This whole fall has gotten completely away from me. So many great things have been going on and I’ve just been too swamped to write a thing. Forcing myself now, because I loved this project and must share!
Our unit “What’s in a Number?” contained a substantial bit of work on exponents, specifically rational exponents. One of my assessment criterion is Applying Math in Real World Contexts, which specifically asks students to model and critique their models, which is something I’ve been interested in for a while (h/t Frank Nochese).
So I came up with a modeling project based on this YouTube video from the always awesome Vsauce:
In the first part the students had to investigate how many ancestors, A they had g generations ago, with themselves as g = 0 (and the number of ancestors being 1 — themselves). The ultimate goal was to write a rule to find the number of ancestors they had in any given generation.
In part two the students had to decide how long a generation lasts (meaning, how long before a new generation starts) and use it to approximate the year of their great-great-great grandparents’ birth, writing a rule to find the birth year of any given generation. Here’s some interesting things that occurred here:
In part three they were asked to approximate the number of ancestors they had in different time periods, such as the year of the founding of the Netherlands (where we are) and around 1200 (the time period in which 0 was introduced to Europe). They had to put together their two models/rules to calculate this, which most did with no problems.
But then I gave them the estimated population of the world in 1200 and asked them to comment on their model with this in mind. I asked them what was good about the model, what was bad, how accurate was it, what could they conclude? Because if they’d done their calculations correctly, they should come up with the fact that they had more ancestors than people alive at that time period (or that more than half of the world was related to them).
Their answers are the really interesting stuff:
I liked this project because it takes something that’s a clear obvious rule A = 2^g and then muddies the water with estimating generation length. It gives the students a chance to actually create their own model and then hopefully analyze it. It’s clear they still need some work at this, but it’s a good start, I think.