Wednesday, August 17, 2016
One time in math class…(when I was a student…)
My favorite lesson as a student was a calculus lesson. We had just learned about how to minimize the surface area of a cylinder given a constant volume. Our teacher asked each us to choose any product, packaged in a cylindrical container that was not in the optimized shape. We wrote a letter to the company (complete with calculus equations and sketches) explaining our concern and telling them about how they could save lots of money with a new package in the optimal shape. We had to show the letters to our teacher before sending them out. We were offered bonus points if we got a response from the company, so we were encouraged to write an influential letter.
Our teacher kept a record of each company that had been written to in the past so that the same companies would not be reused. The most fun part was when we received responses and shared the letters with the class.
My letter was to a lip gloss company and I encouraged them to switch to a pot instead of a tube. They sent a letter back thanking, me for my letter and with some coupons for a free product.
A classmate wrote to a company selling protein powder. They wrote back calling her a genius and sent her a one year supply of free product.
A soup company wrote back saying that the student had forgotten about the fact that their cans get stacked. Therefore, the tops and bottoms of the can need to be thicker to support the weight of stacking. They explained that their packaging was in fact optimized based on the thicker tops/bottoms.
A pineapple company replied telling the student that the shape of their packaging was determined by the shape of the pineapple rings. Since they could not change the shape of the rings, they could not change the diameter of the can.
It was a really cool activity. I've never taught this content, but I will certainly use this lesson if I ever have the chance :)