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Linear Auction Activity

This linear auction activity was a fun way to practice linear vs non-linear functions in Algebra 1. You know an activity is a huge success when you end the day with an overwhelming feeling of teacher bliss.

linear auction activity

The goal for the day was to determine if a function is linear or non-linear based on a table or graph.  We had already started talking about different types of functions (linear, quadratic, and exponential) through the “Win Some Cash!” task that I blogged about earlier this week.  

We had also done quite a bit of graphing practice with linear, quadratic, exponential, and absolute value functions.

Linear Auction Activity

We began class by completing a Frayer Model about the term “linear function.”  After writing the definition and characteristics, the class worked together to create their own examples and non-examples of linear functions.  

Upon completion of this, I had the students move into groups of 2 or 3.  In my class of 24 students, I had them work in groups of 4.

Linear Auction Activity

I passed out the linear auction activity sheet face down to each group.  I announced that I had set a timer for five minutes.  

Students were warned that when the timer went off, the linear auction activity would begin. As soon as the students turned over their papers, there was instant excitement.  

After a few exclamations of joy, the groups quickly got to work without any prompting on my part.  The room was buzzing with conversations and collaboration.

My students knew exactly what to do when they got this activity sheet because this was actually our second auction of the year.  Our first auction was a “Function Auction” at the beginning of this unit.  

In the Function Auction, students had to compete to buy as many functions as possible.  The team that bought the most functions won.  If two teams ended up with the same number of functions, then the team with the most money left won.

When I first shared about the function auction on twitter, someone suggested that the same structure could be used to practice linear vs non-linear functions. I took the idea and ran with it!

I took my function auction template with 12 lots and reduced it to 9 lots for this auction.  I used the Snipping Tool to cut out pictures of graphs and tables from old state test questions that I found online.  

Each group was given $1000 to spend in the auction.  I printed monopoly money off the internet for this purpose.  One of my students gave me a bit of grief today over the fact that I had counterfeited monopoly money which is apparently means I have stooped lower than if I had just counterfeited actual money!  

I set the minimum opening bid at $50.  The minimum amount that students could raise the bid was $20.  I did this because I gave them their $1000 to spend in 20s/50s/100s.  

If you didn’t want to deal with 20s, you could make them raise the bid by at least $50 instead.

As we were doing this linear auction activity today, I thought of an idea to make these auctions go even smoother in the future.

In the past, there has been some debate about which group ended up with the most functions/linear functions (depending on the auction).  

Since this is a competition, students are not always the most honest about how many they won!  

In the future, I will make laminated cards that say things like “Function,” “Not a Function,” “Linear,” or “Non-Linear.” Then, when a group buys a lot, they will get a card reflecting what they purchased.  

I think it will be much easier to determine the winner at the end of the game.

What I love most about this auction style activity is that it encourages collaboration and conversation throughout.  As each lot is auctioned off, we discuss it to determine if the group bought what they thought they were buying.  

Students can take what they learn from each of these “reveals” to decide if they will bid on the next lot.  Group members must discuss what they are thinking with their teammates in order to make decisions.

More Activities for Teaching Linear vs Non-Linear Functions


Wednesday 24th of October 2018

I loved this activity last year and so did my students!!! We've been turning everything we can into an auction.

parallel slopes or not perpendicular slopes or not proportional or not Congruent Angles for parallel lines cut by transversals Continuous vs. discrete Polynomial or Not Arithmetic Sequence or not Geometric Sequence

And they still love it....I don't do it every time but they always want to. They came up with half of them.


Friday 12th of January 2018

I really like this idea. I might use it next week when we start our discussion on linear vs non linear!


Friday 8th of December 2017

Same here...sounds really fun, but don't understand the dynamics. Thank you.

Susan Hewett

Sunday 13th of November 2016

I am confused about teh actual auction. Could you post more info? I am getting ready to start my functions unit and like the idea.


Friday 11th of November 2016

This sounds fun, but I'm still a little confused. Next time you do an auction could you maybe take a video of it?

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