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

Solving Addition and Subtraction Problems to 1000

B2.5 B2.3 A1About 40 minutes

Learning goals

I can use a four-step plan to solve story problems.
I can draw a bar model to decide whether to add or subtract.
I can solve problems where the start, the change or the result is missing.
I can solve two-step problems and check that my answer makes sense.
I can keep trying when a problem is hard.

Words to know

bar model
A drawing with bars that shows the parts and the whole in a story problem.

compare
Find how many more or how many fewer one amount is than another.

two-step problem
A problem that needs two calculations to solve.

number sentence
A math sentence with numbers and symbols, like 245 + □ = 420.

persevere
Keep trying, even when something is hard.

Remember from Grade 2

In Grade 2 you solved story problems to 100. You learned that the missing number could be at the start, the change or the end of a story. Now you will solve the same kinds of problems with numbers up to 1000.

A four-step plan

Good problem solvers follow a plan:

Understand. Read the problem twice. What do you know? What do you need to find?
Plan. Draw a picture or a bar model. Decide: add or subtract? Write a number sentence.
Solve. Use a strategy: mental math, the column method or counting up.
Look back. Does the answer make sense? Compare it with an estimate. Check by using the opposite operation.

Bar models

A bar model shows the whole and its parts.

If you know both parts, add to find the whole.
If you know the whole and one part, subtract to find the other part.

A part-part-whole bar model. The whole is 420. One part is 245. The other part is missing.

Worked example

Example 1: The change is missing

Ava had 245 hockey cards. After her birthday she had 420. How many cards did she get for her birthday?

Understand: The start is 245. The end is 420. We need the change.
Plan: The whole is 420 and one part is 245 (see the bar model). Write 245 + □ = 420, which is the same as 420 − 245 = □.
Solve by counting up: 245 + 5 = 250, 250 + 50 = 300, 300 + 120 = 420. Jumps: 5 + 50 + 120 = 175.
Look back: 245 + 175 = 420. ✓

Ava got 175 cards.

Comparing

When a problem asks how many more or how many fewer, draw two bars, one for each amount. The difference is the extra piece on the longer bar. Find it by subtracting.

A compare bar model. The longer bar is 486. The shorter bar is 312. The dashed box is the difference.

Worked example

Example 2: How many more?

Maple School has 486 students. Birch School has 312 students. How many more students does Maple School have?

Understand: We compare two schools. We need the difference.
Plan: 486 − 312 = □.
Solve: 6 − 2 = 4, 8 − 1 = 7, 4 − 3 = 1. The answer is 174.
Look back: 312 + 174 = 486. ✓

Maple School has 174 more students.

Worked example

Example 3: The start is missing

Some people were at a winter carnival. 268 people went home. 435 people stayed. How many people were at the carnival at the start?

Understand: We don't know the start. Some left and some stayed.
Plan: The people who left and the people who stayed are the two parts. The start is the whole. Write □ − 268 = 435. To find the whole, add the parts: 435 + 268.
Solve: Ones: 5 + 8 = 13, write 3, carry 1. Tens: 1 + 3 + 6 = 10, write 0, carry 1. Hundreds: 1 + 4 + 2 = 7. The answer is 703.
Look back: 703 − 268 = 435. ✓ Estimate: 400 + 300 = 700. Close!

There were 703 people at the start.

Watch out for clue words

Words like left or more do not always mean subtract or add. In Example 3, the words went home sound like subtracting, but we had to add to find the start. Always draw the story to decide.

Worked example

Example 4: A two-step problem

A library had 650 books. It got 175 new books. Then it lent out 290 books. How many books are on the shelves now?

Understand: Two things happen: books come in, then books go out.
Step 1: Add the new books: 650 + 175 = 825.
Step 2: Take away the books lent out: 825 − 290 = 535.
Look back: Estimate 650 + 200 − 300 = 550. 535 is close. ✓

There are 535 books on the shelves.

Kind of problem	Example	Number sentence
Result missing	357 leaves, then 228 more. How many?	357 + 228 = □
Change missing	Had 245, now 420. How many more did she get?	245 + □ = 420
Start missing	Some left, 435 stayed. How many at first?	□ − 268 = 435
Compare	How many more does 486 have than 312?	486 − 312 = □
Two-step	650 + 175, then lend 290	650 + 175 = 825, 825 − 290 = □

Kinds of addition and subtraction story problems.

When a problem feels hard

Everyone gets stuck sometimes, even grown-ups! Take a deep breath. Try these:

Read the problem again, slowly.
Draw it. A bar model or a quick sketch helps a lot.
Try smaller numbers first, like 4 and 2, to see if you should add or subtract.
Talk about it with someone.

Mistakes help your brain grow. Keep going!

Just for fun

125 birds flew away from the bird feeder, and 275 birds stayed. The squirrel watching from the tree said, "Great, 125 fewer birds to share with!"

Hands-on activity

Make your own story problems

You need: paper, a pencil, and something you like to count (toy cars, hockey cards, books on a shelf).

Make up a story problem with numbers between 100 and 1000. Use a real place you know: your school, a hockey rink, the grocery store, a sugar bush.
Make one problem of each kind: result missing, change missing, start missing and compare.
Swap problems with a grown-up or sibling. Solve each other's problems with the four-step plan and a bar model.
Check each answer by doing the opposite operation.

Math talk: "How did you know whether to add or subtract?"

Your turn

Kids collected 357 maple leaves on Saturday and 228 on Sunday. How many leaves in all?

A farmer had 840 pumpkins. She sold 365. How many are left?

The Owls scored 693 points in a reading challenge. The Bears scored 528. How many more points did the Owls score?

Liam has read 186 pages of a 300-page book. How many pages are left?

A bakery made some bagels. It sold 445. There are 155 left. How many bagels did it make?

Grandpa drove 238 km on Saturday and 315 km on Sunday. The whole trip is 800 km. How many kilometres are left?

A school has 274 girls and 289 boys. Is the total more or less than 500? Find the exact total.

More practice: warm-up

A theatre has 400 seats. 150 are taken. How many are empty?

An orchard picked 120 apples in the morning and 300 in the afternoon. How many in all?

A problem asks how many more. Do you usually add or subtract?

Kids made 250 snowballs in the morning and 250 in the afternoon. How many in all?

Mo had 900 points in a game. He lost 100. How many points does he have now?

More practice: on your own

A ferry carried 365 people in the morning and 482 in the afternoon. How many people in all?

A bike path is 750 m long. Ella has ridden 385 m. How far does she have left?

Raj has 175 more stickers than Tia. Tia has 248. How many stickers does Raj have?

Some geese were on a pond. 135 flew away. 290 are still there. How many geese were there at first?

A store had 500 toques. It sold some. Now 324 are left. Write a number sentence with a box, then solve.

Challenge

A school wants to collect 1000 cans for the food bank. Grade 3 brought 276 and Grade 4 brought 348. How many more cans do they need?

Two numbers add up to 600. One number is 100 more than the other. What are the numbers?

Jada says: "There were 845 people at the game. 397 left early. About 450 stayed." Is her estimate reasonable? What is the exact answer?

Check your understanding

Quiz

A rink had 625 skaters. 250 more came. How many skaters are there now?

Tom has 432 marbles. Sara has 289. Which number sentence tells how many more Tom has?

What is 432 − 289?

Some kids were at a park. 120 went home. 380 are still playing. How many kids were there at first?

Ali has $500. He spends $150 and then $200. How much does he have left?

You are stuck on a hard problem. What is a good thing to do?

For parents and teachers

Big idea: Grade 3 students represent and solve addition and subtraction problems with numbers up to 1000 using tools and algorithms (B2.5), and use estimation to judge answers (B2.3). Strand A asks children to persevere, manage frustration and explain their thinking; this lesson practises those skills.

Common difficulties:

Grabbing the numbers and adding. Children often add every number they see. Ask them to draw a bar model first and point to the whole.
Clue-word traps. "Left" or "more" don't always mean subtract or add. Start-missing problems (□ − 268 = 435) are the hardest; they need adding.
Two-step problems. Children often stop after one step. Ask: "Did that answer the question?"
Skipping the check. Encourage estimating first and checking with the opposite operation.

How to help: Make up problems about real life: kilometres on a car trip, pages in a chapter book, points in a game. Praise effort and strategy ("I like how you drew the bar model") as much as correct answers.