Multiplication and Division Strategies: Year 4 Study Guide
Year 4 students know their multiplication facts and use them to work out bigger calculations.
By Year 4, students recall multiplication facts up to 10 × 10 and the matching division facts. They use these to solve harder problems by partitioning numbers: 6 × 14 = (6 × 10) + (6 × 4) = 60 + 24 = 84. This is called the distributive property.
They also use the inverse relationship between multiplication and division. Because 7 × 8 = 56, we know 56 ÷ 8 = 7 and 56 ÷ 7 = 8. Division can leave a remainder, and students decide what to do with it in context.
Building multiplication strategies
Use known facts to find unknown ones. Doubling: 6 × 4 is double 3 × 4. Halving and doubling: 5 × 16 = 10 × 8 = 80. Near tens: 9 × 7 = 10 × 7 − 7 = 63. Splitting: 7 × 13 = 70 + 21 = 91.
| Strategy | Example | Working |
|---|---|---|
| Doubling | 6 × 4 | 3 × 4 = 12, doubled is 24 |
| Near ten | 9 × 6 | 60 − 6 = 54 |
| Split | 8 × 12 | 80 + 16 = 96 |
| Halve and double | 5 × 18 | 10 × 9 = 90 |
Division and remainders
Division shares a quantity equally or finds how many groups fit. 47 ÷ 5: 5 × 9 = 45, so the answer is 9 remainder 2. In a story problem the remainder decides the answer. 47 cupcakes in boxes of 5 needs 10 boxes (round up). 47 cupcakes shared among 5 friends gives 9 each, with 2 left over.
5 × 9 = 45.
47 − 45 = 2.
9 remainder 2.
5 × 9 + 2 = 47.
Fact families and patterns
A fact family links three numbers: 6, 7 and 42 give 6 × 7 = 42, 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6. Patterns help: multiples of 5 end in 0 or 5, multiples of 9 have digits that add up to 9, and multiples of 4 are the double of the double.
Worked examples and common mistakes
Example: A school buys 8 packs of 25 markers. 8 × 25 = 8 × 20 + 8 × 5 = 160 + 40 = 200 markers. Common mistakes: forgetting that division is not commutative (12 ÷ 3 is not 3 ÷ 12), losing track of a remainder, and multiplying only the tens digit. Always ask whether the answer is sensible by estimating.
Check your understanding: model answers
1. 7 × 10 + 7 × 5 = 70 + 35 = 105. 2. 9 remainder 2 (9 × 9 = 81). 3. 40 ÷ 6 = 6 remainder 4, so 7 cartons are needed.
✨ Key Takeaways
- Know the facts to 10 × 10.
- Partition numbers to multiply.
- Multiplication and division are inverses.
- Read the problem to decide what the remainder means.
💬 Questions for Discussion & Reflection
- Work out 7 × 15.
- Work out 83 ÷ 9.
- Eggs come in cartons of 6. How many cartons are needed for 40 eggs?