At The Institute, I teach a weird and wonderful set of subjects, few of which are what I was trained to do. That's what makes the job so interesting although it was a teeny bit stressful when I started work three years ago: being 2 weeks or even 2 days ahead of the students in mastering the syllabus. I've had two sections of 1st Year QM
In a metric world, one of the weirder units of measurement is a bale of 4-inch solids, which consists of 44 (?!) concrete blocks 100mm x 215mm x 450mm. Why 44? It's not because the molecular weight of carbon-dioxide is 44? And to point out that I get 44 flapjacks out of a swissroll tin is to suggest that these popular cookies are like door-stops. No, the answer is apparently that, because the density of concrete is about 2.35g/cu.cm, then 44 blocks weighs about 1 metric ton: it's convenient for loading trucks.
So I thought, I'd pop a question in tne QM exam, for the boys, like:
Q. What is the volume of 44 (100mm x 215mm x 450mm) concrete blocks in scientific notation and SI units [cu.m]? A. 0.426 cu.m. or 4.26 X 10-1
Only one student got it right, having converted it, correctly, to 0.1m x 0.215m x 0.45m x 44. Another was wrong wrong-almost-right at 4.257 X 101. The majority of the students plonked for 4.257 * 108. On the assumption that mm are essentially the same as m. A minority view had 4.257 * 105 as the answer; under the mistaken impression that if
1mm is the 1/1000th part of 1m so
1cu.m is 1000x the size of 1cu.mm; when in reality it is 1000 x 1000 x 1000 times bigger.
Whatever about the maths, the thing that distresses me is that 425,000,000 cu.m. is about the volume of the entire domestic housing stock of the Republic of Ireland ! How could you write that down as an answer for the volume of half-a-hundred blocks; which wouldn't even make a garden shed large enough to shelter a lawn-mower. What to do? Throw the kids out of the classroom! Stop them doing pages of Victorian sum-copy exercises and make them measure timber and mix concrete and order up enough plywood to make a play-house in the garden. They'll soon get the measurements right if the first version of their play-house hasn't sufficient plywood for the roof. You can't invite your dolls to tea if the sandwiches get all wet from the rain.