Multiplication and Division Facts: Year 3 Study Guide
Multiplication and division are two sides of the same idea: equal groups.
Multiplication finds how many in total when there are equal groups. Three bags with five apples in each bag is 3 × 5 = 15 apples. Division goes the other way: 15 apples shared among 3 bags gives 5 in each bag, or 15 ÷ 5 = 3 bags.
In Year 3 the focus is on understanding what the symbols mean and on learning the facts for the 2, 3, 5 and 10 times tables first. Later years build on these to cover the 4, 6, 7, 8 and 9 times tables.
Skip counting patterns
Skip counting is repeated addition at speed. Count by twos (2, 4, 6, 8…), threes (3, 6, 9, 12…), fives (5, 10, 15, 20…) and tens (10, 20, 30…). Patterns help: multiples of 5 end in 0 or 5, multiples of 10 end in 0, and multiples of 2 end in 0, 2, 4, 6 or 8.
Fact families
A set of facts using the same three numbers: 3 × 5 = 15, 5 × 3 = 15, 15 ÷ 3 = 5 and 15 ÷ 5 = 3. If you know one, you know the other three.
| Times table | First six multiples |
|---|---|
| 2 | 2, 4, 6, 8, 10, 12 |
| 3 | 3, 6, 9, 12, 15, 18 |
| 5 | 5, 10, 15, 20, 25, 30 |
| 10 | 10, 20, 30, 40, 50, 60 |
Solving word problems
Read the problem and decide whether the groups are known, or the total is known.
Draw or imagine the groups.
Equal groups, total wanted: multiply. Sharing or grouping a total: divide.
6 trays of 5 pies is 6 × 5 = 30.
30 pies for 6 trays seems right.
Worked examples and common mistakes
Example: Mia has 24 stickers and shares them equally among 3 friends. 24 ÷ 3 = 8. Check: 3 × 8 = 24. Another: how many 5 cent coins make 40 cents? 40 ÷ 5 = 8. A common mistake is to say 5 × 0 = 5 (it is 0). Another is to forget that 12 ÷ 3 is not the same as 3 ÷ 12. Division order matters.
Check your understanding: model answers
1. 4 × 5 = 20, 5 × 4 = 20, 20 ÷ 4 = 5 and 20 ÷ 5 = 4. 2. 8 × 3 = 24 balloons (8 groups of 3). 3. 30 ÷ 5 = 6 pencils on each table.
✨ Key Takeaways
- Multiplication finds the total of equal groups; division shares or groups a total.
- Skip counting builds the times tables.
- A fact family has two multiplication and two division facts.
- Always check division by multiplying back.
💬 Questions for Discussion & Reflection
- Write the fact family for 4, 5 and 20.
- Eight children each have 3 balloons. How many balloons? Show a drawing.
- A teacher has 30 pencils for 5 tables. How many pencils on each table?