Multiplication & division
Connecting the times tables
When you know one times table, you can use it to work out others by doubling, halving or adding. This helps you learn the 2, 4 and 8 tables, and the 3, 6 and 9 tables.
Every fact is groups × group size
In a multiplication table, the group size × how many groups = the product. When you change the group size, you must change the product in the same way. The number of groups stays the same.
Connecting the 2, 4 and 8 tables
Double 2 is 4, so double a 2× fact to get the 4× fact: 2 × 6 = 12, double → 4 × 6 = 24. Double 4 is 8, so double a 4× fact to get the 8× fact: 4 × 6 = 24, double → 8 × 6 = 48. You can also halve to go back down. All multiples of 2, 4 and 8 are even numbers.
Connecting the 3, 6 and 9 tables
Double 3 is 6, so double a 3× fact to get the 6× fact: 3 × 5 = 15, double → 6 × 5 = 30. Doubling the 6× table does NOT give the 9× table. Instead you can add tables: 9 × 4 = 3 × 4 + 6 × 4 = 12 + 24 = 36.
Counting on from any number
Once you know a table, you can count on in that step from any start number. Starting at 5 and adding 4 each time gives 5, 9, 13, 17, 21. This is called the term-to-term rule.
Worked examples
Doubling the 2× table to find a 4× fact
- Start with the 2× fact: 2 × 6 = 12.
- Double the group size from 2 to 4.
- Double the product too: 12 doubled is 24.
Answer: 4 × 6 = 24.
Doubling the 4× table to find an 8× fact
- Start with the 4× fact: 4 × 6 = 24.
- Double the group size from 4 to 8.
- Double the product: 24 doubled is 48.
Answer: 8 × 6 = 48.
Adding tables to find a 9× fact
- You want 9 × 4 but doubling 6× does not work.
- Add the 3× and 6× facts: 3 × 4 = 12 and 6 × 4 = 24.
- Add the products: 12 + 24.
Answer: 9 × 4 = 12 + 24 = 36.
Counting on with a term-to-term rule
- The rule is add 4 and the start number is 5.
- Add 4 each time: 5, then 9, then 13.
- Keep going: 17, then 21.
Answer: The sequence is 5, 9, 13, 17, 21.
Where you see this in real life
- Counting spider legs in eights.
- Counting the sides of squares in fours.
- Working out totals quickly by doubling a table you already know.
Key words
- Double
- Make a number twice as big by adding it to itself.
- Halve
- Split a number into two equal parts to make it half the size.
- Multiple
- A number in a times table, such as multiples of 4: 4, 8, 12, 16.
- Product
- The answer when you multiply two numbers.
- Term-to-term rule
- The rule that tells you how to get from one number in a sequence to the next.