Goal: find and justify the first whole item count that exceeds a fixed stated total. 25 = 2 + 5 + 6 + 7 + 5.
- 0–2: Retrieve Card B's $160 hourly total and $9 per accepted prop. Ask “How many accepted props first give more than $160?”
- 2–7: Model
9n > 160;n > 160/9≈17.78, so the first whole count is 18, giving $162. This is a mathematical boundary, not a productivity target. - 7–13: Learners check 17 props = $153 and 18 = $162. Contrast “at least $160” with “strictly more than $160”; the threshold happens to be 18 for both here, so ask why the words still matter.
- 13–20: Routes: build a $9-per-piece number line using tokens; fill 15–20 rows in the payment board; solve the inequality and verify adjacent whole counts. All routes show the two boundary values and the unknown real work time.
- 20–25: Exit “Why not round 17.78 to 17?” Key: 17 gives only $153. Move: make learner test both adjacent whole counts before selecting a conclusion.
Alternative domain: Fictional photo-editing deliverables. Optional/home: find the first whole count at $7 each exceeding a fictional $50 target; no real gig advice.