Drawing distance
The length measured on the page, map or plan.
🎯 Learning Objectives
By the end of this lesson, you should be able to:
- Explain what a scale compares.
- Describe why maps, plans and models use scales.
- Interpret a simple statement scale.
- Find a real distance by multiplying.
🤔 Start with the Idea
Imagine fitting the road from Harare to Bulawayo onto one page. The road is hundreds of kilometres long, but on a map it may be only a few centimetres. A scale makes this possible.
A scale tells us how a measurement on a drawing, map or model is connected to the corresponding measurement in real life.
📖 What Is a Scale?
A scale is the relationship between a distance on a drawing and the matching distance in real life.
1 cm on the map represents 5 km in real life
The drawing is smaller, but the proportions stay correct. Every map centimetre represents the same real distance.
Real distance
The actual length of the road, room, object or area.
🎮 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 map has the scale 1 cm represents 3 km. Two villages are 7 cm apart on the map.
Step 1: One centimetre represents 3 km.
Step 2: Seven centimetres represent seven groups of 3 km.
7 × 3 = 21 km
Answer: The villages are 21 km apart.
✏️ Practice Questions
Build confidence- A map uses 1 cm = 4 km. Find the real distance represented by 6 cm.
- A plan uses 1 cm = 2 m. Find the actual length represented by 9 cm.
- A route is 5.5 cm on a map with scale 1 cm = 8 km. Find its real length.
✅ Check your answers
- 24 km
- 18 m
- 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.