🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Select a suitable scale method.
- Convert units within multi-step problems.
- Calculate route lengths and plan dimensions.
- Check whether an answer is reasonable.
🤔 Start with the Idea
Practical scale questions combine measuring, unit conversion and proportional reasoning. A clear plan prevents the units from becoming confusing.
🎮 Explore the Scale
Change the map or drawing length and the scale value. Notice how the real distance changes proportionally.
🧠 Let’s Think Together
A rectangular field measures 4.8 cm by 3.2 cm on a map with RF 1 : 5 000. Find its actual dimensions in metres.
Actual length: 4.8 × 5 000 = 24 000 cm = 240 m.
Actual width: 3.2 × 5 000 = 16 000 cm = 160 m.
Answer: 240 m by 160 m.
✏️ Practice Questions
Build confidence- At RF 1 : 20 000, a path is 8.5 cm. Find the real length in kilometres.
- A 30 m room is drawn as 12 cm. Find the scale in the form 1 : n.
- A map route has lengths 2.4 cm, 5.1 cm and 3.5 cm at 1 cm = 4 km. Find the journey length.
✅ Check your answers
- 1.7 km
- 1 : 250
- 44 km
⚠️ Common Mistakes
- Using different units on the two sides of a ratio scale.
- Multiplying when the question requires division, or dividing when it requires multiplication.
- Leaving out the unit or using a linear unit for an area.
- Rounding too early in a multi-step calculation.
🎯 Exam Focus
Write what the scale means before calculating. Show unit conversions clearly, keep full calculator values until the final step, and include the correct unit in the answer.
📌 One-Minute Summary
- A scale connects a drawing or model to the corresponding real object.
- Use multiplication when moving from a drawing measurement to a real measurement.
- Use division when working backwards from real size to drawing size.
- Ratio scales require the same unit on both sides.
- Area changes by the square of the linear scale factor.