OT2: Mathematical problem solving: Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

The idea

This objective is about seeing the mathematics inside a real or unfamiliar situation, then simplifying and abstracting it into a solvable form. To recognise structure, identify quantities, relationships and constraints, and decide which are essential. To simplify, remove irrelevant detail and replace complex features with manageable approximations. To abstract, represent the situation with variables, equations, diagrams or functions. For example, a problem about a leaking tank can be abstracted to a linear model relating volume to time, ignoring minor variations. You must then solve the abstracted problem and interpret the result in context. Assessment may present a scenario and ask you to set up a model, choose variables, or explain assumptions. The skill is shown by clear, justified modelling choices.

What earns the marks

• Identify key quantities, relationships and constraints in a situation.
• Choose appropriate variables, diagrams or notation to represent the situation.
• Simplify by ignoring irrelevant detail and making reasonable assumptions.
• Formulate equations, functions or models that capture the essential structure.
• Solve the abstracted problem and interpret the solution in the original context.

Common mistakes and how to put them right

• Including too much detail and making the model too complex to solve.

  Put it right: Focus on the main relationships and state simplifying assumptions.

• Using variables without defining them, leading to confusion.

  Put it right: Clearly define each variable and its units.

• Forgetting to interpret the mathematical solution back in the real-world context.

  Put it right: Relate the answer to the original situation and check it is sensible.

Exam tips

• Read the problem twice and list the quantities and relationships before starting algebra.
• State any assumptions you make; they are often part of the assessment.
• Check your final answer against the context to see if it is reasonable.