# To Accumulate a Rate — Integrate!

Teaching High School Mathematics

# Linear Graphing Auction

I’ve created a linear graphing activity that was super fun. The kids enjoyed it and I had a great time too.

Here is the pdf of the worksheet: graphingauction

I just did the activity today, 11/2/2016, and here is how it went:

Students were in teams of 3-4. The key is how many teams there are for the equations listed. I had 7 teams in my classes and none of the team were able to purchase lines so that they had a point with three lines through it. If I want that to happen, then I need to create some lines that go through three points but don’t go through many other points to keep their price down. Or create a smaller number of groups.

I gave every student a paper and allowed them to investigate the equations for 20 minutes prior to the auction.

Each group was allowed \$100 to spend on equations during the auction.
If they don’t win an equation they really want, they can purchase it for \$10 more than the winning bid price. This worked well for teams that made it to the end and still had money.

The teams then graphed their lines on a team paper I handed out and they added up their totals.

5th Period Totals: 70,75,75,85,85,85,100

6th Period Totals: 50, 60, 80, 105, 120, 140, 155

Ultimately this is about practicing graphing linear equations, but it was interesting to watch their bidding strategies as well. In both classes a group spent way too much on a good equation early. It made me think that I should put the better equations last, like a real auction. One group spent \$100 on one equation and was done. One group waited until the last 3 equations to try to get them for cheap, but didn’t realize that some other groups still had money and then couldn’t get the equations they wanted.

The class wants to do this again… I’m thinking that we could do it where they provide any 5 equations they want with no auction, or do the auction and they get to add an equation of their own at the end for no cost. Another option would be to do it again with quadratics.

Graphing Auctions!!! I’m loving it!

### 3 comments on “Linear Graphing Auction”

1. Phillip HH
October 29, 2016

I love the creativity. As I process what you have suggested, I have some questions: 1) are the lines and/or points already created or something the students are involved in creating? 2) to earn pts, do they have to get their purchased line to go through the pt or near enough to it? 3) are they using digital tools after they purchase lines or doing things by hand?

• kaleb40
October 29, 2016

1. I love the idea of students creating their own equations. I think this would possibly take away from the auction idea, not that an auction is necessary, but maybe a separate follow up activity could have students creating the equations. What if students get to have 6 equations and they can create them all?

2. They have to go right through the point. None of the given lines even graze a point they don’t go through.

3. I want them to graph everything by hand.

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This entry was posted on October 29, 2016 by in Algebra, problem solving and tagged , , , , , , .