The other day I read Carl Oliver’s post about the safe and the piggy bank. I was reminded of a lesson I did last year in my exponential unit after taking Chris Luzniak’s wonderful course on debate in math and science classrooms. I wanted to make the typical doubling penny problem more debatable. It actually only really required a small change.
a) Win $100,000 a month for 30 months, or
b) Win a penny the first month and have your total doubled every subsequent month, for 30 months.”
This seems like the same problem as the typical formulation, on the surface, but it’s not. The key difference is in the length of time. Usually, the time frame is over a month with daily payments. This is because the number 30 lends itself well to the problem. In that case is pretty unreasonable to not just wait for the full month to get more money by using the penny.
But now though the penny option gets you more money in the long run, you have to wait a really long time before you get anything of value. It takes two years just to get the same amount of money as option A gets you in one month. For some students, that’s just too long to wait. When you need money, you might gladly choose option one for more immediate relief, even if option B gets you more in the end. So it’s a nice debate and would you rather question.
James Cleveland-Tran
The Roots of the Equation 
Comments on: "The Lottery Choice" (4)
With the payout going over a longer period, there’s also a component of interest to consider. You could invest the money you get right away with the larger payment method and see how that affects the total in the end
The length of time is always interesting in these, but with the usual story of the rice and the chess board, that length of time gets way too crazy. Having it double for each of the squares of the chessboard would mean you would almost have to teach a separate lesson on number sense so that they can fathom how big that number really is.
…And thanks for reading!
I really like this — that problem is fun, but once kids see it once they tend to internalize it as “oh, ok, exponential is always the right answer” without having to go to deep into what an exponential function means. Here, at least some informal evaluation is necessary — big step up. Will definitely use this!