OK, maybe it isn’t from the student’s point of view, though I sort of doubt it. 1 million just seems like shorthand for ” a really big number”. Cue Dr Evil (“I will destroy the Earth unless you give me …. one million dollars!!!!”). I also had a guess of 66 billion as well, but from someone trying to show off in some way. You have to filter the serious attempts a bit.

It wasn’t a major point of the lesson, so I didn’t feel too bad about this censorship. Perhaps if you’d already built some sort of rapport with the class, you’d be able to do it without filtering out the silly stuff.

Anyway, after trying it on 6 classes of about 20 (yes, 6), I got 5 good averages (250,000-280,000) and one odd one (150,000). So wisdom of crowds works, most of the time. (with the caveat that I was filtering). Certainly worth a try, and the students were seriously impressed that the average guess was so close to the exact number.

You could also get the students to do the averaging, filter out the silly guesses, and so on. Maybe a discussion about the merits of mean and median?

One interesting approach I got from time to time was groups of two or three students who decided there HAD to be a simple formula for the number of pennies, and insisted on trying to find it. Unfortunately, these (self-selected) groups invariably did not know enough math to understand finite differences, and had difficulty even imposing the pyramid approximation on the problem. If I were a better teacher, or less overworked, I might have been able to guide them better (i.e. derail them faster from their flawed idea of how to tackle the problem); but I just find it interesting that the less prepared students were the ones trying to overreach – or perhaps shortcut the problem – the most.

Any suggestions about how to avoid or exploit such problems in future greatly appreciated. But I have to say that this lesson worked well almost all the time.

(context: I’m a university lecturer trying to run a remedial maths class for 120 students. While they are all reasonably smart, they haven’t all been well served by the math curriculum in the UK; and half of them haven’t done math since they were 15).

I’ve tried this a few times and it works incredibly well (after you delete the silly guesses like 1 million and above).

Why is one million silly?

In three attempts, I’ve had averages of 260,000 to 280,000. Once the students work out the true number of pennies, I always direct them to the whiteboard where I’ve written up the average. Never fails to impress (and never fails to impress me, too).

We used this three act problem in our science classroom last week. The class is for pre-service elementary education teachers. I used your three act method for showing how science processes and thought works. Overall it went well, there where some hangups on how to tackle the math. The main thing was that everyone was engaged as soon as they saw the picture.

Pre-algebra: Factoring.

Algebra 1: Finite differences

Geometry: Pyramid approximations, proportions

Algebra 2: finding the general formula with matrix equations

Pre-calc: Inductive proofs

Calc: Integration minus error methods for finding the formula