OT3: Mathematical modelling: Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

The idea

Refinement means using model outputs and assumptions to improve the model. Evaluate appropriateness by checking if outputs are realistic and assumptions reasonable. For example, a linear population model may predict negative population eventually; refine by using a logistic model. Assess by comparing predictions with real data, considering sensitivity to assumptions, and judging if the model serves its purpose.

What earns the marks

• Identifies simplifying assumptions in a given model and explains how they might affect the model's outputs.
• Suggests specific refinements to the model based on the outputs or assumptions, such as adding a limiting factor or using a different function.
• Evaluates whether the model is appropriate for its intended purpose by comparing outputs with real-world data or expectations.
• Discusses the trade-off between simplicity and accuracy when refining a model.
• Justifies the appropriateness of a model with reference to its context and limitations.

Common mistakes and how to put them right

• Suggesting refinements that are not based on the model's outputs or assumptions.

  Put it right: Link suggested refinements to specific outputs or assumptions that seem unrealistic.

• Evaluating a model as inappropriate without considering its purpose.

  Put it right: Assess appropriateness relative to the model's intended use and required accuracy.

• Assuming that a more complex model is always better.

  Put it right: Discuss the balance between simplicity and accuracy, and consider whether added complexity is justified.

Exam tips

• When asked to refine a model, suggest a specific change and explain how it addresses a limitation revealed by the outputs.
• To evaluate appropriateness, compare model predictions with known data or common sense, and comment on the impact of assumptions.
• Use phrases like 'the model assumes... which may not hold because...' to structure your evaluation.