In fair sharing you knew how many groups and found how many go in each. Division can also ask the other question: you know how big each group is, and you want to know how many groups you can make.
Why it works
Making groups of 4 from 20 means taking away 4 again and again until none are left. Each take-away makes one group. You can take 4 away 5 times, so there are 5 groups. It is still $20 \div 4 = 5$, because $5 \times 4 = 20$. The numbers are the same as sharing; only the question is different.
| The story tells you | Division finds | Example: $20 \div 4 = 5$ |
|---|---|---|
| how many groups (4) | how many in each group | 4 friends share 20 cookies: 5 each |
| how many in each group (4) | how many groups | 20 cookies, 4 per bag: 5 bags |
Key idea
$20 \div 4$ can mean "how many groups of 4 are in 20?" The answer counts groups.
Worked example: How many bags?
There are 24 apples. Each bag holds 6. How many bags are needed?
- The size of each group is known: 6. The number of groups is not.
- Count by 6s to 24: 6, 12, 18, 24. That is 4 groups.
- So $24 \div 6 = 4$.
Answer: $4$ bags
Worked example: Which question?
28 students split into teams of 7. What does $28 \div 7$ tell you?
- The team size, 7, is given.
- So the answer, 4, is the number of teams.
Answer: how many teams (4)
Common mistake
Mixing up the two meanings. After dividing, ask: does my answer count groups or things in a group? Label it: "4 bags," not just "4." If the story already told you the number of groups, the answer is the size of a group, and the other way round.