1ST GRADE MATH • NUMBER AND OPERATIONS IN BASE TEN

Understanding Tens

Learn how ten ones come together to make one group called a ten!

Why Do We Group by Tens?

Have you ever looked at your hands? You have ten fingers! A very long time ago, people used their fingers to count things. Because we have ten fingers, people decided to group things in sets of ten. This is how our number system was born!

Long Ago
Counting on Fingers
People used their ten fingers to count sheep, food, and other things they needed.
Ancient Times
Tally Marks
People scratched lines on rocks or sticks to keep track of numbers. After every ten lines, they made a special mark.
Hundreds of Years Ago
The Abacus
People invented a tool with beads on rows. Each row stood for ones, tens, or hundreds. It helped people count faster!
Today
Our Number System
We still use groups of ten every day! The numbers 0 through 9 are our building blocks. When we get to ten, we start a new group.

So here is the big question: what happens when you have more than 9 things? You make a bundle of ten! Let's learn how that works.

What Is a Ten?

When you count to ten, you are counting ten ones. A "one" is just one single thing. When you put ten ones together, you get a new group. We call that group a "ten." Think of it like putting ten blocks into one bag!

1

Ones Are Single Things

Each block, penny, or bead by itself is one one. You count them: 1, 2, 3, 4, 5, 6, 7, 8, 9.
2

Ten Ones Make a Ten

When you get 10 ones, you can bundle them together. That bundle is called a ten.
3

A Ten Is Worth 10

Even though a ten looks like one bundle, it still has 10 ones inside. The bundle is just a faster way to count!
4

Tens and Ones Work Together

Numbers bigger than 9 use tens and ones. The number 14 is 1 ten and 4 ones!
KEY TAKEAWAY
Think of a ten like a pack of crayons. When you buy crayons, they come in a box of 10. The box holds 10 crayons inside, but you carry it as one box. A ten is just like that box — it is one group that holds 10 ones inside!

See How Ones Become a Ten

Let's look at a picture! Below you can see ten single blocks on the left. On the right, those same ten blocks are bundled together into one tall ten-stick. They are the same amount — just grouped differently!

On the left, you see 10 yellow blocks spread out. On the right, those same 10 blocks are stacked and bundled with a dotted line to show 1 ten. Same amount, different way to see it!

When you see a tall stick of 10 blocks, remember — there are still 10 ones inside. We just put them together to make counting easier and faster!

How Tens and Ones Make Numbers

Every number from 10 to 19 is made of 1 ten and some ones. Let's see the pattern!

TEN AND ONES
10 = 1 ten + 0 ones
The number 10 is exactly 1 ten. There are zero extra ones.
EXAMPLE: 13
13 = 1 ten + 3 ones
The number 13 has 1 ten (that's 10) and 3 more ones. 10 + 3 = 13!
EXAMPLE: 17
17 = 1 ten + 7 ones
The number 17 has 1 ten (that's 10) and 7 more ones. 10 + 7 = 17!
💡 Remember!
In a two-digit number, the first digit tells you how many tens and the second digit tells you how many ones. In the number 15, the "1" means 1 ten and the "5" means 5 ones.

The Tens and Ones Chart

A place value chart helps us see how many tens and how many ones are in a number. The tens place is on the left. The ones place is on the right. Let's look at some numbers in the chart!

Place value chart for teen numbers
NumberTensOnes
1010
1212
1515
1919
1616
This chart shows the number 14. On the tens side (left), there is 1 tall ten-stick in cyan. On the ones side (right), there are 4 small blocks in pink.

Every teen number works the same way. The tens side always has 1 ten-stick. The ones side has the extra blocks. Try it with 16 — you would see 1 ten-stick and 6 ones blocks!

Let's Try One Together!

Let's figure out how many tens and ones are in the number 18. Follow along step by step!

How Many Tens and Ones in 18?
1
Step 1 — Count Out 18 OnesImagine you have 18 small blocks sitting on your desk. Count them: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. That is a lot of blocks!
2
Step 2 — Make a Group of TenTake 10 of those blocks and bundle them together. Now you have 1 ten. Stack them into a tall stick!
1 ten
3
Step 3 — Count the Leftover OnesYou started with 18. You bundled 10. How many are left? 18 − 10 = 8. There are 8 ones left over.
8 ones
4
Step 4 — Write the AnswerSo the number 18 is made of 1 ten and 8 ones. We can write: 18 = 1 ten + 8 ones. The digit 1 is in the tens place and the digit 8 is in the ones place!
18 = 1 ten + 8 ones

Ones vs. Tens — What's the Difference?

Let's compare ones and tens side by side so you can see how they are different and how they work together.

Comparing Ones and Tens
OnesTens
What it looks likeA single small blockA tall stick of 10 blocks bundled together
How much is it worth?110
Where in a number?The right digit (ones place)The left digit (tens place)
Example with 15The 5 in 15 means 5 onesThe 1 in 15 means 1 ten
KEY TAKEAWAY
Think about coins! A penny is like a one — it is worth 1 cent. A dime is like a ten — it is worth 10 cents. One dime has the same value as 10 pennies, just like 1 ten equals 10 ones!

From Tens to Even Bigger Numbers!

You just learned that 10 ones make 1 ten. Guess what? The same idea keeps going! When you get 10 tens, you can bundle them into an even bigger group called a hundred. That's 100! You'll learn about hundreds soon.

Now and Next
What You Know NowWhat Comes Next
10 ones = 1 ten10 tens = 1 hundred (100)
Numbers 10–19 have 1 tenNumbers like 20, 30, 40 have more tens
You can break a number into tens and onesYou can break bigger numbers into hundreds, tens, and ones

The big idea is called place value. Each spot in a number has a value. You already know about the ones place and the tens place. As you grow in math, you will learn about the hundreds place, the thousands place, and beyond!

Practice Problems

Now it's your turn! Try these problems. Think about tens and ones as you solve each one.

PROBLEM 1CONCEPTUAL
What is a "ten"? Explain it in your own words.
PROBLEM 2BASIC CALCULATION
How many tens and ones are in the number 13?
PROBLEM 3INTERMEDIATE
Sam has 1 ten-stick and 6 single cubes. How many cubes does Sam have in all?
PROBLEM 4APPLIED
Maya picked 10 red apples and 5 green apples. She puts all the red apples in one bag. How many tens and how many ones does she have? How many apples is that in all?
PROBLEM 5CRITICAL THINKING
Jake says that 10 ones and 1 ten are different amounts. Is he right or wrong? Explain why.

Let's Remember What We Learned!

Today you learned that 10 ones can be grouped together to make 1 ten. A ten is just a bundle of ten ones — the amount stays the same! We use place value to show where tens and ones go in a number. The first digit tells how many tens and the second digit tells how many ones.

Every teen number (like 11, 14, or 18) is made of 1 ten and some extra ones. This big idea of grouping by tens is how our whole number system works. Next, you will learn how more tens make even bigger numbers like 20, 30, and beyond!

Varsity Tutors • 1st Grade Math • Understanding Tens — CCSS.1.NBT.2.a