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

Solving Multiplication and Division Problems

B2.7 B2.1 A1About 40 minutes

Learning goals

I can tell if a story problem needs multiplication or division.
I can draw a picture, an array or a number line to solve a problem.
I can solve two-step problems that use multiplication or division and adding or subtracting.
I can explain my thinking and check my answer.

Words to know

equal groups
Groups that all have the same number of things.

total
The whole amount, all together.

times as many
A way to compare: 3 times as many as 4 is 3 groups of 4, which is 12.

two-step problem
A problem that needs two calculations.

strategy
A plan or a way to solve a problem.

Let's start with a question

At the hockey arena, the snack bar sells juice boxes in packs of 6. The team buys 4 packs. How many juice boxes?

There are equal groups, and we want the total. That is multiplication: 4 × 6 = 24 juice boxes.

Multiply or divide?

Every equal-groups story has three numbers: the number of groups, the number in each group, and the total. Ask yourself: which one is missing?

Missing the total? Multiply. 4 packs of 6 juice boxes. How many in all? 4 × 6 = 24.
Missing how many in each group? Divide (sharing). 24 juice boxes shared by 4 teams. How many each? 24 ÷ 4 = 6.
Missing the number of groups? Divide (grouping). 24 juice boxes in packs of 6. How many packs? 24 ÷ 6 = 4.

Groups	In each group	Total	Operation
4	6	?	4 × 6 = 24
4	?	24	24 ÷ 4 = 6
?	6	24	24 ÷ 6 = 4

One fact family, three different stories.

Worked example

Example 1: Find the total

A box holds 6 doughnuts. How many doughnuts are in 4 boxes?

Understand: 4 groups, 6 in each group. The total is missing.
Plan: Multiply: 4 × 6.
Solve: Split it: 2 × 6 = 12, and double that: 12 + 12 = 24.
Look back: 6 + 6 + 6 + 6 = 24. ✓

24 doughnuts

Worked example

Example 2: Sharing

28 kids sit in 4 equal rows at an assembly. How many kids are in each row?

Understand: The total is 28 and there are 4 groups (rows). How many in each row is missing.
Plan: Divide: 28 ÷ 4.
Solve: Think: 4 times what makes 28? 4 × 7 = 28.
Look back: 7 + 7 + 7 + 7 = 28. ✓

7 kids in each row

28 kids in 4 equal rows: 7 in each row.

Worked example

Example 3: Grouping

Each canoe holds 3 people. How many canoes do 18 campers need?

Understand: The total is 18 and each group is 3. The number of groups is missing.
Plan: Divide: 18 ÷ 3.
Solve: Jump back by 3s from 18: 15, 12, 9, 6, 3, 0. That is 6 jumps.
Look back: 6 × 3 = 18. ✓

6 canoes

Jumping back by 3 from 18 to 0 takes 6 jumps. 18 ÷ 3 = 6.

Times as many

Sometimes a problem compares two amounts with times as many.

Leah has 4 stickers. Max has 3 times as many. That means Max has 3 groups of 4: 3 × 4 = 12 stickers.

Leah's bar is 4. Max's bar is 3 times as long: 4 + 4 + 4 = 12.

Worked example

Example 4: Two steps

A class has 5 packs of markers with 8 markers in each pack. They also have 3 loose markers. How many markers in all?

Step 1: Find the markers in packs: 5 × 8 = 40.
Step 2: Add the loose markers: 40 + 3 = 43.
Look back: Does 43 make sense? 40 markers in packs plus a few more. Yes. ✓

43 markers

Draw it!

If you're not sure whether to multiply or divide, draw the story. Draw circles for groups, or an array, or a number line. Then ask: "What do I know? What is missing?" Your drawing will show you what to do.

Working together

Solving problems with a partner is a great way to learn. Take turns explaining your plan. Listen to your partner's idea, even if it is different from yours. Say "Can you show me how you got that?" instead of "That's wrong."

Just for fun

An octopus has 8 arms. So 3 octopuses have 3 × 8 = 24 arms. That is a lot of high fives!

Hands-on activity

Kitchen problem solvers

You need: things from the kitchen like a muffin pan, an egg carton, a box of crackers or a bag of apples, plus paper and a pencil.

With your grown-up, make up four story problems using real things: a total problem ("How many muffin cups are in 2 pans of 6?"), a sharing problem ("Share 20 crackers among 4 people."), a grouping problem ("Put 15 apples in bags of 5. How many bags?") and a two-step problem.
Solve each one with a drawing first, then a number sentence.
Act it out with the real things to check.

Math talk: "How did you decide whether to multiply or divide?"

Your turn

There are 6 bags with 5 apples in each. How many apples?

20 mittens make how many pairs?

32 chairs are set in 4 equal rows. How many chairs in each row?

How many legs do 7 tables have if each table has 4 legs?

45 cookies go on plates with 5 cookies on each plate. How many plates?

9 cars each carry 2 people to a soccer game. How many people? Do you multiply or divide?

A class has 3 packs of 10 juice boxes. The class drinks 24. How many are left?

More practice: warm-up

How many fingers on 2 hands with 5 fingers each?

12 grapes shared equally by 2 kids. How many each?

3 boxes of 10 crayons. How many crayons?

4 friends each have 10¢. How much money altogether?

15 stickers shared equally by 5 kids. How many each?

More practice: on your own

A school bus has 10 rows with 4 seats in each row. How many seats?

36 hockey players make teams of 6. How many teams?

Ana saves $5 every week for 8 weeks. How much does she save?

50 granola bars are shared equally among 10 kids. How many does each kid get?

Sam has 6 marbles. Lee has 4 times as many. How many marbles does Lee have?

Challenge

A garden has 4 rows of 7 tulips and 3 rows of 5 daffodils. How many flowers in all?

Pencils come in boxes of 8. The class needs 40 pencils. How many boxes? What if they need 42?

Write a multiplication story for 3 × 9 and a division story for 27 ÷ 3.

Check your understanding

Quiz

A box has 5 rows of 6 chocolates. How many chocolates?

40 kids go on 4 buses equally. Which number sentence tells how many on each bus?

Each tent holds 2 campers. How many tents do 16 campers need?

Kim has 5 books. Jo has 2 times as many. How many books does Jo have?

There are 3 bags of 10 oranges and 4 more oranges. How many oranges?

Which question needs division?

For parents and teachers

Big idea: Grade 3 students represent and solve problems involving multiplication and division using tools and drawings (B2.7). The key is recognizing what is missing: the total (multiply), the size of each group (divide by sharing), or the number of groups (divide by grouping). Strand A skills (persevering, working with others, explaining thinking) are practised here.

Common difficulties:

Picking an operation from key words. Encourage drawing the situation instead.
Mixing up the two kinds of division. Both are fine to solve with 18 ÷ 3; the drawing just looks different.
Stopping after step 1 of a two-step problem.
"Times as many" is new. A bar model with repeated bars helps.

How to help: Turn everyday moments into problems: "We need 3 snacks each for 5 kids. How many snacks?" Ask your child to explain why they multiplied or divided.