Adding Within 20

What you will learn

• Add two numbers with a total up to $20$.
• Count on from the bigger number, make ten first, and use doubles and near doubles.
• Know the five number bonds to $10$.

Before you start: you should be able to count to $20$ and know that the digits $0$ to $9$ show how many. Counting and Place Value covers this.

The idea

Adding means putting things together. If you have $4$ shells in one hand and $3$ in the other, and you tip them all into one pile, you have $4 + 3 = 7$ shells. The little cross sign, $+$, just means “and then put these with them”.

You could count every shell from one. That works. But there are quicker ways, and this lesson shows you five of them.

Count on from the bigger number

Hold the bigger number in your head. Then count on the smaller number, one at a time.

For $6 + 3$: say “six” and hold it. Now count on three more: “seven, eight, nine”. The answer is $9$.

Use your fingers to keep track of how many you have counted on. For $+3$, put up three fingers and fold one down with each number you say.

Swap the order if it helps

$2 + 9$ and $9 + 2$ give the same answer. Putting two groups together gives the same pile whichever one you tip in first.

So for $2 + 9$, do not count on nine times. Swap it round. Start at $9$ and count on $2$: “ten, eleven”. The answer is $11$.

Know your bonds to ten

Two numbers that add up to $10$ are called a number bond to ten. There are only five pairs to learn:

• $1 + 9$
• $2 + 8$
• $3 + 7$
• $4 + 6$
• $5 + 5$

Try this with your hands. Hold up all ten fingers. Fold down any number of them. The fingers still up and the fingers folded down always make a bond to ten.

Make ten, then add the rest

When an answer goes past $10$, split the smaller number so that part of it fills up to ten first.

For $8 + 5$: ask “what does $8$ need to make $10$?” It needs $2$. Take $2$ from the $5$, leaving $3$. Now $8 + 2 = 10$, and $10 + 3 = 13$.

Numbers in the teens are easy to say once you reach ten: “ten and three” is thirteen.

Use doubles

A double is a number added to itself: $5 + 5$, $6 + 6$, $7 + 7$. Doubles are worth learning by heart because they unlock their neighbours.

$6 + 7$ is one more than $6 + 6$. If you know $6 + 6 = 12$, then $6 + 7 = 13$. Sums like this are called near doubles.

Worked examples

Example 1: Counting on

A jar has $7$ marbles. You drop in $4$ more. How many marbles are in the jar now?

1. The bigger number is $7$. Hold it in your head.
2. Put up $4$ fingers for the marbles you add.
3. Count on, folding a finger each time: “eight, nine, ten, eleven”.
4. All four fingers are down, so stop at $11$.

Answer: $7 + 4 = 11$ marbles.

Example 2: Making ten

Work out $9 + 6$.

1. Ask what $9$ needs to make $10$. It needs $1$.
2. Split the $6$ into $1$ and $5$.
3. Add the $1$ first: $9 + 1 = 10$.
4. Add what is left: $10 + 5 = 15$.

Answer: $9 + 6 = 15$.

Example 3: Near doubles

A ladybird has $7$ spots on one wing and $8$ on the other. How many spots altogether?

1. Spot that $7$ and $8$ are next to each other, so this is a near double.
2. Use the double you know: $7 + 7 = 14$.
3. The $8$ is one more than $7$, so add one more: $14 + 1 = 15$.
4. Check by making ten instead: $8 + 2 = 10$, then $10 + 5 = 15$. Same answer, so it is right.

Answer: $7 + 8 = 15$ spots.

When you count on, do not say the starting number again. For $6 + 3$, the first number you say out loud is “seven”, not “six”. Saying “six” as the first count-on gives $8$, which is one too few.

Why it matters

Adding within $20$ is the maths you will use most in a day. Two more people are coming for tea, so how many plates? You have read $8$ pages and $7$ more to go, so how long is the chapter? Dice in a board game, points in a playground race and coins in a purse all need quick adding. Once the small sums feel easy, bigger numbers follow the same rules, so the tricks here will keep working all the way up.