GCSE Maths Problem-Solving Questions

La méthode, étape par étape

1. 1

   Extract the numbers and what they mean

   annotate the question — label every quantity with its unit

   Before choosing a method, write down what you have been given and what is being asked for. Most students who are stuck have not separated those two things, and the gap between them usually suggests the method.

2. 2

   Name the mathematics involved

   'this is a ratio question with a percentage change in it'

   Naming the topics converts an unfamiliar situation into familiar tools. Examiners deliberately dress standard techniques in unfamiliar contexts, and identifying the technique is most of the difficulty.

3. 3

   Work forwards from what you have

   compute anything computable, even if its use is unclear

   Producing intermediate results often reveals the route. It also earns method marks, which are awarded for correct steps regardless of whether the final answer is reached — so this is never wasted effort.

4. 4

   Work backwards from what is wanted

   'to find the cost I need the area, so I need the dimensions'

   Chaining backwards from the required answer identifies what is missing. Meeting the forward chain in the middle is how most multi-step problems are solved, and it is far more reliable than trying to see the whole route at once.

5. 5

   Write everything down and state the answer in context

   'the total cost is £248' rather than '248'

   Method marks require visible working, so nothing should be done mentally. Final answers should carry their units and refer to what was asked, because a bare number sometimes does not earn the final mark.

Why these questions feel different

A standard question tells you what to do — solve, expand, calculate. A problem-solving question describes a situation and leaves the method entirely to the student. The mathematics is usually no harder; the difficulty is that nobody has said which mathematics it is.

This is deliberate, and it is where the higher grades are decided. Students who can execute every technique but cannot recognise which one applies plateau exactly here, and the fix is practice at recognition rather than more practice at execution.

• Annotate: what am I given, what is wanted
• Name the topics involved
• Work forwards — compute what you can
• Work backwards — identify what is missing
• Show all working; method marks are real marks

Partial credit is substantial

A five-mark problem typically awards one or two marks for correct method even when the final answer is wrong or absent. A student who writes nothing because they cannot see the whole route scores zero on a question where two marks were readily available.

This changes the optimal strategy under time pressure. Attempting every question badly beats attempting most of them well, because the early marks in each are the cheapest on the paper.

The shapes that recur

Best-buy comparisons, recipe scaling, journeys combining speed and time, area problems dressed as painting or paving, and compound interest presented as savings decisions. A relatively small set of contexts covers most of what appears.

Recognising the shape is worth practising directly. Students who have seen six best-buy questions treat the seventh as routine, whatever the products happen to be.

How we teach problem solving

We spend as much time on identifying the method as on carrying it out. A common exercise is to give students a set of worded questions and ask only which topics each one needs, without solving any — it isolates the skill that is actually missing.

We also insist that something is written for every question in a mock, however stuck the student feels. Watching two method marks appear on a question they had written off changes how students approach the next paper more than any amount of advice about it.