B. Number · Operations: Adding, Subtracting and Equal Groups

Subtraction Facts to 20

B2.2 B2.1About 30 minutes

Learning goals

I can subtract from numbers up to 20 using a strategy.
I can count back, count up, or go back through 10.
I can use a doubles fact to subtract.
I can recall many subtraction facts quickly.

Words to know

subtract
To take away, or to find the difference between two numbers.

difference
The answer to a subtraction. In 15 − 9 = 6, the difference is 6.

count back
Start at the bigger number and count backward. Good for taking away 1, 2 or 3.

count up
Start at the smaller number and count up to the bigger number. Good when the numbers are close.

related fact
An adding fact that uses the same numbers, like 7 + 6 = 13 for 13 − 6 = 7.

Let's start with a story

There are 15 geese on the pond in the fall. 9 geese fly south for the winter. How many geese are still on the pond?

We need 15 − 9. Counting back 9 one at a time is slow, and it is easy to lose track. Today you will learn faster ways to subtract.

Canada geese on a calm lake in the fall, with some swimming and some flying above the colourful trees. — Count the geese in this photo: there are 14 in all, and 8 are flying away. 14 − 8 = 6, so 6 geese are still on the pond. AI-generated image

Every subtraction fact to 20 has an addition partner. Because you are learning your addition facts to 20, you are learning subtraction facts at the same time! Here are four strategies.

Strategy 1: Count back (for taking away 1, 2 or 3)

17 − 3: Start at 17. Count back 3: 16, 15, 14. So 17 − 3 = 14.

17 − 3: start at 17 and jump back 3 to land on 14.

Strategy 2: Count up (when the numbers are close)

12 − 9: 9 and 12 are close together. Start at 9 and count up to 12: 10, 11, 12. That is 3 jumps. So 12 − 9 = 3.

12 − 9: start at 9 and count up to 12. That is 3 jumps, so the difference is 3.

Counting back or counting up?

Look at the number you are subtracting.

Small (1, 2 or 3)? Count back. 14 − 2: 13, 12.
Close to the big number? Count up. 14 − 12: 13, 14. That's 2.

Strategy 3: Go back through 10

14 − 6: First take away just enough to get to 10. 14 − 4 = 10. We still need to take away 2 more (because 6 is 4 and 2). 10 − 2 = 8. So 14 − 6 = 8.

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14 is a full ten frame and 4 more.

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Take away the 4 extra counters (now 10), then 2 more from the ten frame. 8 are left.

14 − 6: jump back 4 to 10, then back 2 more to 8.

Worked example

Example 1: Back through 10 (the geese)

15 geese are on the pond. 9 fly away. How many are left?

We need 15 − 9.
Take away 5 to get to 10: 15 − 5 = 10.
9 is 5 and 4, so take away 4 more: 10 − 4 = 6.

6 geese are left. Check: 6 + 9 = 15.

Strategy 4: Think addition

16 − 8: Ask "8 plus what makes 16?" You know the double 8 + 8 = 16. So 16 − 8 = 8.

Doubles are super handy for subtracting: if 7 + 7 = 14, then 14 − 7 = 7.

Double	Subtraction fact
6 + 6 = 12	12 − 6 = 6
7 + 7 = 14	14 − 7 = 7
8 + 8 = 16	16 − 8 = 8
9 + 9 = 18	18 − 9 = 9
10 + 10 = 20	20 − 10 = 10

Doubles help you subtract

Worked example

Example 2: Think addition

Solve 13 − 7.

Ask: "7 plus what makes 13?"
I know 7 + 6 = 13 (near double: 6 + 6 = 12, plus 1).
So the missing part is 6.

13 − 7 = 6.

Worked example

Example 3: Take away 10 and 9

Solve 17 − 10 and 17 − 9.

17 − 10: 17 is one ten and 7 ones. Take away the ten, 7 ones are left. 17 − 10 = 7.
17 − 9: 9 is one less than 10, so we took away 1 too many with 10. Give 1 back: 7 + 1 = 8.

17 − 10 = 7 and 17 − 9 = 8.

Just for fun

15 geese were on the pond and 9 flew south. 15 − 9 = 6 geese stayed behind and said, "We'll go next week... right after one more swim!"

Hands-on activity

Ten frame take-away

You need: two egg cartons cut down to 10 cups each (a grown-up does the cutting) or two ten frames drawn on paper, plus 20 small things like dry beans.

Fill one ten frame (10) and put some more in the second frame. Say the number, like 13.
A grown-up says a number to take away, like 5.
Take away from the second frame first until you reach 10, then take the rest from the full frame.
Say the subtraction fact: 13 − 5 = 8.
Then say the addition partner: 8 + 5 = 13.

Do 8 rounds. Take turns being the one who chooses.

Your turn

16 − 2 = ? Count back.

11 − 9 = ? Count up.

12 − 5 = ? Go back through 10.

14 − 7 = ? Use a double.

18 − 10 = ?

15 − 8 = ?

There are 13 muffins. The family eats 4. How many are left?

More practice: warm-up

10 − 3 = ?

12 − 6 = ?

19 − 1 = ?

20 − 10 = ?

13 − 2 = ?

More practice: on your own

17 − 8 = ? Show your strategy.

16 − 9 = ?

11 − 4 = ?

A class has 19 skates on the shelf. 12 skates are taken out to the rink. How many skates are still on the shelf?

Which is the best strategy for 15 − 14: count back or count up? Solve it.

Challenge

Fill in the blank: 14 − __ = 6

Ella says 13 − 5 = 7. Check her answer. Is she right? If not, fix it.

Write three different subtraction facts that have a difference of 9, using numbers up to 20.

Check your understanding

Quiz

What is 12 − 3?

What is 16 − 8?

For 14 − 6, a student does 14 − 4 = 10 first. What is the next step?

What is 11 − 8?

Which addition fact helps you solve 15 − 7?

What is 19 − 9?

For parents and teachers

Big idea: Subtraction facts to 20 are learned together with their addition partners (B2.2), and the strategies come from the properties and relationships in B2.1. Children should be able to choose a strategy that fits the numbers.

Common mistakes:

Counting back and including the starting number. For 12 − 3 they say "12, 11, 10" and answer 10. Teach: say the start number quietly, then count the jumps. A number line shows it clearly.
Counting back by a big number (15 − 9 by ones). Encourage count up or back through 10.
Back through 10: forgetting the second jump (14 − 6: 14 − 4 = 10, then stopping at 10).

How to help: Use the "think addition" question every time: "__ plus what makes __?" Play games where a sum is hidden ("I had 14 grapes, now I have 9. How many did I eat?"). Five minutes a day with ten frames or cards builds recall.