## 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, more difficult subtractions require that children use written strategies as well as mental ones to achieve a correct answer. For example, when subtracting a 2-digit number from a 3-digit number or when finding a difference between two 3-digit numbers, children need to make written jottings to help them.

## What are the skills involved?

In order to use more complicated written 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).

Once these two skills are secure, it is possible to progress to use these in learning the mathematical procedures required for performing more difficult subtractions with larger numbers.

However, if children are stuck at the level of counting on or back in ones when they are performing simpler subtractions, then they will not be able to retain the necessary procedural knowledge to perform the more complex calculations.

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, crucially, that they do use these two skills in doing simple sums, before proceeding with really quite difficult and more lengthy subtractions.

A simple check is to ask the child to do’43 – 35’ and watch how they do this relatively simple calculation.  It should be performed using place value and number facts rather than by counting in ones, i.e. The child should count up from 35 to 43, first counting up 5 to 40 (using number facts) then adding 3 more (knowing that 43 is 40 + 3). The child will then have counted up 8 in all.

If the child relies upon counting in ones to find the answer, then we have discovered that they are not able to use their number facts and their understanding of place value in performing simple calculations. It is therefore unlikely that they will be able to use these skills in working out more complicated subtractions.  So it is best to go back and make sure that these two skills are well understood. Then to practise simpler calculations (see Addition and Subtraction: Mental addition and subtraction).

## So how is this skill taught?

The challenge then is to ensure that every child has a really reliable and robust method for writing harder subtractions and coming up with the correct answer every time.  It follows then that the way we teach these, needs 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 subtraction

At this stage in children’s mathematical careers, it is important that they can subtract any pair of numbers successfully. It is not important that they can use a standard method that their parents or others may have been taught and may or may not remember accurately! These more formal methods will come later, once children have really built up basic and secure mathematical skills and also have a robust understanding of place value with larger numbers.

Therefore we use the children’s mental strategies as the basis for a good method involving written jottings.
This way of subtracting has an added advantage in that it relies upon the use of number facts and also an understanding of place value and so actually reinforces these two vital aspects of children’s mathematical learning.

The basis of the method, as with the mental strategies described in Addition and Subtraction: Mental addition and subtraction, is counting up from the smaller number to the larger. The image that children are drawing upon, and that underpins their competence, is the number line.

• Encourage the child to draw a line with the smaller number at the start and the larger number at the end.
• They then draw hops or jumps – we call these ‘frog-jumps’ to make them memorable!
• The first frog-jump is to the next multiple of 10 (in this case, 60).
• The second frog-jump is to the next multiple of 100 (in this case 300). The final frog jump is to the larger number.

This method has many advantages for children. It is easily memorable – we just remind them that they are doing frog-jumping! It is also much easier for children to count up than to count back. Finally, it is a method that works whatever the numbers.

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