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

The idea

Every measurement is a number together with a unit, and the unit is part of the answer. Length runs 10 mm = 1 cm, 100 cm = 1 m and 1000 m = 1 km; mass runs 1000 g = 1 kg and 1000 kg = 1 tonne; capacity runs 1000 ml = 1 litre, with 1 ml filling exactly 1 cm³. Area and volume factors are the length factor squared and cubed, so 1 m² = 10000 cm² and 1 m³ = 1000000 cm³. Put every length into the same unit before you calculate: for a rectangle measuring 0.5 m by 30 cm, change 0.5 m into 50 cm, then the area is 50 × 30 = 1500 cm². Time is not decimal, so 2.5 hours means 2 hours and 30 minutes. Money answers keep two decimal places, so write £4.50 and not £4.5.

What earns the marks

• Converting every measurement into a common unit before any calculation, even if the arithmetic that follows is wrong.
• Using the squared or cubed conversion factor when changing area or volume units, such as multiplying by 10000 to go from square metres to square centimetres.
• The numerical answer together with the unit the question asks for, since a value carrying the unit of a different measure does not earn the accuracy mark.
• A correct method turning a time in hours and minutes into a decimal number of hours, or turning one back.

Common mistakes and how to put them right

• Converting 1 m² into 100 cm² instead of 10000 cm², because the length factor was not squared.

• Reading 3.45 hours as 3 hours and 45 minutes when it is 3 hours and 27 minutes.

• Mixing centimetres and metres inside one calculation, so the area comes out a hundred times too large or too small.

• Writing a money answer as £6.5 rather than £6.50, or dropping the units from a volume.

Exam tips

• Write at the top of your working which unit you are going to use, then convert everything into it before you start.
• Check the unit the answer is asked for, because it is often not the unit the measurements were given in.
• For area and volume, square or cube the length conversion factor rather than using it as it stands.