Strong band · 120+
Percentages, ratios and the compound items held — including the ones where a discount lands twice and the intuitive answer (20% then 25% is 45%) is wrong. The scale samples applied numeracy rather than mathematics: change from a note, a recipe scaled from four servings to seven, two trains closing at 80 and 70 km/h, the odds of rolling a seven. There is no calculator, so it reads mental arithmetic alongside the reasoning and the two are hard to separate in one number. What it does not sample is mathematics as a discipline — no proof, no algebra beyond the arithmetic. Everyday numeracy measured well, not mathematical talent.
Mid-band · 90–119
The direct items — percentages, area, change from a note — went in; the drop-off sits where a number has to be carried through two steps, or where the intuitive answer is a trap. Successive discounts are the classic one: 20% and then 25% off feels like 45% and is not. This is applied numeracy rather than mathematics, and it is strongly practice-shaped: people who work with numbers weekly sit above people with identical schooling who do not. That gap closes faster than most expect, because the underlying moves — ratio, percentage, average — are few and they repeat.
Below sample · under 90
The number-handling items did not carry this time, and the most useful thing to know is what this scale is not. It is not mathematics as a subject: there is no algebra and no proof here, only applied numeracy — percentages, ratios, averages, change from a note. It is also unforgiving of speed, because there is no calculator, so mental arithmetic and reasoning collapse into one score and a slow, correct thinker can land below a fast, careless one. Of the four scales this is where deliberate practice moves the number most reliably, and where school-era discomfort with numbers explains more of the result than capacity does.