Why is this skill important?
Although at this stage in children’s mathematical careers, it is very important to focus on the development of well understood and firmly embedded mental methods of adding and subtracting numbers, it is nevertheless the case that some calculations are simply too hard to do ‘in our heads’. This should never include the addition or subtraction of any two 2-digit numbers (e.g. 54 + 87 or 83 – 56) which should always be performed by children as a mental calculation – done in our heads! (See Addition and Subtraction: Mental addition and subtraction.)
However, although we are enthusiastic about being able to do many sums in our heads, we do recognise the need for written methods for the harder calculations. When adding several 2-digit numbers or two or more 3-digit numbers children need and should have a reliable method for writing the calculation and getting it right.
What are the skill?
In order to use more complex numerical procedures, children need to possess two pre-requisite skills.
- A thorough understanding of place value (see Number: Place Value and Counting in 10s and 100s).
- A really good recall of basic number facts, especially the number bonds to ten (see Addition and Subtraction: Pairs up to 10 and Know doubles and halves to 20).
Once these two skills are secure, it is possible to use these in learning the mathematical methods required for effective written addition.
However, if children are stuck at the level of ‘counting on in ones’ when they are performing simpler addition, then they will not be able to retain the necessary procedural knowledge to perform the written methods.
It is therefore important to check that children do understand place value – i.e. how the numbers ‘work’, that they do know by heart their number facts, and – importantly – that they can use both these skills when doing easier sums, before proceeding with written methods.
A simple check is to ask the child to do ’36 + 27’ and watch how they do this simple calculation.
A confident child will split the 27 in their head and will first add the 20 to 36, getting 56. They will then split the ‘7’ and add 4 to get to 60, and then 3 more to get to 63. They will not count on in ones to get from 57 to 63.
If the child is still at the stage of counting in ones, then we do know that they are not yet using their number facts and their understanding of place value in performing simple calculations. It is unlikely that they will be able to use these skills in performing written calculations.
So how are these skills taught?
The challenge then is to ensure that every child has a really reliable and robust method for writing harder additions and coming up with the correct answer every time. The way we teach these need to help the children to:
- Understand what they are doing, so that they realise why the procedure they are using ‘works’; i.e. why the calculation gives them the correct answer.
- Remember the process so that they always know ‘what to do next’.
- Use the same method in any situation and with any numbers so that children do not have to learn several methods and then have the difficulty of deciding which one to use.
Teaching written addition
Basically there are two ways of using the standard written method for adding several 3-digit or 2-digit numbers. One is an expanded version, where we write all the stages in the process and so make these visible to children. The second is a concise shortened version where we use a traditional method of ‘carrying’ numbers from one column to the next.
Both are demonstrated here, and it is easy to see that the expanded version may well be easier for children who are finding this hard. It is FAR better for children to use the expanded method and to get their sums right than for them to be pushed too early into the concise method and for them then to forget what they are doing and why, and to become confused and get the sums wrong. This will inevitably result in a lack of confidence.
The moral then is, do not rush children into the concise if they are finding this hard. Expanded works, and it will do the job just fine.
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.