In the fall of 2024, Citizen Math released updated versions of every lesson in our library, plus a few new ones! We know you may have already prepped an earlier version or planned a repeat of last year, so we're continuing to make these earlier versions available through Thursday December 5, 2024.

You can find the new lessons through the regular search, and we hope you love them as much as we do. You can read more about these updates in Our Community.

Click here for the updated version of this lesson!

How much should you bid in an auction? From Sotheby’s to eBay, auctions are a popular way to buy everything from paintings to baby clothes. Of course, the goal of an auction isn’t just to win the item; it’s to pay as little as possible for it.

In this lesson, students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.

- In an auction, a higher bid has a higher probability of winning (than does a lower one) but reduces your profit.
- An optimal bid can be thought of as the bid with the highest expected value.
- In a two-person bid, the optimal bid is approximately half the item’s value; as more people participate, the probability of any given bid winning decreases, so the optimal bid increases.

- Write and graph a quadratic equation to model a real-world situation
- Write and graph higher-order polynomial equations to describe a real-world situation
- Calculate and model expected value in a real-world context