Check: run it backwards
The estimate from the last lesson catches big nonsense. But what about a mistake of one? The result 34 instead of 33 passes an estimate without a beep. For small mistakes you need a finer tool: a check.
A check means running the calculation backwards. Did you subtract? Check it with addition. Division? Check it with multiplication. When the way back takes you to the original number, the result matches.
It works because operations walk in pairs: plus and minus are return tickets for each other, times and divide too. What one operation does, the other undoes.
The best bit is the price: a check takes twenty seconds. In a test it is the cheapest mark you will ever get — a mark for a mistake you caught yourself before the red pen.
Jonáš finishes the test ten minutes early. “Xong!” He hands it in and goes. Tereza finishes at the same time — but instead of handing it in she runs each result through a check.
At the third question the way back does not match: 84 − 39 came out 55, but 55 + 39 is not 84. She finds the clue (she forgot to borrow a ten), fixes it to 45, checks: 45 + 39 = 84. It matches.
The next day: Jonáš has almost a star — except for one silly mistake. Tereza has a clean one. The difference was not in the counting. It was in the last ten minutes.
Do the check by a different path than the one you counted. If you only repeat the same calculation, the head happily repeats the same mistake — the brain likes to ride in worn tracks.
Operations walk in pairs
Minus is checked with plus. You count 73 − 46 = 27. Check: take the result and add back what you subtracted: 27 + 46. It must come out 73, the number you started with. Did it? It matches. Did it not? There is a clue somewhere — either in the calculation or in the check, and you will find that fast.
Plus is checked with minus. You count 38 + 25 = 63. Check: 63 − 25 must give 38.
Divide is checked with times. 48 : 6 = 8, because 8 × 6 = 48. And the other way: times is checked with division.
For addition you have a second way back: add the numbers in the opposite order. 38 + 25 and 25 + 38 must give the same — and because you ride a different route, the same mistake will not repeat.
When to do a check? In a test always, the last five minutes are made for that. In practice at least on questions where you are not sure. And always when the result feels weird — something in your head is whispering, listen to it.
Estimate and check together are a double net: the estimate catches elephants, the check mosquitoes.
Example 1: minus checked with plus
Calculation: 73 − 46. Method: 73 − 40 = 33, then 33 − 6: I split six into 3 + 3, so 33 − 3 = 30 and 30 − 3 = 27.
Check with plus: 27 + 46. Tens: 27 + 40 = 67. Ones: 67 + 6: I split into 3 + 3, so 67 + 3 = 70 and 70 + 3 = 73.
It came out exactly the number I started with. The result 27 has a stamp: checked.
Example 2: a check catches a mistake
Tereza counts 84 − 39 and gets 55. Check: 55 + 39. She counts: 55 + 40 = 95, give one back: 95 − 1 = 94. But she started with 84!
The way back did not take her home — so she looks for a clue in the original calculation. She found it: she counted 84 − 39 as 84 − 30 = 54 and then subtracted the ones carelessly. Right: 84 − 30 = 54, then 54 − 9: split into 4 + 5, 54 − 4 = 50, 50 − 5 = 45.
New check: 45 + 39 = 45 + 40 − 1 = 84. It matches. Twenty seconds of check, one saved mark.
Example 3: times and divide
Calculation: 48 : 6 = ? How many times does six fit into 48? Method by multiples: 6, 12, 18, 24, 30, 36, 42, 48 — that is eight steps. So 48 : 6 = 8.
Check with multiplication: 8 × 6. Eight sixes: 6 + 6 = 12, two twelves are 24, two twenty-fours are 48. It matches, I am back at the start.
This pair will help you all the time: every division in life you can check with one multiplication.
Do not check a result by counting the same question the same way again. A worn track in the head will happily serve the same mistake a second time — and you will believe it twice as much.
Practice: now you do it 🎲
Now try it for real. You will see all the questions at once, like on paper. Bắt đầu with ten. When it goes well, add more.
Subtraction to 100. Check each result on paper with plus — only then write it in the box.
On paper: a checked stamp
Three calculations, three checks. By each checked result draw a small stamp — a tick in a circle.
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Count 91 − 37 and check with plus. Write both paths under each other, so you see how they meet.
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Count 46 + 28 and check two ways: with minus (result − 28) and with swapped order (28 + 46).
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Count 63 : 7 and check with multiplication.
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This result may be wrong: 72 − 45 = 33. Decide with a check — do not fix anything until the check has spoken.
Now you 💪
- I know the pairs: plus–minus and times–divide, and I can ride them backwards.
- I check by a different path, not by repeating the same calculation.
- In a test I leave time for a check instead of handing in early.
Done when: You have three results with a checked stamp and one someone else’s mistake caught by a check.
What to take from this lesson
- Operations walk in pairs: plus–minus, times–divide.
- A check = the way back to the original number.
- Check by a different route — the same route repeats the same mistake.
- An estimate catches elephants, a check mosquitoes. Use both.
- The last five minutes of a test belong to the check, not to handing in.
© 2026 Ing. Martin Polak / AlgoRhino · Điều khoản sử dụng nội dung