Functions and archery

Last time, just after we finished the first Math Circle, I started to fear I’d talked too much about functions. Way too much. And Vera confirmed my fear. Kind of.

“You talked about arrows last time, young boy?”

“Sure I did. I talked about functions.”

“I thought it was arrows. Boys said you were playing with a bunch of arrows. What’s this, it’s certainly not math... Is it archery?” asked Vera.

“Did they mention functions?”

“No.”

“Not a word about functions?”

“Not a word.”

“Did they say what arrows represented?”

“They said they didn’t know.”

Of course they didn’t. But mapping between different objects seems a highly important concept to me. And functions are mappings. So I planned to continue talking about these concepts (archery!) at least a little bit.

Epsilons

In the second Math Circle, I therefore wanted to carry on discussing the concept of mapping. But hopefully in a more pleasurable context — football. However, considering that the younger group (Epsilons) consists only of girls, I was concerned this might not be the best choice after all.

It turned out that girls can be almost as enthusiastic about football as boys. Of course, some of the Epsilons are little sisters of the Delta boys and seem to be heavily influenced by them.

We were taking penalties and were using two boxes as goals. Each of the girls had five attempts. When they scored, they put a sticker on the coordinate system on the wall. The number of stickers represented the number of scored goals. The stickers were put in the column above the shape representing the girl. They all had triangles because they are all three years old, but each of them had a different color.

I talked a bit about how we could visualize it differently — representing the number of goals simply by drawing a point at the appropriate height. Vesna drew it like this:

Vesna’s picture doesn’t reflect the actual results, but that was the best I could get from her. It seemed that after penalties and stickers, they had more than enough of coordinate systems and functions, they just wanted to get out of the room as quickly as possible. And they did.

Deltas

There was a lot of screaming when I mentioned we were going to play football and it was difficult to calm the boys down. But even Rebeka, my oldest daughter and the only girl in the group, was somehow excited. She probably just didn’t want to stand out.

This, however, changed the moment Rebeka failed to score in her first two attempts. She started crying and I couldn’t comfort her. She left the room but actually returned shortly, still crying.

The boys were totally excited and I couldn’t leave them alone. They were discussing the scoring system. Scoring here was actually a bit different than in the first group – we had two goals here too, but one was further away and brought two points if scored. There were screams for successful as well as for unsuccessful attempts.

It was Rebeka’s turn again. And again, she missed. Now the crying intensified. But I realized now – she was hungry. I know her, she just can’t help herself when she is hungry. I knew nothing would help but food. But she didn’t want to have any. She just continued to cry and left the room. Running after her and persuading her to have some food didn’t help. In the meantime, the boys were kicking the ball, shouting wildly. Of course, nobody was discussing the coordinate system.

I came back and asked for results. Gregor won. He is the youngest and it was funny how he got some admiring looks from the older boys.

Besides drawing the coordinate system, we constructed towers of books – one book for each scored goal. Each kid marked their tower with the flag and shape from last time.

There were no goals for Rebeka (third column in the coordinate system on the wall) and me (sixth column), you know why. There are two sheets of paper with the same graph on the wall because I planned to continue this activity in a few weeks and would like to have one coordinate system for a cumulative result.

My wife wasn’t at home at the time, and I couldn’t find Rebeka immediately. But finally, I heard her laughing in the kitchen. She was sitting in Vera’s lap and eating a chocolate. Vera most likely realized in a second what the problem was and solved it. She looked at me reproachfully: “Young boy, your kids are hungry!” But she didn’t mock me this time, for which I was grateful.

In general, I think the kids liked today’s activity. Of course, you never know how much of the coordinate system they actually absorbed. I hope someday they will realize that while we were taking penalty kicks, there was some mapping there, as well.