## The Activities

**Topic: Charts:** Book: The Great Graph Contest by Loreen Leedy.
**Topics: Multiplication, Proofs:** Prove that multiplication is commutative, i.e., x * y = y * x.
**Topic: Programming:** I did several robot dances. The kids needed to write a program for that dance. For example, R(ight turn)RRRJ(ump)F(orward)B(ackward)RRRRJ. Then, they had to find the shortest program they could for that dance, using loops and functions.
**Topic: Origami:** We all worked in parallel, each kid (and I) making two simple models, a rolling toy and an envelope.

## How Did It Go?

All 6 kids made it this week again!

#### The Great Graph Contest

I asked the kids at the beginning what a graph was. Kid 1 said they did graphs at school, and it was where they asked everyone a question and they said yes or no and then they saw who had more. I asked for any other definitions, and Kid 2 said almost exactly the same thing. I said those was one kind of graph but there were others. The kids liked the book better than average I think, several kids said they liked it afterwards.

#### Commutivity of Multiplication

First, I asked which is bigger, 3 * 10 or 10 * 3. Kids 1 and 2 both immediately said “the same!” although the other kids didn’t know. I tried out some other numbers, and Kids 1 and 2 kept saying the same (going in, we thought that maybe none of the kids would know about this). I asked them why it was true, Kid 1 had a circular answer and also said something like “because they’re both 30”. Kid 1’s explanation for why 5 * 4 = 4 * 5 was that 5 * 4 is 5, 10, 15, 20, and then 4 * 5 is 4, 8, 12, 16, 20, so the same! I asked them to prove it with blue blocks. Several of the kids started making piles, Kid 1 started to make rectangles, and a couple kids did nothing. After a while I asked them all to make 3 * 5, which Kid 3 explained as 3 groups of 5. Then I asked them to make 5 * 3. Most of them had 2 sets of piles at this point. Kid 2 said “look, I can use one set of piles to make the other” but just did it adhoc without a pattern. I pointed out Kid 1’s rectangles and asked if they were the same. Kid 4 said something about them being the same squares (sic), and said something about the side lengths. Kid 1, after a bit, said you could look at them from different ways and they would go back and forth. I said “Kid 1 proved it!” and repeated his proof. Then I showed them the proof where you take 1 thing from each pile to make a new pile, and do that until you’re out of blocks. I don’t know if any of them understood it.

#### Writing Dance Programs

I performed several dances for them, and they had to write down the instructions for that dance. I started with a simple dance, F(orward)B(ackward)BFJ(ump). It was harder than expected. I ended up doing it about 5 or 6 times. By that time, all but Kid 1 had it correct (Kid 1 only had one B).

Next, I did R(ight)RRRJFBRRRJ. Again, they had some issues keeping track of what I was doing. After a while a several of the kids had correct programs. Kids 1 and 2 were the fastest, followed by Kids 3 and 4, and then Kids 5 and 6. About this time, Kid 5 said, unprompted, “Moopsy!” I was very excited, because this was what I was looking for (Moopsy was a subprogram from last week), but Kid 5 didn’t follow up and use it. After a little bit I hinted them towards Moopsy, and then several of them were able to quickly write the program in terms of Moopsy.

Finally, I did D(own)U(p)DUDUDUFBFBDUDUDUDU. Kids 1 and 2 finished the whole thing, and Kids 3 and 4 made good progress. Then I asked them who could do with the shortest program. Kid 3 came up with “Do 4 times: DU FBFB Do 4 times: DU”. It’s worth noting that most of the kids didn’t have any syntax; Kid 1 was the only one who wrote each instruction on a different line. A couple kids mentioned Floopsy from the previous week (DUFB), which was usable but not super helpful. Then I said “You can make up your own programs!” Kid 1 did something interesting, Kid 1 erased the whole program and wrote “n” and then said that “n” was the whole program. I said Kid 1 still needed to tell me what “n” meant, and Kid 1 got rather upset and said they didn’t know what I meant. After a bit I was able to explain that I didn’t know how to do “n” so they needed to tell me. But it turned out that wasn’t enough, and that the core problem was that the definition of the length of a program wasn’t clear. So that’s something to be more careful about in the future. Meanwhile, although most of the kids weren’t making progress (Kid 5 was busy writing the names “Poopsy” and “Peesie”), Kid 3 had written “t” and was doing DUDUDUDU. I pointed this out to everyone and asked if they could write the program in terms of “t”, and several of them did. I mentioned Kid 3 could use “do X times” inside “t”, and they did. In the end, Kid 3 ended up defining “s” to be “FBFB”, so the final program was “tst”.

The kids are doing pretty well at programming, although there’s a noticeable range in ability among the kids.

After circle, our daughter kept working on her program with Corey and made a shorter program than we had come up with during circle.

#### Origami

We made two models, as a group, from the books “Origami: Fun with Paper Folding #5 and #8”. The books don’t seem to be available online, but they’re pretty simple models, although a bit harder than the cat and dog we made last time. One of the models was a cute rolling toy, and the other was an envelope. There was lots and lots of “how do I do this step?” but everyone was doing pretty well. The kids are good enough at making folds that I think we can try harder things in the near future, like the standard swan. The kids all were able to handle the symmetry very well, once I showed them how to do one side they could do the other side without problems. However, they did sometimes have problems when they were supposed to turn it and do the same thing on the other side. A couple of the kids knew about “sandwich folds” and “hot dog folds” (for the two different initial ways of folding the paper in half).