Definition
Mathematical modelling
Mathematical modelling turns a real situation into mathematics, uses the model, and checks the result against reality.
Continue from this idea into connected AXIO math.
What it means
You start with something real, decide what matters, and make a useful maths version of it. Then you calculate or reason with that version. Finally, you ask, “Does this answer make sense in the real situation?” If not, change an assumption or the model and try again. The model is the maths you made; modelling is the whole make–use–check–improve process.
Remember it
Think: real world → maths → answer → real world. The last check can send you round again.
Example
A taxi charges £4 to start and £2 per kilometre. Let d be the distance and model the fare by C = 4 + 2d. For 3 km, C = 4 + 2 × 3 = £10. Treat £10 as a prediction, compare it with the receipt and fare rules, and revise the model if a waiting fee or another omitted rule matters.
Watch for
Copying numbers from a story into an unrelated calculation is not mathematical modelling. The calculation must represent the situation and its important relationships.
Common mix-up
A mathematical model is the representation, such as an equation or graph. Mathematical modelling is the whole process of making, using, checking, and improving that representation.
Exact meaning
Mathematical modelling is the process of selecting important quantities and assumptions from a real situation, representing their relationships mathematically, analysing that representation, interpreting the result in context, and revising the model when the check against reality shows it should change.