On another note, I thought the MathCounts problem of the week was not super interesting so I took a poll of the kids after we discussed it today. Interestingly, the kids seemed to generally like it. I mean to think about this some more. Was it because these type questions are more straightforward? Its definitely a caution for me to remember to vary activities. My taste in Math is my own (and perhaps a bit quirky) and I want to make sure to try to appeal to everyone over time.
Today's main Math Club activity was inspired by the following tweets:
We are getting 3 different areas for the shaded part! Who wants to help us out? @KatherineSchack @ddmeyer @robertkaplinsky pic.twitter.com/Xo3gcBcc4h— Mandy Wandling (@Jepsen6B) May 18, 2017
There was mention of the following problem:
@ddmeyer See Tanya Khovanova mentioned a similar problem on her blog a few years back: pic.twitter.com/zTe8UtnyTl— Mike Lawler (@mikeandallie) May 19, 2017
That made me think of the classic Martin Gardiner missing square puzzle:
These problems seemed like a good progression of fishy triangle issues and all seem well suited to group problem solving on the whiteboard. So I had everyone getup and circulate among them during the main part of the hour. I liked the general activity. The most difficult one turned out to be the Tanya Khovanova "triangle". This was the only one the kids didn't fully solve although it brought out some great questions about the Pythagorean Theorem and experimentation with various triangle configurations. As kids cracked the other ones, there were occasional excited shouts "This isn't really a triangle!" I was particularly happy they also connected the problems back to slopes to prove what they discovered.
To close the day out I wanted another game. This time I turned to one I found on Sara Vandewerf's site: 5x5.
I pretty much followed Sara's format. (I always appreciate time estimates for a game in a writeup) We did 5 founds and the kids were just as engaged as promised. Beforehand, I had wondered if all the scores would bunch around a few values. Even with 14 players that didn't generally happen except when going for low scores. As a thought experiment: since all the kids loved the lima beans we used as tokens a few months ago it occurred to me afterwards I could spray paint them gold and give them out as "prizes" in the future. [Would older kids find this corny or fun?]
Some probability work form Waterloo:
Unused: I actually had some more skyscraper brain teasers and a little bit of combinatorics in my back pocket.