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Terms and variables

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

We make squares in a row out of sticks. How many sticks do you need for 100 squares? With a variable (die Variable) and a term (der Term) you can work it out quickly.
📄 Open worksheet (PDF, German)

The video

In the video we make squares out of sticks and find the term \(3 \cdot n + 1\).

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

Contents of the video

  1. 0:01 Introduction
  2. 0:24 The variable
  3. 0:44 A term
  4. 1:08 Putting in values
  5. 1:49 Careful, mistake!
  6. 2:09 Try it yourself

The most important points

Variable and term

A variable is a placeholder for a number, for example \(n\) or \(x\). A term is a calculation with numbers and variables, for example \(3 \cdot n + 1\).

1 stick at the start, 3 new ones for each square: 3 · n + 1.
1 stick at the start, 3 new ones for each square: \(3 \cdot n + 1\).

Putting in values

Put a number in for the variable and calculate. For \(n = 10\): \(3 \cdot 10 + 1 = 31\).

For x = 4, 2 · x - 5 = 3.
For \(x = 4\), \(2 \cdot x - 5 = 3\).

Careful: \(3n\) means \(3 \cdot n\). For \(n = 5\), \(3n = 15\), not 35.

Between a number and a variable there is an invisible times sign.
Between a number and a variable there is an invisible times sign.

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
Page 4/4

Try it yourself

Task

a) Calculate \(4 \cdot n + 2\) for \(n = 3\). b) Calculate \(5 - 2 \cdot x\) for \(x = 4\).

Show solution

a) \(4 \cdot 3 + 2 = 14\) b) \(5 - 8 = -3\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Terme und Variablen (Variable als Platzhalter, Term aufstellen, Werte einsetzen). 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.