This past week, my Algebra 1 students started Unit 3 which is an introduction to all-things Functions. Unit 4 is all about linear functions and graphing. So, Unit 3 is about how to represent relations, how to determine if a relation is a function, how to find the domain and range of a function from a table or a graph, and how to evaluate functions. It's a nice change of pace from the weeks and weeks we've spent solving equations and word problems galore.
I ended up spending an entire 52 minute class period on representing relations. This frustrated me because I thought it would only be half a class period. But, you know how those things go sometimes... The next day, I introduced students to the definition of a function. We made a few examples and non-examples in class together. Now, normally when I would teach this lesson, my next activity would be a card sort where students sorted relations in to functions and not functions. In the past, this has always been super frustrating because too many kids just sit there and say they don't know how to tell if something is a function or not. So, I decided to put the card sort off until the next day and find a practice activity to do to finish out the class period.
Five minutes before class started, I still wasn't sure what this practice activity was going to be. I wasn't super worried because I had a fall back option - mini dry erase board practice. But, I still hoped I'd think of something more exciting. At the last minute, I thought back to an activity I had done as a first year teacher - a solving equations review auction. I decided I could easily tweak this and make it into a function auction. Various relations would be put up for auction. Students would be placed in teams whose goal was to buy as many functions as possible at the auction.
I quickly threw together some auction paddles using rulers, colored copy paper, and a stapler. It just makes the bidding so much more fun! :)
And, for an "auction catalog," I printed of a worksheet from the internet. You could very easily make your own, but I like to do things at the last minute. I liked this worksheet because it had tables, ordered pairs, graphs, and mapping diagrams.
Since my desks are already arranged in groups of four, I made these into the groups for this competition. I explained that there would be an auction, and each team would be given $1,000. The team that purchased the most functions with their $1,000 would win candy.
I asked how many students had been to an auction before, and most had. I asked them if they knew what an auction catalog was. They didn't, and several claimed cattle auctions don't have those.
I passed out the "auction catalog" to each group, and I purposefully gave each group only one copy of the catalog so they would have to work together. Then, I gave them a few minutes to look over the "catalog" and decide on which lots they would be bidding on. It was so fun to walk around the room and watch the kids justifying their reasoning to each other as they discussed which relations they wanted to purchase. I think I got a lot more engagement out of my students by structuring the activity in this way than if I had just put the problems up one-by-one on the SMART Board.
After running the auction with my first Algebra 1 class of the day, I decided the activity needed a bit more structure to make the auction run smoothly and efficiently. I instituted a minimum opening bid of $50. And, I made it so each bid had to raise the previous bid by at least $20. This made things run much better for the rest of the day.
Before running this activity, I intentionally did not introduce my students to the vertical line test for determining if a graph is a function. It was fun to see several groups come up with the test on their own just based on the definition of a function having exactly one output for every input.
In two of the class periods where I ran this function auction, two groups had purchased the same amount of functions. Therefore, it's probably important to come up with a rule for how to break ties. I like to declare the group with the most money left as the winner.
There was the fun-to-watch auction drama of groups not paying attention to what was being auctioned and bidding because they thought we were on a different problem, one member of the group raising the bid way higher than the other groupmates thought they should go, and the smug looks of the members of one group when they realize they are going to get the function for the opening bid of $50 because all of the other groups think it isn't a function. Another favorite - a room silent enough to hear crickets when you ask for opening bids for a relation that isn't a function. :D The kids came in the next day begging to have another auction. That's what I call a successful, low-prep, high engagement activity!