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.
- 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.