A fact family, sometimes known as a number family, is a group of maths facts or equations that use the same numbers.
For example, 3, 2 and 5 can be used to generate a ‘family’ of four addition and subtraction number sentences:
3 + 2 = 5
2 + 3 = 5
5 - 3 = 2
5 - 2 = 3
A common way of introducing pupils to this concept is through presenting them with three numbers in a triangle, and asking them to write the four number sentences of the fact family.
However, this can be daunting for many children – so why not try some of these fun approaches, instead?
Start by looking at a set of three numbers – eg 3, 2, 5 – and helping children to establish which is the greatest.
The obvious way to compare is by using a number line. But a simple (and more tasty) visual comparison can also be made through counting out the three separate amounts of biscuits, chocolates or sweets.
Place them on three plates, then ask, ‘Which plate would you choose? Which plate has the most?’. It is surprising how many children can instantly recognise the option with the most chocolate!
Dominoes are a great way to explore fact families visually. A big display set is really good if working with a whole class. A smaller set is fine for working with groups.
Remove the dominoes that have the same number of dots on each side, to avoid confusion.
Addition
Demonstrate first with one domino: choose one with a low number of spots, eg 1 on one side and 2 on the other side. Count how many spots are on each side, then how many there are altogether.
Show how you can make a number sentence with the domino by writing it directly underneath the domino spots: 1 + 2 = 3
Then turn the domino around and write the new number sentence underneath: 2 + 1 = 3
Play a game, with children working in pairs for added confidence. Have the set of dominoes face down on the table or carpet. Each pair of children selects a domino and turns it over, then they must make two addition sentences with the numbers represented by the dots.
They could take it turns to say the sentences out loud, and/or write them on mini whiteboards.
Subtraction
As with addition, demonstrate first with one domino, eg with 6 spots on one side and 4 on the other. Count the number of spots altogether, and explain how you need to know this number first, as you are going to take away from it.
Cover one side of the domino and show how you are taking away this number of spots. Write the number sentence underneath: 6 – 4 = 2.
Then turn the domino around and cover the other side for the second number sentence: 6 – 2 = 4.
Play the same game as before, but this time, the children must count the total number of spots first, then create two subtraction sentences.
All together
Demonstrate how one domino can be used to generate four number sentences: two addition and two subtraction. Point out how the same three numbers are used each time.
Can anyone spot a pattern? (The addition sentences always end with the greatest number, and the subtraction sentences always begin with the greatest number).
Play the previous game one more time, with each pair now writing four number sentences for their domino. If they do it correctly, they can keep the domino. Repeat until there are no more dominos left.
Using the dominoes they have won, each pair can make a domino snake!
Using prepared black paper rectangles, children can fold the paper in half, then open to paint a centre line and dots on each side. Write the number sentences underneath and arrange as a domino snake in ascending order to create a display.
Children could also draw dominoes and write number sentences on the playground, using chalks.
Another way to generate numbers for fact families is to use dice. Hand each pair of children two dice to roll, and have them count the dots on the upturned faces, separately and all together, to give three numbers (if they roll a double, they will need to try again).
Can they now make four number fact sentences with their three numbers? If they are still finding it difficult, they can use counters or small objects alongside to help – the use of practical physical apparatus can never be underestimated with early maths!
How many fact families can they make?
In this small group game, each child has a whiteboard and a pen. Ask them to draw a big triangle on their board. Shuffle two sets of 0-9 digit cards, and spread them over the floor, face down.
One child turns over two cards. They write the two numbers in the bottom corners of their triangle, then add them together and put the total at the top of the triangle.
The child then says the four number sentences for the three numbers. If correct they keep the cards. Continue around the circle. If anyone turns over two cards the same, they replace them and miss their turn. The winner is the person with the most cards at the end.
Once the concept of fact families is understood, it can be used to help with calculations involving larger numbers – add zeros to make multiples of ten or 100.
Fact families represent the inverse relationship between operations. When children are ready, introduce fact families involving multiplication and division, too (eg 3 x 5 = 15, 5 x 3 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3).
All the activities and games described in this article can also be played with multiplication and division symbols instead of addition and subtraction.
ELG: Building Relationships
● Work and play cooperatively and take turns with others
ELG: Numerical Patterns
● Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity
● Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally.
Year 1 non statutory guidance
● Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 + 7 = 16; 16 − 7 = 9; 7 = 16 − 9). Pupils memorise and reason with number bonds to 10 and 20 in several forms (for example, 9 + 7 = 16; 16 − 7 = 9; 7 = 16 − 9).
Madeleine Fox is an educational writer and former SEN teacher.
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