## The Circumference of a Cylinder

25 Feb

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?

Apparently not.

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 …

### 6 responses to “The Circumference of a Cylinder”

1. February 25, 2016 at 5:18 pm

1 finger for height because the finger points up
2 fingers spread a bit for circum..use thumb and index as a crab pincher
3 = The other option

The tennis can…not all get this…on their own, but it is worth trying for every class every year. They will think about it for years to come, I hope.

I like that label A-F quick poll.

I like to use an empty toilet paper roll, then cut it.
Also, using an empty paper towel roll and marking/guessing where the equal point is a good assignment. Then string them up for a display.

Another idea is to take 2 8.5 by 11 inch pieces of paper. Roll one to make height = circum. Use the other to measure/wrap the circum to verify/create the height. Then tape to hold the form.

2. February 25, 2016 at 6:59 pm

What question type did you use to make that quick poll question?

• February 26, 2016 at 6:27 am

It’s the “label image” question type.

3. February 26, 2016 at 5:26 pm

SIllyness, but isn’t the can of tennis balls actually a little taller than 3 tennis balls stacked vertically because of that bubble on the bottom? It actually looks REALLY close to 3.14 tennis balls in height to me. Curious… I’ll have to measure when I get home.

4. March 13, 2016 at 2:57 pm

Hi Jennifer, thanks for the idea! Used it with 6th – 12th grade math teachers during PD last week. Very interesting results. Here is link to what we did (following your activity): https://drive.google.com/open?id=0B_dntyhD7AF3SDNtbGVsNDNvU0k, and here are poll results (using Polleverywhere.com) – https://drive.google.com/open?id=0B_dntyhD7AF3bnc2S3hlUnpDeUk