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

Adding and Subtracting Are Partners

B2.1 B2.2About 30 minutes
Learning goals
  • I can write a fact family with numbers up to 20.
  • I can use an adding fact to help me subtract.
  • I can check a subtraction answer by adding.
  • I can find a missing number in a number sentence.

Words to know

fact family
A group of adding and subtracting facts that use the same three numbers, like 6 + 8 = 14, 8 + 6 = 14, 14 − 6 = 8 and 14 − 8 = 6.
whole
The total amount. In a fact family, it is the biggest number.
part
One of the pieces that make up the whole. In 6 + 8 = 14, the parts are 6 and 8.
inverse
The opposite. Adding and subtracting are opposites: subtracting undoes adding.
check
To make sure an answer is right by solving it a different way.

Remember from Grade 1

In Grade 1 you learned fact families to 10, like 3 + 4 = 7 and 7 − 4 = 3. In Grade 2 we use bigger numbers, up to 20, and we use fact families as a superpower for subtracting and for checking our work.

Let's start with a story

It is a sunny afternoon at the park. There are 8 kids on the climber and 6 kids on the swings. That is 14 kids in all.

Then the 6 kids on the swings go home. How many kids are still at the park? You already know! 8. The same three numbers, 8, 6 and 14, tell both stories.

🧒🧒🧒🧒🧒🧒🧒🧒👧👧👧👧👧👧
8 kids on the climber and 6 kids on the swings make 14 kids. 8 + 6 = 14.

When two parts make a whole, we can write four facts with the same three numbers. This is a fact family.

  • 8 + 6 = 14
  • 6 + 8 = 14
  • 14 − 6 = 8
  • 14 − 8 = 6

Adding puts the parts together to make the whole. Subtracting takes a part away from the whole and leaves the other part. Adding and subtracting undo each other.

1486
A fact triangle. The whole (14) is at the top. The two parts (8 and 6) are at the bottom.

How to use a fact triangle

  • Add the two bottom numbers to get the top number: 8 + 6 = 14.
  • Subtract: cover one bottom number. Top take away the other bottom number: 14 − 6 = 8.
  • In a fact family the whole is always the biggest number. We subtract from the whole.

Think addition to subtract

Subtracting from a number up to 20 can feel hard. Here is a trick: turn it into an adding question.

For 15 − 7, ask yourself: "7 plus what makes 15?"

If you know 7 + 8 = 15, then you know 15 − 7 = 8.

Worked example

Example 1: Think addition

Solve 13 − 9.

  1. Turn it around: "9 plus what makes 13?"
  2. 9 + 1 = 10, and 10 + 3 = 13. So we added 1 + 3 = 4.
  3. So 9 + 4 = 13.
  4. That means 13 − 9 = 4.

13 − 9 = 4, because 9 + 4 = 13.

56789101112131415+1+3
Counting up from 9 to 13: jump 1 to 10, then jump 3 more. 1 + 3 = 4 jumps in all.
Worked example

Example 2: Check by adding

Ava says 17 − 8 = 9. Is she right?

  1. To check a subtraction, add the answer to the number you took away.
  2. Add the answer (9) and the number taken away (8): 9 + 8 = 17.
  3. We got back to 17, the number we started with.

Yes, Ava is right. 9 + 8 = 17, so 17 − 8 = 9.

Worked example

Example 3: A wrong answer

Noah says 16 − 7 = 8. Check his answer.

  1. Add the answer and the number taken away: 8 + 7 = 15.
  2. 15 is not 16. So the answer is not right.
  3. Think addition: 7 + 9 = 16.
  4. So 16 − 7 = 9.

Noah made a mistake. 16 − 7 = 9, because 9 + 7 = 16.

Missing numbers

Sometimes a number in the sentence is missing. We use a box □ for the missing number. Fact families help us find it.

  • 6 + □ = 13: 6 plus what makes 13? 6 + 7 = 13, so □ = 7.
  • □ − 5 = 9: The missing number is the whole. Add the parts: 9 + 5 = 14, so □ = 14.
  • 12 − □ = 4: 4 plus what makes 12? 4 + 8 = 12, so □ = 8.
Worked example

Example 4: Missing part story

Leo has 11 hockey cards. Some are in his pocket and 5 are on the table. How many are in his pocket?

  1. The whole is 11. One part is 5. We need the other part.
  2. Write it as 5 + □ = 11 or 11 − 5 = □.
  3. Think: 5 + 6 = 11.
  4. So □ = 6.

6 cards are in his pocket. 5 + 6 = 11 and 11 − 5 = 6.

115?
A part-part-whole bar. The whole is 11. One part is 5. The other part is missing: 6.

The equal sign means "the same as"

Remember: = means both sides are the same amount. So this is true:

8 + 6 = 10 + 4

The left side makes 14 and the right side makes 14. Both sides balance!

Math talk (thinking like a mathematician)

When you solve a question, say how you know. For example: "I know 15 − 6 = 9 because 9 + 6 = 15." Explaining your thinking helps you and helps others learn.

Just for fun

What did 14 say to 8 and 6?

"You two complete me!"

Hands-on activity

Fact family houses

You need: paper, a pencil, and 20 small things (buttons, dry pasta or LEGO bricks).

  1. Draw a house with a pointy roof. This is a fact family house.
  2. A grown-up picks two numbers that add up to 20 or less, like 7 and 9.
  3. Count out 7 things and 9 things. Push them together and count the whole: 16. Write 16 in the roof.
  4. Write the four family facts inside the house: 7 + 9 = 16, 9 + 7 = 16, 16 − 9 = 7, 16 − 7 = 9.
  5. Act out each subtraction fact by taking away one part.
  6. Make 3 more houses with new numbers.

Math talk: "Why does every fact in the house use the same three numbers?"

Your turn

1

Write the fact family for 5, 9 and 14.

2

Use an adding fact to solve 12 − 8.

3

Find the missing number: 7 + □ = 15

4

Mila says 18 − 9 = 9. Check by adding. Is she right?

5

Find the missing number: □ − 6 = 7

6

There are 16 crayons in a box. 10 are broken. How many are not broken? Write a fact you used.

7

True or false: 9 + 5 = 10 + 4

More practice: warm-up

1

Which number is the whole in this family: 4, 7, 11?

2

If 6 + 4 = 10, then 10 − 4 = ?

3

If 8 + 5 = 13, then 13 − 8 = ?

4

Find the missing number: 10 + □ = 17

5

Write the two adding facts for 3, 9 and 12.

More practice: on your own

1

Solve 14 − 6. Show how you thought about it.

2

Ben says 15 − 8 = 6. Check his answer by adding. What is the right answer?

3

Find the missing number: 13 − □ = 5

4

A shelf holds 19 books. 10 are storybooks and the rest are about animals. How many are about animals?

5

Write the fact family for 8, 8 and 16. How many facts does it have?

Challenge

1

Find the missing number: 6 + 9 = □ + 5

2

Sara picked some apples. She gave 7 to her neighbour. Now she has 9 left. How many apples did she pick? Write the number sentence.

3

Make up a fact family where the whole is 20 and one part is 13. Write all four facts.

Check your understanding

Quiz

1.

Which fact is in the same family as 9 + 6 = 15?

2.

What is 11 − 4?

3.

How can you check that 17 − 9 = 8?

4.

Find the missing number: 8 + □ = 14

5.

Find the missing number: □ − 7 = 6

6.

Which number sentence is true?

For parents and teachers

Big idea: Addition and subtraction are inverse (opposite) operations. Knowing 8 + 6 = 14 means your child also knows 14 − 6 and 14 − 8. The Ontario curriculum (B2.1) asks children to use this relationship to solve problems and to check calculations.

Common mistakes:

  • Subtracting the wrong way round (writing 6 − 14). Remind them that in a fact family we always subtract from the whole, the biggest number.
  • Checking by adding the wrong numbers. To check 17 − 8 = 9, add 9 + 8, not 17 + 8.
  • Missing numbers at the start (□ − 5 = 9). Children often subtract 9 − 5. Ask: "Is the box the whole or a part?" A bar drawing helps.
  • Seeing = as "the answer goes here". Sentences like 8 + 6 = 10 + 4 build the idea that = means "is the same as".

How to help: Ask fact-family questions in daily life: "There are 13 eggs in two cartons. One has 6. How many in the other?" Encourage your child to say "I know ___ because ___".