Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to convert a map length with a scale.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Multiply whole numbers and convert centimetres to metres.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A map uses a scale of 1:25,000. Two points are 6 cm apart on the map. What actual straight-line distance does that represent in kilometres?
Why this math matters
A map scale relates drawing length and actual length through consistent units. Check the printed scale bar after resizing a plan; the original ratio may no longer apply.
Set up the model
A useful answer starts with clear assumptions:
- The map has a uniform scale.
- The requested distance is straight-line distance, not a road route.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Convert a map length with a scale
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A map uses a scale of 1:25,000. Two points are 6 cm apart on the map. What actual straight-line distance does that represent in kilometres?
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the quantities
1 cm on map = 25,000 cm in reality
A scale written as a bare ratio compares like units.
Apply the relationship
6 × 25,000 = 150,000 cm = 1,500 m
Multiply by the scale factor, then divide by 100 to convert centimetres to metres.
Check and interpret
1,500 m = 1.5 km
The result describes the direct separation of the points.
The result
1,500 m = 1.5 km
The result describes the direct separation of the points.
Common mistakes to catch
- Mixing centimetres and metres inside the scale ratio creates a factor-of-100 error.
- A road distance can exceed the straight-line map distance.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
At 1:2,000 scale, how long is a real 50 m path on the drawing?
Show a hint
Convert the real length to centimetres before dividing.
Reveal answer and explanation
2.5 cm
50 m = 5,000 cm; 5,000/2,000 = 2.5 cm.
Practice 2
A drawing doubles in both dimensions during printing. What happens to its 1:500 scale?
Show a hint
One new centimetre represents half as much real distance.
Reveal answer and explanation
It becomes 1:250
Each feature now occupies twice the paper length, so the reality-to-drawing factor is halved.
Take the idea with you
Check the printed scale bar after resizing a plan; the original ratio may no longer apply.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Choose the base of a percentage change
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