Reading Scales: Thermometers, Jugs, Maps & Graphs

Every scale question — a thermometer, a measuring jug, a ruler on a map, the axis of a graph — starts with the same move: find out what one gap is worth. Take two labelled marks, subtract, and divide by the number of gaps between them. Gaps, not marks: between 0 and 100 there are five marks but only four gaps, so each gap is 25. Test writers know that students divide by the number of marks, and they write the wrong-but-tempting answer into the options. Work out the gap value before you look at where the pointer or the water level is, then count up from a labelled mark.

Thermometer questions usually show two thermometers and ask for the difference, or show one and ask what it will read after a change. The trap is the small tick. Labels every 10 with five gaps between means each small tick is worth 2, not 1; labels every 5 with five gaps means 1; labels every 10 with four gaps means 2.5. Read each thermometer from its own nearest label — 'two ticks above 10' — rather than from the bottom, and then do the subtraction. The official paper's thermometers had unlabelled ticks precisely so that a student who assumes 'one tick, one degree' lands on a wrong option.

A measuring jug in a test does not have to be marked in tens. The official paper labelled a container 0 and 40 mL and drew five gaps, so each mark was 8 mL, and the tempting answers 25 and 30 were in the options. Same rule: subtract the labels, divide by the gaps, then multiply by the mark the water reaches. If the water sits between marks, add half a gap or a quarter of a gap as the picture shows. Jug questions sometimes go on to add blocks that raise the level; then the reading skill is only the first step and you must keep the gap value in your head for the second.

Map questions give a scale like '1 cm represents 20 m' and a ruler drawn in millimetres. The whole difficulty is the unit change. Read the ruler in millimetres, turn it into centimetres by dividing by 10, and only then multiply by the scale: 85 mm is 8.5 cm, and 8.5 lots of 20 m is 170 m. If decimals feel slippery, split it: 8 cm is 160 m and the extra 5 mm is half a centimetre, 10 m, so 170 m. Check the answer against the real world at the end — a distance between two front doors should be a short walk, not nearly two kilometres.

Two graph tricks appear on the test. The first is a bar that ends between gridlines: if gridlines are every 10 and the bar stops halfway, read 35, not 30 or 40. The second is a graph with its scale missing, paired with another graph or a key that lets you recover it. Find one thing you can measure in both — Mia is three gridlines tall in one graph and one-and-a-half circles, six books, in the other — and use it to price a gridline. Then everything else on the graph can be read. Questions like these are chained: read, convert, then answer what was actually asked, which is often a total or a 'how many more'. Quiz and exercises now!