- Topic: Fractions and Infinity: Book: The Cat in Numberland by Ekeland, Chapter 5.
- Topic: Prime numbers: The kids used blocks to prove which numbers 1-70 are not prime. The easy ones were already done in a previous week. This week they proved 49, 51, 55, 57, 65, and 69 are not prime by making a rectangle out of that many cubes.
- Topic: Logic: 20 questions with numbers. The kids got 7 or 8 guesses to figure out my secret number which is between 1 and 36. They were allowed to ask yes/no questions like: Is it higher than 24? With each wrong guess, a bear would move closer to a picnic treat, and steal it if they didn’t get the number in time.
For the prime number activity, we had a chart with the numbers 1 – 70 taped to the wall. If a kid proves a number is not prime, they get to color in that square on the chart.
For the 20 questions game, I printed out cute clipart of picnic treats like cake, hot dogs, and donuts, and also a cartoon bear. Every time the kids asked a question the bear would move one step closer to one of the treats.
How did it go?
The prime number activity was fascinating. I gave each kid a number of cubes (e.g. 49 or 51) and asked them to prove it was not prime. The kids really don’t have a good search strategy yet, so they would randomly try a rectangle with 2 to a side, and then 5 to a side. At one point the kid working on 51 tried to make a square out of the blocks. The kid working on 49 saw that and decided to try it. It worked for 49, but not 51. There were some inklings of an algorithm…for example, one kid tried a rectangle with 2 to a side, and then another kid suggested they try 3 to a side.
The kids love the number guessing game. My secret number was between 1 and 36. We’ve played it before, and now most of the kids know that a question like “Is it 5?” is not good. Some of the kids have started to realize that binary search is a good strategy, but the kids are still convinced that whether something is a good question is determined by the answer. So if someone asked “Is it smaller than 4?”, if the answer was no, the kids would accuse the asker of using a bad question, but if the answer was yes, they would congratulate the asker.