Now that my school finally got a balance, I was able to perform my lab on measuring the mass of a penny, without measuring a single one.
The idea of the lab was to reflect the way in which Millikan was able to determine the mass of an electron by measuring the electromagnetic force required to levitate an oil drop. The force would be proportional to the number of electrons and the charge of each one.
However, both of those were unknowns, making the entire problem somewhat challenging.
The genius of Millikan's solution was that he made the wild and crazy assumption that there was some fundamental charge that was indivisible. In other words, that electrons had a fixed charge. By taking lots of measurements and dividing by integer numbers, it would be possible to find a common number between them all.
It occurred to me this principle would work for anything with a fundamental quantity and an unknown number. Weight (mass) was a convenient way to go.
So I sealed up pennies in 7 different envelopes, had students weigh an empty envelope, subtract that, and determine the mass of the unknown number of pennies in each one.
From there, the easy way would have been to toss the raw data in excel and have it to all the division.
Sadly, the computer lab was taken. Which meant they had to do all the math by hand. Poor kids.
A few of them figured out that I'd given them a hint by telling them that each envelope had somewhere between about 3 and 20 pennies (in reality, the envelope with the least had 4 and the most was 17). From this, they deduced that they didn't have to divide the lightest of the envelopes all the way up to 20 since they would only contain a few pennies.
This saved the smarter students a considerable amount of effort.
Ultimately every group was able to find a fundamental number common to every envelope. The range in that number varied by about .1 grams which is more than I expected, but I made absolutely no effort to find pennies that were all equally free of dirt and uncorroded (although I did find only pennies from the last 25 years as to ensure the same ratio of copper and zinc which would significantly change the weight). This was intentional because I wanted to better simulate real data and give them the opportunity to consider that a significant source of error in their discussion. Sadly, only one of the five groups (two students per group) figured that out.
The rest of the groups seemed pretty clueless on what I meant by "discuss significant sources of error." Many of them put things like, "Follow the instructions" and "Round correctly".
Overall this lab went fantastically well considering it was something I'd came up with out of the blue. It needs some revision. After watching this video, I feel like I should challenge the students to try to develop the methodology more themselves (I made it pretty cookie cutter), but for my students, it would likely be little more than an exercise in frustration.
Additionally, I think there should be a way to graphically represent the data that might help it be more easily approachable, but I haven't worked it out yet.