## Thursday, March 20, 2014

MARCH MADNESS - to Teach Mathematics

My knowledge of basketball goes about as far as my one year on the 6th grade basketball team.  But, what I lack in basketball knowledge I hope I can make up with my knowledge of mathematics.  When I filled out my bracket this year (only to please my overly competitive family) I wanted to use mathematics to help me win the coveted prize, a gift card to my dad's favorite restaurant (you can guess who picked out the prize).  I have two purposes to this post.  First, I want to tell you how I used mathematics to fill out my bracket.   Second, I will give some ideas on how to use march madness in your classroom.

Math and my bracket:
The first thing to know is that there are MANY options for the march madness and the chances of
guessing a totally perfect bracket is pretty much ZERO.

For the first round there are 2^32 ways of guessing, that would be
4,292,967,296.  This is because there are 32 games and 2 possible outcomes for each game.  Yup, 4 billion ways for the first round to turn out.  The second is less, but still 2^16 is 65,536.  Continuing on, there are 2^8 for the third round, 2^4 for the fourth round, 2^2 for the fifth round, and finally 2 ways for the final round to turn out.

We multiply these numbers together to get the total number of ways the tournament could turn out and we get....a number too big to fit on my calculator.

## 9.22 x 10^18

So based on WikiAnswers I found the length from the earth to the moon at it's farthest point from the earth.  From this, I discovered that 9.22 x 10^18 paperclips would make it to the moon and back 363,755,010 times.

That's why my bracket already isn't perfect, as you can tell below.

Asking your students what the probability of having the perfect bracket is could be a great way to get the real world into your classroom.

You can also ask them to find out how I came up 363,755,010 times to the moon and back.  This is a great way to look at and explore conversion lengths.

To fill out my bracket I decided to use statistics from the past to try to predict the future.  I found statistics on this website:

There is more than one way to apply these statistics.  You could just go by percentages and have the team win who has the higher percentage.  I decided where there was a 70% winning rate for one seed against another to pick about 3/4 of these teams to win and 1/4 of them to loose.  This wouldn't be the statistically perfect way to pick, but I wanted to do something a little different.

Next, I followed these statistics from the same website as above,

• "Only once (4% of the time) has all four #1 seeds have made it to the Final Four.
• Three times (12% of the time) no #1 seeds have made it to the Final Four.
• 14 times (52% of the time) a #1 seed has won the entire tournament.
• The lowest seed to win the tournament is a #8 seed.
• The lowest seed to make it to the Final Four is a #11 seed."
I checked my bracket to see if it followed these statistics too.  Essentially this means that I made all the number 9 seeds win the first round.

Finally, I used these to help pick my final four and championship game.  I used the winning percentages to finalize who would win in the final four.