What are ‘additive relations’?
No, they’re not the relatives that turn up unannounced to a function and suddenly you’re adding seats, more food … you know how it goes!
Put simply, additive relations refer to the connections between numbers and the processes of addition and subtraction.
But it’s more than that.
Addition and subtraction are inverse operations. I know…more maths talk… but it’s important for you to understand, so that you can help your child understand.
Inverse operations are those where one ‘undoes’ the other, or as the NSW syllabus defines it, “the operation that reverses the effect of another operation.”
Let me give you an example.
If we have 7 and 3 more, we end up with 10…and if we have 10, and we take away 3, we end up with 7.
It involves understanding how numbers can be represented as combinations of their parts, which helps your child solve a wide range of mathematical problems AND it has practical applications in real-life scenarios, for which I imagine you can now think of your own examples.
This concept is dealt with differently in each stage of your child’s learning. Let’s explore.
Early Stage 1
In Early Stage 1, or Kindergarten, the big idea that they will learn about and talk about is combining and separating quantities, and they’ll use blocks, toys, fingers or other objects to demonstrate their understanding. They begin to develop an understanding of the number bonds to 10, by creating them and then discussing what they have done and the different combinations they have found. Lots of different words are used, but add, subtract and equals are NOT used at all at this stage.
Stage 1
In Stage 1, or Years 1 and 2, they’ll still talk about combining and separating, rather than addition and subtraction, but the words add, subtract and others are introduced. They start to recognise and use the symbols for these processes, and start developing and using flexible strategies to solve addition and subtraction problems. There’s a lot to learn about in Stage 1 and it lays the platform for the more formal learning that comes in Stage 2 and beyond.
Stage 2
In Stage 2, or Years 3 and 4, the big idea is now additive relations, and they’ll start recognising and explaining how addition and subtraction are connected. Their problem-solving skills will develop to incorporate a multitude of flexible strategies, and they’ll work with numbers up to 4 digits, including partitioning, regrouping and renaming numbers. Money and simple budgeting concepts are now introduced.
Stage 3
In Stage 3, or Years 5 and 6, when they learn about additive relations, it is the application of efficient strategies that becomes the focus, as well as the application of known strategies to add and subtract decimals.
Ok, that was a lot …
It should be obvious by now that your child’s understanding is built upon each year, and that there is a well thought out, structured approach to the destination that is efficiency in addition and subtraction. But this does not happen on its own.
Yes, your child’s teachers along the way will play their part, but that’s all it is - a part - a very BIG part admittedly, but a part, nonetheless.
The other part is YOU.
Yes. I mean that YOU have to help them too. They cannot possibly get the practice that is required for these concepts to become permanent fixtures in their heads without your help.
Think about the other activities in which your child might be involved - sport, music, art, dance … - they NEED to practice. And ok, they may have a coach, or a tutor, or something similar to help them practice but YOU are responsible for getting them to practice.
With maths, they need someone to help them practice these ideas until they become permanent.
If you are fortunate enough to be in a position to pay for a tutor, that’s great, but what if they have a problem on a day when the tutor isn’t there? Do they just remain stuck until next week?
OR …
Do you roll your sleeves up and help them?
Not sure how?
That’s ok. Let me show you. It’s what I do.
