Practice Semi-written arithmetic
Semi-written calculation works in clear steps without the full written layout: split numbers into tens and ones and use helper facts such as doubling.
It is faster than the written method and shows what that method really does.
Exercises with solutions
Semi-written calculation means clear steps in your head or on paper, without the full written layout. Split numbers into tens and ones, work step by step and use helper facts such as doubling or building on facts you already know.
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Exercise 1
Calculate semi-written: 48 + 25.
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73
Split 25 into 20 and 5. First 48 + 20 = 68, then 68 + 5 = 73. Tens first, ones second – that keeps your head clear.
Exercise 2
Calculate semi-written: 52 − 27.
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25
First 52 − 20 = 32, then 32 − 7 = 25. You can also count up: from 27 to 52 is 3 up to 30 and another 22, together 25.
Exercise 3
Calculate semi-written: 4 · 25.
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100
Double twice: 2 · 25 = 50 and 2 · 50 = 100. Helper facts with 25 come from quarters of 100.
Exercise 4
Calculate semi-written: 6 · 14.
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84
Split 14 into 10 and 4: 6 · 10 = 60 and 6 · 4 = 24, together 84. That is exactly the distributive law.
Common mistake
Forgetting the second step when subtracting in steps: after 52 − 20 = 32 you still owe the 7, not nothing. When multiplying via splitting, both parts get multiplied – 6 · 14 is 6 · 10 plus 6 · 4, not just 6 · 10.
Free maths worksheets with worked solutions
Numbers to 1000: free German worksheet with solutions (PDF)
Grades 3/4: questions 1–5 practise numbers and simple sums; 6–10 practise semi-written steps that cross the tens and hundreds boundary, with question 10 as a word problem.
PDF and questions in German
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