The worksheets themselves are in German – just as in class. The editor is only available in German so far.
Sets of calculations – worksheets to print
Calculations with a pattern: work them out, discover the pattern and write down what you notice – also continue a set or find the one that does not fit.
- Choose the number of tasks and the difficulty yourself
- With an answer sheet and, if you like, a QR code to the answers
- At three levels (★ to ★★★) and as group A and B
- As a single worksheet or as a task on a mixed worksheet
Sets of calculations: explained simply
A calculation pattern contains problems built around a shared rule. Work them out and investigate what changes from one row to the next.
How to work it out
- Compare the first number, second number and answer with the next row. What stays the same, increases or decreases?
- Explain why the answers follow the pattern. Check your rule against all rows before continuing it.
An example, step by step
3 + 4, 4 + 4, 5 + 4: what do you notice?
| First number | Second number | Answer |
|---|---|---|
| 3 | + 4 | = 7 |
| 4 | + 4 | = 8 |
| 5 | + 4 | = 9 |
| 6 | + 4 | = 10 |
- Calculate: 3 + 4 = 7, 4 + 4 = 8, 5 + 4 = 9.
- The first number increases by 1 each time. The second stays at 4, so the answer also increases by 1.
- The next matching problem is 6 + 4 = 10.
Understand other variations
Addition: the answer can stay the same
3 + 7 = 10, 4 + 6 = 10, 5 + 5 = 10: one number increases by 1 while the other decreases by 1, balancing each other out. If both increase by 1, the sum increases by 2.
Subtraction: which number changes?
12 − 3 = 9, 12 − 4 = 8, 12 − 5 = 7: taking away 1 more leaves 1 less. If both numbers increase equally, the difference stays the same, for example 12 − 3 = 13 − 4 = 9. If only the first number grows, the answer grows too.
Multiplication and division
3 · 2 = 6, 3 · 3 = 9, 3 · 4 = 12: one more group of three increases the answer by 3. In 12 : 3 = 4, 15 : 3 = 5, 18 : 3 = 6, one more group of three increases the answer by 1. Doubling patterns also occur: 3 · 1, 3 · 2, 3 · 4, 3 · 8.
Continue or find the odd one out
To continue, write the complete next problems. An odd one out breaks the rule. In 3 + 4, 4 + 4, 8 + 4, 6 + 4, the problem 8 + 4 does not fit: 5 + 4 belongs there. A calculation can be correct and still break the pattern.
Your turn
Continue and explain: 2 · 3 = 6, 2 · 4 = 8, 2 · 5 = 10.
Show the answer and method
2 · 6 = 12. The second number increases by 1, adding one group of two. The answer therefore increases by 2.
Ready-made worksheets: Sets of calculations
Click the picture to see the worksheet large and print it. “Use” opens it in the editor.