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Teaching mathematics
Teaching mathematics

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2.1 Problem solving using proportional reasoning

Proportional reasoning questions cover a huge variety of real-life applications, from best buys to map scales.

Maps and scales

Maps and scale drawings use proportionality. In order for a map to be useful, it needs a scale which represents how much smaller it is than the place it represents. This means that journey distances can be accurately calculated.

Activity 8 Example problem: model boat

Timing: Allow 5 minutes

A scale model of a sailboat is made to a scale of 1:20 (Figure 13).

  • a.If the model boat is 17 cm wide, how wide is the actual boat?
  • b.If the boat has a sail of height 5 m, how high is the sail on the model?
A photo of a model sail boat
Figure 13 A scale model boat


  • a.The actual boat is 20 times larger, so it will be 340 cm or 3.4 m wide.
  • b.The model boat is 20 times smaller, so the sail will be 0.25 m or 25 cm high