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Scale

This page was translated from German with AI. It has not been checked by a native speaker. Original page in German

Plans and maps are smaller than reality. The scale (der Maßstab) tells you how much smaller or bigger.
📄 Open worksheet (PDF, German)

The video

In the video we draw a room plan \(1 : 100\), read a map \(1 : 10\,000\) and enlarge a ladybird \(10 : 1\).

Subtitles are available in ten languages. Choose them at the bottom right of the video.

Contents of the video

  1. 0:00 Introduction
  2. 0:16 The scale
  3. 0:40 Drawing a door
  4. 1:00 The map
  5. 1:27 Enlarging
  6. 1:50 Careful, mistake!
  7. 2:12 Try it yourself

The most important points

Scale 1 : 100

\(1\,\text{cm}\) on the plan is \(100\,\text{cm} = 1\,\text{m}\) in reality. Plan → reality: \(\cdot 100\). Reality → plan: \(: 100\).

Room 4\,\text{m} \times 3\,\text{m} as a plan 4\,\text{cm} \times 3\,\text{cm}.
Room \(4\,\text{m} \times 3\,\text{m}\) as a plan \(4\,\text{cm} \times 3\,\text{cm}\).

Door \(80\,\text{cm}\): \(80 : 100 = 0{,}8\,\text{cm} = 8\,\text{mm}\) on the plan.

The door is drawn with the set square.
The door is drawn with the set square.

Map and enlargement

Map \(1 : 10\,000\): \(1\,\text{cm}\) is \(100\,\text{m}\); \(6\,\text{cm}\) is \(600\,\text{m}\). Enlargement \(10 : 1\): \(8\,\text{mm}\) become \(8\,\text{cm}\).

School and station: 6\,\text{cm} on the map.
School and station: \(6\,\text{cm}\) on the map.

Careful: \(3\,\text{cm} \cdot 10\,000 = 30\,000\,\text{cm}\), not metres! That is \(300\,\text{m}\).

The worksheet

Here you can see the worksheet for the video (in German). First it explains everything again, then there are practice tasks at three levels. You can also open it as a PDF and print it.

📄 Open worksheet (PDF, German)

The worksheet – Page 1
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The worksheet – Page 2
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The worksheet – Page 3
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Show the worksheet solutions
The worksheet – Page 4
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Try it yourself

Task

Garden plan \(1 : 200\): \(6\,\text{cm}\) long, \(4\,\text{cm}\) wide. How big is the garden in reality?

Show solution

\(1\,\text{cm} \mathrel{\hat{=}} 2\,\text{m}\): \(12\,\text{m}\) long, \(8\,\text{m}\) wide.

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: scale (Maßstab): plan, map, enlargement. Give me five short tasks, one after the other. Always wait for my answer. Then tell me if it is right and explain briefly why. Use simple German sentences.

How this was made: The idea, structure and examples of the series are mine. I made them with the help of AI: a language model (LLM) built the slides of the video following my instructions. The voice was generated with Qwen3-TTS, modelled on my own voice.

The subtitles, the translations, the worksheet and this page were also made with the help of AI. The translations have not been checked by native speakers.

The videos, worksheets, texts and prompts in this series are licensed under CC BY 4.0: you may use, change and share them if you name the source.