Most children can tell you that 3 + 4 = 7.
But do they also know that 4 + 3 = 7?
And if they know those two facts, do they realise they also know that 7 – 3 = 4 and 7 – 4 = 3?
That is the power of Fact Families.
In primary maths, Fact Families help children see that numbers are connected. They show that one known fact can reveal several more. In Big Maths, this matters because it reduces the amount children need to hold in their heads and helps maths feel simpler, clearer and far less overwhelming.
What is a Fact Family?
A Fact Family is a small group of related number sentences that all use the same three numbers.
Take the numbers 3, 4 and 7. They make this Fact Family:
3 + 4 = 7
4 + 3 = 7
7 – 3 = 4
7 – 4 = 3
One set of numbers. Four connected facts. That is a Fact Family.
Try it yourself: enter any three numbers
When both addends are the same, like 5 + 5 = 10. Switching the numbers gives the same fact.
So this family only has two members: 5 + 5 = 10 and 10 – 5 = 5.
Why Fact Families matter so much
Fact Families are important because they cut down what children need to memorise.
Without Fact Families, addition and subtraction facts, multiplication and division facts, can feel like separate pieces of learning. Children may think they have to learn them all individually. But when they understand the relationship between the numbers, they begin to see that one fact gives access to others.
Children’s working memory is limited. If they are using too much mental effort to work out basic number facts, there is less thinking space left for reasoning, problem solving and new learning. Fact Families help reduce that load by turning several separate facts into one connected idea.
How Big Maths makes this even easier
In Big Maths, children first learn Learn Its. There are 72 addition and multiplication number facts that need to be recalled instantly, without hesitation. Each term children learn new Learn Its, ensuring that they know all 72 facts (which means they know all their times tables) by the end of year 4 / primary 5 without any drama or stress.
So from learning one fact, for example:
3 + 4 = 7 (Learn It)
Then they use our Switchers approach. ‘Switchers’ is the Big Maths name for the simple observation that swapping the numbers in an addition sum gives the same answer. You might know this as the Commutative Law… but that term means nothing to a child. It is abstract, forgettable, and the moment you stop using it they forget it entirely. Switchers is a word that does what it says. Children understand it straight away and remember it because it connects to something real.
So now, with just one secure Learn It and its Switcher, the child already knows two facts.
3 + 4 = 7 (Learn It)
4 + 3 = 7 (Switcher)
Then comes the real magic.
The Fact Families concept reveals the inverse facts:
3 + 4 = 7 (Learn It)
4 + 3 = 7 (Switcher)
7 – 3 = 4 (Fact Family)
7 – 4 = 3 (Fact Family)
Suddenly, the child has not learned one isolated fact at all. They have unlocked a whole Fact Family from the same three numbers.
It feels like magic because it is so efficient
To a child, this can feel almost magical.
They start with one Learn It. Switchers gives them the second addition fact. Fact Families then reveals the two subtraction facts. So instead of learning four separate facts, they learn one relationship and see four connected truths. That is not a trick. It is strong mathematical understanding.
What about multiplication and division?
This is where Fact Families become even more powerful.
In Big Maths, the same idea does not stop with addition and subtraction. It also works with multiplication and division.
If a child knows a multiplication Learn It, and understands Switchers, they do not just know one fact. They already know much more.
Take these three numbers:
3, 7 and 21
If a child knows:
3 × 7 = 21
then Switchers gives them:
7 × 3 = 21
And Fact Families reveal the inverse facts:
21 ÷ 3 = 7
21 ÷ 7 = 3
So one secure multiplication fact can unlock a whole family of related facts.
3 × 7 = 21 (Learn It)
7 × 3 = 21 (Switcher)
21 ÷ 3 = 7 (Fact Family)
21 ÷ 7 = 3 (Fact Family)
That is why this matters so much for fluency. Children do not need to experience multiplication and division as separate bits of learning. They can see that the numbers are connected, and that one known fact opens the door to several more.
Exactly the same principle applies:
Know one fact well.
Use Switchers.
Let Fact Families reveal the rest.
That is how children come to realise that by knowing addition and multiplication facts securely, they already know far more than they think they know.
How Learn Its and Fact Families supercharge Fluency and Mental Maths
In Big Maths, Jigsaw Numbers is one of the strategies we use to make mathematical relationships easy to see. Jigsaw Numbers helps children to see that two parts fit together to make a whole, so by using their Learn Its, they can identify Jigsaw Numbers to 1,000 for any 3 digit number. Children can see, and trust the relationship before they are expected to explain it abstractly. That visual structure helps make Fact Families more concrete, especially when children are first learning to connect the numbers.
The strength of this approach is that the structure stays the same as numbers get bigger. Children are not constantly meeting new methods. They are applying the same understanding again and again.
A practical classroom example
Suppose a child knows this Learn It:
7 + 3 = 10
Switchers immediately gives them:
3 + 7 = 10
Fact Families then reveals:
10 – 7 = 3
10 – 3 = 7
Once children are secure with that, teachers can deepen understanding by varying the presentation:
10 = 7 + 3
10 = 3 + 7
7 = 10 – 3
3 = 10 – 7
Then by using missing number questions:
7 + ☐ = 10
☐ + 7 = 10
10 – 7 = ☐
10 – ☐ = 7
The numbers stay the same. The structure stays the same. The challenge shifts slightly. That is what real mathematical fluency looks like.
In summary…
Fact Families help children see that maths is connected. They show that a known fact is not a dead end. It is a doorway. Switchers gives them a second fact from Learn Its, Fact Families then reveal the inverse facts. 1 fact = 4 facts!
That is why Fact Families matter so much, they reduce cognitive load, strengthen number sense, and build confidence. And they help children realise that maths is often much easier than it first appears.
One fact can open the door to three more.