May The Best Team Win?

Driving home today, there was an interesting discussion on sports-talk radio about championship teams in various sports. The genesis of the discussion was the lingering anger/disappointment/jealousy we Phillies fans harbor over the Saint Louis Cardinals winning the World Series this year (the stereotype is true….we are generally angry people). Despite having the best regular-season record, and the best record in team history, the Phillies were out in the first round.

Part of the discussion centered around the wild-card in baseball, and how the introduction of the wild-card (and more next year), makes it far more difficult for the “best” team to win. This stands in contrast to the NBA, where the best team is not often upset early, and the NFL, where the byes give a large advantage to top teams.

So, what does the data suggest? Coming home, I looked up the champions for the past 25 years in all 4 major (yes, hockey counts….so shut it!) sports. I also did a quick check and found the team’s regular season ranks, according to wins (or points, in hockey). Here’s what we get:


Some interesting trends here. The host on my local sports-radio channel was making a compelling argument this it is easier to win if you are a top team in the NBA, and the numbers bear that out.  Also, note how poorly the team with the best regular-season record in major league baseball fares.

Math-wise, what can we do with this data? The chart has some nice talking points for conditional probability:

  • What is the probability you win the NBA title, give that you are the top seed?
  • What is the probability you were the top team, given that you won the World Series?
  • What is the probability you were the #2-4 seed, if you won the Stanley Cup?

What else can you do with this?


Making Friends and Breaking Pringles, the Exciting Conclusion!

Yesterday was the day of reckoning for the Pringles!  Donna’s class and the kids I am working with met on Skype, awash in anticipation over the status of the mailed Pringles.  I started the proceedings by opening the two shaky-looking boxes.  The first looked quite sad and crushed, and peeling back the cardboard revealed just some rolled up bubble-wrap (bubble warp will become a theme in this blog!)….but…..can you believe it….the chip survived intact, and was quite delicious.  In the second box, the was a different outcome, as at least 20 pieces of chip were spread out all over the desk….


Next to be opened was the box my kids made. Encased in floral foam with cotton balls inside, the chip did not quite survive, with 2 main pieces. A disappointment, yes. But something to learn from for next time.

The final box to be opened was the one from out New Jersey-Giants-Yankees-trash-talking friends. Opening this box was quite a chore, with lots of masking tape, a styrafoam cup for a holder, and even a surprise pencil included for support. How did it fare? (thanks to Donna for the video coverage)

Another intact chip!

In the end, Donna’s class are the inter-galactic Pringles Chip winners, at least for one day.

Epliogue: the day after the skype chat, a 4th box from New Jersey arrived late. It too contained an intact chip, using plastic cups to serve as a Pringles cocoon. Nice job by Donn’a class.

Algebra Technology

What to do Before a Hurricaine

Perhaps the best part of my job as math coach is working with teachers of various grade levels on lessons; developing “hooks” for discussion and inquiry, and being invited into classroom to share exciting stuff.  It’s a neat feeling to have kids say hello in the hallway, and ask when I will be around to visit their class again.  This week, final exams are being held at out high school, which means that new courses begin next week.  This presents a great opportunity to challenge teachers to think differently about how they start off with their classes.  How can review of previous material be done in a way to both allow for a discussion of previously-covered concepts, but also set the table for a class culture of productive idea-sharing?

Dan Meyer’s blog, has been a great source of inspiration to me, and I shared his TED talk with my district’s secondary math staff at an inservice this year.  The talk led to an interesting discussion about the questions we ask in the classroom, and healthy debate on how we can re-think lines of questioning.  And while Dan is an advocate for all sorts of useful and productive classroom technology integration, what I appreciate most are his self-made videos and demonstrations.  One of the simplest, yet effective, videos shows a hexagonal tank being filled with water, then later emptied.  The video leads to the natural question “how long will it take for the tank to fill”, and leads to all sorts of nice math ideas like linear growth, prediction, and error.

Being a brave soul with decent, but hardly expert, tech skills, I set out to do a video on my own, in order to inspire my colleagues.  Sure, I could have just used Dan’s videos, but the “what the heck is he doing out there?” look from my neighbors is just too much to pass up.  Besaides, the “anyone can do this” factor is strong here.  Find neat stuff in your environment, and go with it.  So, with a jug from Wal-Mart, some cherry juice mix, a laptop, and my home camera (nothing too fancy), I set out in my backyard hours before hurricaine Irene.  I tried my best to emulate the best of Dan Meyer, but with my own flavor:

I first used this video as an ice-breaker in the in-service days before school, in July. Stopping the video a minute in, I asked math staff to predict how long it would take for the tank to empty, using the neat site to have teachers contribute answers via cell phone.  (To be honest, this worked well at our high school, but was problematic at our middle school, where wireless connection gremlins tripped me up).

So, how to use this as an opener for a course, perhaps Algebra II?  I found today that if the video is shown on a whiteboard, then drawing a vertical guideline on the side of the jug and placing tic marks can allow for some nice data collection as the water level decreases.  Importing the video into a SMART notebook could allow for a nice scale to be drawn on the jug.  Either I’d like to find a way to super-impose a line on the video, or I may go the low-tech route and place tape on the side of the jug and reshoot.

What directions can a discussion of this video take?

  • Independent vs Dependent variables (is the water level dependent on the time, or vice versa?)
  • Differentiating linear and non-linear models
  • Using technology to analyze data and develop regression models
  • Making predictions based on models

Any other thoughts or ideas?