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Negative numbers

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

In winter the thermometer often shows less than zero degrees, for example \(-3\) °C. You get to know the negative numbers (die negativen Zahlen) on the number line and put them in order.
📄 Open worksheet (PDF, German)

The video

In the video we lay the thermometer down: this gives the number line (die Zahlengerade).

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

Contents of the video

  1. 0:00 Introduction
  2. 0:21 The number line
  3. 1:03 Ordering
  4. 1:44 Opposite number and absolute value
  5. 2:05 Careful, mistake!
  6. 2:29 Try it yourself

The most important points

The number line

To the right of zero are the positive numbers, to the left the negative ones: \(-1, -2, -3\) … Zero is neither positive nor negative.

-4: four steps to the left. 2: two steps to the right.
\(-4\): four steps to the left. \(2\): two steps to the right.

Ordering

The number further to the right is bigger: \(-2 > -5\) and \(1 > -1\). From small to big: \(-4 < -1 < 0 < 2 < 3\).

Read the number line from left to right.
Read the number line from left to right.

Opposite number and absolute value

\(3\) and \(-3\) are opposite numbers (die Gegenzahlen). The absolute value (der Betrag) is the distance to zero: \(|-3| = 3\).

Both numbers are 3 away from zero.
Both numbers are 3 away from zero.

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) Which number is bigger: \(-7\) or \(-3\)? b) Order from small to big: \(2, -6, 0, -1\).

Show solution

a) \(-3\), because it is further to the right. b) \(-6 < -1 < 0 < 2\)

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: negative Zahlen (Zahlengerade, ordnen, Gegenzahl, Betrag). 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.