Why is this skill important?
There is a technique to adding a line of numbers – sensible accountants do not just add them in any old order but apply intelligent tricks! Children need to be taught these and to begin to practise them at this stage. Knowing these calculation tricks helps them to become numerically fluent and to remain mathematically agile. This skill also enables children to keep rehearsing and reinforcing their bonds to ten and other numbers facts.
What is the skill?
The skill here resides in skimming along the line of numbers to be added and looking for pairs of numbers which we recognise and where we know the total without having to do any work! These pairs we are looking to spot include:
- Two or more numbers which add together to make 10, e.g.
6 + 4 or 2 + 3 + 5
- Doubles and near doubles, e.g. 5 + 5 or 5 + 6
- Place value additions (no-work sums), e.g. 34 + 10 or 30 + 4
Once a child knows to look for these pairs, they can also be shown how to minimise the work needed by starting with the largest number. Thus when they are adding 5 + 7 + 4 + 12 + 3 = they can spot the following pairs: 7 + 3 (10) and 5 + 4 (9) making the calculation 12 + 10 + 9, where the first part (12 + 10) requires no work. 22 + 9 is the final calculation.
So how is this skill taught?
Clearly this skill relies upon knowing by heart all the doubles and the bonds to ten and other numbers. The main teaching required therefore is to focus on ensuring that children really have these facts at their fingertips. It can help children in the short term to provide a poster of the number bonds to 10 so that they can use this as a prompt when they are looking along the numbers to be added.
It is also very important to remind children that addition is commutative – this means that it can be done in any order. It does not matter in which order we add numbers, whereas, of course, it makes a great deal of difference in which order we subtract numbers. 3 + 15 gives the same total as 15 + 3 so it makes good sense to start with the larger number and then add the smaller number to it. However, 5 – 3 does not give at all the same answer as 3 – 5!
Ask children to do the following sum: 3 + 6 + 12 + 7 to assess the following:
- Does the child spot the pair of numbers that make ten?
- Do they start with the larger number (12) when adding?
- Do they recognise that adding ten or twenty is easy?
Depending on the answers to these questions, it will be necessary to help the child by:
- Helping them to remember the bonds to ten by rehearsing these and also having a poster displaying them beside you as you do the additions (see resources).
- Rehearse adding pairs of unequal numbers such as 5 + 13 or 4 + 25 on a calculator so that it is clear that it makes no difference which order the numbers are added – the total is the same!
- Practise adding 10 or 20 or 30 etc. to numbers using a 1-100 number grid so that children can see what is happening – we are going down the grid not along it!
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.