Subtraction Is a Missing Number Puzzle!

Section 1

Where Did This Idea Come From?

People have been adding and subtracting for a very, very long time! Long ago, people used rocks, sticks, and their fingers to count things. They needed to figure out how many things were left when some went away. Over time, clever teachers found a secret: subtraction and addition are best friends. They are two sides of the same coin! Let's look at how people learned this.

Long, Long Ago

People used their fingers to count. If you had 5 apples and gave away 3, you could fold down 3 fingers to find out you had 2 left. 🖐️

Ancient Times

People in Egypt and Babylon used marks on clay to add and subtract. They noticed that taking away is the opposite of putting together!

Hundreds of Years Ago

Teachers started to use the minus sign (−) and the plus sign (+). They wrote number sentences like 10 − 8 = 2 and 8 + 2 = 10.

Today!

Now we know a cool trick: to subtract, we can think about what number is missing in an addition problem. That's what you are going to learn today! 🌟

Here is the big question this lesson answers: When you see 10 − 8, can you find the answer by asking, "What number plus 8 makes 10?" Yes, you can! Let's find out how.

Section 2

The Big Ideas

Before we start solving, let's learn four big ideas. These ideas are like tools in a toolbox. Once you know them, subtraction will be much easier!

Addition Puts Together

When you add, you put groups together to get a bigger number. Like 3 + 5 = 8. You start with 3, add 5 more, and get 8!

Subtraction Takes Apart

When you subtract, you take some away. Like 8 − 5 = 3. You start with 8, take away 5, and have 3 left!

They Are Opposites!

Addition and subtraction undo each other. If 3 + 5 = 8, then 8 − 5 = 3. They are like zipping up a coat and unzipping it. 🧥

The Missing Number Trick

To solve 10 − 8, just ask: "8 + what = 10?" The missing number is your answer! This is the unknown-addend trick.

✦ ✦ Key Takeaway

Think of subtraction like a puzzle with a missing piece. If you have a puzzle that should have 10 pieces, and you can see 8 pieces already in place, how many pieces are missing? Just 2! That's the same as 10 − 8 = 2, because 8 + 2 = 10.

Section 3

See It With a Picture!

Let's look at a picture that shows how 10 − 8 works. We have a row of 10 circles. 8 of them are blue (the part we know), and we need to find out how many more make 10. The missing circles are shown with a dotted outline.

Diagram showing 10 circles: 8 filled blue circles and 2 empty dotted circles, illustrating 10 minus 8 equals 2

Look at the picture above. The 8 blue circles are the part we already have. The 2 dotted circles are the missing part. Together, they all make 10. So 10 − 8 = 2!

Section 4

How Does the Trick Work?

Here is the secret. Every subtraction problem can be turned into an addition problem with a missing number. Let's see how!

The Subtraction Way

10 − 8 = ?

We ask: "What is left when we take 8 away from 10?"

The Addition Way (Unknown Addend)

8 + ? = 10

We ask: "What number do I add to 8 to get 10?"

Both questions give the same answer: 2! This is because addition and subtraction are opposite operations. When you know 8 + 2 = 10, you also know 10 − 8 = 2 and 10 − 2 = 8. These three facts are a fact family.

Fact Family

8 + 2 = 10 2 + 8 = 10 10 − 8 = 2 10 − 2 = 8

All four facts use the same three numbers: 2, 8, and 10.

The fancy word "addend" just means a number you add. In 8 + 2 = 10, both 8 and 2 are addends. When one addend is missing, we call it the unknown addend. Finding the unknown addend is the same as subtracting!

✦ ✦ Key Takeaway

Think of it like a see-saw! 🎢 One side has 8 blocks. The other side needs to have 10 blocks to balance. How many more blocks do you put on? 2 blocks! Subtraction just asks, "How many more blocks do I need?"

Section 5

More Examples to See

Let's look at a number line to see how this works with different numbers. A number line is like a ruler that shows numbers in order.

Number line from 0 to 10 showing hops from 7 to 10, illustrating that 10 minus 7 equals 3 because 7 plus 3 equals 10

On the number line, we started at 7 and hopped forward until we got to 10. We hopped 3 times. So 7 + 3 = 10, which means 10 − 7 = 3!

Let's see a few more examples in a table.

Subtraction Problem	Think: Addition!	Answer
9 − 5 = ?	5 + ? = 9	4
7 − 3 = ?	3 + ? = 7	4
6 − 2 = ?	2 + ? = 6	4
8 − 3 = ?	3 + ? = 8	5
10 − 4 = ?	4 + ? = 10	6

Do you see the pattern? Every time, we flip the subtraction into an addition question and find the missing number!

Section 6

Let's Solve One Together!

Here is a problem. Let's solve it step by step.

Problem: Sam has 9 stickers. He gives 6 stickers to his friend. How many stickers does Sam have now?

Step 1 — Write the subtractionSam had 9 stickers and gave away 6. We write: 9 − 6 = ?

Step 2 — Turn it into an addition questionInstead of taking away, let's think: "6 plus what number equals 9?" We write: 6 + ? = 9

Step 3 — Find the missing numberLet's count up from 6. We go 7, 8, 9. That's 3 more! So the missing number is 3.

Step 4 — Check it!Does 6 + 3 = 9? Yes! ✅ So 9 − 6 = 3.

Step 5 — Answer the questionSam has 3 stickers left. 🌟

Section 7

Two Ways to Subtract — Which Do You Like?

There are two ways to think about subtraction. Both give the right answer! Let's compare them.

	Taking Away	Finding the Missing Addend
What you do	Start with the big number. Take some away.	Start with the small number. Count up to the big number.
Example: 10 − 8	Start at 10. Count back 8. You land on 2.	Start at 8. Count up to 10. You count 2 hops.
When it is easiest	When you take away a small number (like 10 − 1).	When the two numbers are close together (like 10 − 8).
Feels like…	Eating cookies from a jar. 🍪 Yum!	Climbing stairs to reach the top! 🪜

✦ ✦ Key Takeaway

Both ways work! The missing-addend way is super helpful when the numbers are close together. Instead of counting backward a lot, you just count forward a little. It's like taking an elevator up 2 floors instead of walking down 8 floors. 🛗 Much easier!

Section 8

What Will You Learn Next?

Now that you know subtraction is like a missing-addend puzzle, you are ready for even bigger ideas! Let's peek at what's coming.

What You Know Now	What You'll Learn Soon
Subtract numbers up to 10	Subtract numbers up to 20!
Use counting up to find a missing addend	Use ten frames and other tools to subtract faster
Fact families with 3 numbers	Bigger fact families and related facts
Simple word problems	Harder word problems with more than one step

The cool thing is this: the missing-addend trick works with big numbers too! If you ever need to find 100 − 97, you can think, "97 plus what equals 100?" That's just 3! This idea will help you for many years of math. 🚀

Section 9

Practice Time! 🎉

Try these problems. Click "Show Answer" when you are ready to check your work!

PROBLEM 1 — TELL ME WHY

If you know that 5 + 4 = 9, what subtraction fact do you also know?

PROBLEM 2 — FIND THE ANSWER

Solve 8 − 5 = ? by thinking of it as an addition problem.

PROBLEM 3 — A LITTLE HARDER

What number goes in the box? 7 + ☐ = 10. Then use that to tell me what 10 − 7 equals.

PROBLEM 4 — WORD PROBLEM

Mia has 10 crayons. She puts 6 crayons in her box. How many crayons are still on the table? Use the missing-addend way to find out.

PROBLEM 5 — THINK ABOUT IT!

Why is counting up from 8 to 10 easier than counting back from 10 eight times? Can you explain it to a friend?

Summary

What We Learned Today

Today you learned a super helpful math secret: subtraction is the same as finding a missing addend! When you see a problem like 10 − 8, you can change it into 8 + ? = 10 and count up to find the answer. The answer is 2 because 8 + 2 = 10.

You also learned that addition and subtraction are opposites — they are part of the same fact family. Knowing that 8 + 2 = 10 also tells you that 10 − 8 = 2 and 10 − 2 = 8. This missing-addend trick is especially handy when the numbers are close together, because counting up a little is easier than counting back a lot. Keep practicing, and this trick will feel as easy as snapping your fingers! 🫰