Mathematical Vocabulary: Addition and Subtraction
"We don't bother using the vocab because they don't know what they [the words] mean when they come to Year 7. We just teach it without using those words."
This comment from a secondary maths teacher opened my eyes (and my mind!) about the teaching of mathematical vocabulary in primary school. Two thoughts came to mind...
Thought 1- Why don't children know the language?
Thought 2 - What more could pupils achieve in if they did know the correct vocabulary?
Secondary teachers shouldn't feel they have to re-visit the primary curriculum instead of hitting the ground running. I know how hard the primary teams work and I think that empowering the young people in our schools to understand and begin to use the correct technical vocabulary will have us winning all round. I also understand that if Maths is not your most confident subject, you may worry about teaching the wrong thing...so you've come to the right place!
Here is a quick summary of the key vocabulary to be used relating to addition and subtraction, that we all should use. By all, I mean teachers, pupils, teaching assistants, the headteacher...everybody. Ultimately there is no real benefit to anyone to refer to each number in a calculation as 'that number' and pointing.
Year 1 children will explore parts and wholes. They should quickly learn that each of those parts is called an addend and the whole is called the total. Explore the word addend. Are there any words hidden in it? Ahh yes - add. Remind me what add means? You can then explore the operation of adding as combining two groups. Children should notice (through practise!) that addends can be added in either order and the total will stay the same. Explore with the total - is it always the largest number in our calculation? How do you know?
Children will need to hear the words many times modelled by you before they are likely to use it themselves...and that's fine!
Vocabulary in subtraction is a little more tricky and will take more modelling and more practise. But your life teaching subtraction will become soooooo much easier when children understand, I promise. So addend was the only tricky word needed in addition - its the same word for the same purpose. There are three different words to use when subtracting - minuend, subtrahend and difference.
You can explore the vocab with the children as part of your teaching sequence - draw generalisations by posing questions such as what do we notice about the minuend? Well, it's the largest part of the calculation.
The simplest way to apply the vocab is like this:
The minuend is the largest set in a subtraction calculation. The subtrahend is a part subtracted. The remaining set is the difference.
In the above example, you could consider a set of 5 apples (minuend). 3 apples are eaten (subtrahend). There are 2 apples left (the difference between what was in the set to begin with and what was eaten).
As we know, subtraction is not commutative and neither is the vocab. If the story changed to '5 apples were in a set then 2 were eaten', we still call the 3 the difference. We have to think of the purpose of each number - what it is representing.
The next two examples use the same vocabulary even though the structure is different.
Subtraction - comparison structure
Pupils in Year 2 can begin to use this language. Again, it will take confident modelling and exploration about what the numbers can and can't do. Hopefully your pupils will realise that subtraction is not commutative as the numbers each have a different purpose; unlike the addends that are commutative (order can be changed and total stays the same).
That's all there is to it! Give it a try and model model model!
Top tip : Colour code the numbers to help children understand the relationships and therefore what the numbers can and can't do when it comes to rearranging.
My top go-to documents (click to link) for getting the language right in primary are:
NCETM PD Materials Spine 1 (Number, Addition and Subtraction) - The teacher guidance PDF will tell you what to say and when to introduce vocab. It revolutionised my Maths teaching!
DfE Mathematics Guidance (KS1 and KS2) - Look out for the Language Focus box
I'd love to hear how you get on.