Grade by Grade
B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates

Division Facts and Fact Families to 144

B2.2 B2.1About 35 minutes
Learning goals
  • I can use a multiplication fact to find a related division fact, up to 144 ÷ 12.
  • I can write a fact family with 11s and 12s.
  • I can solve sharing and grouping problems with division facts.

Words to know

dividend
The number being divided. In 84 ÷ 12 = 7, the dividend is 84.
divisor
The number you divide by. In 84 ÷ 12 = 7, the divisor is 12.
quotient
The answer when you divide. In 84 ÷ 12 = 7, the quotient is 7.
fact family
The multiplication and division facts that use the same three numbers.

Let's start with a story

132 students go to a winter carnival. The teachers make teams of 11. How many teams are there?

This is 132 ÷ 11. Think: 11 times what makes 132? You learned that 11 × 12 = 132. So there are 12 teams.

Every division fact has a multiplication partner. If you know your multiplication facts, you know your division facts!

Two ways to think about division

  • Sharing: 84 cookies are shared equally on 12 plates. How many on each plate? 84 ÷ 12 = 7.
  • Grouping: 84 eggs are packed in cartons of 12. How many cartons? 84 ÷ 12 = 7.

Both stories use the same fact: 12 × 7 = 84.

84 dots in 7 rows of 12. You can see 84 ÷ 12 = 7 (7 rows) and 84 ÷ 7 = 12 (12 in each row).

Fact families

The numbers 7, 12 and 84 make a fact family:

  • 7 × 12 = 84
  • 12 × 7 = 84
  • 84 ÷ 12 = 7
  • 84 ÷ 7 = 12

The product (here 84) is always the number you start with when you divide.

84712× ÷product on top, factors belowOne fact family, four facts:7 × 12 = 8412 × 7 = 8484 ÷ 12 = 784 ÷ 7 = 12
A fact triangle for 7, 12 and 84. Cover the 84 and multiply the bottom numbers; cover 7 or 12 and divide 84 by the other number.
Worked example

Example 1: Think multiplication

Solve 108 ÷ 12.

  1. Ask: 12 times what is 108?
  2. Try 12 × 9 = 90 + 18 = 108. ✓

108 ÷ 12 = 9

Worked example

Example 2: A grouping story

A coach has 96 pucks. She puts them in buckets of 12. How many buckets does she fill?

  1. Grouping: how many 12s are in 96? That's 96 ÷ 12.
  2. 12 × 8 = 80 + 16 = 96.

8 buckets

Division rules to remember

  • 0 ÷ any number (not 0) = 0. If there's nothing to share, everyone gets 0.
  • Any number ÷ 1 = that number. One group gets everything.
  • Any number (not 0) ÷ itself = 1. 12 ÷ 12 = 1.
  • You can't divide by 0. There's no way to share into 0 groups, so 12 ÷ 0 has no answer.

Stuck? Build from 10

If you get stuck on a division fact, start from a fact you know. For 132 ÷ 12, think: 12 × 10 = 120. 132 is 12 more than 120, so it's one more group: 11.

Just for fun

Riddle: Why did the cookies refuse to be divided by 0?

Because there was nobody to share them with!

Hands-on activity

Sharing and grouping with 60

You need: 60 small items, like dry beans, pennies, buttons or pieces of cereal (keep small items away from young children), and some cups or small bowls.

  1. Share the 60 items equally into 12 cups. How many in each cup? (60 ÷ 12 = 5)
  2. Put them back. Now make groups of 12. How many groups? (60 ÷ 12 = 5)
  3. Try making groups of 5, 6 and 10. Write each division sentence.
  4. Write the fact family for 5, 12 and 60.

Math talk: "Why did sharing into 12 cups and making groups of 12 give the same answer?"

Your turn

1

72 ÷ 12 = ?

2

99 ÷ 11 = ?

3

144 ÷ 12 = ?

4

48 ÷ 12 = ?

5

110 ÷ 11 = ?

6

0 ÷ 12 = ?

7

132 ÷ 12 = ?

8

Write the fact family for 7, 12 and 84.

More practice: warm-up

1

24 ÷ 12 = ?

2

33 ÷ 11 = ?

3

36 ÷ 12 = ?

4

22 ÷ 2 = ?

5

60 ÷ 12 = ?

More practice: on your own

1

96 ÷ 8 = ?

2

84 eggs are packed in cartons of 12. How many cartons?

3

121 ÷ 11 = ?

4

Write the fact family for 9, 11 and 99.

5

108 ÷ 9 = ?

Challenge

1

Find the missing number: □ ÷ 12 = 12.

2

A baker has 120 muffins. How many boxes of 12 can she fill? How many boxes of 6? Why is the second answer double the first?

3

Kai says 0 ÷ 12 = 12. Is he right? Explain.

Check your understanding

Quiz

1.

What is 96 ÷ 12?

2.

What is 121 ÷ 11?

3.

Which fact helps you solve 84 ÷ 12?

4.

132 students make 12 equal teams. How many students are on each team?

5.

What is 0 ÷ 9?

6.

What is 144 ÷ 12?

For parents and teachers

Big idea: Along with multiplication facts to 12 × 12, students in Grade 5 are expected to know the related division facts (B2.2). The fastest way to a division fact is to think of its multiplication partner: "84 ÷ 12 is 12 times what?"

Common difficulties:

  • Not seeing the link to multiplication. Always ask "What times 12 makes 84?"
  • Writing the division backwards (12 ÷ 84). Remind your child that the big number (the total) comes first.
  • Thinking 0 ÷ 12 is 12. Use a sharing story: no cookies, 12 friends.

How to help: Turn multiplication flash cards into division ones by covering one factor. Play "I'm thinking of a number: 12 times my number is 108". Ask your child to explain sharing and grouping stories for the same fact.