The aim is that children use mental methods when appropriate but, for calculations that they cannot do in their heads, they use an efficient written method accurately and with confidence. These will be introduced to children AFTER they have understood the term subtraction by using objects and pictures to reinforce the idea. Children will always have had experience of using a numbered number line as well.
To subtract successfully, children need to be able to:
- recall all addition and subtraction facts to 20
- subtract multiples of 10 (such as 160-70) using the related subtraction fact, 16-7, and their knowledge of place value
- partition 2-digit numbers into multiples of 10 and 1 in different ways (e.g., partition 74 into 70 + 4 or 60 + 14)
It is important that children’s mental methods of calculation are practised and secured alongside their learning and use of an efficient written method for subtraction.
It is very important to teach difference when teaching subtraction, because we are not always trying to take away something. For instance; I have £37 and I want to buy a radio costing £49. How much more do I need? We are finding the difference, not taking away, and if we don’t introduce and use this term from the outset then children will find it confusing later. Do not use the term leave (i.e. 5 take away 3 leaves 2) because eventually children need to know that 5-3=2 and 2=5-3 but it won’t make sense if the term ‘leaves’ is used.
Children should be encouraged to notice similarities and differences in contexts not related to numbers, such as in the example of the snails.
Vocabulary for Subtraction
Learning pathway for subtraction
Early subtraction through play
In the first stage children will explore the reduction of an amount through their play supported by adults questioning what is happening. Example questions:
Make set of 5 cars and remove 1. How many are there now?
I had 9 apples but my rabbit ate 3 of them. How many do I have now?
Counting back 10-1
Say the number names counting down from any given number. “Start at 8 and count back to 3.”
Counting back should also be done through songs such as ten green bottles, 5 little speckled frogs etc.
Children need to know that counting back has a difference of one. Stem sentence:
Consecutive numbers have a difference of one
Subtract 1 from a number up to 10
Children know that subtracting one gives us one less.
Children know that counting back has a difference of one and use this to solve subtraction equations where the subtrahend is 1.
When you subtract one from a number, the number gets one smaller
Subtract 2 from a number up to 10
Children notice that subtracting 2 from an odd number gives the previous odd number. Subtracting 2 from an even number gives the previous even number.
Finding half of a number up to 10
Children practically explore halving of even numbers up to 10 by dividing the quantity (whole) into 2 equal groups (parts). This can be supported through play and the use of part-whole models.
One half of ___ is ___
It is important to emphasize saying “ONE half of…”
Record subtraction expressions and then equations.
(Expressions do not have the = symbol)
Children will recognise a reduction story and represent this through the CPA approach.
First there were __, then there were __ less. Now there are __.
Children recognise and use the - symbol referring to it as “minus”.
Children recognise and use the language of minuend (the whole amount) and subtrahend (the amount subtracted) when talking about their calculations.
Children use manipulatives, models and then written methods to record subtraction equations.
The stem sentence for reading a subtraction equation is:
___ minus ___ gives the difference of ___
The effect of zero in a subtraction equation
When zero is subtracted from a number, the number remains unchanged.
Subtracting a number from itself gives a difference of zero.
Recording half of numbers up to 10.
Children recognise that halving is the opposite of doubling.
Children now explore and record halving in an equation. Recognising that the subtrahend is half of the minuend and the difference is the remaining half of the minuend.
8 - ? = 4
Subtracting from numbers up to 20, through/from ten methods.
Method 1 (left) Method 2 (right)
subtraction through ten subtraction from ten
Subtract a one digit number from a number up to 99 (not crossing into the next 10)
The children will now be using dienes and place value charts to support their calculations.
Subtract a multiple of 10 from a 2 digit number
The children will now be encouraged to use known number facts rather than counting back to solve these subtraction equations. This is seen in the stem sentences below that they are encouraged to use.
Subtract 2 subtrahends `one ten and one one’
Children will be introduced to the first, then, then, now structure.
They will explore the order of the subtrahends to notice differences and similarities.
Subtract a 2 digit number from a 2 digit number ( not crossing into the 10)
The children will use dienes to support the partitioning of the subtrahend. They will begin by looking at expressions (not using = or finding the difference) and then they will record and complete full equations.
The children will then explore other pictorial models to support their understanding of this learning outcome.
Subtracting a 2 digit number from a 2 digit number when crossing the ten
The children notice the ones of the subtrahend are more than the ones of the minuend and take the following steps:
1.Partition the subtrahend into tens and one….20 and 7
2.Subtract the tens….86 - 20 = 66
3.Notice how many ones need to be subtracted from the minuend to get to the next multiple of ten and partition the ones accordingly… 6 and 1
4. Subtract to the next multiple of 10…. 66 - 6 = 60
5.Subtract the remaining part…. 60-1=59
Subtract two consecutive numbers.
Children should now be able to apply their knowledge that consecutive numbers have a difference of one to solve the equation quickly.
Subtract 2x two digits numbers where the ones are the same
Children should check for and notice if the ones of the subtrahend and minuend are the same. If they are, then the children should apply the most efficient strategy to subtract the ones first and then the tens.