Understanding Tens - 1st Grade Math

SECTION 1

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.

SECTION 2

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!

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.

Ten Ones Make a Ten

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

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!

Tens and Ones Work Together

Numbers bigger than 9 use tens and ones. The number 14 is 1 ten and 4 ones!

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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!

SECTION 3

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!

SECTION 4

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!

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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.

SECTION 5

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!

Number	Tens	Ones
10	1	0
12	1	2
15	1	5
19	1	9
16	1	6

Place value chart for teen numbers

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!

SECTION 6

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 Ones

Imagine 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 Ten

Take 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 Ones

You 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 Answer

So 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

SECTION 7

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.

	Ones	Tens
What it looks like	A single small block	A tall stick of 10 blocks bundled together
How much is it worth?	1	10
Where in a number?	The right digit (ones place)	The left digit (tens place)
Example with 15	The 5 in 15 means 5 ones	The 1 in 15 means 1 ten

Comparing Ones and Tens

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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!

SECTION 8

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.

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

Now and Next

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!

SECTION 9

Practice Problems

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

Question 1: CONCEPTUAL

What is a "ten"? Explain it in your own words.

Show answer

A ten is a bundle or group of 10 ones. When you have 10 single things and put them together, that group is called a ten. It is like putting 10 blocks into one bag. The bag still holds 10 blocks, but now you count it as 1 ten.

Question 2: BASIC CALCULATION

How many tens and ones are in the number 13?

Show answer

The number 13 has 1 ten and 3 ones. You can make one group of 10 from the 13, which leaves 3 left over. So 13 = 1 ten + 3 ones. The digit 1 is in the tens place and the digit 3 is in the ones place.

Question 3: INTERMEDIATE

Sam has 1 ten-stick and 6 single cubes. How many cubes does Sam have in all?

Show answer

Sam has 16 cubes in all. The 1 ten-stick is worth 10 cubes, and then there are 6 more single cubes. You add them together: 10 + 6 = 16. So 1 ten and 6 ones equals 16.

Question 4: APPLIED

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?

Show answer

Maya has 1 ten and 5 ones. The bag of 10 red apples is her 1 ten. The 5 green apples are her 5 ones. In all, she has 10 + 5 = 15 apples. We can write this as 15 = 1 ten + 5 ones.

Question 5: CRITICAL THINKING

Jake says that 10 ones and 1 ten are different amounts. Is he right or wrong? Explain why.

Show answer

Jake is wrong! 10 ones and 1 ten are the same amount. They both equal 10. The only difference is how they are grouped. Ten ones means 10 separate things. One ten means those 10 things are bundled together into one group. The value does not change — just the way we organize and count them.

SUMMARY

Let's Remember What We Learned!

Summary

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!