Using Mathematics in Context - Te Whakamahi Pāngarau i roto i te Horopaki
Using mathematics in context tests whether you can pull the right numbers from a realistic situation and apply number, measurement or statistics correctly. Contexts include personal finance, workplaces, community decisions and travel.
Core rules and concepts
- Identify the relevant information and discard distractors. Check that all quantities use compatible units and time periods.
- GST in New Zealand is 15%. To add GST, multiply by 1.15. To remove GST from a GST-inclusive price, divide by 1.15. The GST component alone is 3/23 of the inclusive price.
- Simple interest: I = P × r × t, with r as a decimal and t in years. Compound amount: A = P(1 + r)^n.
- Wages: ordinary hours × hourly rate; overtime hours × overtime rate. Time-and-a-half means ×1.5.
- For decisions, compare total costs or break-even points rather than headline rates.
- State the decision and support it with the calculated figures.
Worked example
A worker is paid $23.50 per hour for 32 ordinary hours and time-and-a-half for 6 overtime hours. Find total pay. Ordinary pay = 32 × 23.50 = $752.00. Overtime rate = 23.50 × 1.5 = $35.25. Overtime pay = 6 × 35.25 = $211.50. Total pay = 752.00 + 211.50 = $963.50. Check: the overtime rate is higher than the ordinary rate, and 6 hours at about $35 is about $210, so the total is reasonable.
Traps
- Applying the overtime rate to all hours instead of only the extra hours.
- Adding GST to a price that already includes it.
- Using 15% of the GST-inclusive price as the GST amount; the correct fraction is 3/23.
- Mixing weekly and annual figures.
- Giving a calculation with no decision or conclusion.