OT2: Mathematical problem solving: Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle.

The idea

The problem-solving cycle is a structured approach: specify the problem, collect information, process and represent it, then interpret results. If interpretation shows the problem is not solved, you repeat the cycle. For example, to find the maximum volume of a box made from a 20 cm by 30 cm card, you specify variables, collect dimensions, process by forming a volume function, represent graphically, interpret the maximum, and if the answer seems unreasonable, you refine assumptions and repeat. This cycle is assessed through multi-step problems requiring clear communication of each stage.

What earns the marks

• Clearly define the problem and identify what needs to be found, including any constraints or assumptions.
• Select and collect relevant information, such as given data, formulae, or measurements, and recognise when additional information is needed.
• Process information using appropriate mathematical techniques, and represent it in a helpful form such as an equation, table, graph, or diagram.
• Interpret results in the context of the original problem, checking reasonableness and units, and decide whether the cycle needs repeating.

Common mistakes and how to put them right

• Skipping the specification stage and jumping straight into calculations.

  Put it right: Write down what you are trying to find and any assumptions before starting.

• Ignoring the interpretation stage and not checking whether the answer makes sense.

  Put it right: After calculating, relate the result back to the problem context and consider if it is realistic.

• Failing to recognise when the cycle needs repeating after an unsatisfactory result.

  Put it right: If the result is unreasonable or does not answer the problem, revisit earlier stages with new information or a revised approach.

Exam tips

• Show your working for each stage of the cycle, as marks are often awarded for clear communication of the process, not just the final answer.
• When representing information, choose a form that makes the problem easier to solve, such as a graph for optimisation or a table for patterns.
• Always interpret your final answer in the context of the question, including units and a brief sentence explaining what it means.