Math = Love: Linear Auction

## Thursday, November 10, 2016

### Linear Auction

Today's Algebra 1 lesson left me with an overwhelming feeling of teacher bliss.  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.

We began class by completing a Frayer Model about the term "linear function."  After writing the definition and characteristics, the class worked together to make examples and non-examples.  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.

I passed out the activity sheet face down to each group.  I announced that I had set a timer for five minutes.  When the timer went off, the 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.

So, what was this magical activity that students were so excited to see?

It was a "Linear Auction."

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 that 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.

The idea of adapting this function auction idea to being a linear auction was stolen from someone, but I don't remember who.  After blogging/tweeting about my function auction, I seem to remember someone talking about adapting it for linear vs. non-linear, but I can't remember who it was.  And, I can't find the blog comment or tweet.  If it was you, please leave a comment, and I'll give you proper credit!

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.  Here are the functions I chose:

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 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.

I've uploaded the file for this activity here.