Mensuration and calculation: use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money etc.)

The idea

This topic requires you to choose and use standard units for length, area, volume or capacity, mass, time and money, and to apply the related concepts that link them. For length, work in mm, cm, m and km; for area, use mm², cm², m² and km²; for volume and capacity, use mm³, cm³, m³ and litres, remembering that 1 cm³ = 1 ml and 1 m³ = 1000 litres. Mass is measured in mg, g, kg and tonnes, time in seconds, minutes, hours and years, and money in pounds and pence. You must convert correctly, for example 3.5 m = 350 cm, 2 m² = 20 000 cm², and 4.2 litres = 4200 cm³.

What earns the marks

• Selects the appropriate standard unit for a given measurement context, such as cm for a pencil length or m³ for a room volume.
• Converts between metric units of length, area, volume/capacity, mass, time and money using correct multiplicative factors.
• Applies the relationship between volume and capacity, including 1 cm³ = 1 ml and 1 m³ = 1000 litres.
• Uses squared and cubed unit notation correctly, for example cm² and m³, and distinguishes area from volume units.
• Interprets and compares quantities given in different units by converting to a common unit before choosing an answer.

Common mistakes and how to put them right

• Treating area and volume conversions as if they were length conversions.

  Put it right: Square the length factor for area and cube it for volume, so 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³.

• Confusing capacity and volume units, for example writing 1 litre = 1 m³.

  Put it right: 1 litre = 1000 cm³ and 1 m³ = 1000 litres.

• Using non-standard or mixed units in a calculation, such as adding metres to centimetres without converting.

  Put it right: Convert all quantities to the same unit first.

• Ignoring the unit given in the answer options and selecting a numerically correct value with the wrong unit.

  Put it right: Check both the number and the unit in every option.

Exam tips

• Underline the unit required in the question and the units in the options before doing any arithmetic.
• Write down the conversion factor you are using, for example 1 m = 100 cm, so you can check the direction of the conversion.
• For area and volume, convert the linear measurement first and then square or cube it, rather than multiplying the area or volume by a linear factor.
• Estimate the size of the answer in real terms, such as whether a bottle holds about 2 litres or 2 m³, to reject impossible options.