Why is this skill important?
Doubles and corresponding halves are pairs of numbers that need to be known by heart in order to make it possible to do calculations quickly and accurately in our heads. Once children know that 8 + 8 is 16, they will recognise and use this fact in a wide variety of other calculations, e.g. in adding several numbers; 8 + 41 + 8 + 22 becomes a lot easier as 41 + 22 + 16, or in multiplying, 48 x 2 is (40 x 2) + (8 x 2) or in adding near doubles such as 16 + 17 (16 + 16 = 32 so 16 + 17 = 33).
The doubles to 20 and halves of numbers to 40 should be known so well that children do not even have to think about them! Like other number facts (see Addition and Subtraction: Pairs up to 10) they need to be on automatic pilot!
What are the skills?
Both doubling and halving rely largely on memory, where simple repetition is the key to knowing by heart. However, it is also important that children realise that:
- Doubling a whole number ALWAYS gives an answer of an even number.
- Halving an even number gives a whole number answer.
- Halving an odd number gives a mixed number answer, e.g. half of 7 is 3½, and half of 17 is 7½.
- Doubling two-digit numbers can be achieved by doubling the tens and then the ones and adding the results.
If children do not realise these basic mathematical facts, they are likely to make errors later on when they have to use doubling and halving as important techniques in performing mental multiplication and division calculations.
For example, when multiplying by 25 they would do so by multiplying by 100 and halving twice, or when dividing by 8 by halving three times as in 1,000,000 ÷ 8 = 125,000.
So how are these skills taught?
Clearly repetition is key to memorisation. Since children memorise in different ways – some aurally/orally by chanting the doubles, some visually by seeing the pairs of numbers on the page, and some kinaesthetically by movement or the use of manipulable resources.
To combine the aural and kinaesthetic, it is easy to help children recall the first five doubles using fingers.
- Hold matching thumbs up, rest of fingers folded down, and say ‘double one is two’.
- Then unfold one finger, so that the thumb and one finger on each hand stand up. Say ‘double two is four.’
- Continue like this, standing one finger more on each hand to chant the remaining doubles up to double five.
Having children make all the pairs to double 20 using coins (10p and 1p only) is also very helpful as the money provides a visual stimulus as well as being a real life context.
- So they lay out, for example, 12p using a 10p and two 1p coins.
- They then physically double this, so that they have two 10ps and four 1ps.
- You can do this for different teen numbers, e.g. doubling one 10p and four 1ps (14p) or one 10p and nine 1ps (19p).
Chanting the doubles is always a good way of inserting these into the memory, starting with ‘two and two is four, three and three is six’ and so on all the way up to, ‘twenty and twenty is forty’.
Make the connection between the doubles to 10 and the doubles to 20.
- Double ten is twenty.
- Double six is twelve.
- So double sixteen is thirty-two (20 + 16), etc.
Coins are a very good way of doing this visually, or else towers of ten cubes plus loose cubes will also make this very accessible for children who struggle.
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
Say numbers 10 100 1000
Pairs up to 10
Skill with single digit numbers
Mental addition & subtraction
Know doubles & halves to 20
Add 2 or 3 digits with writing
Counting back to subtract
Subtract by counting up
Say numbers 10 100 1000: Say immediately the numbers 10, 100, 1000 more or less than any number up to 10,000
Pairs up to 10: Know by heart the pairs of numbers to make all the numbers up to and including ten
Skill with single digit numbers: Add several single-digit numbers spotting pairs to 10 and doubles
Mental addition & subtraction: Add or subtract two 2-digit numbers in their heads without writing anything down (and without groaning!)
Know doubles & halves to 20: Know by heart the doubles of all numbers up to 20 and the corresponding halves
Add 2 or 3 digits with writing: Add several 2-digit or 3-digit numbers using a written method
Counting back to subtract: Subtract a small number from a large number by counting back, e.g. 345 – 26 (take off 20, then 6)
Subtract by counting up: Subtract two numbers by counting up to find the difference, e.g. 345 – 287 by counting from 287 to 300 then to 345
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.