On the surface it seemed like a great way to explore composition of functions until I realized...STEPS 2 & 3 ARE NOT FUNCTIONS!
After a few deep breaths I concluded that it didn't really matter. Truly, who really cares if anything is a function. The refinement from relation to function seems like something we do for mathematical convenience.
Step 1: Putting money on the card.
Prompt: Name the domain, range, and rule of assignment.
Pretty cool conversation about piecewise functions here. Also, the range is anything but trivial. I divided the class into two groups: half assumed they had the cards already. The other half assumed they needed to buy the card.
Please excuse any clumsy notation.
Step 2: Play games and win points.
We explored the games we all played by watching a few videos we took and looking at the pictures we all contributed to our lensmob album. BTW, thanks to Frank Noschese for the great lensmob suggestion!
Prompt: Pick a game and name the domain, range, and rule of assignment.
The only actual functions were from those games that did not distribute tickets.
Because you pay a flat fee and you can get a variable amount of tickets, it complicated my original idea about a explicit conversation about function composition. It is possible, however, that the conceptual gains were greater because they were not functions.
There were a couple of really interesting games. Take, for example, what we called "Ball Drop."
The fact that you can get bonus plays makes the range very tricky to figure out! (Or maybe not? Think about it.)
Step 3: Turn tickets in for prizes.
The nice thing about this step is that the range no longer includes numbers.
Not much to this part; the heavy lifting has already been done.
All-in-all, it was a fun lesson with the potential to increase students' conceptual understanding of relations and functions. I was very happy with how it turned out, and will do it again!