Subtracting Within 20

What you will learn

• Subtract within $20$ by counting back, going back to ten, or counting up to find the difference.
• Use an adding fact to work out and check a subtraction.
• Tell when a question is asking for “how many are left” and when it is asking for “how far apart”.

Before you start: you should be happy adding within $20$. See Adding Within 20 first.

The idea

Subtracting is adding run backwards. There are $9$ ducks on a pond and $3$ of them fly off. How many are left? That is $9 - 3 = 6$. The little dash sign, $-$, means “take these away”.

Subtracting also answers a different sort of question. You have $9$ ducks and your friend has $6$. How many more do you have? That is $9 - 6 = 3$. Finding how far apart two numbers are is called finding the difference, and it uses the same sign.

Here are four ways to do it.

Count back

Start at the bigger number. Count backwards the number you are taking away. The number you land on is the answer.

For $11 - 3$: say “eleven” and hold it. Count back three: “ten, nine, eight”. The answer is $8$.

Use fingers to keep count, just as you do when adding. Put up $3$ fingers and fold one down with each number you say.

Go back to ten first

When the answer drops below $10$, take away enough to land on ten, then take away the rest.

For $15 - 7$: what takes $15$ back to $10$? Taking away $5$. Take $5$ from the $7$, which leaves $2$ still to take. Now $15 - 5 = 10$, and $10 - 2 = 8$.

This is the make-ten trick from adding, run in reverse.

Count up to find the difference

When the two numbers are close together, counting back is slow. Instead, start at the smaller number and count up to the bigger one. The number of jumps is the answer.

For $14 - 9$: start at $9$. Jump $1$ to reach $10$. Jump $4$ more to reach $14$. That is $1 + 4 = 5$ jumps, so $14 - 9 = 5$.

Use what you know about adding

Adding and subtracting undo each other. If $7 + 5 = 12$, then $12 - 5 = 7$ and $12 - 7 = 5$. Three facts for the price of one.

So when you see $13 - 8$, ask “eight and what makes thirteen?” Eight and five, so the answer is $5$. Your number bonds do the work.

This is also the best way to check. After any subtraction, add your answer back to the number you took away. You should get the number you started with.

Worked examples

Example 1: Counting back

A plate has $12$ crackers. Theo eats $4$. How many crackers are left?

1. The starting number is $12$. Hold it in your head.
2. Put up $4$ fingers for the crackers Theo eats.
3. Count back, folding a finger each time: “eleven, ten, nine, eight”.
4. All four fingers are down, so stop at $8$.

Answer: $12 - 4 = 8$ crackers.

Example 2: Back to ten

Work out $16 - 9$.

1. Ask what takes $16$ back to $10$. Taking away $6$.
2. Split the $9$ into $6$ and $3$.
3. Take away the $6$ first: $16 - 6 = 10$.
4. Take away what is left: $10 - 3 = 7$.
5. Check by adding: $7 + 9 = 16$. Correct.

Answer: $16 - 9 = 7$.

Example 3: Finding the difference

Amara is $11$ and her cousin Jude is $8$. How many years older is Amara?

1. The question asks how far apart $8$ and $11$ are, so this is a difference.
2. Start at $8$ and count up to $11$: “nine, ten, eleven”. That is $3$ jumps.
3. Check by adding: $8 + 3 = 11$. Correct.

Answer: Amara is $3$ years older.

When you count back, do not say the starting number. For $11 - 3$, the first number you say is “ten”, not “eleven”. Saying “eleven” as the first count-back gives $9$, which is one too many.

Why it matters

Subtracting tells you what is left and what is missing. How many days until your birthday? How much change should you get back? How many more stickers do you need to fill the page? Who won by how many points? It also lets you check your adding, because the two always agree. Everything here works the same for bigger numbers later on, so these small sums are building the habit, not just the answers.