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Class Openers

Class Opener – Day 8 – 9/11 Memoial

Can it really be 13 years since the Twin Towers were attacked?  I clearly recall my old classroom, where a teacher across the hall told me I needed to turn on CNN.  Now the students in front of me today have little recollection of that day: they were 1 or 2 years old.  But they are all familiar with the day’s events, and I hope today’s opener brings some math context to this awful day.

I shared my post on Meaningful Adjacencies, the method used to arrange the names on the 9/11 Memorial, both online and during a “My Favorites” session at Twitter Math Camp this summer. And I am thrilled that many contacted me this week looking for resources and information.

In the activity, students are asked to list their 5 favorite TV shows on a card, then appraoch the board. Their task is to connect with classmates, and placee their card so that people with similar interests are as close as possible to each other. After they have completed the board, I show a video which demonstrates parallels between this activity and the arrangement of names on the WTC Memorial.

Class

One of my classes organized themselves into 3 “pods”, thinking that their interests were isolated. But by finding “Family Guy” as a shared interest, we can challenge small pods to come together and embrace similarities.

Board2

September 11 will never be an easy day, but having this activity to share with kids and think about the important task of memorializing those fallen makes it special.

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Class Openers

Class Opener – Day 7 – Probability Fail

Today’s opener comes from the site Math-Fail, which I use often for quick visuals and discussion starters.  This particular post is called Probability Fail:

Fail

There was quite a buzz in my room as students discussed whether this question was “real”, or one of my tricks (aside – they seem to be wise to my style by this point – always be skeptical!). But I have no reason to believe the task is anything but authentic, unfortunately. To see what they thought, I had the class answer the question and assessed their thoughts by a show of hands:

How many of you think the answer is A?

A few tentative hands rise.

How many of you think the answer is B?

More hands, yet still uneasiness.

How many of you think this question is just plain stupid?

Many, many hands….

So, what’s the problem with this question? I was thrilled that the first student to volunteer refered to “independence” – that coins don’t talk to or influence each other.  But what about those 8 heads? Is it possible that heads are “hot”, and more likely?  Or maybe tails is “due”.  Fun discussion today, which leads to a true story about a colleague I have shared many times with classes:

HOW TO LOSE $150 IN 4 MINUTES

Our school is about 90 minutes away from Atlantic City, and when our staff was younger we would take semi-regular bus trips to the gambling mecca for a night to let off steam and enjoy some beverages together.

RouletteThis story centers around a dubious strategy for betting on roulette; in particular, using the results board to your advantage.  Here is the strategy my colleague (a highly repected and intelligent social studies teacher) provided:

  • Stand in the center of the roulette table area. Often there are 4 or 5 tables together.
  • Observe the board results. Locate a table which has had a “run” of a particular color; 4 or more of the same color.
  • Place money on the other color to win, as it is “due”
  • If you lose, repeat your bet. When you win, you will have recouped all losses and made a profit

Realizing my colleague’s strategy was full of holes, I was interested to see the theory of “run” put to the test.  We located a table where there had been 5 red results in a row. Time to make a profit!

$10 on black….spin, spin, spin…..RED!

$20 on black…spin, spin, spin…..RED!

$40 on black….spin, spin, spin…..RED!

$80 on black…spin, spin, spin…..RED!

And then we left the casino floor…$150 poorer yet with a valuable probability lesson behind us!

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Class Openers

Class Opener – Day 6 – Foul Balls

In today’s opener, the Cleveland Indians provide the hook:

The article from ESPN.com provides the math:

The odds are one in a thousand just to catch one foul ball at any give game, according to ESPN Stats & Information. So what are the odds of one person catching four at a single game?

A cool one in a trillion, or simply a great day in Cleveland.

Pretty long odds. Almost suspiciously long.

Digging deeper, we can find out where ESPN came up with their trillion odds (linked from theblaze.com):

Trillion

After students looked over this arguement, I asked them how many of them had caught foul balls at a baseball game before.  Where did they sit?

I was behind home plate.

I was near third base.

I was in the upper level near first base.

PNC parkFew people from the top sections, the outfield (where clearly a foul ball would not be an issue), and some other goofy sections ever have a chance at a foul ball.  This led to general agreement that some sections are “ideal” for catching foul balls, while others are not so great.  It appears that our Cleveland friend was probably sitting in one of the “hot” sections. The cool site IdealSeat provides heat maps for a number of MLB stadiums, showing you where to sit in order to optimize our chances of catching a baseball. Based on this evidence, is it safe to assume that the probability of catching a ball at a game is 1/1000? We agreed it was probably something lower, based on the lucky man’s seat location.

This is also a great time to talk about the multiplicationrule for independent events, where we agreed that the rule was (for the most part) applied correctly, though with some uneasiness.

I’ve reached the point where anytime probability or odds are quoted on the TV news or in a newspaper or magazine, I immediately am skeptical of the claim. I hope I transfer this desire to dig deeper to my classes.