Compose And Decompose 11 To 19 — CCSS.K.NBT.1: Compose and...

SECTION 1

Where Did Teen Numbers Come From?

People have been counting for a very long time! Long ago, people used their fingers to count. They had ten fingers, so they thought ten was a very special number. That is why we group things by tens today!

When people needed to count more than ten things, they had to find a smart way to do it. They made teen numbers! Teen numbers are 11, 12, 13, 14, 15, 16, 17, 18, and 19. Each one is a group of ten plus some more.

Long Ago

Counting on Fingers

People used their 10 fingers to count things like sheep and food.

Then

Grouping by Tens

People learned to make groups of 10 to count faster. This is called base ten.

Later

Writing Numbers

People created number symbols like 1, 2, 3 so they could write down how many they counted.

Today

Teen Numbers in School

You learn that every teen number is 10 + some extra ones. This helps you get ready for bigger math!

So here is the big question: if you have 14 blocks, how can you show that 14 is really just 10 blocks and 4 more blocks? That is exactly what we will learn!

SECTION 2

Big Ideas About Teen Numbers

Before we start, let's learn some important words. When you compose a number, you put parts together to make it. When you decompose a number, you break it apart into smaller pieces.

Compose Means Build

Put 10 ones and some extra ones together to build a teen number. Example: 10 + 3 = 13.

Decompose Means Break Apart

Take a teen number and break it into 10 and some extra ones. Example: 15 = 10 + 5.

Always a Group of Ten

Every teen number has exactly one group of ten ones inside it. No more, no less!

Some Extra Ones

After the group of ten, there are 1 to 9 extra ones left over. That extra part tells us which teen number it is.

✦ KEY TAKEAWAY

Think of a teen number like a full egg carton (that holds 10 eggs) plus a few extra eggs sitting next to it. If you have 10 eggs in the carton and 6 eggs beside it, you have 16 eggs in all. The carton is always the group of 10!

SECTION 3

See It! Teen Numbers as Tens and Ones

Let's look at a picture that shows how the number 14 is made of a group of 10 and 4 extra ones. The blue circles show the group of ten. The pink circles show the extra ones.

This picture shows the number 14 broken into a group of 10 (blue circles) and 4 extra ones (pink circles). We write it as 14 = 10 + 4.

Count the blue circles. There are 10! Now count the pink circles. There are 4! When you put them all together, you get 14. That is how we decompose 14!

SECTION 4

The Teen Number Equation

Every teen number follows the same pattern. We can write it as a math sentence called an equation. An equation uses an equals sign (=) to show that two things are the same.

TEEN NUMBER PATTERN

Teen Number = 10 + Extra Ones

The Teen Number is any number from 11 to 19. The Extra Ones is the number from 1 to 9 that you add to 10.

EXAMPLE: COMPOSING 16

10 + 6 = 16

Start with 10. Add 6 extra ones. You get 16! This is called composing because you are putting parts together.

EXAMPLE: DECOMPOSING 16

16 = 10 + 6

Start with 16. Break it into 10 and 6. This is called decomposing because you are breaking the number apart.

💡 Fun Tip!

Composing and decomposing are like opposites! Composing puts things together. Decomposing takes things apart. They are like building and un-building a tower of blocks!

SECTION 5

Every Teen Number From 11 to 19

Let's see every teen number and how it breaks apart into 10 and extra ones. Look at the table below. Every single teen number has a 10 inside it!

All teen numbers decomposed into 10 + extra ones

Teen Number	Group of Ten	Extra Ones	Equation
11	10	1	11 = 10 + 1
12	10	2	12 = 10 + 2
13	10	3	13 = 10 + 3
14	10	4	14 = 10 + 4
15	10	5	15 = 10 + 5
16	10	6	16 = 10 + 6
17	10	7	17 = 10 + 7
18	10	8	18 = 10 + 8
19	10	9	19 = 10 + 9

This bar chart shows every teen number. The blue bar is always the same size (10). The pink bar grows from 1 to 9 as the teen numbers get bigger.

Do you see the pattern? The blue part stays the same every time. Only the pink part changes! That pink part tells us how many extra ones there are.

SECTION 6

Let's Try It Together!

Let's decompose the number 17 step by step. Imagine you have 17 crayons on a table.

Decompose 17 Into Tens and Ones

Step 1 — Count All the CrayonsYou have 17 crayons on the table. Count them: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17!

Total: 17 crayons

Step 2 — Make a Group of TenNow put 10 crayons into one group. You can line them up or put them in a cup. You made a group of 10!

Group of ten: 10 crayons

Step 3 — Count the LeftoversLook at the crayons still on the table. Count them: 1, 2, 3, 4, 5, 6, 7. There are 7 extra ones left over.

Extra ones: 7 crayons

Step 4 — Write the EquationNow write a math sentence. You had 17. You broke it into 10 and 7. So you write:

17 = 10 + 7

Step 5 — Check Your WorkCount all the crayons again. 10 in the group plus 7 extra ones. 10 + 7 = 17. ✓ It matches! You did it!

✓ 10 + 7 = 17

SECTION 7

Ways to Show Tens and Ones

There are many ways to show how teen numbers break apart. Some ways use things you can touch. Other ways use pictures or numbers. Let's compare them!

Different tools to compose and decompose teen numbers

Tool	How It Works	Best For
Counting Blocks	Use real blocks. Put 10 in a tower. Leave the extras next to it.	Touching and feeling the number
Ten Frame	A box with 10 spaces. Fill it up, then count extras outside.	Seeing 10 as a full group
Drawing Circles	Draw 10 circles in one group. Draw extra circles in another group.	Showing your work on paper
Equations	Write a math sentence like 15 = 10 + 5.	Using numbers and symbols

✦ KEY TAKEAWAY

Think of a ten frame like a parking lot with 10 spaces. When all 10 spaces are full, any extra cars have to park outside the lot. The cars inside are your group of 10. The cars outside are your extra ones!

SECTION 8

Getting Ready for Bigger Numbers

Right now, you are learning about numbers from 11 to 19. But this same big idea works for even bigger numbers! In first grade, you will learn about numbers like 20, 30, and beyond. The idea of grouping by tens will help you with all of those numbers.

How teen number skills grow into bigger math

What You Know Now	What You Will Learn Next
Teen numbers have 1 group of ten	Bigger numbers can have 2, 3, or more groups of ten
14 = 10 + 4	24 = 20 + 4 (that's 2 groups of ten!)
You use objects and drawings	You will learn place value with a tens place and ones place
You compose and decompose with 10	You will add and subtract using tens and ones

Learning to break apart teen numbers is like learning to ride a bike with training wheels. Once you can do it with small numbers, you will be ready to do it with big numbers too!

SECTION 9

Practice Problems

Now it is your turn! Try these problems. Remember, every teen number is made of 10 + some extra ones.

PROBLEM 1 — CONCEPTUAL

Is the number 15 made of a group of ten and some extra ones? How do you know?

PROBLEM 2 — BASIC CALCULATION

Decompose 13. Write the equation: 13 = 10 + ___.

PROBLEM 3 — INTERMEDIATE

You have 10 red apples and 8 green apples. How many apples do you have in all? Write a composing equation.

PROBLEM 4 — APPLIED

Maria has 16 stickers. She puts 10 stickers on one page and the rest on another page. Draw a picture showing both pages, and write the decomposing equation.

PROBLEM 5 — CRITICAL THINKING

Sam says that 10 + 9 = 20. Is Sam right? Explain why or why not.

SUMMARY

What We Learned

Every teen number (11 through 19) is made of one group of ten ones and some extra ones. When you compose, you put 10 and the extra ones together to build the teen number, like 10 + 5 = 15. When you decompose, you break the teen number apart, like 15 = 10 + 5.

You can show composing and decomposing by using objects (like blocks or crayons), drawings (like circles in groups), or equations (math sentences with numbers and an equals sign). This skill helps you understand place value and gets you ready for adding and subtracting bigger numbers!