Goal: calculate mark-up on cost and margin on selling price for Card K, with both denominators visible. 25 = 2 + 5 + 6 + 7 + 5.
- 0–2: Read cost $72, price $90, gap $18. Ask why $18 cannot be called a percentage until a denominator is chosen.
- 2–7: Model mark-up
18÷72×100=25%, then margin18÷90×100=20%. In each case, mark the denominator on the base grid. - 7–13: Learners reconstruct price from cost plus gap and explain in one sentence why both percentages can be correct here. This is a gross gap, not net margin after expenses.
- 13–20: Routes: lay the $18 gap strip beside $72 then $90 labelled bases; fill a two-row ratio table; give a spoken/typed explanation with two fractions and units. All routes distinguish denominator and business limit.
- 20–25: Exit “Which denominator belongs to margin?” Key: selling price, $90. Move: ask learner to point to what the named percentage is “of.”
Alternative domains: invented app-icon printing or repair-shop parts. Optional/home: with fictional cost $20 and selling price $25, find both percentages; no real shop data. Two optional swaps.