Why is this skill important?
This skill is about providing a solid foundation to underpin children’s strategies in performing multiplication and division calculations. Counting in steps of particular size, e.g. counting in 2s or 5s, are the main vehicle for familiarising children with a list of the multiples of that number. It is extremely important that children:
(a) Come to understand what a multiple is – and subsequently what a factor is and what a common multiple consists of.
(b) Memorise the multiples up to the tenth multiple of all the numbers up to 10.
Without these two skills, it is almost impossible for children to move on and perform the more difficult calculations in both multiplication and division.
What is the skill?
In thinking about the skills involved in counting in uniform steps of different numbers, it is important first to be clear about the related terminology.
- A multiple is a number which is in a particular count – e.g. a multiple of three is a number in the threes count: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, etc.
- A factor is a number, which divides into a multiple without leaving a remainder, e.g. 3 is a factor of 15; it is also a factor of 135…
For children in the lower juniors, counting in steps of a uniform size (every step is the same size) is the best way to become familiar with and to then memorise a list of multiples. Counting in 3s helps children to learn the multiples of 3: three, six, nine, twelve, fifteen, eighteen, etc. Counting in 5s helps children to learn the multiples of 5: five, ten, fifteen, twenty, etc.
Once children know these multiples, it is much easier for them to say whether a number has a particular factor or not, e.g. 5 is a factor of 35 because 35 is a number I say in the ‘fives’ count.
So how is this skill taught?
This skill resides basically in memorising or learning by heart. 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 numbers in unison aloud. When working with an individual child, the best way of doing this is by chanting in turns. I say 4, and then David says 8, I then say 12, he says 16 and so on. Bouncing the numbers 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 these numbers on the page. They can envisage things they have repeatedly looked at. Having posters or ‘ladders’ of the different counts stuck in obvious places – on the bathroom walls, in the kitchen, etc. can really help. Or make them a bookmark of a count with which they are having particular difficulty, e.g. the threes or fours.
- Written – For these children, writing the multiples in a particular count 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.
Use whichever of these techniques are appropriate for the child, 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 counts.
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.