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March Madness Brackets ala Mathematics

My idea of a resource is broad...texts, events, videos,...even classroom-tested ideas! The latter descibes this week's resource.

D.E. (Seattle) recently sent me the following note, asking if I could somehow share it with others. In his words, it describes a "good algebra-trig/PC application." And, it is appropriate for this time of year---March Madness...Thus, it is a resource you can adapt and use next year.


A little math moment…
I’ve been given the job of setting up the computer spreadsheet to track our march madness competition (well, my principal’s competition). It’s a cheapie: $10 to enter, all $ given out as prizes, 1st, 2nd, and 3rd. I get free entry with my work. Completely bombing this year. What can you do, when you pick Vanderbilt, Temple, Missouri, and Florida State?

Quick background:

  1. You just pick 8 teams
  2. If they win, you get points:
    • 1, 2, 3, 4, 5, and 6 for each round
    • times their seed. For example: Kansas has won four games: 1 + 2 + 3 + 4 = 10 points, but they are a #2 seed, so they are worth 10 x 2 = 20 points
    • So the best team to pick (thus far) has been Louisville, who is worth 10 x 4 = 40 points. 2nd best team to pick was North Carolina State, who only won two games (1 + 2 = 3 points), but were an #11 seed, so they got people 33 points.
So I built a spreadsheet to track this. To help keep track of how others are doing, I wanted a process by which it would figure out who still had teams left. So, on the front page, the program lists the teams and figures out if they’re still in, by counting the number of games the team has won, then matching that to the # of rounds played (manually entered by the user). Unfortunately, our principal (a smart man in almost all respects) would forget to update the round, so people would have the wrong report for how many teams they had left. So, I figure, I need to automate this. I need the computer to figure out, based on the number of games played, what round it is.

So: here’s the real-world data to fit a function to: (X = # of games played and Y = # of rounds finished)

x324856606263
y123456

We want to fit a function to this data. What makes this problem good is that if kids look at the picture, then they’ll jump out with “exponential”…though it doesn’t work. Instead, the kids need to realize that each time the x’s go halfway to 64, the y’s go up 1. This means it’s logarithmic when comparing it to x = 64 (which is the vertical asymptote). So, it’s better if we compare the x’s distance to 64:

64-x32168421
y123456

Now, we can do logarithmic regression from here, but let’s figure it out. We want the function to go through (1, 0) to be a standard log graph, so let’s go with:

64-x32168421
y-6-5-4-3-2-10

And, if we flip the y’s:

64-x32168421
-y+6543210

So now we’re set: -y + 6 = log2(64-x) or y = 6 - log2(64-x).


Gems of Geometry is a gem itself.