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The coordinate system

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

In the game Battleship (Schiffe versenken) you must say exactly where a ship is. For this you need two numbers. You learn the coordinate system (das Koordinatensystem): plotting and reading points.
📄 Open worksheet (PDF, German)

The video

In the video we draw the x-axis and the y-axis. Then we go from the zero point to the points.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:20 The axes
  3. 0:54 Plotting points
  4. 1:37 Reading points
  5. 2:18 Careful, mistake!
  6. 2:37 Try it yourself

The most important points

The coordinate system

The x-axis (die x-Achse) goes to the right, the y-axis (die y-Achse) goes up. They meet at the zero point (der Nullpunkt, the origin).

The x-axis, the y-axis and the zero point.
The x-axis, the y-axis and the zero point.

First x, then y

A point has two coordinates (die Koordinaten): \(A(3\,|\,5)\). First you go 3 to the right (x-coordinate), then 5 up (y-coordinate).

A(3\,|\,5) and B(7\,|\,2): first to the right, then up.
\(A(3\,|\,5)\) and \(B(7\,|\,2)\): first to the right, then up.

Careful: \((2\,|\,6)\) and \((6\,|\,2)\) are different points. The order matters.

If you go up first, you end up at the wrong point.
If you go up first, you end up at the wrong point.

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

Try it yourself

Task

a) You go 4 to the right and 1 up. What is the point? b) Where is the point \((0\,|\,5)\)?

Show solution

a) \((4\,|\,1)\) b) on the y-axis, 5 up

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: das Koordinatensystem (x-Achse, y-Achse, Nullpunkt, Punkte eintragen und ablesen, erst x, dann y). Stelle mir nacheinander fünf kurze Aufgaben. Warte immer auf meine Antwort. Sag mir dann, ob sie richtig ist, und erkläre kurz, warum. Benutze einfache deutsche Sätze.

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.