Estimate the answer before you count

An estimate is a safety net: a rough answer in advance that catches nonsense before you hand it in.

Estimate first, then calculate

Tightrope walkers have a net under the rope. Not because they cannot walk — because one wrong step should not mean the end.

An estimate is your net under counting. Before you count exactly, you say roughly what should come out. Then you count. And at the end you compare: is the exact result close to the estimate? If yes, it is probably right. If it is somewhere else entirely, there is a mistake — and you catch it before you hand it in.

An estimate takes a few seconds, because you count with nicely round numbers. No carries, no borrowing. Just tens.

You know this already from lesson four, where an estimate watched the calculator. Today we let it onto all counting — because tap typos and runaway digits happen on paper too, not only on a display.

Filip counts 48 + 37 and writes 715. He goes on happily. Ema looks over his shoulder: “Wait. Fifty and forty is ninety. How did you get seven hundred?”

Filip looks at his writing — and sees it. He added the ones: 8 + 7 = 15, then just wrote the 7 from the tens next to it. He glued digits together instead of a proper add. Without Ema’s sentence he would have handed in 715. That sentence was no magic: she just rounded both numbers and added the tens. Five seconds of work, one piece of nonsense caught in flight.

💡

Always write the estimate, even just small in the corner: “≈ 90”. An estimate that stays in the head mysteriously bends to the result after you count. A written estimate cannot be cheated.

How to estimate: round numbers

The whole trick has three steps.

Step 1: round the numbers. Move each number to the nearest ten. 48 becomes 50, 37 becomes 40, 62 becomes 60. Rule: ones 5 and up — up, ones 4 and down — down.

Step 2: count with the round ones. 50 + 40 = 90. You can do that in your head, because round numbers are just tens in disguise: 5 tens + 4 tens = 9 tens.

Step 3: after the exact calculation, compare. The exact result should be close to the estimate — a bit to the side, not a floor away. You got 85 and the estimate was 90? It fits. You got 715 and the estimate was 90? Alarm, look for a clue.

How close is “close”? By rounding you move each number by 5 at most, so for adding two numbers the exact result differs from the estimate by 10 at most. When the gap is bigger, something creaks.

And watch one thing: an estimate catches mistakes, but it does not guarantee there is none. Small slips (off by one) sneak through. A check catches those — that is in the next lesson. Estimate and check are partners, not rivals.

Example 1: 48 + 37 with a net

Estimate: 48 ≈ 50, 37 ≈ 40. Sum of the round ones: 50 + 40 = 90. In the corner: “≈ 90”.

Exact calculation in parts: tens first, 48 + 30 = 78. Then ones: 78 + 7. I split seven into 2 + 5, because 78 + 2 = 80 is round. So 80 + 5 = 85.

Compare: 85 against the estimate 90. Gap of 5, that is fine — the net does not jump in. If 715 came out like Filip’s, the gap would shout at the whole notebook.

Example 2: subtraction with an estimate

Count 62 − 29.

Estimate: 62 ≈ 60, 29 ≈ 30. Round: 60 − 30 = 30. I expect something around thirty.

Exact calculation with a trick: 29 is almost 30, so I subtract 30 straight away — that is easy: 62 − 30 = 32. But I subtracted 1 more than I should, so I give the one back: 32 + 1 = 33.

Compare: 33 against the estimate 30. Close, it fits. And notice — rounding helped twice: once in the estimate, once as a trick in the calculation itself.

Example 3: a shop with three numbers

Ema buys a notebook for 19 Kč, crayons for 24 Kč and a pad for 52 Kč. Is a hundred enough?

Estimate: 19 ≈ 20, 24 ≈ 20, 52 ≈ 50. Round: 20 + 20 + 50 = 90. It looks like a hundred is enough, but it is tight — on tight things an exact calculation pays.

Exactly: 19 + 24 = 43 (because 19 + 24 = 20 + 24 − 1 = 43). Then 43 + 52: tens 40 + 50 = 90, ones 3 + 2 = 5, together 95 Kč.

A hundred is enough and she gets 5 Kč back. The estimate answered the main question in five seconds, the exact calculation tuned the detail.

⚠️

An estimate is not the answer. Do not write a rounded number in a test or in the box on the sheet — the estimate is a net under the rope, but you still have to walk the rope with an exact calculation.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. Start with ten. When it goes well, add more.

For each question first write an estimate from round numbers, then count exactly on paper and compare. Five in a row.

Practise the questions

On paper: a net under three questions

Three questions, for each the whole ritual: estimate in the corner, exact calculation, compare.

Count 57 + 36. First an estimate from round numbers, write it, then exactly, then compare.
Count 81 − 44. The same ritual. Notice on purpose how the estimate watches that the result should be around forty.
This calculation is wrong on purpose: 46 + 28 = 92. Make an estimate and write in one sentence how the estimate gives the mistake away. Then find the right result.
Write this rule in your notebook: I always write an estimate, even when I trust myself. Especially when I trust myself.

Now you 💪

I can round a number to the nearest ten and I know when up and when down.
I write the estimate in the corner before I start counting exactly.
When the result and the estimate split by a lot, I look for a clue and I do not argue with the net.

✅

Done when: You have three questions with a written estimate, an exact calculation and a compare — and one someone else’s mistake caught in the net.

What to take from this lesson

An estimate is a safety net: a rough answer in advance catches nonsense.
Round to tens and count in your head — it takes a few seconds.
Write the estimate. In the head it bends after the calculation.
A big gap between estimate and result = look for a clue.
An estimate catches big mistakes, a check (next lesson) the small ones.