I was recently asked to give a math lesson to a group of 7th graders, which I don’t normally do, on the topic of rates, which, again, I don’t normally do. But I was really excited by the prospect, because I’d noticed something weird at my local grocery store, namely the price of pine nuts (in Dutch “pijnboom pitten”).
I showed the students the three options for buying pine nuts at the main Dutch supermarket, Albert Heijn, and simultaneously highlighted and obscured important information for them:
Then I asked them the following three questions for them to work out in groups:
- Which of the three packages would you advise me to buy. Justify your answer (and buy justify I mean give a valid reason with some calculations to back up that reason).
- I believe your advice is good, but I choose to buy a different package anyway. Why might I do that?
- Why do you think that Albert Heijn has different pricing for these three packages?
I gave them ten minutes to work on it. Half of the groups had a good sense of where they should start and quickly came to the correct answer. Other groups didn’t have a good sense of where to start, so I asked scaffolding questions like “what makes something a better deal? How can you quickly tell if the medium is a better deal than the small?” and “what important information is given on the price tag? What do you think I covered up?”
You end up with the sort of surprising answer that the medium package is the best deal, even though one assumes (or maybe 7th graders don’t yet have that assumption) that buying in bulk results in a better deal.
So the 3rd, non-math question became the most interesting. The students suggested that Albert Heijn had done market research on the most common amount of pine nuts people want to buy and priced accordingly. They also suggested that the plastic of the medium package, which looked flimsy, cost less than the nice, sturdy looking plastic box that the large package came in. They also suggested that maybe people like the resealable box, so that’s why it’s more expensive.
If I’d had longer, we could’ve delved into this idea more, that the price of something is not just the raw price of the goods itself but the materials used, the convenience of it, etc. I think these sort of discussions are important to have in today’s society and that in math class we should be grappling with the sort of questions of the real cost of goods and services. I could imagine a much larger unit about, among other things, environmental justice. Do you have any other good non-math questions that you’ve asked in math class?