Using Numeracy in Real-Life Contexts: choosing the maths and communicating the answer
This strand is where the other three are applied without a label telling you which one to use. Questions are set in unfamiliar situations - a community fundraiser, a bus timetable, a power bill, a savings plan - and the marks are for deciding what to calculate, carrying it out, and stating the answer in a way that makes sense in the context. Expect multi-step problems where the arithmetic is easy but the reasoning is not.
Core rules
Unpack before computing: what is given (with units), what is asked (with units), and what connects them. Most multi-step problems chain a rate, a percentage or a conversion.
- Wages: pay = rate × hours; overtime uses a multiplier (time-and-a-half = ×1.5).
- GST in New Zealand is 15%: add it with ×1.15, remove it with ÷1.15.
- Successive percentage changes multiply and never add: 20% off then 10% off is ×0.8 ×0.9 = 0.72, which is 28% off, not 30%.
- Best buy: compare unit prices (cost per 100 g, per litre, per wash), not pack prices.
- Rounding must respect the context: money to cents, whole items upwards, and the final answer must be plausible.
Worked example
A 460 km trip in a car using 7.2 L per 100 km, with fuel at $2.85 per litre. Dividing 460 by 100 gives 4.6 hundreds of kilometres. Fuel = 4.6 × 7.2 = 33.12 L. Cost = 33.12 × 2.85 = $94.39. A quick estimate - roughly 32 L at about $3 per litre, so about $96 - confirms the answer is sensible before it is written down.
Traps that cost marks
- Answering a different question from the one asked, such as giving cost per person when the total cost was required.
- Mixing units inside a chain - hours with minutes, grams with kilograms.
- Rounding money at an intermediate step and carrying the error forward.
- Ignoring qualifiers like ‘at least’, ‘maximum’ or ‘per day’, which change the rounding direction.