Multiplication and Division: Times Tables and Written Strategies

Multiplication is a quick way to do repeated addition. It means combining equal groups. For example, 3 × 4 means 3 groups of 4, which is 4 + 4 + 4 = 12. We often say 'times' instead of 'multiplied by'. The answer to a multiplication problem is called the 'product'.

Division is about sharing equally or grouping. It tells us how many equal groups can be made or how many items are in each group when shared equally. For example, 12 ÷ 3 means sharing 12 items into 3 equal groups (each group gets 4 items) or seeing how many groups of 3 can be made from 12 items (4 groups). The answer to a division problem is called the 'quotient'.

Times tables are lists of multiplication facts for a specific number. Knowing your times tables by heart (like 2s, 3s, 5s, 10s for Year 3, and up to 10 × 10 for Year 4) makes multiplication and division much faster and easier. They are the building blocks for more complex calculations.

Multiplication and division are inverse operations, meaning they 'undo' each other. If you know a multiplication fact, you also know related division facts. For example, if 3 × 4 = 12, then 12 ÷ 3 = 4 and 12 ÷ 4 = 3. This is called a 'fact family'.

This property means that the order of the numbers in a multiplication problem does not change the product. For example, 3 × 4 gives the same answer as 4 × 3. This can help you remember fewer facts!

For multiplying larger numbers by a single-digit number, we use a written method called short multiplication. We multiply each digit of the larger number by the single-digit number, starting from the ones place and moving to the left, carrying over any tens as needed.

For dividing larger numbers by a single-digit number, we use a written method called short division (sometimes called the 'bus stop' method). We divide each digit of the larger number by the single-digit divisor, starting from the left (largest place value), carrying over any remainders to the next digit.