Calculation
Times Tables to 12 × 12 and Related Division Facts
Year 3 · Year 4 · Year 5 · Year 6
- ✓Recall multiplication facts for multiplication tables up to 12 × 12 rapidly and accurately.
- ✓Recall corresponding division facts for multiplication tables up to 12 × 12.
- ✓Understand and apply the relationship between multiplication and division as inverse operations.
- ✓Use knowledge of times tables and division facts to solve mathematical problems.
Key concepts
Multiplication is a quick way of doing repeated addition. For example, 3 × 4 means 3 groups of 4, or 4 + 4 + 4, which equals 12. The numbers you multiply are called 'factors', and the answer is called the 'product'. Learning your times tables means knowing the products of pairs of numbers up to 12 × 12 by heart.
Division is the opposite of multiplication. It involves splitting a number into equal groups or finding out how many groups of a certain size can be made from a number. For example, 12 ÷ 3 means sharing 12 into 3 equal groups (each group has 4) or finding how many groups of 3 are in 12 (there are 4 groups). The number being divided is the 'dividend', the number you are dividing by is the 'divisor', and the answer is the 'quotient'.
Multiplication and division are inverse operations, meaning they 'undo' each other. If you know a multiplication fact, you automatically know two related division facts. For example, if you know that 3 × 4 = 12, then you also know that 12 ÷ 3 = 4 and 12 ÷ 4 = 3. This relationship is very useful for checking answers and solving problems.
Key facts to remember
- 1Multiplication is repeated addition.
- 2Division is the inverse (opposite) of multiplication.
- 3Any number multiplied by 0 is 0 (e.g., 5 × 0 = 0).
- 4Any number multiplied by 1 is itself (e.g., 9 × 1 = 9).
- 5Any number divided by 1 is itself (e.g., 10 ÷ 1 = 10).
- 6Any number (except 0) divided by itself is 1 (e.g., 7 ÷ 7 = 1).
- 7The order of numbers in multiplication does not change the product (e.g., 3 × 5 = 5 × 3 = 15). This is called the commutative property.
- 8Regular practice is essential for rapid recall of all times tables up to 12 × 12.
Worked examples
Example 1
What is 9 multiplied by 7?
Answer
63
Knowing your times tables by heart helps you answer quickly.
Example 2
If 8 × 6 = 48, what are the two related division facts?
Answer
48 ÷ 8 = 6 and 48 ÷ 6 = 8
Every multiplication fact (except for squares like 7 × 7) has two related division facts.
Example 3
Find the missing number: 72 ÷ ? = 9.
Answer
8
Using the inverse operation is a powerful way to solve missing number problems.
Common mistakes
- ✗Confusing multiplication and division operations, especially in word problems.
- ✗Forgetting the special rules for multiplying or dividing by 0 or 1.
- ✗Not recalling facts quickly enough, which can lead to errors when under time pressure.
- ✗Incorrectly applying the commutative property to division (e.g., thinking 12 ÷ 4 is the same as 4 ÷ 12).
- ✗Making simple calculation errors due to lack of practice or rushing.
Exam tips
- ★Practise your times tables and related division facts every day. Use flashcards, online games, or recite them aloud.
- ★Learn the division facts alongside the multiplication facts. If you know 6 × 7 = 42, immediately think of 42 ÷ 6 = 7 and 42 ÷ 7 = 6.
- ★Use known facts to work out unknown ones. For example, if you know 5 × 8 = 40, you can find 6 × 8 by adding another 8 (40 + 8 = 48).
- ★Always check your answers using the inverse operation. If you multiply to get an answer, divide to check it, and vice versa.
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