Story Based Math Problems and Proportional Reasoning

Last week in our math course, we saw presentations of three condensed lessons. The topics covered were finance, graph transformations, and calculating volumes. Although all were good, I was to focus on the “volumes” lesson for this post. Nam (the presenter) based his lesson on the film adaption of the book “Holes”, which is a very common presence in the junior school English class. For those who haven’t read it, Holes is a young adult novel about a boy named Stanley who is wrongly convicted of theft and sent to a sort of juvenile disciplinary camp where the inmates are forced to dig a hole every day out in the desert. The depth of the hole and the diameter must be equal to the length of the inmate’s shovel. Nam started the class with a clip from the movie in which Stanley accidently gets in trouble with another inmate for grabbing a shovel slightly shorter than the rest of them. The question Nam posed to the class is, “does it really matter if the shovel is a bit shorter”. He then had us try and figure out how much less dirt we would have to dig over the course of a year if we used the shorter shovel (it turned out to be about a month’s worth of holes). I liked this set up for a lesson because it starts with familiar territory. Practically everyone in the class had read Holes so when we worked on this problem, we already had a context in mind for the problem. I also liked that I was surprised by the answer, I didn’t expect the difference in volumes would be so significant. All in all, it showed me the effectiveness of using stories to engage students with a problem (as opposed to the more generic types of word problems we often encounter). If I had one thing to improve upon, it would be the organization of the problem. The problem was posed in feet and inches and we were made to convert everything to metric units. This made the problem a bit numbers heavy. Additionally, it was a bit ambiguous what was meant by “how fewer holes …” since we had two different volumes. This is nitpicky of course, and easy to fix. An alternate approach could be to do away with inches and metres altogether and use the standard shovel length as your unit length. For example, if the shorter shovel was 7/8 of the standard shovel, the smaller hole has (7/8)³ the volume of a standard hole. This greatly simplifies the calculation and may be a useful way of incorporating proportional reasoning.