graph paper, and had them draw points at specific coordinates and connect the dots to draw shapes.  We did a triangle, then a simple face.  I made a mistake transcribing the numbers to the whiteboard, which cracked the kids up.
The following Monday, as Heidi was dropping Audra off to class, a number of parents said how much fun their child had in Math Circle, and how they were disappointed there was no homework over the weekend. (woohoo!)  So I drew one up and sent it out. As part of it, I wrote a program that plotted the homework to make sure I didn’t make any mistakes (actually, so I knew where the mistakes were).

There was a week off, followed by this most recent meeting on Nov. 2nd. I decided to finally do some non-robot, mathlike exercises.  I read the activity name “function machine” in the math circles book by Bob and Ellen Kaplan, and decided to design what it would be myself:  I brought some empty cereal boxes and cut slots in them, and labeled one “input”, the other “output”.  Once the group had settled down, I told them that this “number machine” took slips of paper with numbers on them, did something to the paper, and spits it out the output slot.
I started by being f(x)=x+2, then f(x)=2x.  It was hilarious!  The kids were really excited at first just to go through the process, shortly after when they realized the output was related to the input, and finally when they figured out the relationship between the input and the output. Next I tried f(x)=x/2.  I knew I was out on a limb with this one…I got a 2, a 4, a 3 (1 1/2!), and at 10, everyone guessed correctly using different language than I’d have guessed – “Takes away half!”
Then we broke into groups of 4 or fewer, each with a parent volunteer (thanks!!). They first decorated their own number machines (this was a good break in the pace), then took turns being functions. The kids did great.  It was amazing to see the excitement when they thought they had the answer, and sent in a number to test their hypothesis. When it was my turn, I did f(x) = 2x+1, and they were vexed.  I could tell when they were frustrated with something when the numbers I got were over 20.  10,000 isn’t going to tell you much about a number machine’s function that 0 or 5 wouldn’t.  At that point, I suggested thinking about what a “doubler” machine would return.  After four more tries, one girl got it, and was thrilled when she turned out to be right.  I hope that wasn’t too much of a hint.  Given the chaos of the moment, I don’t think a subtler hint would have gotten through.
For homework,  I’m going to try doing some number machine activities around the breakfast routine for a while.  Colin (our 4-year-old) likes participating just to see the machine do things.  Generally his numbers have four or more digits. Awww.
Anyway, this has turned out to be a wonderful experience for me — all of the kids seem to truly light up.  I’ve got two weeks to come up with a good follow-on activity.

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