## Why is this skill important?

Many calculations need to be done mentally, that is to say, in our heads without writing anything down. Children need to be taught specific strategies to enable them to do these sums in their heads. It is therefore important that they have a reliable, robust and well understood method for adding or subtracting any two 2-digit numbers (in their heads) that will serve them well, whatever the particular numbers in a calculation and whatever the context in which it arises.

## What are the skills and how are they taught?

In fact, there are two skills here: mental addition of two numbers and mental subtraction of two numbers.

Mental addition of two numbers can be done in two ways:

1. Adding the tens then the ones:
1. Identify the larger number, e.g. for 26 + 88, we first identify 88 as the larger number.
2. Counting on in tens to add the tens part of the smaller number; e.g. for 88 + 26, we add the tens (20) to get 108.
3. Add the ones to reach the total, e.g. for 88 + 26, we then add the ones (6) to get 114.

NB. Some children may try to count on in ones for this last part but it is important to discourage this. Get them to ‘bridge ten’ – that is, to see how many we add to get to the next multiple of ten, then how many more need to be added. 108 + 2 = 110, 110 + 4 = 114

1. Partitioning both numbers and adding the tens and the ones part separately.
1. Identify the larger number, e.g. for 26 + 88, we first identify 88 as the larger number.
2. Split both numbers into ‘tens’ and ‘ones’, e.g.
88 is 8 tens and 8 ones, and 26 is 2 tens and 6 ones.
3. Add the tens: 20 + 80 = 100
4. Add the ones: 8 + 6 = 14
5. Add the two totals: 100 + 14 = 114

NB. This is more stages than the first method and so is slightly harder to do in ones’ head. Children who struggle should be encouraged to use the first method.

Mental subtraction of two numbers can also be done in two ways. However, in this case, it is strongly advisable to focus largely if not exclusively on the first method. This is a good fall-back method that can be used with any mental subtraction in any context.

1. Shopkeeper’s addition or counting up:
1. Identify the number to be subtracted, e.g. for 92 - 47, we identify 47 as the number to be subtracted.
2. Regard this number as the start of a line that goes from it to the larger number. We are going to count up along this line.
3. Say the number which adds to this starting number to make the next ten, e.g. 47 + 3 = 50, so 3 is what we first count up.
4. Now count up from that multiple of ten to the larger number, e.g. 50 + 42 = 92 so we count up 42 to get to 92.
5. Decide how much you have added, or counted up, in all, e.g. we added 3 then 42, so we counted up 45 in all.
45 is the answer.

With any subtraction, children can use this ‘counting up’ method, starting with the smaller number and counting up, first to the next ten and then to the larger number. The addition is easy, and this is a far more foolproof method than taking away or counting back, e.g.
53 – 16

• Start at the smaller number
• Count up from 16 to 20 – that’s 4
• Count from 20 to 53 – that’s 33
• 33 + 4 is 37

Easy!

2. Counting back or taking away.

1. Identify the smaller number and look at how many tens we need to take off the larger number, e.g.
92 – 47 we need to take away 40 or 4 tens.
2. Take these tens from the tens digit in the larger number, e.g. 92 – 40 = 52
3. Identify the ones digit in the smaller number, e.g. there are 7 ones in 47.
4. Subtract these ones from the number we had left. This may involve counting back to the multiple of ten, e.g.
52 – 7 = 52 – 2 – 5 = 45.

NB. This last step is hard as children are having to bridge ten going backwards!

The only subtraction calculations where it is advisable to count back rather than count on are where you are subtracting a very small number or a multiple of ten, e.g. 94 – 12 or 94 – 50. For counting back or taking away, the ones digit in the number being subtracted should be smaller than the ones digit in the first number.

Counting up is therefore a safe and easy mental method that can be used by all children in all circumstances. Make sure they understand 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: 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.

7-9: Lower Juniors

9-11: Upper Juniors