How Division Works
Division is breaking a big group into smaller, equal parts.
We can do it with Fair Sharing or Repeated Subtraction.
Fair Sharing
Fair Sharing is useful when we know how many groups we want, but we don't know how many items go in each group.
Example: We have 12 chocolates and 3 friends. How many chocolates does each friend get?
The Action: "One for you, one for you, one for you..." until they are all gone.
Result: 12 divided into 3 equal groups gives 4 in each group.
Repeated Subtraction
Repeated Subtraction is useful when we know how many are in each group, and we want to discover how many groups we can make.
Example: We have 12 cookies. We give 3 cookies to each person. How many people get cookies?
12 − 3 = 9 (that’s 1 person)
9 − 3 = 6 (that’s 2 people)
6 − 3 = 3 (that’s 3 people)
3 − 3 = 0 (that’s 4 people)
We subtracted 3 a total of 4 times. So, 12 ÷ 3 = 4.
Which way is better?
Both ways give the same answer! Just a different use for each.
12 ÷ 3 = 4
- Fair Sharing: 12 items shared between 3 groups gives 4 in each group.
- Groups Of: 12 items in groups of 3 in each group makes 4 groups.
Fact Family
The numbers 3, 4, and 12 belong to the same fact family. Division and multiplication are closely connected.
- 3 × 4 = 12
- 4 × 3 = 12
- 12 ÷ 4 = 3
- 12 ÷ 3 = 4
Play with the Idea
images/divide-marbles.js