Codes: AC9M10A04, AC9M10A02. Goal: evaluate a model's assumptions and test a change without silently moving the goalposts. Prepare: cost board, brief.
- Set problem · 2 min. “Suppose the household now needs only four months. Is B still the price-only choice?”
- Recall · 5 min. Calculate A(4)=$560 and B(4)=$680. Explain why A is cheaper for four months while B is cheaper at ten.
- Model review · 6 min. The two formulas increase by fixed amounts each month, so a linear model fits the invented price rules. A percentage fee each month would require a different growth model; none is stated here.
- Modify · 7 min. Give an invented variation: B's setup is reduced by $60 to $420 while monthly cost stays $50. Write
B_new(m)=420+50m; solve equality with A:240+80m=420+50m→m=6, total $720. Compare with original crossing at 8. - Evaluate · 3 min. Ask whether the reduced setup proves B has better value. No: the exercise omits service and rights; price is only one criterion.
- Exit · 2 min. Everyone states one changed assumption, new crossing and one real-world question to verify.
Access: value table before algebra, paired line model, typed or dictated reasoning. Mark which representation revealed the change.