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Drawing oblique drawings

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

You draw cubes and cuboids as oblique drawings (das Schrägbild) on squared paper.
📄 Open worksheet (PDF, German)

The video

In the video a cube is drawn step by step. The squares and the square diagonals are counted.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:18 The rules
  3. 0:54 Drawing a cube
  4. 1:40 Drawing a cuboid
  5. 2:11 Careful, mistake!
  6. 2:29 Try it yourself

The most important points

The rules

Edges to the right and upwards: real size, \(1\) cm \(=\) 2 squares (Kästchen). Edges backwards (the depth, die Tiefe): slanted, \(1\) cm \(=\) 1 square diagonal (Kästchendiagonale). Edges you cannot see: dashed (gestrichelt).

Left: 1 cm to the right and upwards; right: the depth, 3 cm = 3 square diagonals.
Left: \(1\) cm to the right and upwards; right: the depth, \(3\) cm \(=\) 3 square diagonals.

Drawing a cube

1. Front face in real size. 2. Edges backwards from top left, top right and bottom right. 3. Join the corners at the back. 4. The three edges at the corner back bottom left dashed.

Cube with a = 4 cm: 8 squares at the front, 4 square diagonals backwards.
Cube with \(a = 4\) cm: 8 squares at the front, 4 square diagonals backwards.
Mistake on the left: 2 diagonals per cm – the cuboid is much too deep.
Mistake on the left: 2 diagonals per cm – the cuboid is much too deep.

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
Page 1/5
The worksheet – Page 2
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The worksheet – Page 3
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The worksheet – Page 4
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Show the worksheet solutions
The worksheet – Page 5
Page 5/5

Try it yourself

Task

Cuboid: 5 cm long, 2 cm high, 3 cm deep. a) How many squares long? b) How many squares high? c) How many square diagonals backwards?

Show solution

a) 10 squares b) 4 squares c) 3 square diagonals

Keep learning with a language model

You are my maths teacher. I am learning German as a second language. Our topic: oblique drawings of cubes and cuboids on squared paper (nach rechts und oben 1 cm = 2 Kästchen, nach hinten 1 cm = 1 Kästchendiagonale, unsichtbare Kanten gestrichelt). 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.