B. Number · Operations: Adding and Subtracting to 1000, Multiplying and Dividing

Estimating Sums and Differences to 1000

B2.3 A1About 30 minutes

Learning goals

I can find the closest hundred or the closest ten to a number.
I can estimate a sum or a difference.
I can use an estimate to check if an answer makes sense.
I can tell when an estimate is enough and when I need an exact answer.

Words to know

estimate
A smart guess that is close to the exact answer.

round
Change a number to the closest ten or hundred to make it easier to work with.

closest hundred
The hundred (like 300 or 400) that a number is nearest to on a number line.

reasonable
Makes sense. A reasonable answer is close to your estimate.

exact
The precise answer, not a guess.

Remember from Grade 2

In Grade 2 you found the closest ten, like 34 is closest to 30. You used it to estimate: 28 + 19 is about 30 + 20 = 50. Now we will estimate with numbers up to 1000, using the closest hundred and the closest ten.

Let's start with a question

Two classes are going to a concert. One group has 168 people and the other has 215 people. The hall has 500 seats. Is there room for everyone?

You don't need the exact answer! 168 is about 200. 215 is about 200. 200 + 200 = 400. That is less than 500, so yes, there is room.

An estimate answered the question quickly. (The exact total is 383.)

An empty concert hall with many rows of red seats facing a stage with a piano. — A concert hall has hundreds of seats. You don't need to count every one to estimate whether two classes will fit. AI-generated image

The dashed line is the 500 seats. The estimate, 200 + 200 = 400, ends before the line, so everyone fits. The exact total, 383, fits too.

Finding the closest hundred

Which hundred is 347 closer to: 300 or 400? Look at the number line. 347 is between 300 and 400. The middle is 350. 347 is before the middle, so it is closer to 300.

347 is between 300 and 400. It is before the middle (350), so it is closest to 300.

A quick rule for the closest hundred

Look at the tens digit.

Tens digit 0, 1, 2, 3 or 4: the number is closer to the hundred below. 347 → 300.
Tens digit 5, 6, 7, 8 or 9: go to the hundred above. 382 → 400.
A number exactly in the middle, like 350, is just as close to both. We usually go up: 350 → 400.

For the closest ten, look at the ones digit the same way: 274 → 270, 586 → 590.

Number	Closest ten	Closest hundred
347	350	300
382	380	400
615	620	600
850	850	900
129	130	100

Rounding to the closest ten and to the closest hundred.

Worked example

Example 1: Estimate a sum

Estimate 312 + 489.

312 is closest to 300.
489 is closest to 500.
300 + 500 = 800.

About 800. (The exact answer is 801. Very close!)

Worked example

Example 2: Estimate a difference

Estimate 723 − 287.

723 is closest to 700. 287 is closest to 300.
700 − 300 = 400.
Want a closer estimate? Use the closest ten: 720 − 290 = 430.

About 400, or about 430 using tens. (The exact answer is 436.)

Estimate to check your work

After you solve a question, estimate. If your answer is far from the estimate, something went wrong. Check again!

Worked example

Example 3: Does this answer make sense?

Sam says 456 + 278 = 634. Is his answer reasonable?

Estimate with tens: 456 is about 460 and 278 is about 280.
460 + 280 = 740.
634 is about 100 away from 740. That is too far!
Sam should add again: 456 + 278 = 734.

Sam's answer is not reasonable. The exact answer is 734, which is close to the estimate of 740.

When is an estimate enough?

An estimate is enough when the question says about, or asks Is there enough? or Is it more than...?
You need the exact answer when you must know the number, like how many tickets to print or how much change to give.

Thinking like a mathematician

Before you solve any big adding or subtracting question, ask yourself: "About how much will the answer be?" Then compare at the end. This habit catches lots of mistakes.

Just for fun

What did 489 say to 500?

"Close enough!"

Hands-on activity

Flyer estimates

You need: a store flyer or a store website (with a grown-up), paper and a pencil.

Find two bigger items with prices between $100 and $500, like a bike at $289 and a tent at $415.
Estimate the total using the closest hundred: 300 + 400 = $700.
Find the exact total with your grown-up: $289 + $415 = $704.
Was your estimate close? Now estimate the difference: "About how much more does the tent cost?" 400 − 300 = about $100. (Exact: $126.)
Do 4 more pairs of items.

Math talk: "Did rounding to the closest ten give a closer estimate than rounding to the closest hundred?"

Your turn

Round 382 to the closest hundred.

Round 649 to the closest hundred.

Round 274 to the closest ten.

Estimate 418 + 375.

Estimate 812 − 395.

Estimate 289 + 506.

Kai says 603 − 298 = 405. Use an estimate to check.

More practice: warm-up

What is the closest hundred to 720?

What is the closest hundred to 180?

Round 550 to the closest hundred.

What is the closest ten to 437?

Estimate 210 + 380.

More practice: on your own

Estimate 465 + 329 two ways: with hundreds and with tens.

A library has 734 books. It gives away 289. About how many books are left?

Is 386 + 245 more than 500? Use an estimate.

Estimate 158 + 247 + 391.

You need to print a ticket for every person at the winter carnival. Should you estimate or find the exact number? Why?

Challenge

Two numbers each round to 300 (closest hundred). What is the smallest their sum could be? The biggest?

Jo estimates 349 + 349 as 300 + 300 = 600. The exact answer is 698. Why is her estimate so far off? Give a better estimate.

A store had 950 maple cookies. It sold 412 on Saturday and 389 on Sunday. About how many cookies are left?

Check your understanding

Quiz

What is the closest hundred to 461?

What is the best estimate for 297 + 412?

What is the best estimate for 805 − 398?

When is an estimate useful?

What is the closest ten to 586?

Amira says 314 + 285 = 899. What does an estimate tell you?

For parents and teachers

Big idea: Estimation is part of the Grade 3 mental math expectation (B2.3). Children round to the closest ten or hundred, estimate sums and differences up to 1000, and use estimates to judge whether answers are reasonable.

Common difficulties:

Rounding to the wrong place (461 → 460 when the question asks for the closest hundred). Ask: "Closest ten or closest hundred?"
Looking at the wrong digit. For hundreds, look at the tens digit; for tens, look at the ones digit.
Thinking an estimate is "wrong" because it isn't exact. Explain that a good estimate is close, not exact.
Estimating after solving (and just copying the answer). Encourage estimating first.

How to help: Use a number line drawn on paper from 300 to 400 and ask where 347 goes. When shopping, ask "About how much will these two things cost?" Praise reasonable estimates even if they are not the same as yours.