Tuesday, April 28, 2015
4/28 Magic Squares
After a very challenging week last time, my goal for this session of the math club was to do something fun/low key and then go over some of the solutions to the purple comet meet as a group. I started by debriefing the kids about the contest. The biggest issues they had were around working as a team which is fairly typical especially with coed groupings like the ones we used last time. I'm leaning towards doing some of the problems in a non-competitive setting next year rather than the full contest but I'll make a judgment based on next years kids. I had one new student who just started last week which was unfortunate timing for forming a first impression. On the other hand, I had one of the stronger kids who missed the contest complete most of the problems at home.
While finishing up snack I handed out today's warm up a magic square progression. I found a web site that generates some worksheets: http://www.worksheetworks.com/puzzles/magic-squares/integer.html going from a sample to a 3x3, 4x4 and then 5x5. On the back I added a magic hexagon from: http://fivetriangles.blogspot.com/2015/04/235-hexagon-puzzle.html. First we talked about the basic rules and did a few squares from the sample. Then I let kids start working on their own with a request to see if they could see any relations between the first 2 3x3 squares. Victory, first I had one girl notice that all the squares in each one were multiples of the same factor. Then a second realized you could transform each square from the first into the second by multiplying by the same ratio. 3x3 squares have only 1 family of solutions unlike all the other larger versions. This generally worked really well. Everyone was quiet and focused and the kids had started to attempt the hexagon right about the time we had to move on.
We then walked through the first 10 problems using the overhead projector. This was a bit more limited than the normal discussions with only 3-4 kids volunteering solutions and it was about the upper limit for how much I can keep the kids focused on each other. Improving my ability to facilitate peer discussion is one of my long term goals. I don't really plan to do the back half of the questions in class. Instead I will email the pdf of the solutions since I think these were the ones that were mostly too difficult and least likely to be productive as a discussion.
Looking forward I've found another interesting activity. https://news.cs.washington.edu/2013/05/11/the-washington-state-algebra-challenge/ I have to do a bit more investigation but hopefully this will pan out.