- Topic: Biographies, Mathematicians: Book: The Boy Who Loved Math: The Improbable Life of Paul Erdos, by Heiligman.
- Topic: Division, Counting: Find all numbers between 1 and 100 that are divisible by 3, 4, 5, 6, 7, 8.
- Topic: Programming: Do dance move programming, following functions. Then write a dance for me.
The Commands and Functions
The Dance Programs
Do 3 three times:
Do 4 times:
Do 2 times:
How did it go?
All 6 kids were at circle again! I don’t think we’ve ever had such consistent attendance before!
The Boy Who Loved Math
The kids were all interested in the book. It’s about what a strange person Paul Erdos was, and how much he loved math. I made sure to point out that he was studying the same things they were in circle: primes, combinatorics, etc. They thought it was funny that he didn’t know how to take care of himself. They were also intrigued that he died at a Math conference.
Find all numbers between 1 and 100 that are divisible by 3, 4, 5, 6, 7, 8. First I told the kids that ‘divisible by’ means you can make that many piles out of the that number of cubes. I grabbed a handful of 10 cubes and made two piles. Each pile had the same number of cubes, so the kids said that 10 is divisible by 2. Then I added one more cube, and they saw that 11 is not divisible by 2.
Next I gave each kid their own number between 3 and 8, and a bag of 100 cubes, and asked them to write down all numbers between 1 and 100 that are divisible by their number. I put each kid somewhere on the floor. Several of the kids did not initially understand what they were supposed to do, so I sat with each and explained one on one.
Kid A started off confused but then I showed him how 8 is divisible by 8, by making 8 piles each containing one cube. Then I added a cube to each pile until we got to 16, which he saw was divisible too. At that point he figured out that he did not need cubes and starting counting by 8. He went all the way to 304 before he ran out of time.
Kid B had 5. She understood the activity after I talked to her one-on-one. Interestingly, she wanted to write the number in letters and digits: thirty 30. When I checked back after a few minutes she had gotten up to 40. I asked her if she saw any patterns, and she said, yes, it’s counting by 5s. I suggested she could fill out the rest of the paper without using blue blocks, which she did.
Kid C had 7. She came up with 7 and 14 by herself, but then she had written 23. I said she should check that one, and she started it again. It took awhile before she realized that counting by 7s would work, and even then, she had some trouble adding 7 to the higher numbers. I demonstrated by counting 7 on my fingers: 22 – 23 – 24 – 25 – 26 – 27 – 28, and then she successfully used that strategy to count by 7s to 98.
Kid D had 4. She used the blocks very efficiently to get up to 56, counting by 4s. Then she mixed up her piles and got frustrated, but as she was starting to count out 56 blocks again, she realized she could count by 4s which she did up to 100. She and Kid A (who had 8) finished first so I had them compare their charts. They noticed that Kid A had written fewer numbers than Kid D, and they said it’s because her number is smaller. Kid D said that whoever had the smaller number would have to write down more numbers.
Kid E made a very elaborate chart like this:
1 yes no
2 yes no
3 yes no
4 yes no…
She used the cubes to test out whether each number was divisible by 3. I asked her if she saw any pattern, and she said it was always yes no no, yes no no. I asked if she could find all the numbers now without using cubes, but I think she continued to use cubes. She only got up to 19, because she had such an elaborate chart.
Kid F was counting by sixes, using the cubes, however her cube strategy was very inefficient: For example she made 6 piles with 2 cubes in each, and then she counted all the cubes into one big pile to see how many she had. This meant she’d have to lay out the cubes from scratch to find the next number. She ended up with 6, 12, 24, 48. I’m not sure if she was intentionally doubling the number each time.
The Programming Dance
David came up with this idea for our four year old son. David would say directions: forward, forward, turn right, backward…and our son would do them. Then David came up with idea of making functions, e.g. ‘Fizzle’ means down up forward forward. My kids loved this, so I decided to do it for circle.
I asked the kids if they like to dance? All the girls shouted yes…Our one boy said no. I said I had a computer dance for them. Then I showed them the chart on the wall, and we did each command. Next I pointed to ‘Floopsy’, and I said it meant we had to do all commands under it.
Then I gave each kid a copy of Program 1. All the girls stood together in front of the command list and did the commands. The boy didn’t want to dance so I said he didn’t have to. For the next one, I had him read the program and I did the dance. Then all the girls asked if they could do it too, so I handed a copy out to each.
Then I skipped to Dance 4. They quickly realized they had to refer to the command wall to remember what Floopsy meant. At this point, the boy got interested and started to do the dances too.
Everyone begged to do all the dances, and no trouble with the idea of functions, or the loops. They were pretty good at counting how many times they had done ‘Floopsy’ for example.
At this point one of the kids suggested that we should do all six dances in order. Everyone else agreed, so they sorted their dances and started. Everyone else was a bit chaotic because they all started at different times, but they were all engaged.
After this, I said they had 5 minutes to write a program dance that I would do. They all cheered, and happily sat down to write a silly dance for me. My daughter finished her dance first and it was something like:
Do 16 times
I started to do it, and laughed incredulously when I saw 16 times! But everyone insisted I must do it, so I really did do it about 16 times. This inspired the other kids who wrote various things for me to do 100 times or 200 times. One kid then said she’d make me do it infinity times, and she knew how to write infinity as a sideways 8.
At this point, the kids introducing silly other commands, which I discouraged. They particularly wanted to add ‘Shake your butt’, which I refused to do. After that, everyone got pretty silly, writing variations on shake your butt.
Circled ended with lots of loud laughing and shouting, and excited kids taking home their dances…so success!