Mathematical modelling questions in examinations work by asking students to turn a real or imagined situation into a mathematical system, use that system, and then judge what the result means. The model may be an equation, graph, probability distribution, geometric representation, rate law or optimisation problem. Its usefulness depends on assumptions: what is treated as constant, negligible, proportional, random, continuous or measurable.
Understanding how mathematical modelling exam questions work improves real-world problem solving, rates, finance, statistics, geometry, functions, calculus and optimisation because it adds a layer beyond calculation. The learner must decide what to include, what to ignore, which relationship is defensible and whether the answer remains sensible when returned to the context.
This world-facing guide extends How Mathematics Examination Works, word problems and multi-step questions, and functions, sequences and calculus exam questions. It focuses on the model–assumption–interpretation chain rather than owning generic real-world numeracy.
The 50-second answer
SITUATION → QUANTITIES → ASSUMPTIONS → MODEL → CALCULATE → INTERPRET → VALIDATE → REVISE IF NEEDED.
1. A model is deliberately simpler than reality
A constant-speed journey model ignores acceleration. A linear cost model may ignore bulk discounts. A population-growth model may assume a constant proportional rate. These simplifications can be useful when they match the question’s purpose; they become weaknesses when the ignored feature materially changes the answer.
2. Assumptions are mathematical inputs
“Volumes add exactly,” “the rate remains constant,” “every outcome is equally likely” and “the object is a perfect cylinder” are not background decoration. They determine which formulas and probability rules are valid.
3. Variables should represent quantities, not anonymous letters
Define t as hours after departure or n as number of participants. Units and meaning make later interpretation possible. An equation solved for x is not finished if nobody remembers what x represents.
4. Data can estimate parameters
A straight-line model y=a+bx may use observed data to estimate intercept and rate. The fitted parameters describe the model; they do not automatically reveal a causal mechanism.
5. Model choice should follow mechanism
A fixed amount added each period suggests linear change. A fixed percentage applied to the current amount suggests exponential change. Choosing by visual familiarity rather than change mechanism can produce a model that fits one point and fails everywhere else.
6. Constraints define feasible answers
A continuous optimisation model may produce 11.6 containers, but the real decision requires a whole count. A negative time or length may be algebraically available and contextually impossible. Feasibility belongs to the model.
7. Validation compares model output with reality or given conditions
Substitute known cases, compare predicted and observed values, inspect units and test edge cases. A model that cannot reproduce the information used to construct it has a problem before extrapolation even begins.
8. Extrapolation increases assumption risk
A relationship observed over a small range may not continue indefinitely. Costs can acquire thresholds, populations meet resource limits and physical relationships can change regime. State the limitation rather than treating a formula as a law outside its evidence.
9. Sensitivity asks what happens when assumptions move
If a travel-time answer changes dramatically when speed changes by one percent, the model is sensitive to that parameter. Testing nearby values can reveal which assumptions deserve the most careful measurement or justification.
10. Interpretation closes the modelling loop
A numerical optimum, probability or forecast must be translated back into the context with units and conditions. The final sentence should say what the model predicts or recommends under its assumptions—not what reality must inevitably do.
Part II. One hundred twenty modelling decisions
11. Variable definition
For variable definition, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
12. Parameter definition
For parameter definition, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
13. Units
For units, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
14. Dimensional consistency
For dimensional consistency, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
15. Fixed cost
For fixed cost, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
16. Variable cost
For variable cost, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
17. Linear models
For linear models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
18. Direct proportion
For direct proportion, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
19. Inverse proportion
For inverse proportion, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
20. Piecewise models
For piecewise models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
21. Quadratic models
For quadratic models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
22. Exponential growth
For exponential growth, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
23. Exponential decay
For exponential decay, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
24. Logarithmic models
For logarithmic models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
25. Power laws
For power laws, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
26. Recurrence models
For recurrence models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
27. Difference equations
For difference equations, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
28. Continuous models
For continuous models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
29. Discrete models
For discrete models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
30. Integer constraints
For integer constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
31. Non-negativity
For non-negativity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
32. Capacity constraints
For capacity constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
33. Budget constraints
For budget constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
34. Time constraints
For time constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
35. Geometric constraints
For geometric constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
36. Probability models
For probability models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
37. Equally likely assumptions
For equally likely assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
38. Independence assumptions
For independence assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
39. Sampling assumptions
For sampling assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
40. Normal models
For normal models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
41. Regression models
For regression models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
42. Correlation
For correlation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
43. Causation
For causation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
44. Interpolation
For interpolation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
45. Extrapolation
For extrapolation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
46. Calibration
For calibration, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
47. Parameter estimation
For parameter estimation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
48. Initial conditions
For initial conditions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
49. Boundary conditions
For boundary conditions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
50. Constant rate
For constant rate, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
51. Average rate
For average rate, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
52. Changing rate
For changing rate, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
53. Speed models
For speed models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
54. Work-rate models
For work-rate models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
55. Flow models
For flow models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
56. Mixture models
For mixture models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
57. Density models
For density models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
58. Financial models
For financial models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
59. Simple interest
For simple interest, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
60. Compound interest
For compound interest, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
61. Depreciation
For depreciation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
62. Break-even models
For break-even models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
63. Revenue models
For revenue models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
64. Profit models
For profit models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
65. Demand models
For demand models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
66. Supply models
For supply models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
67. Scale models
For scale models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
68. Similarity models
For similarity models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
69. Area-volume scaling
For area-volume scaling, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
70. Population models
For population models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
71. Epidemic-style growth abstractions
For epidemic-style growth abstractions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
72. Resource limits
For resource limits, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
73. Logistic-style constraints
For logistic-style constraints, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
74. Optimisation
For optimisation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
75. Objective function
For objective function, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
76. Feasible region
For feasible region, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
77. Linear programming
For linear programming, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
78. Local optimum
For local optimum, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
79. Global optimum
For global optimum, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
80. Sensitivity
For sensitivity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
81. Scenario analysis
For scenario analysis, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
82. Best case
For best case, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
83. Worst case
For worst case, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
84. Uncertainty
For uncertainty, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
85. Measurement error
For measurement error, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
86. Rounding uncertainty
For rounding uncertainty, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
87. Bounds
For bounds, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
88. Tolerance
For tolerance, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
89. Robustness
For robustness, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
90. Validation
For validation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
91. Verification
For verification, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
92. Residuals
For residuals, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
93. Goodness of fit
For goodness of fit, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
94. Outliers
For outliers, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
95. Model bias
For model bias, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
96. Omitted variables
For omitted variables, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
97. Confounding
For confounding, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
98. Simplifying assumptions
For simplifying assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
99. Negligible effects
For negligible effects, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
100. Idealisation
For idealisation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
101. Frictionless assumption
For frictionless assumption, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
102. Perfect mixing
For perfect mixing, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
103. Constant temperature
For constant temperature, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
104. Uniform density
For uniform density, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
105. Randomness
For randomness, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
106. Stationarity
For stationarity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
107. Periodicity
For periodicity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
108. Symmetry assumptions
For symmetry assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
109. Homogeneity
For homogeneity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
110. Isotropy abstraction
For isotropy abstraction, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
111. Independence of agents
For independence of agents, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
112. Queue models
For queue models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
113. Scheduling models
For scheduling models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
114. Network models
For network models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
115. Shortest path
For shortest path, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
116. Allocation models
For allocation models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
117. Packing models
For packing models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
118. Routing models
For routing models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
119. Decision thresholds
For decision thresholds, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
120. Risk models
For risk models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
121. Expected value
For expected value, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
122. Utility abstraction
For utility abstraction, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
123. Simulation
For simulation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
124. Monte Carlo idea
For Monte Carlo idea, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
125. Numerical approximation
For numerical approximation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
126. Spreadsheet models
For spreadsheet models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
127. Calculator models
For calculator models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
128. Graphical models
For graphical models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
129. Diagram models
For diagram models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
130. Equation models
For equation models, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
131. Model comparison
For model comparison, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
132. Parsimony
For parsimony, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
133. Overfitting
For overfitting, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
134. Underfitting
For underfitting, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
135. Domain of validity
For domain of validity, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
136. Edge cases
For edge cases, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
137. Stress tests
For stress tests, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
138. Reverse checks
For reverse checks, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
139. Prediction intervals
For prediction intervals, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
140. Interpretation
For interpretation, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
141. Recommendation scope
For recommendation scope, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
142. Ethical/data limitations
For ethical/data limitations, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
143. Communication of assumptions
For communication of assumptions, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
144. Revision of model
For revision of model, identify what feature of the situation the mathematics is representing and what has been simplified. State the quantities, units and conditions before choosing an equation or computational method. A model is only as interpretable as its variable definitions.
Assumption drill. Write one assumption required for the model to remain useful and one plausible real-world feature it ignores. Then ask whether changing that ignored feature would materially alter the answer within the range the question considers.
Mechanism drill. Explain why the selected relationship fits: constant absolute change, constant proportional change, conservation, capacity, geometric similarity, random selection or another mechanism. Do not choose a model solely because its graph resembles a few observed points.
Validation drill. Test a known case, unit, boundary or observed value. If the model cannot reproduce information it should explain, inspect the assumptions, parameters or implementation before extending it to new cases.
Interpretation drill. State the result using language such as “under this model” or “assuming…” where appropriate. Distinguish a model prediction from a guaranteed real-world outcome and keep any integer, physical or domain constraint attached to the conclusion.
Part III. Forty original modelling laboratories
Laboratory 1. taxi cost
Situation. Fixed6 plus2.5 per km.
Model/result. C=6+2.5d.
Assumption or mechanism. Assume stated rate constant with distance. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 2. break even
Situation. Cost100+5x,revenue9x.
Model/result. x=25.
Assumption or mechanism. Break-even solves equal cost and revenue. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 3. compound growth
Situation. Population500 grows4% per stage.
Model/result. P=500(1.04)^n.
Assumption or mechanism. Assume proportional rate remains4%. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 4. linear growth
Situation. Tank gains12L/min.
Model/result. V=V0+12t.
Assumption or mechanism. Constant absolute inflow. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 5. decay
Situation. 800 retains85% each period.
Model/result. A=800(.85)^n.
Assumption or mechanism. Constant remaining proportion. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 6. capacity
Situation. 91 people,8 per vehicle.
Model/result. Minimum12.
Assumption or mechanism. Discrete constraint modifies continuous quotient. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 7. budget
Situation. 35+8n≤150.
Model/result. Maximum14 participants.
Assumption or mechanism. Whole count and inequality define feasibility. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 8. mixture
Situation. 20L concentrate+water; add water to ratio1:4.
Model/result. Water final80L.
Assumption or mechanism. Perfect mixing/additive volumes as stated; concentrate conserved. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 9. journey
Situation. 150km at constant60km/h.
Model/result. t=2.5h.
Assumption or mechanism. Constant-speed idealisation. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 10. average speed
Situation. 60km at30 then60 at60.
Model/result. 40km/h.
Assumption or mechanism. Model uses total distance/total time. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 11. scale
Situation. Map1:50000,4cm.
Model/result. 2km.
Assumption or mechanism. Uniform scale assumption. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 12. similarity
Situation. Length factor3/2.
Model/result. Area factor9/4.
Assumption or mechanism. Similar figures assumption. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 13. cylinder
Situation. Tank model radius2,height5.
Model/result. V=20π.
Assumption or mechanism. Ideal cylinder. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 14. financial
Situation. 1000 at5% compound3y.
Model/result. 1157.625.
Assumption or mechanism. Interest applied once per stated period. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 15. depreciation
Situation. Car value30000 retains80% yearly.
Model/result. V=30000(.8)^n.
Assumption or mechanism. Constant percentage depreciation abstraction. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 16. regression
Situation. Line y=2.1x+5 fitted to data.
Model/result. Predict inside observed range cautiously.
Assumption or mechanism. Fit describes association, not causal law. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 17. extrapolation
Situation. Same line used far beyond range.
Model/result. Prediction has greater model risk.
Assumption or mechanism. Relationship may change. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 18. probability
Situation. Fair die.
Model/result. Each face1/6.
Assumption or mechanism. Fairness supplies equal likelihood. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 19. without replacement
Situation. Bag changes after draw.
Model/result. Conditional branch probabilities.
Assumption or mechanism. Composition is state variable. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 20. sampling
Situation. Random sample100 from large population.
Model/result. Use sample summaries cautiously for inference.
Assumption or mechanism. Representativeness depends on design. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 21. optimisation
Situation. Rectangle perimeter20.
Model/result. A=x(10−x), max25 atx5.
Assumption or mechanism. Feasible positive side lengths. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 22. packaging
Situation. Volume fixed; minimise material.
Model/result. Objective surface area subject to volume constraint.
Assumption or mechanism. Ideal geometry ignores seams/thickness unless specified. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 23. work rate
Situation. A6h,B3h together.
Model/result. 2h.
Assumption or mechanism. Constant independent rates assumed. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 24. flow
Situation. Pipe10L/min for12min.
Model/result. 120L.
Assumption or mechanism. Constant flow and no loss. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 25. density
Situation. Uniform material mass540g,volume200cm³.
Model/result. 2.7g/cm³.
Assumption or mechanism. Uniform-density model. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 26. temperature conversion
Situation. Celsius to Fahrenheit.
Model/result. F=9C/5+32.
Assumption or mechanism. Linear conversion, not physical heat model. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 27. currency
Situation. 1A=1.25B.
Model/result. 10B=8A.
Assumption or mechanism. Rate assumed fixed for transaction; real fees ignored unless supplied. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 28. queue
Situation. Service1 customer every3min.
Model/result. 20/hour under constant uninterrupted service.
Assumption or mechanism. Ignores variability and downtime. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 29. schedule
Situation. Three tasks durations2,3,4h sequential.
Model/result. Total9h.
Assumption or mechanism. Assumes no overlap. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 30. parallel tasks
Situation. Same tasks fully parallel.
Model/result. Completion4h.
Assumption or mechanism. Assumes independent simultaneous resources. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 31. shortest path
Situation. Weighted network.
Model/result. Choose path with minimum total edge weight.
Assumption or mechanism. Weights must represent relevant cost. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 32. expected value
Situation. Gain10 p.2,lose2 p.8.
Model/result. EV=.4.
Assumption or mechanism. Long-run expectation not guaranteed single outcome. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 33. risk
Situation. Failure probability.01 over independent trials.
Model/result. Use complement for at least one failure.
Assumption or mechanism. Independence assumption matters. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 34. bounds
Situation. Length8.2 nearest.1.
Model/result. 8.15≤L<8.25.
Assumption or mechanism. Measurement represented by interval. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 35. sensitivity
Situation. Cost C=100+5x; rate changes5 to5.5.
Model/result. At x100 cost rises50.
Assumption or mechanism. Parameter perturbation reveals sensitivity. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 36. scenario
Situation. Demand100,120,150.
Model/result. Evaluate model separately for each.
Assumption or mechanism. Scenarios are conditional cases, not probabilities unless assigned. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 37. residual
Situation. Observed20,predicted18.
Model/result. Residual2 under observed−predicted convention.
Assumption or mechanism. Sign convention should be stated. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 38. outlier
Situation. One point far from fitted trend.
Model/result. Inspect before deleting.
Assumption or mechanism. Could be error or real regime; evidence needed. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 39. simulation
Situation. Estimate probability by10000 model trials.
Model/result. Relative frequency approximates model probability.
Assumption or mechanism. Simulation error remains. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Laboratory 40. validation
Situation. Model predicts known benchmark.
Model/result. Compare prediction with benchmark before new forecast.
Assumption or mechanism. Known case is a calibration/validation checkpoint. This sentence explains why the mathematics belongs to the situation rather than merely reporting a calculation.
Stress test. Change one assumption or parameter and decide whether the same model remains appropriate. If it does, recalculate. If it does not, state which relationship must change before continuing.
Validation. Test units, a known case, a boundary or a nearby observed value. Then write the conclusion with its assumptions visible. The model should not claim more certainty or range than its construction supports.
Part IV. A 20-day modelling programme
Day 1. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 2. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 3. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 4. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 5. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 6. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 7. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 8. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 9. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 10. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 11. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 12. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 13. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 14. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 15. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 16. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 17. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 18. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 19. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Day 20. Build, challenge and revise one model
Choose one familiar situation and define the target, variables, units and two explicit assumptions before writing an equation. Identify whether change is additive, multiplicative, conserved, constrained or random. Only then select the mathematical representation.
Calculate one result and validate it against a known case, unit, bound or observation. Next, perturb one important parameter by a small amount and observe how much the output changes. Record which assumption or parameter has the greatest leverage.
Finish by writing a two-sentence conclusion: what the model says, and the condition under which that conclusion should be trusted. If the condition is unrealistic, revise the model rather than hiding the limitation.
Part V. Frequently asked questions
What is a mathematical model?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
Why do models need assumptions?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I choose variables?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I know whether a linear model is appropriate?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
When is exponential growth appropriate?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What is the difference between discrete and continuous models?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do constraints change an answer?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I validate a model?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What is sensitivity analysis?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What is a parameter?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What is an initial condition?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
Why is extrapolation risky?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What is the difference between verification and validation?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I interpret a regression line?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
Does correlation prove causation?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I handle measurement uncertainty?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
What makes an optimisation answer feasible?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I write assumptions in an exam?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I improve modelling questions?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
How do I know when a model is too simple?
Start with purpose and mechanism. A useful model is not the most complicated one; it is a representation detailed enough for the question while remaining interpretable and testable. State what is held constant, what is allowed to vary and what evidence would make you revise the relationship.
For practice, keep the same numerical data but change one assumption. Decide whether the original model survives. This reveals which parts of the solution come from arithmetic and which come from the model’s view of the situation.
A creative-writing lens: every world has rules
A fictional world also simplifies reality by selecting which details matter. Once a story establishes that a train takes forty minutes, later scenes should respect that constraint unless something changes. Mathematical modelling is far stricter and quantitative, but the useful analogy is consistency: assumptions create consequences, and changing an assumption changes what follows.
Use the eduKate ecosystem as a route
Use the Mathematics Learning Hub for prerequisite techniques, Additional Mathematics Hub for advanced functions and optimisation, and How to Solve Maths Word Problems and Multi-Step Questions for translation from prose. For wider real-world numeracy, use How G1 Mathematics Works | Real-Life Numeracy, Problem Solving and SEC K110 Readiness where relevant to that learner.
Scope note and final answer
Modelling expectations vary by syllabus and level. Follow current official instructions. The examples here are original teaching material, not official questions, validated forecasts or mark allocations. Adrian, Jo, Ben, Aisha, Ryan, Mira, Clara and Ethan are fictional teaching characters.
The central habit is: do not ask only whether the calculation is correct; ask whether the mathematical world you built deserves to represent the situation. State assumptions, test the model and keep the final conclusion inside the boundaries of what the model can support.