- Topic: Probability: Book: A Very Improbable Story by E. Einhorn.
- Topic: Probability: First, I secretly put 2 red and 8 blue stones into a small drawstring bag. Each kid took turns pulling one stone out, looking at it, and then putting it back. The question was, are there more reds or blues? I repeated it with 4 red / 6 blue, and also 5 red / 5 blue. Finally, I made two bags, one with 10 red / 10 blue, and the other with 11 red / 9 blue, divided the kids into two teams, and asked them to figure out which bag had more reds. I gave the kids paper and pencil and they decided to make charts to keep track of the results.
- Topics: Numbers, Sorting: I had about 20 different numbers on squares of paper, 0, 1, 3, 4, 6, 8, 12, 13, 100, 105, 1001, 1052, 1053, 1000000, -5, and -100. First, I handed each kid one number and asked them to sort themselves. We did this several times, starting simple and then using some of the trickier numbers. Then, instead of handing them the numbers, I taped a number to each kids’ back, and without telling each other what the numbers were, they needed to sort themselves. We did this a few times as well.
- Topics: Tangrams, Geometry: I gave each kid six different tangram puzzles. For the kids who finished earlier, I had them work on the letter “A” from Tangrams: 330 Puzzles.
How Did It Go?
We had four kids this week. It was a good circle, a few of the kids got a little antsy when we were discussing the results of the bag counting, but otherwise they were all engaged the whole time.
A Very Improbable Story
The kids liked the cat on the head :).
The kids immediately grasped the idea of looking for whichever color came out more often. Not surprisingly, they were overconfident — once, after only 3 draws one kid concluded red was the winner and dumped out the bag, only to find out that there were 5 of each.
For the team activity, one of the teams delegated one person to pull the stones and the other to record, while the other was taking turns drawing out stones. The former strategy was about 2x faster, so I suggested the other team use it as well. It was very interesting to see the two charts (pictured above). One was a standard tally chart, except with 6 instead of 5 in each group. For the other, the kid started by writing a bunch of numbers, and then checking them off as stones were pulled out of the bag. The results came out pretty nicely — exactly 50% for the 10/10 bag, and 55.6% for the 11/9 bag (expected 55%). However, the kids were a bit confused by the fact that team 1 had counts of 15 red and 15 blue vs. 30 red and 24 blue for team 2 — at one point, one kid concluded that team 2 had more reds AND blues. In fact, the only way I got them to conclude that team 2 had more reds was to ask them to guess what was in each bag. Their guess for team 1 was 10/10, while their guess for team 2 was “6 more reds than blues” (not coincidentally, they had drawn red out 6 times more than blue). I asked them how many reds there would be if there were 6 more reds than blues, and 20 total — this was actually quite hard for them and I had to help them a lot (the initial guess, 16, didn’t work). Of course, 13/7 doesn’t match their observed results. So, there’s clearly a lot more them to learn for the fine shades of probability!
This activity was pretty easy for them, even with the numbers taped to their backs. They had a lot of fun, particularly when I gave them negative numbers or really big numbers. They did a great job not telling each other — the closest they came was saying one kid’s number was really low (when it was -100).
This group has done these puzzles before, but that wasn’t an issue, they didn’t remember the solutions. They were better than last time, but the puzzles still definitely weren’t trivial. The bonus puzzle is much harder because it wasn’t to scale, but they made a good effort and made progress.