Decompose Numbers To 10 — CCSS.K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). - Kindergarten Math

SECTION 1

Why Do We Break Numbers Apart?

People have been counting and breaking numbers apart for a very long time! Long ago, people used rocks, sticks, and fingers to count things. They learned that a group of objects can be split into smaller groups. This idea helps us add and subtract.

Long Ago • Counting With Fingers

People first used their fingers to count. They noticed they had 5 fingers on each hand. They could split 5 fingers into groups like 2 and 3!

Old Times • Using Objects to Count

People used pebbles and beads to count. They put beads into two piles to see how a number could be split apart.

School Days • Writing Number Sentences

Teachers started showing kids how to write equations like 5 = 2 + 3. This way, everyone could share how they broke numbers apart.

Today • Decomposing Numbers

Now you get to learn this too! Breaking apart numbers is called decomposing. It helps you get ready for adding and subtracting.

So here is our big question: If you have a number like 5 or 7, how many ways can you break it into two parts? Let's find out!

SECTION 2

What Does It Mean to Decompose a Number?

The word decompose means to break apart. When we decompose a number, we split it into two smaller numbers. Those two smaller numbers are called a pair. When we put the pair back together, we get the number we started with!

Decompose Means Break Apart

Take one number and split it into two smaller numbers. Example: 6 can become 4 and 2.

More Than One Way

Every number can be broken apart in many ways. The number 6 can be 5 + 1, 4 + 2, or 3 + 3!

Use Objects or Drawings

You can use blocks, crayons, circles, or anything you like to show how you broke the number apart.

Write an Equation

An equation is a number sentence. Write it like this: 6 = 4 + 2. The equals sign means 'is the same as.'

The Parts Add Up

The two parts must always add up to the number you started with. If they don't, try again!

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KEY TAKEAWAY

Think of decomposing like sharing cookies with a friend. If you have 5 cookies, you could give your friend 1 and keep 4. Or give 2 and keep 3. Or give 3 and keep 2. Each way of sharing is a different way to decompose 5!

SECTION 3

See It! Breaking 5 Apart

Let's look at the number 5. The picture below shows all the ways we can break 5 into two parts. Each row shows a different pair!

Each row shows 5 circles. The red circles are one part and the white circles are the other part. The dashed line shows where we split the group. Notice there are six different ways to decompose 5!

Look at the picture above. In each row, we have 5 circles. We color some red and leave the rest white. The red ones are one part, and the white ones are the other part. Every row is a different way to decompose 5!

SECTION 4

Writing Number Sentences (Equations)

When we decompose a number, we can write it as an equation. An equation is a number sentence with an equals sign. The equals sign (=) means 'is the same as.' Let's look at some equations for the number 5.

DECOMPOSITION OF 5

5 = 1 + 4

The number 5 is the whole. The numbers 1 and 4 are the parts. The parts add up to the whole: 1 + 4 = 5.

ANOTHER WAY

5 = 2 + 3

Same number 5, but different parts! This time the parts are 2 and 3. They still add up to 5.

THE RULE

whole = part + part

Every decomposition follows this pattern. The whole number goes on one side. The two parts go on the other side with a plus sign between them.

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Remember!

The equals sign does NOT mean 'the answer is.' It means 'is the same as.' So 5 = 2 + 3 means 5 is the same as 2 + 3.

SECTION 5

Number Bonds — A Special Picture

A number bond is a special picture that shows how a number breaks apart. It has one circle on top for the whole number and two circles on the bottom for the parts. Lines connect them. Let's see a number bond for the number 7!

Six number bonds for the number 7. The yellow circle on top is the whole. The blue and purple circles on the bottom are the parts. Each bond shows a different way to decompose 7.

Look at the number bonds above. The big yellow circle on top always says 7. The two smaller circles on the bottom show the parts. Notice that 7 = 3 + 4 and 7 = 4 + 3 are both shown. The parts are just switched around! We call this a turnaround fact.

SECTION 6

Let's Decompose 8 Together!

Now let's practice with the number 8. We will find different ways to break 8 into two parts. Follow along step by step!

Decomposing the Number 8

1
Step 1 — Start With the Whole

We have 8 apples. Let's draw 8 circles to show our apples: ⚪⚪⚪⚪⚪⚪⚪⚪. Count them — there are 8!

Whole = 8
2
Step 2 — Pick One Way to Split

Let's color the first 3 apples red: 🔴🔴🔴⚪⚪⚪⚪⚪. We have 3 red apples and 5 white apples. That is one way to decompose 8!

8 = 3 + 5
3
Step 3 — Try Another Way

Now color the first 6 apples red: 🔴🔴🔴🔴🔴🔴⚪⚪. We have 6 red apples and 2 white apples. That is a different way!

8 = 6 + 2
4
Step 4 — Find a Special Way

What if both parts are the same? Color 4 red: 🔴🔴🔴🔴⚪⚪⚪⚪. We have 4 red and 4 white. The two parts are equal!

8 = 4 + 4
5
Step 5 — Write All the Equations

Now write all the ways: 8 = 0 + 8, 8 = 1 + 7, 8 = 2 + 6, 8 = 3 + 5, 8 = 4 + 4, 8 = 5 + 3, 8 = 6 + 2, 8 = 7 + 1, 8 = 8 + 0. That is 9 ways!

9 decompositions of 8

SECTION 7

Ways to Show Decomposing

There are many tools you can use to decompose numbers. Some are great for working with your hands. Others are great for writing on paper. Let's compare them!

Tool	How It Works	Best For
Counters / Blocks	Put real objects into two groups. Move them around to try new ways.	Hands-on learners who like to touch and move things.
Drawings (Circles)	Draw circles on paper. Color some in and leave the rest empty.	Showing your work on paper or a worksheet.
Number Bonds	Draw a circle for the whole on top and two circles for the parts below. Connect with lines.	Seeing the whole and parts at the same time.
Equations	Write a number sentence like 6 = 2 + 4.	Recording your answer quickly and neatly.
Fingers	Hold up fingers on two hands. Count fingers on each hand.	Quick thinking — numbers up to 10!

Different tools for decomposing numbers

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KEY TAKEAWAY

Think of it like a pizza! If you have a pizza cut into 6 slices, you can put some slices on one plate and some on another. No matter how you split them, you still have 6 slices total. That's decomposing!

SECTION 8

Getting Ready for Addition and Subtraction

Decomposing numbers is a big step! Once you know how to break numbers apart, you are ready for addition and subtraction. Let's see how they connect!

What You Know Now	What Comes Next
5 = 2 + 3 (decomposing)	2 + 3 = 5 (addition!)
8 = 5 + 3 (decomposing)	8 − 5 = 3 (subtraction!)
Finding all pairs for a number	Knowing addition facts by heart
Numbers up to 10	Numbers up to 20 and beyond!

How decomposing connects to addition and subtraction

When you decompose 8 into 5 + 3, you already know an addition fact: 5 + 3 = 8! And you also know a subtraction fact: 8 − 3 = 5. Decomposing helps you understand how numbers work together. You are building a strong math brain!

SECTION 9

Practice Problems

Now it's your turn! Try these problems. Remember: decompose means break a number into two parts.

Question 1: CONCEPTUAL

What does it mean to decompose a number? Can you explain it in your own words?

Show answer

To decompose a number means to break it apart into two smaller numbers (parts). When you put the two parts back together, you get the number you started with. For example, if you decompose 6, you can break it into 2 and 4, because 2 + 4 = 6.

Question 2: BASIC CALCULATION

Decompose the number 4 in two different ways. Write an equation for each way.

Show answer

Here are two ways: 4 = 1 + 3 and 4 = 2 + 2. In the first way, one part is 1 and the other part is 3. In the second way, both parts are 2. There are other ways too, like 4 = 0 + 4 and 4 = 3 + 1. All the parts add up to 4!

Question 3: INTERMEDIATE

Find ALL the ways to decompose the number 6 into two parts. Write each way as an equation. How many ways did you find?

Show answer

The ways are: 6 = 0 + 6, 6 = 1 + 5, 6 = 2 + 4, 6 = 3 + 3, 6 = 4 + 2, 6 = 5 + 1, and 6 = 6 + 0. That is 7 ways in all! Notice that 6 = 3 + 3 is special because both parts are the same number.

Question 4: APPLIED

You have 9 crayons. You want to put them in two boxes. Write three different equations to show three different ways you could split the crayons between the two boxes.

Show answer

Here are three ways: 9 = 4 + 5 (4 crayons in one box and 5 in the other), 9 = 7 + 2 (7 in one box and 2 in the other), and 9 = 3 + 6 (3 in one box and 6 in the other). No matter how you split them, the two numbers always add up to 9. You could also try 9 = 1 + 8 or 9 = 0 + 9!

Question 5: CRITICAL THINKING

Mia says that the number 10 can only be decomposed in 5 ways. Is Mia right or wrong? How many ways can you actually decompose 10? Explain your thinking.

Show answer

Mia is wrong! The number 10 can be decomposed in 11 ways: 10 = 0 + 10, 10 = 1 + 9, 10 = 2 + 8, 10 = 3 + 7, 10 = 4 + 6, 10 = 5 + 5, 10 = 6 + 4, 10 = 7 + 3, 10 = 8 + 2, 10 = 9 + 1, and 10 = 10 + 0. A helpful pattern: for any number, the number of ways to decompose it is one more than the number itself. The number 10 has 11 ways!

SUMMARY

What We Learned

Summary

In this lesson, you learned that to decompose a number means to break it into two smaller parts. Every number from 0 to 10 can be decomposed in more than one way. You can show your work using objects, drawings, number bonds, or equations. An equation looks like this: 5 = 2 + 3. The equals sign means 'is the same as.'

Remember, the two parts always add up to the whole. Decomposing numbers helps you get ready for addition and subtraction. Keep practicing with objects, fingers, and pictures. The more ways you find, the stronger your math brain gets!