Mathematical modelling, problem solving and reasoning

Module 1 is not a separate block of content. It runs alongside Modules 2 and 3 and describes how you use the mathematics from those modules to deal with real situations. A modelling or problem-solving response moves through four recognisable stages. Formulate: decide what is being asked, define variables with units, choose a model and state your assumptions. Solve: apply the technique accurately, by hand or with technology.

Interpret: translate the mathematical answer back into the context, with units and sensible rounding. Verify: check the answer against the original information and ask whether it is reasonable.

Formulating is often the hardest step. Read the situation and list the known quantities, the unknown quantity and any conditions. Give each variable a letter and a unit, for example n = number of items sold or C = total cost in dollars.

Then decide which kind of model fits: a linear rule for a constant rate, a matrix for information arranged in rows and columns, a compound interest model for money that earns interest on interest, summary statistics for comparing groups, or a measurement formula for area or volume.

Interpreting means answering the question that was asked, not just the equation you wrote. If a model gives n = 119.4 items, the practical answer depends on the question: to cover costs you would need 120 items, because only whole items can be sold. A conclusion should be a full sentence in context, and it should follow from your results rather than from what you expected before calculating.

When you write up a task, label each stage so a reader can follow your reasoning from question to conclusion.