Why is this skill important?
This skill is simply about getting an important ‘times table’ under children’s belts, and secured early in their education. The times tables are a constant bugbear in mathematics education. Children learn them, then forget them, re-learn them, then forget them just as easily, and so on. One way of tackling this is to have five of the tables that do not rely upon short-term memory but are just known to the child. This secure foundation can also give confidence to a child who has real trouble remembering all the tables facts.
If children know 5 tables without any effort, they in fact know ¾ of their tables facts. This is apparent if we look at the multiplication grid below.
The yellow shaded spaces are the table facts that are known if the child knows the 1x table, the 2x table, the 5x table, the 10x table and the 9x tables.
The reason for this is that multiplication is commutative (see Multiplication and Division: Multiplication as repeated addition). This means that it can be done either way round. 5 x 7 gives the same answer as 7 x 5. This means that if the child does not know their 7x table, but does know their 5x table, they can do 5 lots of 7 as 7 lots of 5.
Children already know the ‘counts’ (see Multiplication and Division: Counting in steps) for the 1s, the 2s, the 5s and the 10s. They learned these in the infants and know they can count in 1s, 2s, 5s and 10s without even thinking about it. They can do 7 x 5 by counting in fives up to the 7th multiple. The same for 6 x 2, 8 x 10, and so on. Learning the 9x table gives them one other table and makes the total of known tables facts seventy-five – which is three quarters of those they have to know.
What is the skill?
The skill here resides in recognising that the multiples of nine form a very special pattern.
For a start, the digits always add up to 9. This is even true for large multiples of 9. For example, 4365 is in the 9x table – if you went on far enough! We know this because the digits all add up to 9.
4 + 3 + 6 + 5 = 18 and 1 + 8 = 9.
Secondly, in the 9x table, the tens digits count from 1 to 9 and the ones digits count back from 9 to 1.
Thirdly, because of the way in which the sum of the digits is always 9, it is easy to do the nine times table on our fingers! If one finger is folded down, that means we always have nine standing up – and these can give us the answers to the multiplications in the nine times table.
So how is this skill taught?
This skill resides basically in using fingers to aid the memorisation of the nine times table facts.
- Say the multiplication required, e.g. 3 x 9
- Hold all ten fingers up.
- Turn down the finger to match the first number in the multiplication, e.g. 3rd finger.
- Look at the fingers on the left, e.g. 2 of them. These are the tens, e.g. 20
- Look at the fingers on the right, e.g. 7 of them. These are the ones, e.g. 7
- Put the two together to read off the answer, e.g. 27
Repeat for any multiplication.
For the related division facts, e.g. 72 ÷ 9 = 8
- Hold up the fingers.
- Turn down the finger that leaves you the correct number of tens on the left, e.g. the eighth finger in this case as we need 7 fingers standing for the 70 in 72.
- Look at which finger you have turned down, e.g. number 8. This is the answer to the division.
Practise Together: These activities are intended to be shared. Read the Explanation of the skill being practised and then play the game or share the task. Watch out for the points highlighted in the Explanation and if necessary, help your child, following the advice in ‘How this skill is taught’ section. Shared activities are not only more fun – they enable you to actively support your child’s learning.
Explanation & Worksheets:
Test: Take a test, questions from this area
Multiplication as repeated addition
Counting in steps
Division as inverse of multiplication
The grid method
Divisions with remainders
Division beyond tables
Multiplication as repeated addition:
Understand that multiplication is a way of doing repeated additions, e.g. 4 x 5 is the same as 5 + 5 + 5 + 5
Counting in steps:
Count confidently in twos, , threes, fours fives and tens: 3, 6, 9, 12, etc.
Perform multiplications involving 9 using finger-method
Know the 2x, 3x, 4x, 5x and 10x tables off by heart
Division as inverse of multiplication:
Understand that division is the reverse of multiplication, so that we read 24 ÷ 6 as how many sixes in twenty-four or ? x 6 = 24
The grid method:
Use the grid method to find an answer to larger multiplications, e.g. 4 x 27 or 13 x 8
Divisions with remainders:
Perform divisions with remainders, e.g. 38 ÷ 4
Division beyond tables:
Perform divisions with remainders, e.g. 38 ÷ 4
Number Concepts: Count in different ways, understand how numbers work, become fluent in the ways of numbers
Adding and Subtracting: Mentally add or subtract numbers with confidence and develop written ways of adding and subtracting larger numbers or more of them!
Multiplying and Dividing: Know the times tables and use these to perform mental multiplication and divisions; develop written methods for multiplication and division.