Estimating Sums and Differences

An estimate is a fast, rough answer. It tells you roughly where the real answer should land.

Round, then work

For 287 + 412, round to 300 and 400. The estimate is 700.

Use it as a check

The exact answer is 699. That is close to 700, so it is believable.

It catches big mistakes

If you had got 1,099, the estimate would tell you something went wrong.

What an estimate is for

An estimate is not a worse version of the real answer — it is a different tool. It tells you roughly what to expect so that when the exact calculation lands somewhere wild you notice immediately. Doing the estimate first is what makes it useful; doing it afterwards only confirms what you already wrote.

How to make one

Round each number to a convenient place, then calculate with the rounded numbers. For 287 + 412, round to 300 + 400 = 700. The real answer is 699, which is close, so it passes. If you had got 1,699 you would know a digit went astray.

Knowing which way you are off

If you rounded both numbers up, your estimate is too big and the real answer will be smaller. If you rounded both down, it is too small. Noticing the direction makes an estimate sharper — you are not just near the answer, you know which side of it you are on.