# Group theory for kids?

## Epsilons

Iztok joined the Epsilons for the first time today. And I immediately made a couple of silly mistakes.

I knew Iztok was coming, so I’d prepared a triangle for him. And that was the first mistake. Not sure how I’d forgotten, but he is four years old. I repeatedly mentioned him being three years old while showing him a triangle. He just silently observed it. After a while, Vesna, my second-oldest daughter, reminded me he was actually four.

I apologized and quickly made a rectangle. Then I asked Iztok to draw something on it. I think I made two additional mistakes here. First of all, this was a nice opportunity to let him cut the rectangle out of a sheet of paper by himself. I’d known by now how much kids like cutting, coloring, and pasting. Secondly, at some point in past, I’d learned Iztok didn’t like drawing, his mother had told me. But it totally slipped my mind. So, he simply ran out of the room. I went after him, but I was unsuccessful when trying to get him back.

Four girls were waiting for me. Kind of. Vesna was racing around the room and screaming, but at least she didn’t escape out of it. We started drawing circles by using a compass. I let them touch the compass to feel how sharp it is and explained this was to fix one of the legs where the center of the circle is supposed to be.

We then switched to the concept of rotations.

We started with a triangle. We positioned a triangle in the triangle drawn in a circle. To fix the triangle at the center, we used the compass. For each rotation one of the kids was holding it. My help was needed, otherwise it simply wouldn’t be fixed.

The starting position:

After one rotation:

After two rotations we were at the starting position again. We discussed how many rotations we needed to get the fruits aligned again.

What about a rectangle?

Again, we counted the number of rotations we needed to get the ice creams aligned again. One rotation here means rotation from one vertex to another – 90 degrees.

Kids liked holding the compass, but it was also distracting. I am not sure how much of my explanations of rotations they understood. I think I should be explaining less and just let them try out.

I had another set of "instruments" prepared.

Constructing a rotating triangle turned out to be the most interesting part:

The final product:

After a while, the girls had enough of triangles, rectangles, and rotations, and just wanted to get out. They left the room screaming and I let the older kids in.

## Deltas

We had just started when Vesna came and informed me that Andreja, one of the Epsilons, had wet herself. I had no other choice but to accept that this was part of the Math Circle too, and I took care of it. In between, the screaming and laughing Deltas were all over the place. Not without significant effort I silenced them and started with similar questions about rotations as in the first group. Here, answers were immediate and mostly correct. A few times I was impressed with how quick they were to grasp it.

Together we constructed a hexagon and an octagon. A couple of times, actually. Everybody, especially boys, wanted to construct a rotation tool at least once.

Some of the kids knew where we land after six, eight and even eighteen or twenty rotations. The others lost interest and I couldn’t make them follow again. When Marko, who always shows the most interest, asked me if we could now play football for a bit, I knew it was enough. Of course, we played football for a bit.