Tuesday, January 31, 2017

1/31 Chessboard Problems or manipulatives on the cheap

This week's planning revolved around my desire to pivot away from the more conventional topics of last week.  I needed to give the kids more exposure to exponents but that being accomplished I wanted a lot more whimsy this week. I was casting around in some of my more Math Circle oriented resources but then I ended up watching a lecture by Maria Droujkova @ https://www.bigmarker.com/GlobalMathDept/Avoid-Hard-Work-Natural-Math-Adventures?show_register_box=true. Among the discussion, one particular problem caught my eye: the knight's tour which is done on a chessboard. I then independently found a different chessboard problem that I liked featured in a numberphile video. I also remembered a chess station I manned last year in the Julia Robinson Festival. All told, that was more than enough material and I thought it would make a fun themed day. The final problem was producing enough pieces for 12 kids to use.

Inspiration struck at the grocery store. For only a few dollars I purchased hundreds of dry lima beans. They worked perfectly on some printed out chessboards and the only issue was making sure they didn't end up all over the floor.

As you can see from above, I also bought some candy to reward the kids for reaching our problem of week point goal. The last few weeks, participation has been edging up again and I'm feeling good again about its function.

I also ended up borrowing a video projector so I could show the following video:

I played the first 5 minutes or so and then broke out the lima beans and had the kids work on solutions to the problem for the next 10 minutes. At the very end, I started to get questions about whether this was impossible. My response was can you come up with reasons for why that seems to be the case. We then reconvened for the back of the video. As usual media makes for very easy to manage Math Club sessions. I could very easily see running a permanent format where one did a 10 minute video every week.  I particularly like the focus on math practices and proofs embedded within this clip. Its almost perfect for the kids at this stage in their math careers.  Two immediately on point moments occurred first when the video asked whether it was possible to prove something impossible. I heard a lot of "yes' murmurs from the room.  Then later on when the video started talking about the infinite geometric series 1 + 1/2 + 1/4  ... I stopped to ask the kids what they thought that ended up summing to. Sure enough as the video would call out most answers were a fractional bit less than 2.

For the last 20 minutes or so we then turned to the Knight's Tour Problem. I explained the basic rules in a huddle, promised everyone this puzzle was solvable and then everyone was off.

All told, I was very satisfied with the engagement again this week. I have another Olympiad coming up in a few weeks but I hope to repeat another "pure" Math Circle session before then.

Bonus: http://www.msri.org/attachments/jrmf/activities/ChessCovers.pdf

a pythagorean puzzle from @solvemymaths.

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