Topics · Primary Maths · Length, Mass & Volume
Length, mass and volume: units, conversions and reading scales
Three different things to measure, one set of habits. Know which units belong to which measure, convert by multiplying or dividing by 10, 100 or 1000, and work out what one small mark on a scale is worth before reading it.
- 517 exam papers analysed
- appears in 98% of P6 Maths papers
- ~4 min read
01 Which units measure what
Mixing up the three is a surprisingly common way to lose a mark, and the fix is only to notice which family a unit belongs to.
Length — millimetre (mm), centimetre (cm), metre (m), kilometre (km). How long, how tall, how far.
Mass — gram (g), kilogram (kg). How heavy. Mass is the word papers use; “weight” means something slightly different and is not what is being measured here.
Volume — millilitre (ml), litre (l), and cubic centimetres (cm³) for solids. How much space, or how much a container holds.
02 Converting: what to multiply by
Every conversion is a multiply or a divide by 10, 100 or 1000. Going to a smaller unit gives a bigger number, because it takes more small things to make the same amount.
- 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
- 1 kg = 1000 g. 1 litre = 1000 ml.
- Big unit to small unit: multiply. 2.5 km = 2.5 × 1000 = 2500 m.
- Small unit to big unit: divide. 450 g = 450 ÷ 1000 = 0.45 kg.
- Check the direction with common sense. A number that got smaller when you moved to a smaller unit means the operation went the wrong way.
03 Reading a scale — where the marks are lost
The numbered marks are never the problem. The small unnumbered ones between them are, because a child who assumes each small mark is 1 gets every reading wrong on a scale that goes up in anything else.
Work out what one small mark is worth first. Find two numbered marks, subtract, and count the gaps between them — not the lines, the gaps.
Below, 0 to 1 is divided into 5 gaps, so each small mark is 0.2. The arrow sits three marks past 2, which makes it 2.6 — not 2.3.
04 Compound units
Papers write measurements two ways and expect you to move between them. 2 m 35 cm and 2.35 m are the same length; 1 kg 200 g and 1.2 kg are the same mass.
Watch the columns when converting. 1 kg 50 g is 1.05 kg, not 1.5 kg — grams run to 1000, so 50 g needs its place held, exactly as cents do in money.
Before adding or subtracting, put everything in one unit. Adding 2 m 35 cm to 80 cm by lining up the numbers as written is how a right method produces a wrong answer.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- massmore than onemasses
How heavy something is, measured in grams and kilograms. The word papers use rather than “weight”.
- capacitysaykuh-PASS-uh-tee
How much a container holds, measured in millilitres and litres.
- millimetre, written mmsayMIL-i-mee-tuhmore than onemillimetres
A tenth of a centimetre. Ten of them make 1 cm.
- kilometre, written kmsayKIL-uh-mee-tuhmore than onekilometres
A thousand metres. Used for distances between places.
- kilogram, written kgsayKIL-uh-grammore than onekilograms
A thousand grams.
- scalemore than onescales
The row of marks on a ruler, weighing machine or measuring jug. Work out what one small mark is worth before reading it.
- compound unitmore than onecompound units
A measurement written in two units at once, like 2 m 35 cm or 1 kg 200 g.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Measuring with a ruler, comparing lengths and masses, and reading simple scales.
Practise P2 Length, Mass & Volume — 10 questions →83% of P2 papers
- P3
Units and the first conversions, and measurements written in two units.
Practise P3 Length, Mass & Volume — 10 questions →65% of P3 papers
- P4
Converting between all the units, and adding and subtracting compound measurements.
Practise P4 Length, Mass & Volume — 10 questions →87% of P4 papers
- P5
Measurement inside area, perimeter and volume problems, and decimals in measurements.
Practise P5 Length, Mass & Volume — 10 questions →84% of P5 papers
- P6
Multi-step problems mixing units, and rate and speed built on distance and time.
Practise P6 Length, Mass & Volume — 10 questions →98% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“Each small mark on the scale is 1.”
Only sometimes. Count the gaps between two numbered marks and divide. Five gaps between 0 and 1 makes each mark 0.2, so three marks past 2 is 2.6, not 2.3.
“1 kg 50 g is 1.5 kg.”
1.05 kg. There are 1000 g in a kilogram, so grams take three columns — 50 g is 0.050 kg. 1.5 kg would be 1 kg 500 g.
“2.5 km is 250 m.”
2500 m. A kilometre is 1000 metres, so multiply by 1000. Moving to a smaller unit always makes the number bigger.
“I added 2 m 35 cm and 80 cm and got 2 m 115 cm.”
Centimetres carry at 100, so 115 cm is 1 m 15 cm. The answer is 3 m 15 cm. Converting everything to one unit first avoids this entirely.
“The answer is 450.”
450 what? A measurement without its unit is not an answer, and grams and kilograms are a thousand times apart.
Now try it
50 questions across 5 levels, marked as you go with the working shown.