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

*Mathsemantics*, which book hinges on the observation that even quite handy number-wonks go all to pieces when the problem is embedded in a sentence and/or you have to define your units and/or you have to have an order-of-magnitude clue about what the answer should be.

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 10

^{1}. The majority of the students plonked for 4.257 * 10

^{8}. On the assumption that mm

*are essentially the same as*m. A minority view had 4.257 * 10

^{5 }as the answer; under the mistaken impression that if

1mm is the 1/1000th part of 1m so

1

**.m is 1000x the size of 1**

__cu__**.mm; when in reality it is 1000 x 1000 x 1000 times bigger.**

__cu__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.

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