Learn with Amar
Teaching video
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Browse grades and teaching videos01 · Read and understand
What you will learn
- Interpret a scale as a conversion rate.
- Track and cancel units.
- Reverse the conversion when the represented distance is known.
Before you start
Multiply decimals by whole numbers and convert 1,000 metres to one kilometre.
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 classroom map uses a scale of 1 cm to 250 m. A straight segment between two landmarks measures 3.6 cm on the map. What distance does it represent?
Why this math matters
A scale connects two measurements of the same feature. Treating it as a conversion rate keeps map centimetres separate from represented metres. The calculation is a proportion because multiplying one distance multiplies the other by the same factor.
Set up the model
A useful answer starts with clear assumptions:
- The map has not been resized after its scale was specified.
- The measured segment uses the map's stated scale; it does not necessarily equal the length of a winding travel 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.
Turn a map measurement into a real distance
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A classroom map uses a scale of 1 cm to 250 m. A straight segment between two landmarks measures 3.6 cm on the map. What distance does it represent?
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.
Write the relationship
represented distance = map length × 250 m/cm
Each additional map centimetre represents another 250 metres. The scale rate names both measurement systems.
Convert the given length
3.6 cm × 250 m/cm = 900 m
Map-centimetre units cancel. The resulting unit is metres in the represented setting, not centimetres on the paper.
Check the proportion
900 m / 250 m per cm = 3.6 cm; 900 m = 0.9 km
The reverse conversion reconstructs the measured map length. Expressing the result in kilometres changes its unit, not the distance.
The result
The segment represents 900 m, or 0.9 km.
A copy enlarged to twice its original size would need an updated scale. Reading the old text scale from a resized image can produce a plausible-looking but incorrect distance.
Common mistakes to catch
- Do not mix map centimetres with represented centimetres without labelling them.
- A straight line between landmarks can be shorter than the actual path travelled.
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 cm to 500 m, what does 2.4 cm represent?
Show a hint
Multiply the map length by the metres-per-centimetre rate.
Reveal answer and explanation
1,200 m, or 1.2 km
2.4 × 500 = 1,200. Divide by 1,000 to convert metres into kilometres.
Practice 2
At the original 1 cm to 250 m scale, how long is a map segment representing 1.5 km?
Show a hint
Convert kilometres to metres before dividing by 250.
Reveal answer and explanation
6 cm
1.5 km = 1,500 m. Then 1,500/250 = 6 map centimetres.
Take the idea with you
Before measuring a printed or onscreen drawing, confirm its scale still applies at the displayed size.
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: Write a parcel-cost rule before calculating
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