Auctions can be a fun and engaging activity in math class. The first auction I ever tried with a class was a unique bid auction that I learned about from Dan Meyer. I called it a "Lone Wolf" auction after seeing a discussion about this type of auction from Shawn Cornally. Students really enjoyed it and it generated some great discussions about strategies. We collected some data and were able to look at some displays to analyze the game. I haven't used many auctions as part of a mathematics activity. I was always concerned that too much time would be taken up by the logistics of the auction and there would not be enough time devoted to mathematical analysis. I learned some strategies for focusing on mathematical reasoning by reading how other teachers have facilitated auctions to make engaging math activities. Here are a few below: Function AuctionSarah Carter created a function auction activity for students to deepen their understanding of what makes a relation a function. Students bid on lots containing a variety of relations... some functions and some not. The team with the most functions at the end of the auction wins. Students work as a team to try to identify which lots contain the most functions and what a reasonable price for each lot might be given their starting funds. Sarah found this to be more engaging than a traditional function/not-function worksheet. The activity generates a lot of student conversation and discussion about functions. Dice AuctionNat Banting created a dice auction activity to get students thinking about the probabilities of outcomes when rolling two dice (this activity was won the 2020 Rosenthal Prize). In his description of the activity, Nat makes sure to include plenty of time for student teams to discuss their strategy and to try to assign a reasonable price to each event. He also builds in some reflection questions for students to answer at the end of the activity. This activity reminds me somewhat of the Borel Dice board game. Definite Integral AuctionI decided that an auction might be an engaging way for students to practice evaluating definite integrals in calculus class and so I created a definite integral auction activity. I incorporated some of the ideas from both Sarah's and Nat's auction activities. My auction is described below. As in Sarah's activity, I included time for students to talk and strategize by starting with five minutes to review the "auction catalogue". This page shows all the values that will be auctioned. As in Nat's auction, I scheduled in time at the halfway point for students to assess their situation and review the remaining lots. This gives students time to calculate their current integral and determine how they might increase its value even further. I also included some of Nat's reflection questions at the end to consolidate the activity. I got some additional ideas from Lola Morales (@lolamenting) when she posted on Twitter how she was going to use this activity in her classroom. If you have any tips or suggestions about auctions in math class, I'd love to hear about how you facilitate these types of activities. EL
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