- Topics: Codes, Arithmetic, Logic: We did the first activity from Sideways Arithmetic from Wayside School by L. Sachar. In this activity, you have to solve letter-number substitution problems like “elf + elf = fool”, “egg + egg = page”, “top + tot = opt” and “ears + ears = swear”.
- Topic: Arithmetic: We revisited the activity where you have to make as many different numbers from 1-60 using only 5’s and the four basic arithmetic operations (plus parentheses). This time I gave them a prize based on how many they could come up with working together.
How Did It Go?
I started circle with a talk about the goals of math circle, with three points: 1) The activities are supposed to be hard and strengthen your brain (mentioning that just like soccer, you practice to get better and stronger), 2) The activities often will be things you haven’t done in school, and 3) Even if you think an activity is boring, if you say that it might affect the other kids, plus if you try hard you might find it’s actually interesting.
Whether due to this talk or not, circle went much better this time. The activities were fairly tricky and all five kids contributed to both activities and paid attention most of the time.
Elf + Elf = Fool
The first one I had to give them some fairly strong clues before they realized that ‘f’ had to be 1. After that they mostly figured out the rest. “egg + egg = page” is quite a bit harder, the kids came up with all the key ideas but I steered them some. “top + tot = opt” went even better, and by the 4th or 5th one some of the kids were getting pretty comfortable.
We’ve done this a couple times before with less progress than I had hoped, but this time went much better. Besides the pep talk, I did two things differently: I had a chart on the wall where they could add their answers, and I gave them 1 prize at 25 answers, 2 at 40, and 3 if they got all 60. In about 25 minutes they got 32 unique answers. They also figured out the idea of adding or subtracting (5 / 5) repeatedly, but they didn’t use it to grind out all 60 numbers. Initially they had (5 / 5) + (5 / 5) + (5 / 5) for 3, I challenged them to find a better way and they eventually got (5 + 5 + 5) / 5. We’ll probably give them a chance to get the rest next time. Also, a good variant we should do in the future is giving them a challenge like “Make 5, 13, 19, 27, and 41 using as few total 5’s as possible” with prizes based on how few — there’s lots of really interesting math in figuring out the factors and figuring out what nearby numbers can be made cheaply (similar to dynamic programming if you’re familiar with that concept from computer science).