The Area Problem

Last Friday, October 27, I tried a totally open-ended inquiry activity in Recitation which I called "The Area Problem". In the activity, students were given three identical "blobs" and told to estimate the area as best they could. But there were three rules:

1. Each group could only use objects that they had on their person, so group members had to pool their resources.

2. The only math they were allowed to use was numbers and basic operations: +, -, x, /.

3. They had to be able to state the area with some units of measurement.

Some common solutions were the iPhone dimension app, airpod cases, and pen caps. One group got really creative and imagined that the blob was deformed into a square. They attempted to come up with area based on the perimeter (which they measured using a headphone cable). One other creative group used cough drops, and another Altoids.

On the other hand, there were some students who had calculus in high school and immediately tried to use Riemann sums (through graph paper, a ruler, etc). These students were resistant to using any other estimation method because they felt Riemann Sums were "the right way" to do it. 

It was super interesting to see these different approaches, and overall, I think the activity was a success, especially for it being the day after their Unit 3 Test, which was mildly brain-frying, as the Calculus I Unit 3 Test tends to be. There just isn't a good way to make a short test on those concepts, because so many of them are important applications.