## The Activities

**Topics: Numbers, Large Numbers:** The Cat in Numberland, Chapter 1, by I. Ekeland.
**Topic: Large Numbers:** First, I asked the kids to come up with numbers with increasing sizes (first 1 digit, then 2 digits, …). After they stopped being able to come up with things, I wrote powers of 10 up to a quintillion. I also wrote a googol and had them help me count the zeroes. Next, each kid wrote down the biggest number they could on a sheet of paper. I asked them which kid’s number was largest, and then I asked if it was the largest possible number. Then I guided them through a proof by contradiction that there is no largest number.
**Topic: Programming:** We revisited the Dance Programming activity. First I called out commands (Down, Up, Jump, Spin) and the kids did them. Then I taught them a few programs I had made that used the four commands plus “Do X times {… }” loops and function calls. Next I had them each say a 3-command function for us all to do. Finally, I asked each kid to write down a named function, with the rule that if you used a “Do X” loop X was at most 5. Then I made a program that called all their functions and a couple of the kids did it.

**Topic: Programming:** We revisited the Cargo Bots activity. I made a new version of the board, download here. First, we moved a single block from one end to the other; then two blocks; and finally, they needed to move two blocks of different colors from one end to other so that the final ordering was the same (i.e., if red is on top initially, it should be on top at the end as well).

## How Did It Go?

We had four kids this week. This circle went pretty well, we had some good discussions and some good problem solving. The kids sometimes thank us after circle(usually prompted by parents) , this time one of them said “Thanks for giving circle to me.”

#### The Cat in Numberland

This was a popular book with the older circle. There was a part about how not all numbers can play division together — two of the four kids got the idea. When it got to the part about infinity, several of the kids already knew something about infinity. One kid said “My friend says that her mom is always right, and her mom says infinity is a number.”

#### Large Numbers

Most of the kids had trouble coming up with a number above 1000. Even the kids that knew larger numbers like 1,000,000 couldn’t make arbitrary seven digit numbers. The kids enjoyed counting out 100 zeroes when I was writing a googol. The kids varied in their approaches to writing large numbers. Some did 1 followed by lots of zeroes, others wrote somewhat random sequences. I wrote a large number as well — I started with 9’s for obvious reasons, but I discovered that 9 is pretty slow to write, and so I switched to 1’s which are really fast to write.

Next, I asked them which number was biggest; I’m pretty sure it was mine, but one of the kids had filled up their page with larger numbers, so they picked that one. I asked whether it was the biggest number. 3 of the kids said no, one said yes. I asked whether they could make a bigger number. They didn’t really come up with adding 1, but they did suggest adding more digits, including adding on someone else’s sheet of numbers. Then I said the idea of proof by contradiction (assume the opposite, find a problem), and said “Suppose you took all paper in the world and filled it with numbers. Could you make a bigger number?” After a bit, one of the kids said “You could cut down more trees and make more paper so you could add more numbers.” So I think some of them got the idea. Since they had suggested taping together sheets, I taped together all the sheets that we had made and laid it on the floor. For the rest of circle, when a kid finished their work and was waiting on someone else, they asked to go over and add more numbers to their sheets.

#### Dance Programming

For an activity involving jumping up and down, the kids payed pretty good attention. They all understood sequences of instructions, and I think they understood loops and functions. When it came time to write a program, only one used a loop; the loop they wrote was a copy of one of my functions with a different number. It’s a good thing I limited X to 5, because they immediately said “I wanted to do 100.” No one figured out the weakness in my problem specification — nested loops.

#### Cargo Bots

One of the kids missed the first time we did this but caught up fairly quickly. All the kids were able to solve the first two problems, at different speeds. A common mistake on the two-block problem was forgetting to move the crane back to the beginning for the second block. The two-color two-block problem was way harder. One of the kids came up with some interesting rule-breaking solutions, such as using their other hand. After a while I gave them a hint by making a program that flipped the stack onto the middle square of the track. From this, one of the kids (same one who came up with the alternate solutions) realized if they repeated this again, they would solve the problem. They had some bugs along the way, which I demonstrated by tracing through their program, and they were able to keep fixing things until they got a correct solution (with a few unneeded instructions). Another kid understood the solution and tried to copy what the first kid had done and got pretty close. The other kids were still far off and hadn’t gotten the idea of double flipping.