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Hannah has 6 orange sweets and some yellow ones.

Overall, she has n sweets.

The probability of her taking two orange sweets is 1/3

Prove that n²-n-90=0


(Taken from this year's GCSE Maths paper)

Started a more 'fun' proof using binomial coefficient and then went 'nah, why don't I just do it the easy way' :D

6/n x 5/n-1 = 1/3.

I can't get over the furore this has caused, notwithstanding it's a poorly worded question.

How is it poorly worded?

Seems to be some pretty poor furore! :D

The link between the third and fourth sentences is not easy to follow. What does that equation have to do with 1/3?

Not everybody can equate maths to real life. Test people's ability to do the maths, rather than their ability to understand the question.

I don't understand why the question is bad?  Seems okay to me - construct a formula and simplify it to get to the proof?

But all maths is related to some kind of question, no? If someone can solve that formula but not understand the question then....

I think the complaint wasn't that it was difficult per se - but that it wasn't consistent with the difficulty level they were being taught to and had appeared in previous year's exam papers.

Of course, but my reading of the feedback on the internet and in the news is that people struggled to understand what the question was asking of them. The maths bit is fairly straightforward (if you've been studying algebra). Here's an alternative last sentence...

Hannah has 6 orange sweets and some yellow ones.

Overall, she has n sweets.

The probability of her taking two orange sweets is 1/3.

Show that the probability of her picking two orange sweets in her two next selections can be rewritten as n²-n-90=0

not sure that helps Tal

ironically I couldn't have answered the question when I was 16 but can have a decent go now

(6*5/2)/(n*(n-1)/2)=1/3

45/(n*(n-1)/2)=1

45=(n*(n-1)/2)

90=n*(n-1)

0 = (n*(n-1))-90

0 = n2-n-90

(I think)


edit bloody brackets

I don't like orange sweets.

Good job Hannah does, then.

I think people are always going to have barriers when asked to prove something now.  

It was definitely one of my pet hates and I did a maths degree.  Proofs are a doddle if you remember them, but not so much when you have to do them from scratch.  

Getting asked to prove something from scratch is just going to appear really hard to a lot of children.  It is getting over that psychological barrier that helps you see the question for what it is something that is not something that is easy to do under the stressful conditions of a significant exam.  I expect it would be something that I'd have found difficult at 16.  I am sure it was quite a bit after that where I learned to just move on to the next question if something was too difficult.  

FWIW It doesn't even look that easy when I saw the question for what it was.

Does it drive you mad when those irritating like-farming memes go round facebook and the vast majority of people would answer a question like 2 + 2 x 0 + 2 as 2 rather than 4?

That must mean that the majority of people would also completely fail a question like the one in the OP

The probability of picking the two sweets can be expressed as:

6/n * 5/(n-1) = 1/3

Numerator 6 * 5 = 30 so the denominator must be 90

n(n-1) = 90

n(n-1) - 90 = 0

n^2 - n - 90 = 0


Really don't see what the fuss is about. Question is worded absolutely fine.

If people think that's bad they're going to be in for a shock in a couple of years time. This question is easy compared with what is planned to come.

(Edit - Simplified the simplifying)

What constitutes a furore?

In my day kids might hang about outside the exam room to whinge about questions with their friends.
Nowadays, a few of them use Twitter or other social media to do the same and national newspapers which are struggling for stories make an online article out of it.
(Personally I prefer videos of cats doing cute things).

Surely the whole point of an exam is to have some tough questions. If everybody could answer all the questions then it wouldn't serve much purpose.


Right, now that that's sorted, the grumpy old git is off for his afternoon nap.

I was thinking much the same about the furore, I guess the definition is something the BBC picks up on?

It's more than a row but less than a fracas.

It's a weird question. The equation itself is easy to solve but I don't understand the relevance of all the text before it.

How many sweets has she picked up? I can't see anywhere where it says she has picked up 2 only.  She could have picked up 8.  Always hard to get the kids to just pick up 2 and 8 seems a much more likely answer if daddy isn't there.

??

Every bit of info is required

 combos of 2 from 6 divided by combos of 2 from n = 1/3.

Use that to prove n2-n-90=0

That was the ambiguity I saw, however, I think its reasonable to ask children of that age to use some reasoning to interpret a bit of ambiguity.  They could even prefix their answer with a statement of their interpretation.

Here is the actual question:

(http://i.imgur.com/NI3V0Ni.jpg)

lol Tal makes a perfectly reasonable question look bad

QESweets

(http://i.imgur.com/eDre0b2.jpg)

Greater than a contretemps, but less than a set-to.

Rather more than a brouhaha but somewhat less than pandemonium?

What does n²-n-90=0 actually mean? That's what I think is poorly explained. Well, it's not explained at all, is it?

My suggested last sentence tells the person sitting the exam what they are being asked to do. It doesn't give them a helping hand or anything like that; all the work has to come from the student.

This is only GCSE. How many interviews have you sat in where a question is asked without apparent context and the interviewee has no opportunity to ask what is meant, nor will the interviewer ask follow-up, probing questions to steer the conversation towards the area they're interested in?

your suggestion was

Show that the probability of her picking two orange sweets in her two next selections can be rewritten as n2-n-90=0

unfortunately that is nonsense

You could perhaps say "using the above information show that n2-n-90=0" but that's about it.

As I said my equivalent was o level many moons ago and probability/combinations wasn't covered, not sure it was even covered in highers, so the question does seem a bit hard for GCSE.

More than a wrangle but less than a melee.

There is no doubt that this question is presented differently to your standard probability question on a GCSE paper. However, this topic is supposed to be hard (even A/A* with tree diagrams) and the questions are often not reflective of this. I can understand students and teachers being surprised that this type of question was included on the paper but then again at least they are finally pitching the topic where it should be. I think it's a good, but challenging (for the kids who can normally nail probability) question. The issue is that the students who struggle with algebra will feel cheated out of 3 marks which they normally get every time on these papers.

FWIW, I think it should be out of 4 not 3.

Also, agree with Doobs, children are generally poor at proof. One of the main reasons why I use it as often as I can in my lessons.

Is this really that hard?

Can most 16yo not answer this?

Well it was a lot easier when we saw the real question.  The real question looks tough but fine to me.  No point in giving them 17 easy questions. 

I don't know what usual looks like these days though.

When I read the question, I honestly didn't get what it was asking me to do.

Once that was clear, the actual maths I was fine with.

In a pressure situation, at sixteen, I could well see myself wasting five minutes or so on that question completely needlessly, getting myself into a tizz and doing far worse than I should.

As I said in the OP, I don't think the maths - the thing really being tested - is inappropriate for that level. There need to be questions in there for the A/A* divide, after all.

I did take it from the independent this morning.

That's what you get for copying, I suppose.

Children are scared by the words 'show that'

This is why I left school with no qualifications

I know people who have taken various exams in the last few years and that's the impression I get. The first thing they do is go on twitter to discuss/complain.

This kind of question seems entirely appropriate for that level, the only difference to normal seems to be that the BBC decided it was a story.

It means that if you take n then square it, take away n and then take away 90 you get 0.

I don't get the issue? This is standard maths terminology that any GCSE student sitting this paper will be familiar with.