How Many Ancestors Do You Have?

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:

  • Some students misinterpreted this — one student said a generation was a 100 years because that’s how old people live to!
  • Most reasoned about 25-30 years per generation. Many of them said 30 years was a good amount of time because it’s how old their parents were when they had them.
  • Just under half of them made comment on the fact that this was not a very good/accurate assumption because in “the olden days” women had children much younger.”
  • About a third of the students took into their own age (the fact that g = 0 is in its 15th year) into account, but many of them had rules that said things like their parents were born only 25 years ago, oops.
  • 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:

  • Some students are just trained to justify themselves constantly so they say things like, “My answers are very accurate because I used a calculator.” As if that is what makes things accurate!
  • Some students who calculated that they had more ancestors than people alive did not appear to notice this fact. Do they really critically look at their answers? Or are they just concerned with getting to a “right” answer?
  • One student said his model didn’t take into account cultural norms like taking multiple wives (I thought this was interesting) or child brides or that a generational length can vary tremendously around times of war
  • About 2/3 of the students said it’s impossible to be accurate without knowing the exact length of a generation, even though they felt they had a good model.
  • A few people said that their model didn’t take into account incest — the fact that at some point people must’ve been having offspring with people related to them.
  • One student who had about a third of the world related to him said that if this model was true for him and the other 7 billion people alive today, we all had to be related, and that not only that, if you go back far enough you’d be related to every person. He even had a nice diagram to illustrate this point.
  • 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.

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    About katenerdypoo

    Middle Years and Upper Grades math teacher in the Netherlands teaching both within the Dutch national curriculum and the IB MYP and DP.
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