AC9M10M05Year 10MeasurementPractised in part

AC9M10M05 — Year 10 Measurement

Official Curriculum Content Description:

use mathematical modelling to solve practical problems involving proportion and scaling of objects; formulate problems and interpret solutions in terms of the situation; evaluate and modify models as necessary, and report assumptions, methods and findings

Coverage notice: Practised in part

What this practice covers: multi-step direct and inverse proportion

What is omitted: scaling of objects; formulating, evaluating and modifying a model

Worked Examples (1)

Example 1Multi-Step Proportional Reasoning
If 22 shearers shear 3030 sheep in 33 hours, how long will 66 shearers take to shear 9090 sheep?
Common mistake: Treating shearers and time as directly proportional instead of inversely proportional, giving 27 hours.
Correct Answer:3 hours3\text{ hours}
Accepted: A unit is optional (hours accepted).
Worked Solution:
1. Shearers and time are inversely proportional: scale shearers to 66. 11 shearer shears 3030 sheep in 2×3=62 \times 3 = 6 hours. 66 shearers shear 3030 sheep in 6÷6=16 \div 6 = 1 hour. 2. Sheep and time are directly proportional: scale sheep from 3030 to 9090. 66 shearers shear 9090 sheep in 1×9030=3 hours1 \times \frac{90}{30} = 3\text{ hours}.

Ready to practise this descriptor?

Work through unlimited interactive questions for this curriculum skill, with instant answers and step-by-step methods.

Start unlimited online practicePrint Year 10 worksheet