B. Number · Adding and Subtracting

Subtraction Facts and Fact Families

B2.1 B2.2About 30 minutes

Learning goals

I can see the two parts and the whole in a number story.
I can write a fact family of 2 addition and 2 subtraction facts.
I can use an addition fact to find a subtraction fact.
I can check a subtraction answer by adding.

Words to know

part
One of the smaller groups that make up the whole.

whole
All of it together. The two parts add up to the whole.

fact family
A group of addition and subtraction facts that use the same three numbers, like 3, 5 and 8.

related facts
Facts in the same fact family. If you know one, you can find the others.

Adding and subtracting are a team

On Thanksgiving, Grandpa puts 5 pumpkin tarts and 3 apple tarts on a tray. That's 8 tarts in all.

There are two parts (5 and 3) and one whole (8).

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5 pumpkin tarts and 3 apple tarts make 8 tarts.

A part-part-whole picture. The top bar is the whole. The bottom bars are the parts.

From this one picture, we can write four facts:

5 + 3 = 8
3 + 5 = 8
8 − 3 = 5 (eat the 3 apple tarts, 5 are left)
8 − 5 = 3 (eat the 5 pumpkin tarts, 3 are left)

These four facts are a fact family. They all use the same three numbers: 3, 5 and 8.

Where does the big number go?

In a fact family, the biggest number is the whole.

When you add, the whole comes after the equal sign: part + part = whole.
When you subtract, you start with the whole: whole − part = part.

A fact family triangle. The whole (8) is at the top. The parts (5 and 3) are at the bottom corners. Cover any number and the other two help you find it.

Worked example

Example 1: Write a fact family

Write the fact family for 2, 7 and 9.

Find the whole. The biggest number is 9. The parts are 2 and 7.
Write the two adding facts: 2 + 7 = 9 and 7 + 2 = 9.
Write the two subtracting facts. Start with the whole: 9 − 2 = 7 and 9 − 7 = 2.

2 + 7 = 9, 7 + 2 = 9, 9 − 2 = 7, 9 − 7 = 2

Worked example

Example 2: Think addition to subtract

What is 10 − 6?

Turn it into an adding question: 6 + ? = 10.
You know the partners of 10! 6 and 4 make 10.
So 10 − 6 = 4.

10 − 6 = 4, because 6 + 4 = 10.

Think 6 + ? = 10. The ten frame shows 6. There are 4 empty spaces, so 10 − 6 = 4.

Worked example

Example 3: Check your subtracting

Leah says 9 − 4 = 5. Is she right?

Check by adding the answer back: 5 + 4.
5 + 4 = 9. That is the number we started with.
Because we get back to 9, the answer is correct.

Yes! 9 − 4 = 5 is correct, because 5 + 4 = 9.

Undo it to check it

Subtracting undoes adding, and adding undoes subtracting. If you take 4 away and then put 4 back, you have what you started with. That is why adding is a great way to check subtraction.

Jump forward 4 from 5 to land on 9 (5 + 4 = 9). Jump back 4 from 9 to land on 5 (9 − 4 = 5).

Subtraction facts from 10

Because you know the partners of 10, you already know these subtraction facts!

Partners	Subtraction fact	Subtraction fact
9 and 1	10 − 1 = 9	10 − 9 = 1
8 and 2	10 − 2 = 8	10 − 8 = 2
7 and 3	10 − 3 = 7	10 − 7 = 3
6 and 4	10 − 4 = 6	10 − 6 = 4
5 and 5	10 − 5 = 5	10 − 5 = 5

Partners of 10 give us subtraction facts from 10

Just for fun

Why did 3, 5 and 8 have a picnic together?

Because they belong to the same fact family!

Hands-on activity

Cup hide

You need: 8 small objects (like buttons) and a cup.

Count out 8 buttons together.
The grown-up hides some under the cup while you close your eyes.
Open your eyes and count the buttons you can see.
Say how many are hiding. Example: "I see 5, so 3 are under the cup, because 5 + 3 = 8."
Lift the cup to check!
Write the fact family for that round.

Play again with 6, 7, 9 and 10 buttons.

Math talk: "How did knowing an adding fact help you?"

Your turn

Write the fact family for 1, 4 and 5.

You know 3 + 4 = 7. So what is 7 − 4?

8 − 2 = ? (Think: 2 + ? = 8)

10 − 3 = ?

Max says 6 − 2 = 3. Check by adding. Is he right?

Which number does not belong in the fact family for 2, 6, 8? 2 + 6 = 8, 8 − 2 = 6, 8 − 6 = 3

Make a fact family with the whole 10 and the part 4.

More practice: warm-up

You know 2 + 5 = 7. What is 7 − 5?

10 − 8 = ?

In the fact family 4, 2 and 6, which number is the whole?

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4 tarts and 2 tarts make 6 tarts. Fill in the blank: 6 − 2 = __

True or false: 5 + 1 = 6 and 6 − 1 = 5 are in the same fact family.

More practice: on your own

Write the fact family for 3, 6 and 9.

9 − 7 = ? (Think: 7 + ? = 9)

A fact triangle has the whole 10 at the top and the part 2 in a corner. What is the missing part? Write a subtracting fact.

Grandma baked 8 muffins. The family ate some. Now 3 are left. How many muffins did they eat?

Rosa says 7 − 3 = 4. Check by adding. Is she right?

Challenge

The fact family for 4, 4 and 8 has only 2 facts, not 4. Why?

Find the mistake. Leo wrote the fact family for 2, 5 and 7:

2 + 5 = 7
5 + 2 = 7
7 − 2 = 5
5 − 2 = 7

Find the missing numbers: 6 + ? = 10 and 10 − ? = 6. Are they the same number? Explain.

Check your understanding

Quiz

Which fact is in the same family as 4 + 5 = 9?

You know 6 + 3 = 9. What is 9 − 3?

How can you check that 7 − 2 = 5?

In the fact family 3, 7, 10, which number is the whole?

Which fact is in the same family as 2 + 8 = 10?

What is 9 − 5? (Think: 5 + ? = 9)

For parents and teachers

Big idea: Addition and subtraction are inverse operations, which means one undoes the other. The curriculum (B2.1) wants children to use this relationship: to find subtraction facts by thinking of addition, and to check answers.

Common mistakes:

Putting the smaller number first in subtraction (writing 3 − 8 = 5). Remind them: in subtraction you start with the whole, the biggest number.
Counting back for every subtraction fact. Counting back is slow and easy to get wrong. Encourage "think addition": for 9 − 7, ask "7 plus what makes 9?"
Not seeing the parts and whole. Draw the bar model or triangle and point: "Which number is all of them together?"

How to help: Play the Cup Hide game often. It builds instant subtraction facts. When your child subtracts, ask "How could you check?" and let them add to prove it.