A few weeks ago, we had a lesson on one of my favorite topics to have little kids play around with – functions! When covering this topic with little ones, a very important first step is to create a cool function machine:

(Last year we made one by putting two chairs back to back and covering them with a blanket – while not as cool looking, it was quite functional, other than the blanket occasionally falling off.)

“Play” proceeded as follows. One person got inside the machine and was the operator. He/She then came up with a rule that everyone else had to guess experimentally, by putting in various inputs into the machine and receiving/recording the outputs. With a few exceptions, our functions all dealt with numbers. With the youngest group (4-5 yo), we used craft sticks for input/output, and with the older groups (6-10 yo) we had them write numbers on small pieces of paper.

The inputs and outputs were recorded on the board until someone guessed the rule. Most kids, when playing the role of the operator, wanted to make up rules that involved addition. However, we encouraged/helped them come up with more exciting ones. This is what the board looked like after a few of the more involved ones. Can you figure them all out?

The boy (6 yo) who came up with the divide by 2 function in the first picture did a great job of illustrating the concept of domain. When someone tried to put in an odd number (amazingly the first few were all even) a voice came from the machine declaring, “Only even numbers allowed.” When a 9 yo from a different group wanted to come up with the same function, I helped him widen the domain by modifying what was done to the odd numbers (last picture).

As I already mentioned, many kids came up with functions that involved addition, but I was surprised that only one kid tried doing subtraction (and that one didn’t go too well). His function was minus 1, but unfortunately the very first input he got was 0. He wasn’t sure what to do with this, so he decided to switch to a function that returned random answers. When we caught on and told him that he had to have a consistent rule that others could guess, we ended up with one crying kid. Any advice on the best way to handle those type of situations?

Overall though, the kids really got into the activity. I wasn’t surprised that everyone enjoyed being the machine operator (among other things, it certainly made them feel important), but it was nice to see that they were equally engaged in the “guessing” part. I loved hearing exclamations such as “It’s impossible!”, “What??”, “No way!”. And even “This is hard!” showed that they were thinking.

Next time we have a lesson on this topic I’d like to discuss inverses with them (had two great discussions with Katie on the subject a little while back, here and here) as well as compositions of functions. Other suggestions?