Orange sweets Maths exam question UNFAIR!!!

[Xamonas Chegwé]

This question has, apparently, caused quite the twitter frenzy.

Screen Shot 2015-06-05 at 23.25.59.png (90.35 KiB) Viewed 3967 times

Personally, I did it in my head in a few seconds - but I'm a Maths teacher, so DUH!

Seriously though, I can't see what all the fuss is about. It really isn't that difficult and shouldn't be beyond the skills of any GCSE student that is a genuine candidate for an A grade.

The answer is in the picture in the news story below, so don't peek if you want to see if you can solve it first.
http://www.bbc.co.uk/news/education-33017299

[pcCoder]

This was also posted at RatSkep. At initial glace it seemed like it may be difficult but then I solved it pretty quickly. It doesn't seem at all unfair for a secondary education. What would GCSE map to in the US, high school?

[Xamonas Chegwé]

This was also posted at RatSkep. At initial glace it seemed like it may be difficult but then I solved it pretty quickly. It doesn't seem at all unfair for a secondary education. What would GCSE map to in the US, high school?

Yep. High-school diploma level.

[mistermack]

It's a lot simpler than it appears at first sight.

That's probably why people are moaning about it. They were daunted and gave up too soon.

[Xamonas Chegwé]

Apparently, most of the complaints are that it is "nothing like anything in the past papers we were given!"

No, it's not. It's there to test your ability to actually think, reason, work shit out and, for fuck sake, actually do some Maths!

The Maths itself is simple. It tests probability and algebra that is well within GCSE level. It also tests the students' ability to convert a problem stated in English into a Mathematical context - this is a key skill and something that students perennially struggle with - hence why they found this question "hard".

[Tero]

I just hate these things. Why not ask to solve for n?

[cronus]

Encourages a unhealthy diet, doesn't it?

[JimC]

Apparently, most of the complaints are that it is "nothing like anything in the past papers we were given!"

No, it's not. It's there to test your ability to actually think, reason, work shit out and, for fuck sake, actually do some Maths!

The Maths itself is simple. It tests probability and algebra that is well within GCSE level. It also tests the students' ability to convert a problem stated in English into a Mathematical context - this is a key skill and something that students perennially struggle with - hence why they found this question "hard".

Very true, in my experience. However, I think that part of the fault is that too many maths courses (often because they are so crammed with content) spend most of their time on specific skills such as solving various types of equations, and do not systematically take students through the ways to approach worded problems and apply problem solving skills. In recent years, I've made a conscious effort to include more of this when I teach maths.

[Calilasseia]

Here's what I posted elsewhere for this ... JimC will doubtless approve

Step by step:

[1] If there are n total items to select from randomly, and k items (0<=k<=n) are of a given type, then the probability of selecting one of those k items from that collection of n total items is k/n.

[2] After the first selection takes place above, if the selected item is one of the k items of the specified type, then one is left with a total n-1 items, of which k-1 are of the given type.

[3] If a second selection now takes place, then the probability of selecting one of the k-1 items of the given type from the remaining n-1 items is (k-1)/(n-1).

[4] Since these are independent selection events, the total probability of selecting two of the k items of the given type from the available n items at the start, is therefore (k/n)×[(k-1)/(n-1)] = [k(k-1)]/[n(n-1)]

[5] If that total probability is specified as P, then we have:

P = [k(k-1)]/[n(n-1)]

Therefore n(n-1) = [k(k-1)]/P

[6] We are given that k=6, and P=1/3. This gives us:

n(n-1) = (6×5)/(1/3) = 90

Therefore the resulting equation is n2-n-90 = 0.

Factorising this equation gives us (n-10)(n+9) =0. This has solutions n=-9 and n=10.

Since the total number of items n has to be greater than 0, the desired solution is n=10. There are 10 sweets in total in the selection set, of which 6 are orange, 4 are yellow. As a check, the probability of the first selection of an orange sweet is 6/10, and the probability of the second selection of an orange sweet is 5/9. This gives us a probability for the two selections of (6×5)/(10×9) = 30/90 = 1/3.

[JimC]

Spot on, Cali!

Yep, students need to be exposed to this type of problem, where a sequence of logical steps leads to the answer. When teaching this, I like to ask the class for a possible next step, after any particular point, to encourage them to think for themselves. That said, they do of course need some preliminary teaching on the basics of probability via simpler, single step problems.

[Svartalf]

OK, I'm completely worthless at maths, I had no idea how to solve the problem and even Cali's explanation did not help me.

[NineBerry]

But what if we know that Hannah doesn't like orange sweets but only yellow sweets? Then this problem has no solution!

And do the sweets contain sugar or not and did she brush her teeth afterwards?

[PsychoSerenity]

I understand why it would have thrown many of them. It's not a probability question or an algebra question, but an unexpected combination of the two. I'd certainly say it's a high grade question for GCSE. It needs a bit of creative thinking - which is difficult in stressful exam conditions, - rather than just following a simple process that they've learned to solve a given type of question.

Having said that, they should have been taught to tackle problem-solving type questions - that's what maths is for!

[Xamonas Chegwé]

I understand why it would have thrown many of them. It's not a probability question or an algebra question, but an unexpected combination of the two. I'd certainly say it's a high grade question for GCSE. It needs a bit of creative thinking - which is difficult in stressful exam conditions, - rather than just following a simple process that they've learned to solve a given type of question.

Having said that, they should have been taught to tackle problem-solving type questions - that's what maths is for!

There are always a few questions of this type, PS. In fact, it is a requirement of the syllabus! See the last paragraph especially.

[mistermack]

OK, I'm completely worthless at maths, I had no idea how to solve the problem and even Cali's explanation did not help me.

I'm not sure if I did it right, but I got the required answer :

Probablity of first sweet being orange is six in n
Probability of second sweet being orange is five in n-1

Probability of both happening is 6/n x 5/(n-1) = 30/n(n-1)
So 1/3 = 30/n(n-1)
So 1 = 90/n2-n (multiplying both sides by 3)
So n2-n = 90 (multiplying both sides by (n2-n))
So 0 = n2-n-90 (subtracting 90 from both sides)