Tuesday, May 23, 2017

5/23 Triangle Conundrum

In the middle of last week, the MOEMS awards for the year arrived. So I started handing out patches and medals. I'm fairly happy with our overall performance at the Middle School level. Almost all the fifth graders who were present for all 5 tests was in at least the top 50% of 6-8th graders and we had one boy crack the top 10%,  This was not as high a level of achievement as last year when we used the Elementary level but confirmed that this was providing a good level of challenge and was not too difficult. Week to week, almost everyone could access at least 1-2 problems (often more) and we had good discussions about the entire set. As I said before, the MOEMS format has grown on me over the last 3 years. I think I will bring this with me to the middle school level.

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:

There was mention of the following problem:

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.

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