A few weeks ago I did a series of lessons with the kindergartners about one of my favorite topics to do with this age group: functions! I recall being quite surprised when I introduced the concept to my daughter when she was five and she really understood it. She wanted me to come up with more and more rules for her to figure out, and these guys were no different!
Here are some of the functions that they had to guess. Usually, I would draw the first few input/output pairs and the students would try to guess the rule. Then I would draw a few more inputs and the students would tell me what to write/draw for the output. Sometimes the students couldn’t explain the rule in words but I could tell that they understood it because they could predict outputs for various inputs.
As you can see, I got more creative with the drawings of the actual machines. The students were very excited to tell me what type of hair or nose to draw. And then they got to create some functions machines of their own!
In this machine, a wolf and a chicken went in, two wolves and two chickens came out.
This machine changed functions half way through. First it was the doubling machine: One mouse went in, two came out; two candies went in, four came out. But then the student got bored of that function and turned it into a related one: small turtle goes in, large turtle comes out.
The following lesson, we talked about pairs of functions that undo each others work (posts about the discussions with Katie on this topic here and here). We started with a very simple pair: one turns squares into circles and the other one turns circles into squares (color and size is kept the same).
Sometimes they quarrel: One says “don’t turn my circles into squares” while the other one replies, “don’t you dare turn my squares into circles.” But other times they are friends because they can undo each other’s mistakes.
Here is one where I gave the students the first function and they had to come up with and tell me what to draw for the inverse:
And finally, a pair of inverse functions that the students came up with completely on their own:
I loved it! We talked a bit about what one would need to do to turn bad candy into healthy candy (remove all the chemicals, extra sugar, and artificial colors) and vice versa. I asked the students why we’d want to have a machine that turns healthy candy into bad candy and they said that bad candy is more yummy :-(.