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

Mental Math: Adding and Subtracting to 1000

B2.3 A1About 35 minutes

Learning goals

I can add and subtract hundreds and tens in my head.
I can split numbers into hundreds, tens and ones to add.
I can make a friendly number to add or subtract quickly.
I can count up to subtract.
I can explain the strategy I used.

Words to know

mental math
Doing math in your head, sometimes with a few quick notes.

strategy
A plan or a way to solve a problem.

friendly number
A number that is easy to work with, like 100, 250, 400 or 500.

split
Break a number into parts, like 325 = 300 + 20 + 5.

count up
Start at the smaller number and jump up to the bigger number to find the difference.

Remember from Grade 2

In Grade 2 you did mental math with numbers up to 50. You added tens, like 27 + 20 = 47, and you jumped to the next ten, like 29 + 1 = 30. In Grade 3 the numbers get bigger, up to 1000. The good news: the same tricks still work!

Let's start with a story

The Grade 3 class is collecting cans for the food bank. On Monday they have 340 cans. On Tuesday they get 200 more. How many cans now?

You don't need paper. Think: 3 hundreds and 2 hundreds make 5 hundreds. So 340 + 200 = 540. The tens and ones did not change.

That is mental math: solving in your head with a smart strategy.

Strategy 1: Add or take away hundreds and tens

When you add or subtract only hundreds, only the hundreds digit changes. When you add or subtract only tens, only the tens change (unless you cross a hundred).

340 + 200 = 540 (3 hundreds + 2 hundreds = 5 hundreds)
760 − 400 = 360
425 + 30 = 455 (2 tens + 3 tens = 5 tens)
580 − 50 = 530

Strategy 2: Split into hundreds, tens and ones

Break both numbers into hundreds, tens and ones. Add each part. Then put the parts back together.

Worked example

Example 1: Split and add

Solve 325 + 142 in your head.

Split: 325 = 300 + 20 + 5. And 142 = 100 + 40 + 2.
Hundreds: 300 + 100 = 400.
Tens: 20 + 40 = 60.
Ones: 5 + 2 = 7.
Put them together: 400 + 60 + 7 = 467.

325 + 142 = 467

Strategy 3: Jump on a number line

Keep the first number whole. Add the second number in jumps: first the tens, then the ones.

Worked example

Example 2: Jump on a number line

Solve 248 + 35.

Start at 248.
Jump 30 (three tens): 248 + 30 = 278.
Jump 5: 278 + 5 = 283.

248 + 35 = 283

Start at 248. Jump 30 to 278, then jump 5 to 283.

Strategy 4: Make a friendly number

Numbers like 398 or 199 are very close to a friendly number (400 or 200). Use the friendly number, then fix the answer.

Adding 398? Add 400, then take away the extra 2.
Subtracting 199? Subtract 200, then add back the extra 1.

Worked example

Example 3: Use a friendly number to add

Solve 398 + 145.

398 is 2 less than 400.
Add 400 instead: 400 + 145 = 545.
We added 2 too many, so take 2 away: 545 − 2 = 543.

398 + 145 = 543

Start at 145. Jump 400 to 545. Then step back 2 to 543.

Worked example

Example 4: Use a friendly number to subtract

Solve 425 − 199.

199 is 1 less than 200.
Subtract 200 instead: 425 − 200 = 225.
We took away 1 too many, so add 1 back: 225 + 1 = 226.

425 − 199 = 226

Strategy 5: Count up to subtract

When two numbers are close together, count up from the smaller number to the bigger one. The total of your jumps is the answer. This works because adding and subtracting are partners.

Worked example

Example 5: Count up

Solve 400 − 365.

Start at 365. Jump to the next ten: 365 + 5 = 370.
Jump to 400: 370 + 30 = 400.
Add the jumps: 5 + 30 = 35.

400 − 365 = 35. Check: 365 + 35 = 400.

Count up from 365: jump 5 to 370, then 30 to 400. 5 + 30 = 35.

Strategy 6: Change the order to make friendly pairs

When you add, you can add in any order. Look for numbers that make a hundred together.

75 + 180 + 25: 75 + 25 = 100. Then 100 + 180 = 280.

Math talk: explain your strategy

There is more than one good way! After you solve a question, say what you did. For example: "I did 400 + 145 = 545, then took away 2 because 398 is 2 less than 400." Listening to someone else's strategy can teach you a new trick.

Just for fun

Why did 299 dress up as 300?

Because friendly numbers are easier to add! (Just remember to take that 1 back off at the end.)

Hands-on activity

Mental math card game

You need: a deck of playing cards (take out the face cards; Ace = 1 and 10 = 0) or 20 small papers with the digits 0 to 9 written twice, paper and a pencil.

Flip 3 cards to make a 3-digit number, like 4, 6, 2 = 462.
A grown-up says a change: "+ 200", "− 30", "+ 99" or "count up to 500".
Solve it in your head. Say your answer and your strategy out loud.
Check together on paper. Give yourself a point for a correct answer and another point for explaining your strategy.
Play 10 rounds. Then switch: you make up the changes for your grown-up!

Math talk: "Which strategy was fastest for + 99? Why?"

Your turn

450 + 300 = ?

820 − 400 = ?

236 + 50 = ?

364 + 225 = ? Split the numbers.

199 + 245 = ? Use a friendly number.

600 − 580 = ? Count up.

25 + 168 + 75 = ? Look for a friendly pair.

More practice: warm-up

200 + 500 = ?

900 − 300 = ?

470 + 20 = ?

650 − 50 = ?

What number is 100 more than 384?

More practice: on your own

456 + 38 = ? Use jumps.

532 − 199 = ?

700 − 465 = ? Count up.

148 + 252 = ?

350 + 290 = ?

Challenge

Show two different mental strategies for 498 + 367.

Find the missing number: 645 + □ = 1000

Mo says 403 − 398 is a hard question. Show him a fast way.

Check your understanding

Quiz

What is 530 + 200?

What is 297 + 156?

What is 800 − 790?

What is 60 + 340 + 40?

Leo solves 452 − 199 by first doing 452 − 200 = 252. What should he do next?

What is 315 + 142?

For parents and teachers

Big idea: The Ontario curriculum (B2.3) asks Grade 3 students to use mental math strategies to add and subtract numbers that add up to no more than 1000, and to explain the strategies they use. Mental math builds number sense and is the fastest way to check written work.

Common difficulties:

Changing the wrong digit (340 + 200 = 360). Ask: "Are we adding hundreds, tens or ones?"
Fixing the wrong way with friendly numbers. For 398 + 145, children may add 2 instead of taking 2 away. Ask: "Did you add too much or too little?"
Counting up and forgetting a jump. Have your child write each jump down and add them at the end.
Using only one strategy. Celebrate different ways. Ask "Is there another way?"

How to help: Use real numbers you see: house numbers, pages in a book, kilometres on a road sign. Ask "What's 100 more? 20 less? How far to 500?" Let your child jot notes; mental math does not have to be silent.