We talked about pi earlier this week in geometry, and we used Andrew Stadel’s water bottle question to start.
I’m not one to pull of the wager that Andrew used (unfortunately, my students will agree that I am a bit too serious for that), but we still had an interesting conversation.
Compare the circumference and height of the water bottle.
Here’s what they estimated by themselves.
Then they faced left if they thought height > circumference, straight if =, and right if height < circumference. (I saw Andrew lead this at CMC-South year before last … I certainly didn’t think of it myself.) They found someone who agreed with their answer, and practiced I can construct a viable argument and critique the reasoning of others.
Next they found a second person who agreed, and practiced I can construct a viable argument and critique the reasoning of others again. (By this time, we decided it was easier to raise 1, 2, or 3 fingers based on answer choice rather than turn a certain direction as it was a challenge for some to see someone turned the same direction.) Finally, they found someone who disagreed, and practiced I can construct a viable argument and critique the reasoning of others.
I sent the poll again.
It didn’t change much.
So without discussion, I sent a poll with a bit more context … a cylindrical can holding 3 tennis balls. Would the can of tennis balls help them reason abstractly and quantitatively?
Here’s what they thought by themselves.
And here’s what they thought after talking with someone else.
The clock was ticking. I still wanted us to talk about pi. I asked someone who correctly answered to share her thinking with the rest of the class to convince them. And we used string to show that the water bottle circumference was, in fact, longer than its height.
I intended to follow up with this Quick Poll. But I was in a hurry and forgot. Maybe next year.
You can find more number sense ideas from Andrew here.
I’ll look forward to hearing about how they play out in your classroom, as the journey continues …