Numeracy: Number, Measurement, Space and Data
What numeracy questions test
Numeracy spans number and algebra, measurement and geometry, statistics and probability, and - at higher levels - proportional and algebraic reasoning. Questions are usually set in words, so the first skill is translation: turning a sentence into an operation.
Concepts to master
- Place value and operations: order of operations (brackets, indices, multiplication and division left to right, addition and subtraction left to right).
- Fractions, decimals, percentages: convert to whichever form makes the comparison easy. 0.6, 3/5 and 60% are equal.
- Ratio and rate: scale both parts together. For a recipe for 4 scaled to 10, multiply every quantity by 10/4 = 2.5.
- Perimeter, area and volume: perimeter is a length (units), area is square units, volume is cubic units. Area of a triangle is half base times height; the height must be perpendicular to the base.
- Angles: angles on a straight line sum to 180°, at a point to 360°, and in a triangle to 180°. Vertically opposite angles are equal.
- Averages: mean is the total divided by the count; median is the middle value when ordered; mode is the most frequent. An outlier pulls the mean but barely moves the median.
- Probability: a probability is favourable outcomes over total equally likely outcomes, always between 0 and 1.
Traps
- Unit mismatch: minutes and hours, centimetres and metres, grams and kilograms. Convert before calculating.
- Answering the wrong question: the question asks for the remaining amount, not the amount used.
- Misreading scale on graphs: check whether each gridline is 1, 2, 5 or 10 units.
- Rounding too early: keep full precision until the final step.
Worked example
A tank holds 240 litres and is 3/8 full. How many more litres are needed to fill it? Full fraction remaining is 1 − 3/8 = 5/8. Then 5/8 × 240 = 150 litres. As a check, 3/8 × 240 = 90 litres already present, and 90 + 150 = 240.