OT3: Mathematical modelling: Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).

The idea

Interpretation means translating numerical or algebraic outputs back into the real-world context. For a given model, identify what each variable and parameter represents, then explain what the output value means in context, including units and limitations. For a student-constructed model, first state the model and its assumptions, then interpret. For example, if a model predicts the population of a town after 10 years as 25,000, interpret this as the expected population, noting it assumes constant growth rate and no migration. Always relate outputs to the original situation, not just the mathematics.

What earns the marks

• Correctly identifies the meaning of each variable and parameter in the model within the original context.
• Translates numerical or algebraic outputs into a clear statement about the real-world situation, including appropriate units.
• Explains the limitations or assumptions that affect the interpretation of the output.
• For a student-constructed model, clearly states the model and its assumptions before interpreting the output.
• Uses the context to give a meaningful interpretation, not just a restatement of the calculation.

Common mistakes and how to put them right

• Ignoring units when interpreting outputs.

  Put it right: Include and check units to ensure the interpretation is meaningful.

• Interpreting outputs without considering the model's assumptions.

  Put it right: Explicitly state how assumptions affect the validity of the interpretation.

• For a student-constructed model, failing to define variables and parameters clearly.

  Put it right: Define all symbols and their context before interpreting outputs.

Exam tips

• Read the question carefully to identify what the output represents in the given context.
• Write your interpretation as a clear sentence that a non-mathematician could understand, including units.
• If you constructed the model, briefly state the model and its assumptions before interpreting the output.