Division and Fact Families: Grade 3 Study Guide
Division is the opposite of multiplication. If you know your multiplication facts, you already know most of your division facts.
Division splits a total into equal parts. There are two kinds of division story. In a sharing story, 12 stickers are shared equally among 4 friends, so each friend gets 3 (12 ÷ 4 = 3). In a grouping story, 12 stickers are put into bags of 4, so you fill 3 bags (12 ÷ 4 = 3 again).
The numbers in a division sentence have names: the dividend (the total, 12), the divisor (the number you divide by, 4) and the quotient (the answer, 3). You do not need to memorize these words in Grade 3, but they help when talking about your thinking.
Division undoes multiplication
Because 3 × 4 = 12, we know 12 ÷ 4 = 3 and 12 ÷ 3 = 4. A division problem can be turned into a missing-factor problem: to solve 24 ÷ 6 = ?, ask yourself 6 times what makes 24? Since 6 × 4 = 24, the answer is 4.
Fact families
A fact family is a set of related facts that use the same three numbers. Knowing one fact gives you all four.
| Family of 3, 4, 12 | Sentence |
|---|---|
| Multiply | 3 × 4 = 12 |
| Multiply (turn-around) | 4 × 3 = 12 |
| Divide | 12 ÷ 3 = 4 |
| Divide | 12 ÷ 4 = 3 |
Solving an unknown
Use a symbol or letter for the number you do not know, such as ? × 5 = 35 or 40 ÷ ? = 8. Think of the fact family: 35 ÷ 5 = 7, so ? is 7. For 40 ÷ ? = 8, think 8 × 5 = 40, so ? is 5.
Is it sharing or grouping? What is the total?
Total known, size of groups known: divide.
Multiply your answer by the divisor. You should get the total back.
Worked examples
Example 1. A teacher puts 20 crayons equally into 5 cups. How many in each cup? 20 ÷ 5 = 4, because 5 × 4 = 20.
Example 2. A baker packs 36 rolls into bags of 6. How many bags? Think: 6 times what is 36? 6 × 6 = 36, so 6 bags.
Example 3. What is the missing number in ? ÷ 3 = 9? Use the fact family: 3 × 9 = 27, so ? is 27.
Common mistakes
A common error is to switch the numbers: 4 ÷ 12 is not the same as 12 ÷ 4. The total goes first. Another mistake is forgetting that the remainder idea comes later. In Grade 3 the numbers divide exactly, so if an answer does not work, recheck your multiplication fact. Finally, never divide by 0. Try sharing 6 cookies among 0 friends. There is no answer that makes sense.
Check your understanding: model answers
1. 5 × 6 = 30, 6 × 5 = 30, 30 ÷ 5 = 6 and 30 ÷ 6 = 5. 2. 28 ÷ 7 = 4 boxes. This is grouping, because we know the size of each group (7). 3. 6 × 8 = 48, so 48 ÷ ? = 6 means ? is 8. Check: 48 ÷ 8 = 6.
✨ Key Takeaways
- Division shares a total equally or finds how many equal groups there are.
- Multiplication and division are inverse operations.
- A fact family uses the same three numbers in four related facts.
- Check a division answer by multiplying back.
💬 Questions for Discussion & Reflection
- Write the four facts in the family for 5, 6 and 30.
- 28 pencils are put into boxes of 7. How many boxes? Is this sharing or grouping?
- Solve 48 ÷ ? = 6 and show how you checked.