How dumb is Britain?

[EEPhil]

According to the on-line version of the local rag "'Impossible' maths exam question stumps parents" (Well 75% of parents and 100% of pupils) https://www.nottinghampost.com/news/nottingham-news/impossible-maths-exam-question-stumps-7972521

The question that is so impossible is:

That is so easy. Even with my maths being rusty and my memory failing me at times, it took less than 30s to solve this. (And no, I didn't look at the spoiler at the bottom of the article). Is it thick pupils or poor teaching, or both? No wonder we're in such a mess.

 

[alanofcleeves]

Totally agree, 1st term algebra stuff, age about 12 I would have said.

I expect the syllabus covers things we didn't do in our day but there's no escaping the fact that this is EASY.

 

[prpr]

Is it thick pupils or poor teaching, or both?

Probably both, or certainly "can't be bothered" on at least one side or both.

No wonder we're in such a mess.

Quite.

But which way did you do it?
(2x+6)(x+7) + 4(x+1)
(x+1)(x+11) + (x+5)(x+7)
(2x+6)(x+11) - 4(x+5)

 

[prpr]

I expect the syllabus covers things we didn't do in our day

Discuss the feelings of the numbers 0,3,5,7,8 and 9 which are not used in this question and what could be done to help them be more inclusive.

 

[EEPhil]

But which way did you do it?
(2x+6)(x+7) + 4(x+1)
(x+1)(x+11) + (x+5)(x+7)
(2x+6)(x+11) - 4(x+5)

(2x+6)(x+7) + 4(x+1).
Of course, I found the 4(x+1) first so that equation should be the other way around.

 

[EEPhil]

No wonder we're in such a mess.

Quite

The Liz and Queasy [sic] school of economics for a start!

 

[alanofcleeves]

Discuss the feelings of the numbers 0,3,5,7,8 and 9 which are not used in this question and what could be done to help them be more inclusive.

Algebra's full of this sort bias. Total 'x' fixation.

 

[prpr]

Algebra's full of this sort bias.

But at least it all has balance.

so that equation should be the other way around.

Can you spell commutativity? Wonder how many of the little 'darlings' or their parents can or know what it means.

 

[RobH1]

I don't think this a surprise at all, nobody has to think for themselves, they have a smart phone for that.

I agree with A of C in post #2, I clearly remember very basic algebra being introduced in our final year at primary school in preparation for secondary, 11/12 years of age.

 

[Black Hole]

But which way did you do it?
(2x+6)(x+7) + 4(x+1)

Just glancing at it quickly, that's the version I had in my head.

Total 'x' fixation.

Me too!

 

[Luke]

Probably both, or certainly "can't be bothered" on at least one side or both.

Quite.

But which way did you do it?
(2x+6)(x+7) + 4(x+1)
(x+1)(x+11) + (x+5)(x+7)
(2x+6)(x+11) - 4(x+5)

I wonder if anyone's fist choice was to use the 4(x+1) from method 1, the (x+5)(x+7) from method 2 and then add (x+7)(x+1) for the remaining area.

[ The method that initially lept out at me was method 3: (2x+6)(x+11) - 4(x+5) ]

 

[MikeSh]

it took less than 30s to solve this.

I hadn't done it in 30s, so I decided you win and retired to read the following posts.
(I'm sure I could have got there, but after 1/2 bottle of red and without pencil and paper I felt like a modern schoolkid.)

 

[prpr]

I wonder if anyone's fist choice was to use the 4(x+1) from method 1, the (x+5)(x+7) from method 2 and then add (x+7)(x+1) for the remaining area.

Interesting. I thought about this option 4 later, but discounted it as it involves breaking the problem in to 3 rectangles rather than 2 and there's nothing to be gained from doing so - it just makes more work for yourself and increases the possibility of error.

 

[EEPhil]

But at least it all has balance.

Can you spell commutativity? Wonder how many of the little 'darlings' or their parents can or know what it means.

No! But I do know what it means.

 

[Black Hole]

I have a small crumb of sympathy. I can solve the above, but cannot recall any situation in my entire life (including an engineering career) where I have needed to size an irregular object to have a specific surface area. Where I shake my head is when they can't even add up their shopping bill before they get to the checkout, know what change is due out of a tenner... or want a receipt for what they've spent. (I bought something for cash a few weeks ago, and was handed my change as if that was the end of the transaction. I waited, and the operator looked at me querying. "Receipt please." "Oh, sorry, I can't give you one now." So the checkouts don't even produce one unless specifically told to!)

On the subject of puzzles, here is this year's GCHQ Christmas card (widely circulated in the media). I sat over it with a mate of mine, and with two heads we cracked it in maybe half an hour or so. I might go back and look at last year's again now.

 

[Luke]

Interesting. I thought about this option 4 later, but discounted it as it involves breaking the problem in to 3 rectangles rather than 2 and there's nothing to be gained from doing so - it just makes more work for yourself and increases the possibility of error.

I suspect most people will go for either method 1 or method 2, but someone could just continue the exiting lines through the shape in the hope that it provides more bit size chunks. and take it from there instead of evaluating, or realising, there is a simpler method.

I have a small crumb of sympathy. I can solve the above, but cannot recall any situation in my entire life (including an engineering career) where I have needed to size an irregular object to have a specific surface area.

Not even to buy, or cost, paint, wallpaper, patios, drives, tiles, carpets or other flooring, or icing for a cake?

 

[MikeSh]

but cannot recall any situation in my entire life (including an engineering career) where I have needed to size an irregular object to have a specific surface area.

I agree. But this is a test of their maths/algebra ability. It's that ability that can then be transferred to real world problems.

 

[MikeSh]

Not even to buy, or cost, paint, wallpaper, patios, drives, tiles, carpets or other flooring, or icing for a cake?

I have used algebra while estimating stuff, but I've never needed to show that the total area was equal to a formula.

 

[Luke]

I have used algebra while estimating stuff, but I've never needed to show that the total area was equal to a formula.

That is out of context to what I was replying to.

 

[Black Hole]

That is out of context to what I was replying to.

Oh no it isn't (oh yes it is...)! Sort of, maybe.

If I wanted to find the area of that shape (or whatever), I wouldn't write an equation for it, I would just work it out for that specific case (no "x" required). Using "x" moves the specific to the general (but only general in as much as the variability is in x, so that's a limited range of shapes), and the only reasonable application of that is to be able to find a parametric shape which has a desired area and not the area of a parametric shape.

Deriving an equation (which doesn't then require a solution) means the little darlings aren't even taxed with the quadratic formula!