Why is this skill important?
Multiplication is simple enough for children whilst it remains within the bounds of the times tables. Even those children who have trouble remembering their tables, can always count in the multiples, e. g. counting in fives to find the answer to 8 x 5 = ?
However, once children move on to multiply numbers above the tables’ facts, they have to have a reliable method that is easily transferable to any situation and any set of numbers. The method we teach children also has to be memorable. It is unsatisfactory if children can remember what to do only for the duration of the lesson or the week in which they happen to be doing this type of calculation. If they have forgotten it, or are confused when asked to do a multiplication out of the classroom context, then the method taught is really not working!
Grid multiplication does not only provide a robust and secure strategy for doing mental or written multiplications where the numbers involved are larger than 12 x 12. It also has the advantage that, in its very operation, it reinforces children’s understanding of place value and the way numbers work. In addition, it further develops an aspect of reasoning about the operation which will be very useful when children come to do algebra and quadratic equations when they reach secondary school maths. So grid multiplication has come to be the most commonly taught procedure at this stage in children’s education and one many children will stick with throughout their mathematical education.
What is the skill?
Multiplying using a grid is basically a way of separating the parts of a number – the hundreds, tens, and ones – and dealing with each of these separately.
This method can be utilised even when we are multiplying a two-digit by a two-digit number.
So how is this skill taught?
There are some pre-requisite skills that children need to have acquired before they can be taught grid multiplication successfully. Without these basic skills in place, there is little chance of children understanding and following the method. Nor are they likely to be able to remember it and draw upon the procedure when they need to perform multiplication calculations in a variety of different circumstances and with a variety of different numbers. These basic pre-requisite skills are:
- Understanding place value in two-digit and three-digit numbers. This refers to understanding how hundreds, tens and ones are related and how our number system works (see Number: Place value).
- Good recall of 2x, 3x, 4x, 5x, 9x and 10x tables.
- A thorough understanding of multiplication as repeated addition, namely that 4 x 7 is four lots of seven.
- A realisation that you can do multiplication either way round: 4 x 6 has the same answer as 6 x 4.
Once these pre-requisite skills are in place, children can be taught grid multiplication by progressing through three levels.
- Multiplying a teen-number by a single-digit number, e.g. 14 x 5.
- Multiplying any two-digit or three-digit number by a single-digit number, e.g. 46 x 3 or 137 x 6.
- Multiplying a two-digit or three-digit number by a two-digit number, e.g. 45 x 13 or 145 x 13.
First level: a teen-number by a single-digit number
Children are taught to partition the teen number into a ten and some ones, e.g. 14 is one ten and four ones: 14 = 10 + 4
They are then shown how to lay out the multiplication and multiply the parts separately.
The second level involves an understanding of three-digit numbers and a more robust knowledge of the times tables.
Once children are secure at this level, then they can try the multiplication of a two-digit number by a two-digit number. This demands a much higher level of competence with the actual procedure. Therefore it is absolutely crucial that children are very confident operating at the previous level, and also that they have a really secure foundation in their memorised tables facts before attempting these more complicated multiplications.
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.