Estimating the result · Code with Martin

Round, calculate from the head and catch a nonsense result before you hand it in.

Estimate: a nonsense detector

You work out 298 + 503 under each other and get 1 801. Do you hand it in? No! Something smells here — and an estimate will tell you what.

An estimate is a quick rough calculation from the head: you round the numbers and calculate the round ones. 298 is almost 300, 503 almost 500. Round sum: 800. And suddenly you see that 1 801 is nonsense — you probably shifted a column.

An estimate is not a stand-in for the calculation. It is a safety net. The order of work looks like this:

Estimate (from the head, in a few seconds).
Calculate exactly (under each other, on paper).
Compare. Do they fit together? Hand it in. Do they not? Look for the mistake.

Adults do this all the time: at the till, with invoices, with a calculator — because even a calculator calculates wrongly when you tap in the wrong numbers. An estimate is the only check that runs with no tools at all.

Filip calculates on a calculator how much four tickets of 48 Kč cost. He taps it in and reports: “Nine hundred and sixty!” His sister raises an eyebrow: “Four times a fifty is two hundred. How could it be almost a thousand?” Filip looks at the display: he tapped 4 × 240 instead of 4 × 48 — his finger jumped. Correctly: 192 Kč. From then on he does his sister’s trick every time: before he reads the display, he says a round estimate. A calculator calculates fast, but only an estimate knows that it calculated the wrong thing.

💡

Say the estimate before you start calculating exactly. When you do it only after the calculation, the head cheats and rounds so that it comes out.

How to estimate adding, subtracting and multiplying

Estimate of a sum: round both addends to hundreds (or tens) and add the round ones.

298 + 503 → 300 + 500 = about 800.

Estimate of a difference: the same, only subtract.

612 − 289 → 600 − 300 = about 300.

Estimate of a product: round and use the big times tables from the zeros lesson.

4 × 48 → 4 × 50 = about 200.

How to compare an estimate with a result? Do not expect an exact match — an estimate is rough on purpose. You ask: is the result in the same league? Estimate 800 and result 801: same league, fine. Estimate 800 and result 1 801: different league, there is a mistake somewhere.

Which way does the estimate go wrong? You can know that! When you rounded both numbers up, the real result will be smaller than the estimate. When down, it will be bigger. With 4 × 48 ≐ 4 × 50 I went up → the real thing will be a bit under 200. 192 came out — exactly as the estimate promised.

That thinking is the most valuable thing about estimating: not only “about how much”, but also “which way I go wrong”.

Catching a mistake in adding

A friend calculated 298 + 503 = 1 801.

Estimate: 300 + 500 = 800.

Compare: 1 801 is more than double the estimate. Different league → mistake.

Exact calculation under each other: 298 + 503: ones 8 + 3 = 11, I write 1, one on; tens 9 + 0 + 1 = 10, I write 0, one on; hundreds 2 + 5 + 1 = 8. Result 801.

The friend most likely added an extra thousand by mistake. The estimate caught the mistake in five seconds.

Shopping estimate with a reserve

In the basket: 129 Kč, 89 Kč and 245 Kč. You have a five-hundred. Is it enough?

Estimate up (to be sure): 130 + 90 + 250 = 470.

I rounded everything up, so the real price is at most 470. A five-hundred is surely enough.

This is a smart trick: when you estimate money, round prices up. The estimate then promises: it will not be worse than this. Exactly: 129 + 89 + 245 = 463 Kč. The promise held.

Estimate of a product

Example: 6 × 78.

Estimate: 78 ≐ 80, so 6 × 80 = 480. I went up → the real thing will be under 480, but close.

Exactly: 6 × 78 = 6 × 70 + 6 × 8 = 420 + 48 = 468.

Compare: 468 is a bit under 480. Exactly as planned — I trust the result.

If I got say 768, the estimate would shout: different league, recalculate!

⚠️

Never write an estimate as the result! The exact number belongs in the notebook. An estimate is your private detector — it is written to the side, in pencil, with a wavy line or ≐, and above all it is compared.

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.

Warm-up: round to hundreds. Without fast rounding there is no fast estimate.

Practise the questions

On paper

For each question three lines: estimate, exact calculation, compare.

Estimate and then calculate exactly: 402 + 297, 715 − 388, 3 × 92.
Decide by estimate only, with no calculating: is 200 Kč enough for shopping of 78 Kč and 96 Kč? Write the estimate and the decision.
Trick: a friend claims that 5 × 61 = 355. By estimating decide whether to believe it, then recalculate.
Make up a question where the estimate comes out exactly the same as the calculation. (Hint: the rounded numbers are already round.)

Now you 💪

You know the order: estimate → exact calculation → compare.
You can tell from an estimate that 298 + 503 = 1 801 is nonsense.
You know which way the estimate goes wrong when you round up.

✅

Done when: Before every big calculation you make an estimate and after it you compare whether the result is in the same league.

What to take from this lesson

Estimate = round and calculate the round ones from the head.
Order: estimate, exact calculation, compare.
League does not match? There is a mistake somewhere — look.
Rounding up → the real thing will be smaller. With money round up to be sure.
An estimate checks a calculator too: it only calculates what you tap in.