Popcorn!

This question was inspired by the popcorn picker 3 act task. I showed act 1 yesterday and asked the class to think about which holds the most popcorn, an 8.5”x11” paper made into a tube in portrait orientation (we called this hotdog) or in landscape orientation (we called this hamburger).

The students asked if we’d have popcorn the next day…so I agreed.

Today my popcorn popper was in full gear as the students worked through the task.

Some decided to work in cm and others in inches. It was great to see students flock to the formula sheets and use their skills with algebra and equation solving to isolate and solve for different variables. They knew how to calculate the radius when given the circumference.

They knew to calculate the volume, and did a great job communicating their work and checking it over.

To begin with we had people in 3 distinct camps: the tubes will hold the same amount, the tall one will hold more, the short one will hold more.

In the end, we all agreed that the short tube would hold more based on the math. It was time to test it out.

We added popcorn to the tubes. Then dumped them out and counted. There were 50 more pieces in the shorter tube.

The reason this works is that the radius is really important. The radius is squared. Squaring a bigger number makes it grow a lot, so this has a big impact on the volume. Height in the volume calculation is not squared, so an increase in height does not cause as big of an increase in volume.