Why is this skill important?
This skill is about realising the concept that underlies one major aspect of multiplication. Multiplication may be construed, mathematically speaking, as repeated addition and as scaling. The first of these is encapsulated in this skill – and relates to the fact that one way of reading 6 x 4 is as 6 lots of 4. The second relates to the fact that 6 x 4 can also be read as 6 multiplied by 4 or six scaled up by a factor of four. In the primary school, we really only address scaling as doubling – either doubling once (scaling up by a factor or 2) or doubling twice (scaling up by a factor of 4). Understanding these two aspects of multiplication will become increasingly important as children get further into their mathematical careers.
What is the skill?
As children are introduced to multiplication in the infants, they learn how to count in regular steps of two, five and ten.
- 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22…
- 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…
- 10, 20, 30, 40, 50, 60, 70…
Once they have memorised these fundamental counts, they can draw on these to perform simple multiplications.
- 4 x 2 is the fourth number we say in the ‘2s’ count.
- 4 x 5 is the fourth number we say in the ‘5s’ count.
- 4 x 10 is the fourth number we say in the ‘10s’ count.
This translates easily into the repeated addition:
- 4 x 2 is a quick way of writing 2 + 2 + 2 + 2 = 8
- 4 x 5 is a quick way of writing 5 + 5 + 5 + 5 = 20
- 4 x 10 is a quick way of writing 10 + 10 + 10 + 10 = 40
So how is this skill taught?
The skill is taught through three stages:
- Learning the counts. Counting in steps, first of 2, then of 5, then of 10, and then of 3, and 4, and 6, etc. Children need to learn to count in steps of the different multiples, e.g. 3, 6, 9, 12, 15, 18…
As much as anything, this helps them to recognise the multiples, which is crucial in doing division. How many 3s in 23, is made a great deal easier if you know that 21 is a multiple of 3 – it is in the 3s count.
- Recognising the repeated addition. Seeing 4 + 4 + 4 as three lots of 4 is the start of multiplication for most children. This is often presented graphically as three rows of four, or three trays of four buns, or three strips of four stickers like this.
- However, it is also very important that children are shown that 3 x 4 gives the same answer as 4 x 3 or 3 + 3 + 3 + 3. Mathematically, this aspect of multiplication is known as commutativity. We say that multiplication is commutative, meaning that it can be done either way round. 5 x 7 gives the same answer as 7 x 5. Of course, division is not commutative and 35 ÷ 7 does not give the same answer (5), as 7 ÷ 35 (1/7).
Ask children to tell you what a multiplication means, to find out if they can re-phrase 3 x 7 as three lots of 7 or as 7, three times.
- 7 + 7 + 7
- 3 x 7
If they just tell you that 3 x 7 means three times seven, this may indicate that they have no understanding of what the ‘x’ sign means. This will then inhibit the development of strategies for more complicated mental calculations in multiplication. If we realise that 19 x 13 is nineteen sets of 13, then it becomes an obvious technique to try to find 20 sets of thirteen and then subtract one 13.
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.