Carpet Laying Calculation

On Fri, 18 Dec 2015 13:30:10 +0000, pamela wrote:

You'll struggle to find this kind of thing in print any more, thanks to dumbing down. The questions come from a 1950s Grammar School maths book. You can probably find plenty of similar books dirt cheap on Ebay and they are ***MILES*** better than anything published today. In fact for any subject where the science is settled, I now *always* go for something written in the 30s, 40s & 50s. The clarity and precision of language was *way* better back then, too.
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On 18:56 18 Dec 2015, Cursitor Doom wrote:

I couldn't agree with you more. What's the title of the book you have and I'll start by doing a search for that?
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On Fri, 18 Dec 2015 20:26:33 +0000, pamela wrote:

Your timing is impeccably bad. I just arrived with my family today for the holidays and the book is now 196 miles away. Still, if I set off for home at 9.30am in the morning travelling at 50mph... Seriously, remind me on or after the 4th Jan and I'll dig it out.
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On Friday, 18 December 2015 23:34:56 UTC, Cursitor Doom wrote:

That sounds more 60s. In the 1930s you'd probably average 20mph
NT
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In the 1930s my mother drove from London to Edinburgh non-stop. I doubt if she took 20 hours!
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On Sunday, 20 December 2015 16:37:37 UTC, charles wrote:

why? In the 1920s most 'roads' were mud tracks. In the 30s it would have been B roads much of the way, typically in a Ford T or often something much older. I would expect average of under 30, probably around 20.
NT
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On 23:32 18 Dec 2015, Cursitor Doom wrote:

Be good to know it's title so I can impose its delights and discipline on one of my young relatives.
I asked my 16 year old relative, who's a good but not brilliant at maths, to try the carpet laying problem. A WEEK later he is still trying to solve it. The algebra is entirely within his ability but he can't solve it. I don't have to tell you, it's the sort of thing taught to bright 13 or 14 year olds in the past and a single one of their exam papers may have had several questions like it.
The stuff they get in school today is wishy-washy and, if that wasn't bad enough, they are given endless hints to lead them through every step of the working out right up to the solution.
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Doesn't he understand about the notion of having N equations with N unknowns, and that you can in that situation easily calculate what each of the unknowns is? That you can use one equation to substitute for an unknown in all the others?
Perhaps they aren't taught to think these days. Perhaps he's not twigged that although there were two bits of information given about how the area alters if you change the room dimensions (giving you two equations), there is the unstated information that he should know anyway: that the area is the product of the length and width. That gives you the third equation.
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On 21/12/2015 10:41, Tim Streater wrote:

I would not expect the general case of n equations to be taught until A-Level. I doubt it ever was. The general case for n equations, if I recall correctly, requires them to be linear and linearly independent.
This problem was slightly difficult in that it was naturally non linear only becoming linear after algebraic manipulation.
The maths kids are taught today is much the same as it always was. The difference is the teaching targets specific formats of exam question which kids are specifically trained to answer. This is the best way to get kids to pass exams.
In the past most of us were taught the theory and were expected to be able to apply it to general cases. I'm not convinced our teachers couldn't have trained us to pass exams, just as they do today, it is just that they didn't. Hence the kids who passed the same types of exam back then tended to be generally cleverer with a better understanding.
The only thing I think that has changed is that teachers have become better at teaching stupid kids how to pass exams.
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On Mon, 21 Dec 2015 12:28:29 +0000, Nick wrote:

Yes, it magically raises exam standards and produces brighter pupils. A bit like re-labelling a sink school an "Academy" in fact.
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On 12:35 21 Dec 2015, Cursitor Doom wrote:

Modern exams are too often a collusion between bad teachers and poor pupils. Between them they skip all the boring stuff about actually learning a subject and, instead, the pupil is walked by the hand through the coursework which then gets overmarked. Thank goodness the GCSEs after this one will have less marks from coursework.
Pupils are taught to become experts in identifing which question gives how many marks. In my day we just learned a load of stuff in class for several years and towards the exams did some past papers. If we had gained an inkling of what the marking scheme was we would probably have felt that such inside knowledge was tantamout to cheating.
Today a wail of protest goes up if the predicted grade is not achieved and demands for re-marking soon follow.
I'd better stop there!
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On 10:41 21 Dec 2015, Tim Streater wrote:

No, he doesn't. To be fair, that sort of abstract generalisation of a result was only for the very brightest kids.

More worrying, he showed it to some friends who are doing 1st year A level maths and they can't see how to solve the carpet problem either. Or so he claims. Of course he may be making a creative excuse because if an A level student can't solve that while waiting for the toaster to pop then they're on the wrong course.
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On Mon, 21 Dec 2015 10:18:53 +0000, pamela wrote:

A suggestion: try putting the problem into its initial algebraic form for him. If he then zips through it in a flash, you'll know his problem is not the maths but the process of translating a physical world problem into the pure math realm. Been there; done that.
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On 23:32 18 Dec 2015, Cursitor Doom wrote:

Hey Cursitor, I overlooked this.
Is there still any chance to get the name of your 1950s grammar school maths book? Hope so. Thanks.
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Why would that ever come up in real life?
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Most obviously when reusing carpet because SWMBO didn't like it etc.
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But the above involved the actual room being three different sizes. That could only happen if his SWMBO was unsure whether to go open plan or put up a new wall.
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But not when considering where the unwanted carpet could be best used to minimise the wastage.
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You'd have exact measurements, not "that room's a bit less than this one".
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Not with the worst of the diyers who can't find or don't have anything to do the exact measurements with and who just do a crude estimate.
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