How to learn the addition facts

Addition facts are the sums of two single digits, from 1 + 1 to 9 + 9. A child who knows them by heart can add much bigger numbers too, because long addition is these same small sums, one column at a time. There are fewer to learn than it seems, and a few tricks cover most of them.

The rule

Learn the number bonds to 10 and the doubles first. Every other addition fact is one small step from one of them.

How to work one out

Put the bigger number first. 3 + 8 is the same as 8 + 3, and starting from 8 means fewer steps.
If one number is 1, 2 or 3, count on from the bigger one. For 7 + 2, start at 7 and say 8, 9.
If the two numbers are the same, it is a double. If they are next to each other, use the double and add 1. 6 + 6 = 12, so 6 + 7 = 13.
Otherwise, make 10. Split the smaller number so that one part fills the bigger one up to 10, then add what is left: 7 + 5 = 7 + 3 + 2 = 12.
Say the whole fact when you have it, "7 add 5 is 12". Saying it often is how a fact moves from working out to just knowing.

Worked examples

What goes with 6 to make 10?

6 + 4 = 10

A frame of ten squares with 6 filled leaves 4 empty, so 6 and 4 are a number bond to 10. There are only five pairs to learn: 1 and 9, 2 and 8, 3 and 7, 4 and 6, and 5 and 5.

What is 7 + 5?

7 + 5
= 7 + 3 + 2
= 10 + 2
= 12

7 needs 3 to make 10, so split the 5 into 3 and 2. 7 + 3 = 10, and 10 + 2 = 12. So 7 + 5 = 12.

What is 6 + 7?

6 + 6 = 12
6 + 7 = 12 + 1 = 13

6 and 7 are next to each other, so use the double. 6 + 7 is one more than 6 + 6, which makes 13. Double 7 take away 1 gives the same answer, 14 − 1 = 13.

What is 2 + 9?

2 + 9 = 9 + 2
9 … 10, 11

Swap them round and count on 2 from 9, saying 10, 11. So 2 + 9 = 11. Counting on 9 from the 2 would take nine steps, and it is easy to lose count.

Adding 9 and adding 10

Adding 10 to a single digit is the easiest fact of all: 10 + 6 is 16, said just the way it is written.

That makes 9 easy too. Add 10 and then take 1 away: 9 + 6 is 10 + 6 = 16, take away 1, 15. The same trick works for 8: add 10 and take 2 away, so 8 + 7 = 17 − 2 = 15.

Number bonds to 20

Once the bonds to 10 are solid, the bonds to 20 follow from them: 6 and 4 make 10, so 16 and 4 make 20. In England children meet the bonds within 20 in Year 1, and are expected to know all the addition facts to 20 by the end of Year 2.

Why the tricks work

We write numbers in tens and ones, so anything added to 10 is easy: 10 + 2 is 12, no working needed. Making 10 moves part of one number over to the other. In 7 + 5, the 3 moves across to the 7. Nothing is added or lost on the way, so 7 + 5 and 10 + 2 are the same 12.

Order does not matter in adding. Put 3 counters next to 8 counters and there are 11, whichever pile you count first. That halves the work: from 1 + 1 to 9 + 9 there are 81 sums, but only 45 different facts, because 3 + 8 and 8 + 3 are one fact.

A near double works because 7 is 6 + 1. So 6 + 7 is 6 + 6 + 1, the double you know with one more on top.

Where mistakes happen

Counting on from the first number every time. For 2 + 9, counting nine steps from 2 is slow and easy to lose track of. Starting at 9, it is two steps.
Counting the number you start on. For 8 + 3 the count is 9, 10, 11, so the answer is 11. Saying 8, 9, 10 gives 10, one too few.
Using the wrong double. 6 + 7 is double 6 add 1, or double 7 take away 1. Mixing the two, double 7 add 1, gives 15 instead of 13.
Always practising the facts in order, 1 + 1, 1 + 2, 1 + 3 and on. A child then has to run through the list to find 7 + 5. Mixed questions are what make each fact stand on its own.

Questions people ask

How many addition facts are there?

From 1 + 1 to 9 + 9 there are 81, but only 45 different ones, because order does not matter. Adding 1, 2 or 3, the doubles and the bonds to 10 cover most of those, which leaves a small handful to work on by making 10.

Are number bonds the same as addition facts?

A number bond is two numbers that make a total, usually 10 or 20: 6 and 4 make 10. It is an addition fact seen from the total, and it gives you the take-away facts for free: 10 − 6 = 4 and 10 − 4 = 6. The subtraction facts page shows how.

Is it called something else in America?

American schools usually say math facts, or addition facts, and teach the same tricks as making ten and doubles plus one. Number bonds is used there too.

Is it all right to count on fingers?

At first, yes. Fingers are how most children start. The aim is to move on to the tricks above, because counting every time is slow, and in a long sum it makes a child lose their place.