Maths homework, the German way

The questions

1. Question 1 of 6How is 984 divided by 8 written in a German exercise book?

   

   • 984 under a bracket with 8 outside
   • 984 : 8 = 123, all on one line
   • 8 / 984
   • 984 ÷ 8 with the answer underneath

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   Answer: 984 : 8 = 123, all on one line

   In Germany it goes on one line with a colon as the division sign, and the answer comes after the equals sign. The working goes underneath, one digit per box on squared paper (Mahiko).

   Source: Mahiko (DZLM): Schriftlich dividieren, parent guide (German, Feb 2022, PDF)

   Written division in German school

2. Question 2 of 6In a German maths book, what does a raised dot ( · ) mean?

   • Divide
   • Times
   • Decimal point
   • Plus

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   Answer: Times

   In Germany a dot means "times": 1 · 8 = 8. The colon ( : ) means "divided by".

   Source: Mahiko (DZLM): Schriftlich dividieren, parent guide (German, Feb 2022, PDF)

   Written division in German school

3. Question 3 of 62257 : 7 leaves 3 over. How does a German primary school write that?

   • r 3
   • 322 Rest 3
   • 322.43
   • 322 3/7

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   Answer: 322 Rest 3

   German primary school writes "Rest": 2257 : 7 = 322 Rest 3 (Mahiko). In England, Year 6 children also learn to write a remainder as a fraction or decimal (GOV.UK).

   Source: Mahiko (DZLM): Schriftlich dividieren, parent guide (German, Feb 2022, PDF); GOV.UK: National curriculum in England, mathematics programmes of study

   Written division in German school

4. Question 4 of 6What is the "Umkehraufgabe" teachers ask for?

   • A second division
   • The reverse sum: multiply the answer back to check
   • A times-table test
   • Homework for parents

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   Answer: The reverse sum: multiply the answer back to check

   Multiply the answer back: 123 · 8 = 984, so it is right. With a remainder, add it at the end. PIKAS lists this check and a quick estimate (Überschlag) as things your child should be able to do.

   Source: PIKAS (DZLM): Schriftliche Division, Klasse 4 (German, Nov 2022, PDF)

   Written division in German school

5. Question 5 of 6816 : 8. Which answer shows the most common slip PIKAS warns about?

   • 102
   • 12
   • 101
   • 108

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   Answer: 12

   PIKAS names place value and zeros as typical mistakes. If the number brought down is too small, your child must write a 0 in the answer: 816 : 8 = 102, not 12. So 12 is the slip.

   Source: PIKAS (DZLM): Schriftliche Division, Klasse 4 (German, Nov 2022, PDF)

   Written division in German school

6. Question 6 of 6Has Lower Saxony abolished written division in primary school?

   • Yes, completely
   • No: it is prepared in steps, with half-written division at the centre, and finished at secondary school

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   Answer: No: it is prepared in steps, with half-written division at the centre, and finished at secondary school

   Lower Saxony's ministry says written division is not abolished, but in primary school it is now prepared in partial steps, with half-written division (halbschriftliches Dividieren) at the centre.

   Source: Niedersächsisches Kultusministerium: Niedersachsen schafft die schriftliche Division nicht ab (German)

   Written division in German school