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Estimate and check

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

Is your result right? The estimate (der Überschlag) shows it roughly, the check (die Probe) exactly. You learn rounding, the estimate for all four operations and the inverse operation (die Umkehraufgabe).
📄 Open worksheet (PDF, German)

The video

In the video an estimate finds the mistake in Tom's problem.

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

Contents of the video

  1. 0:00 Introduction
  2. 0:15 Rounding
  3. 0:41 Estimate
  4. 1:10 Finding the mistake
  5. 1:28 Check
  6. 2:08 Careful, mistake!
  7. 2:29 Try it yourself

The most important points

Rounding for the estimate

Keep the first digit, all other digits become 0. Look at the second digit: 5 or more: round up. Less than 5: round down. \(485 \to 500\), \(296 \to 300\), \(431 \to 400\).

The rule for rounding.
The rule for rounding.

Estimate for all operations

\(485 + 296 \approx 500 + 300 = 800\) · \(912 - 487 \approx 900 - 500 = 400\) · \(38 \cdot 52 \approx 40 \cdot 50 = 2\,000\) · \(1\,934 : 48 \approx 2\,000 : 50 = 40\).

The estimate for plus, minus, times and divided by.
The estimate for plus, minus, times and divided by.

The check

Do the inverse operation: plus \(\to\) minus, minus \(\to\) plus, times \(\to\) divided by, divided by \(\to\) times. Example: \(781 - 296 = 485\), so \(485 + 296 = 781\) is right.

The check with the inverse operation.
The check with the inverse operation.

Careful: when multiplying, count all the zeros: \(40 \cdot 50 = 2\,000\), not \(200\). Tom's result \(485 + 296 = 681\) does not fit the estimate \(800\). The right result is \(781\).

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
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) Make an estimate: \(697 + 312\). b) Check \(84 \cdot 15 = 1\,260\).

Show solution

a) \(700 + 300 = 1\,000\) (exactly \(1\,009\)) b) \(1\,260 : 15 = 84\), the check is right.

Keep learning with a language model

Du bist meine Mathe-Lehrkraft. Ich lerne Deutsch als Zweitsprache. Unser Thema: Überschlag und Probe (Runden, Umkehraufgabe bei Plus, Minus, Mal und Geteilt). 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.