Why is this skill important?
It is obvious to everyone from leading mathematicians to the children themselves that not knowing ones tables’ facts poses a severe problem as the calculations get harder and more varied. It is simply crucial that children have these facts at their fingertips. However, in todays’ world, memorisation is much more of an issue than it was for our own parents and even for us. Young children no longer routinely memorise rhymes or prayers for example, so their memory is trained before they even enter formal schooling. Once they are in school, all too often the only ‘learning off by heart’ that they do is in the classroom. Daily life no longer provides such opportunities or necessities. Therefore the memorisation that children do at school is all the more crucial to their educational success, as it not only provides them with a foundation of mathematical facts, but also enables that training of the memory itself, which develops their powers of recall for the future.
As we have said in relation to other skills, It is extremely important that children:
(a) Learn their times tables multiplication facts up to the tenth multiple of all the numbers up to 10.
(b) Come to understand what a multiple is – and subsequently what a factor is and what a common multiple consists of.
(c) Learn the related division facts to each of the multiplication facts. Thus children need to know that 42 ÷ 6 is 7 and that 42 ÷ 7 is 6 as well as that 6 x 7 = 42.
What is the skill?
As with Multiplication and Division: Counting in steps, it is important first to be clear about the related terminology.
- A multiple is a number which is an answer in a particular table – e.g. a multiple of three is an answer in the 3x table: 1 x 3 = 3, 2 x 3 = 6, 3 x 3 = 9, 4 x 3 = 12, etc. 3, 6, 9 and 12 are the first four multiples of 3.
- A factor is one of the numbers being multiplied in a times table fact. It is a number, which divides into a number without leaving a remainder, e.g. 3 is a factor of 15, as 3 x 5 = 15. 5 is also a factor 15. Both 3 and 5 are also factors of 135…
For children learning their tables, they need to memorise not only the list of multiples in each table, but also the number of each multiple. Thus they not only need to know the chant, 5, 10, 15, 20, 25, 30, 35, 40, 45… etc. They also need to be able to say instantly, how many 5s are 35. Seven fives are thirty-five. In addition, they need to be able to say how many fives there are in 35, and how many sevens:
35 ÷ 7 = 5 and 35 ÷ 5 = 7.
So how is this skill taught?
Having to learn off by heart what amounts to 100 tables facts can seem an overwhelming task and very daunting for some children. So it is very important to stress that we do NOT have to learn that many facts.
First we must remind children that they can always turn a multiplication around ~ five eights is the same total as eight fives, 5 x 8 ≡ 8 x 5. So if the child cannot remember five eights, they will almost certainly know eight fives.
Second it is important to reassure children that they already know the 1x, 2x, 5x, 10x and 9x tables (this latter can be done on their fingers – see Multiplication and Division: Finger nines). They do NOT have to learn these. And this actually accounts for three quarters of the tables facts required.
Third, it is always a good technique for those children who have trouble memorising, to encourage them to double up. So…
- learn the 2x table and double to get the 4x table.
- learn the 3x table and double to get the 6x table.
The multiplication square below shows the tables facts we know in yellow and those we hope to memorise thoroughly in green. There remain very few that have to be learned as ‘special facts.
The special facts (in blue and white) include the following:
6 x 6 = 36, 7 x 7 = 49 – these are learned in the upper juniors as square numbers.
- 7 x 6 = 42 and 8 x 6 = 48 both of which can be quickly worked out by doubling the matching 3x tables facts ~ 7 x 3 = 21 and 8 x 3 = 24.
- 7 x 8, which is best remembered as 56 is 7 x 8 (i.e. 5, 6, 7, 8).
- 8 x 8 = 64 is best learned using the mnemonic ‘I ate and I ate and was sick on the floor’!
By being careful, therefore, we can whittle the facts to be learned down to a manageable number – and provide help with memorisation.
As we have pointed out before, different children memorise in different ways and it is very important to find the best way for each individual child.
- Aural – some children learn things by heart if they chant the tables in unison aloud. When working with an individual child, the best way of doing this is by taking it in turns to say a line, e.g. you say ‘one times four is four’ and the child says, ‘two times four is eight’, and you say, ‘three times four is twelve’, and they say, ‘four times four is sixteen’. Bouncing the tables chant back and forth like this is the best imitation of a ‘chant’ in unison which is only possible with the whole class.
- Visual – some children prefer to see the tables on the page. They can envisage things they have repeatedly looked at. Having times tables posters up in obvious places – on the bathroom walls, in the kitchen, etc. can really help. As can working together to make a tables poster for a times table with which they are having particular difficulty, e.g. the threes or fours.
- Written – for some children, writing the tables out will undoubtedly assist them in committing these to memory. Use coloured felt-tips or even large paintbrushes to make the writing large and eye-catching!
- Kinaesthetic – some children prefer to use movement as their main technique when memorising a set of numbers. For these children, counting along their fingers may well be a useful strategy. ‘Three’ (holding up one finger), ‘six’ (holding up a second finger), ‘nine’ (holding up a third finger), ‘twelve’ (holding up a fourth finger). The fingers tell us ‘how many’ threes (or whatever) are in that total, e.g. four threes are twelve because we are holding up four fingers and saying 12.
Whichever of these techniques are appropriate for the child should be used, and sometimes it is a cocktail of them all which is most effective. Experiment and see which strategies really help the child with the memorisation of these crucial number facts.
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.