Problem solving framework

Problem solving timeline

Mathematical problems often include different types of maths. They are usually non-routine which means they are unlikely to have appeared before.

The following six step framework provides an approach that can be used to tackle the majority of problem solving questions.

1. What do I have to do?

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Read the question through twice. It can be easy to miss something the first time. Highlight or underline key words and information.

2. What information do I need?

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Decide which bits of information are most useful. Start to think about which type of maths might be used to solve the problem.

Also, think about what form the answer will take. Is it asking for money, time or distance for example? Does the answer have to be a whole number? Will the answer have any units? If so, don’t forget to include them.

3. What information don’t I need?

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Sometimes some information given in the question is not needed.

It is important to decide at the start if there is any information which does not need to be taken into account when working out the answer.

4. What maths can I do?

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This is where it is necessary to start tackling the problem. The earlier steps are designed to break up the problem. In every problem-solving question there is usually a way into the problem:

  • There may be a fraction, percentage, ratio or expression included in the question. This usually provides a good place to start.
  • Sometimes the type of answer that is being looked for helps you begin. For example, if the question asks for an area, perimeter or angle, this might be enough to start a chain of maths.
  • Mark information such as lengths and angles on any diagrams.

Use the highlighted information to get started on the question, even if an initial approach isn’t the right way to start, just do some maths with the information that you have to try and get ‘into’ the problem.

Some problems require different maths topics to solve them, for example setting up an equation to find the measurements of a shape. Look out for opportunities to use a range of maths skills to solve a problem.

5. Is my solution correct?

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There are checks that should always be done:

  • Think about whether your answer seems reasonable.
  • Is it possible to check the answer you got? Small errors can lead to incorrect answers. Check any working out, even if it was done on a calculator.
  • Can you check the answer backwards too? Work backwards and see whether the answer agrees with what you were told in the question. For example, in a question on ratio the total amount is given at the start. Check that any answers add up to this total amount.
  • Check no answers have been rounded until the very end. Rounding too early can lead to final answers being incorrect.

6. Have I completed everything?

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  • Should the answer have any units on it like cm, kg or m2?
  • Has all the information that was highlighted at the start been used? If not, is there a reason why? Was it extra information that was irrelevant or should it have been used somewhere?
  • Does the answer seem reasonable and make sense? For example, if part of the problem was to calculate the mean of the numbers 7, 8, 10 and 15 and you reach an answer of 100, it is clearly not the right answer.
  • Has the question been answered? Does the answer make sense when you read the question back? For example, if the question asked for a speed and instead a distance was found, this is not the final answer.
  • Have you shown all of the steps in the workings out? Even if a calculator has been used, show everything that was entered into the display.