- Topics: Division, Primes: Book: The Number Devil by H. Enzensberger, first half of third chapter.
- Topics: Primes, Multiplication: Following the chapter from the Number Devil, each kid did a sieve of Eratosthenes up to 70.
- Topics: Games, Probability: Using percentile dice (two 10-sided dice which together roll a number from 0 to 99), we played this game: going around the circle in turn, each kid picks a number. I roll the dice, and whoever is closest gets a point (if there’s a tie, each kid gets half a point). After doing this a few times, we did the same thing except that instead of rolling the dice, we computed how many numbers would make each person win, and they got that many points. E.g., if the numbers were A: 10, B: 45, and C: 85, then A wins from 0-27 for 28 points, B wins 28-65 (tie on 65) for 37.5, and C wins 65-99 (tie on 65) for 34.5 points.
How Did It Go?
We had 4 kids this week.
The Number Devil
This chapter talks about the connection between multiplication and division, and about prime numbers. It introduces the sieve of Eratosthenes. One interesting thing that came up is one of the kids, who knows division already, first said that they hadn’t done division this way before, but then later said that they probably knew this way of doing it because they knew how to do division.
Sieve of Eratosthenes
We’ve tried this before, and this time the kids were definitely better. But some of the kids still made multiple mistakes, particularly when counting by threes. I tried to explain why it makes sense to cross out every third number, but I’m not sure they fully understand that counting by 3’s gives you multiples of 3.
The number picks were pretty random for a while; one of the kids guessed lucky numbers, and most of them liked to pick larger numbers. They did all realize they should pick between 0-99. After a bit, one kid realized that guessing right next to another guess might be a good idea — but it then backfired on them when the next person did the same thing. They soon decided that they all wanted to go last — with good guessing, it’s not an advantage to go last, but with the way they were guessing, it definitely was. I had initially planned to use the dice the whole time, but quickly realized that the variance was too high — one of the kids was winning by a sizable margin despite not having made the best picks. So I switched to giving points based on number of ways to win (I did all the calculations, it would have been hard for them). Some of the kids understood this pretty well, but some of them were pretty confused and didn’t know what I was doing. For one thing, they hadn’t seen notation like 45-58 before, and the idea of writing down all the numbers that would win for them wasn’t obvious.