I tried to use the German Tank Experiment multiple times. It was an epic fail the first time, because the students can Google the actual experiment and get the answer in, as my daughter would say, “point 31678” seconds.
So I modified it to a different number, after explaining the historical context (basically, I use this to show that the statisticians kicked the mathematicians butts — the mathematicians were WAY high). Then I asked the librarian how many Algebra I textbooks we have; they replaced the tanks.
Then I made that many little notecards so the kiddos could “capture” them. There were more than 1000 books, so that wasn’t fun.
After the “capture” of five books, the students were asked to estimate how many there actually were in the population.
They didn’t know where to start. At best, they took the mean of the five numbers. Not even the maximum. Their number sense has never been good…
So I modified it again. The kiddos aren’t the best with their TIs, so I could store a number in a letter without them finding it easily (I used 348 tanks, so 348 STO–>N). I chose a number close to, but not equal to, the actual German Tank Problem so my little Googlers would not go snooping.
I then asked them to have the TIs “capture” five: RANDINT (1,N,5).
Then I gave them the following:
They have to take their captured tanks and calculate around 12 statistics, then make their best guess about which statistic gives the best guess. One of the statistics is the actual statistic used, but they don’t know which one. They have to justify why that particular statistic makes the most sense.
Most of the time, they guess correctly. The ones that don’t usually have a pretty funky sample, as in “all low numbers”.
I don’t necessarily think this is a good/respectful use of the problem. I do show them the Wikipedia page with the proofs written out, mostly to make them see that Statistics is very, very mathy.
But I do think it’s a pretty good number sense activity.