Compare the rule with concrete cases
Original fictional score gives two points for each of the first three units and one point for each further unit. Six units give 3×2 + 3×1 = 9. A whole-quantity rule using the rate of the reached band would give six. The output unit is points.
| Units | First portion points | Further portion points | Marginal total |
|---|---|---|---|
| 2 | 2 × 2 = 4 | 0 | 4 |
| 3 | 3 × 2 = 6 | 0 | 6 |
| 6 | 3 × 2 = 6 | 3 × 1 = 3 | 9 |
Work through the distinction
Name the band boundaries and whether earlier units keep their earlier rate. The boundary case alone will not reveal an incorrect whole-quantity interpretation; a beyond-boundary case will.
What score do five units receive under the original rule?
Show the worked answer
Eight: 3×2 + 2×1. Only the two units beyond three use the one-point band.
Acceptance wording to adapt
For integer units n≥0, give 2 points per unit for the first min(n,3) units and 1 per unit for the remaining max(n−3,0). Earlier units retain their band when n grows.