Popcorn Picker

I was invited to run a 3 act task with a colleague’s class this morning. We did popcorn picker. Here’s act 1

Each page was 8.5×11 inches. One was made into a tube by joining the short sides. The other was made into a tube by joining the long sides. The question is: which one holds more popcorn, or are they the same?

Students worked at the boards in random groups of 3. Some struggled to engage in the task at first, but others gave it a solid effort right from the start.

The task involves calculating volume of a cylinder, but before that happens there’s some calculations needed to get the radius of each cylinder. A major misconception that I noticed today was that students thought that the radius was half of the circumference. When I brought over a paper and made a tube and gave a ruler to check, it was easy to see that we needed a different approach. Some made a breakthrough when we got the equation for circumference. Others needed a bit of prompting, but we got there eventually with most groups.

We had a good chat at the end, looking around the room, we saw where we could add some clarification to the work (some needed some arrows and a starting point indicator, some needed equations written, or titles and sub headings).

In the end, we know that if two cylinders have the same lateral surface it does not mean that the volume is the same.