The Twelve Days of Statistics

A little late about this, but bookmark this one for next year!

Last year, I posted the Twelve Days of Algebra, which I got from ICTM several years ago. But my Stats students were a little hurt when I had to sing them the 12 Days of Algebra in Stats. So we fixed that right up.

My awesome resident took lyrics that some former students had worked on and refined them and now we have:

Behold, happy 10th day of Stats class!

[Lyrics by Miranda De Young, 2013]

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Probability for Babies

Ok, not babies, but not AP Stats students, which is what I’m usually rambling about.

I teach two sections of Algebra 1, and I like to use that last-day-before-Christmas for some fun with probability.

Once students end up in my AP Stats class, there’s a lot of fixing to do. They’re pretty sure they know probability. Its simple stuff really. Six blue marbles? 8 red? Done. Except that the “probability” they’ve had beaten into then (for how many years!) isn’t all that useful. Probability is not, be definition, neat and tidy. Its LONG-RUN. It’s THEORETICAL. It doesn’t tell you what “will” or “won’t” happen, it tells you what might happen.

I still remember talking to the nurse in college, and saying I wanted to stop taking the pill because it made me gain weight. I’d started it in March of my freshman year to help with my cramps and a few months later the improvement was minimal but I’d promptly gained 10 pounds. The nurse’s reply?

“This is a time in a lot of young women’s life when they gain weight.”

“What, March? I don’t think so.”

“Gaining weight on the pill is a myth. Only 2% of women actually do.”

Subtext: 2%= Impossible. I couldn’t actually gain weight because of the pill, because only 2% do, and 2% is close to 0, so no one does for real. She was totally serious. It did not occur to her that I could be in that 2% (I was. I ignored her, stopped taking, and the weight promptly disappeared.)

I want my students to explore situations like that, even if we can’t “answer” them.

Sure, I know some more sophisticated ways to calculate probability. But that doesn’t make simulating some halfway-there situations doesn’t have value too.

Here are some of the ways I’ve played with my kids, and awesome ones I’ve seen from others around the MTBoS.

  • Jackpot
  • Fire!
  • Roulette (get an iPad app, project it, and let them make bets, then simulate on the calculator)
  • Bumpy Flight: an excellent set up from Mathalicious. I’d have my students make a prediction, then simulate it using slips of paper, technology or whatever else they can come up with. Pooling our results is informative enough, and we can even make a recommendation at the end.
  • Greed: Everyone stand up. 5 loses, everything else gets points. Roll (let’s say…a 3) and tell they can keep their 3 points and sit down or they can risk it and keep standing–but as soon as you roll a 5 you lose it all. Play a couple rounds. See who won the most overall and what their strategy is.

Last year, we did Greed, Roulette and Jackpot, but I definitely want to throw Fire! in my rotation too. I love that these are fun, get kids thinking, and starting getting across the idea that the same probability doesn’t mean the same result.

Jackpot

I’ve talked some about Probability and I’m sharing a couple of simple ways to explore probability with your students. While you not be able to get exact answers, these are great ways to test out how probability really works, and whether what is “supposed” to happen actually does.

So you know Jackpot. It’s a Holiday classic on the Country station here, and super easy to simulate.

Listeners call in and the nth caller gets to guess how much is in the Jackpot. If you guess the exact amount, you win. Otherwise they tell you if you’re too high or low. There’s several times a day you can call in, and the idea is that listeners are keeping track at home.

Here’s how I run it in my class:

  • Everyone write down a number between 0 and 1000.
  • Choose someone to make a guess.
  • Say, “Sorry ____, thats too low/high” in your best cheesy gameshowhostvoice.
  • Get your Vanna White up to the board. All you actually need to know is how many guesses have been made, but its more fun to have them write the amount too (someone may even catch that it would be helpful to record if its too high or low, but I never point that one out).
  • Continue calling students for guesses.
  • Once you finally get it, have Vanna record the # guesses and winning total. Even the winner if you want.
  • Tell them all to write down a new guess, then repeat the above.
  • Hopefully by the next round they realize its totally pointless to write down an initial guess; they should be revising as they go.
  • Then split them into groups of 3-4, and show them how to use randint on their calculators.

There are a couple places you could go with this:

  • Have them go from 1000 to 10000 and see how many more guesses it will take
  • Make a class dotplot or other representation of how many guesses it took
  • Tell them you plan on doing this in an upcoming assembly but they can pay you off to get to guess at a certain time. Think about it on your own first, then talk it over with your partner. Discuss as a class why they picked that number of guesses. (Some kids will want to guess 5th to make sure they ALWAYS get a guess, others will want to go 10th because if it does get to them they feel they’re likely to get it.)
  • See if any groups can figure out how to make an optimal number of guesses.

This is pretty informal, but my kids love it and it gets them thinking about how the same situation doesn’t mean every detail is identical.

What are some fun ways you have to get kids thinking about probability?