That EdExcel GCSE maths problem (the one about the orange sweets)

I understand the fuss: the question will certainly have thrown students because there’s no precedent question in any previous past paper. And the same goes for some of the other questions in that paper too.

But that’s not to say it shouldn’t have been included. It takes us right to the core issue about how we teach maths in the classroom in this day and age.

The new National Curriculum for maths states its aims as:

“The national curriculum for mathematics aims to ensure that all pupils:

  1. become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
  2. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
  3. can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions”

The issue is, in the past we as maths teachers have focussed far too much on the first of these aims, concentrating on the fundamentals, focussing on repeated exercises and applying the same methodology for exam preparation by working through past exam papers.

The new national curriculum wants us to spend much more time applying these fundamentals to solve problems and reason mathematically. And I suspect this was the thinking when the EdExcel team included the question in the exam paper this week. Incidentally, this is something close to our heart at DoodleMaths.

Our philosophy is that the learning of these fundamentals (which is largely best done by rote) needs to be taken out of the classroom where possible: we have the technology now to be able to deliver an adaptive, individualised study programs which teach children these fundamentals in a way that is personalised to them, their strengths and weaknesses, and the pace at which they learn. Crucially, this frees up teacher time up to do what only they can do in the classroom: teach children to reason mathematically, problem solve and develop their powers of mathematical modelling.

Whilst tech can help with the fundamentals, it will never be able to do this. I’ll get off my soap box now, since most visitors to this blog will be after the solution, I’m guessing. So here it is. I’m off for an orange sherbet.

“There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0″ 

EdExcel Higher Maths Paper, 4th June 2015

Here's the solution to EdExcel's famous orange sweet problem.

Here’s the solution to EdExcel’s famous orange sweet problem!

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