Build 100: Ten Tens Make a Hundred - 2nd Grade Math

SECTION 1

How People Started Counting to 100

Long ago, people needed to count lots of things. They counted sheep, apples, and coins. When they had many things to count, they found a smart way to do it. They put things in groups of ten because we have ten fingers!

Ancient Times • Finger Counting

People used their ten fingers to count. This made ten a special number.

1000s • Base Ten System

People made a counting system using groups of ten. Ten ones make one ten!

1600s • Place Value

Smart people figured out that the place where we write numbers matters.

Today • Learning 100

Kids like you learn that ten tens make one hundred!

Today we will learn how ten groups of ten make the big number 100. This helps us count lots of things quickly!

SECTION 2

What Makes 100 Special

The number 100 is made of smaller parts. Let's learn the important ideas about building 100!

Groups of Ten

We can put ten things together to make one group. This group is worth 10!

Counting by Tens

We can count: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Each number is one more group of ten!

Ten Tens Equal 100

When we have ten groups with ten things in each group, we have 100 things total!

Place Value

In the number 100, the 1 is in the hundreds place. The two 0s show there are no extra tens or ones.

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KEY TAKEAWAY

Think of 100 like a big box of crayons! If you have 10 small boxes with 10 crayons in each box, you have 100 crayons total. Each small box is like a group of ten, and ten of these boxes make the big number 100!

SECTION 3

See How Ten Tens Make 100

Let's look at a picture that shows how ten groups of ten make 100. We will use dots to see this clearly!

Look at the ten colorful boxes! Each box has 10 dots inside. When we count all the groups (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), we get ten groups of ten, which equals 100 dots total!

In this picture, you can see ten different colored boxes. Each box has exactly 10 dots. If we count all the dots from all the boxes, we get 100! This shows us that 10 × 10 = 100.

SECTION 4

The Math Behind Building 100

Let's learn the math that shows how ten tens make 100. We can write this in different ways!

ADDING TENS

10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100

We add ten to itself ten times. Each 10 represents one group of ten things.

MULTIPLICATION

10 × 10 = 100

This means we have 10 groups with 10 things in each group. 10 × 10 = 100.

PLACE VALUE

1 hundred + 0 tens + 0 ones = 100

In the number 100, the 1 is in the hundreds place. The two 0s show zero tens and zero ones left over.

All of these ways show the same thing: when we have ten groups of ten, we get the special number 100!

SECTION 5

Different Ways to Build 100

There are many ways to build the number 100! Let's see different building blocks we can use.

This picture shows six different ways to make 100! The most important way is 10 groups of 10 (shown in blue), but we can also use groups of 20, 25, 50, or even 100 ones. At the bottom, you can see how addition and subtraction can also make 100!

The diagram shows us that 100 is a very special number! We can make it in many ways, but the most important way for second grade is ten groups of ten. This helps us understand place value and how our number system works.

SECTION 6

Let's Build 100 Step by Step

Let's work through an example together! Imagine we have a big bag of 100 marbles and we want to organize them into groups.

Organizing 100 Marbles

1
Step 1 — Start with 100 marbles

We have a big pile of 100 marbles. This is too many to count easily, so we need to organize them.

100 marbles total
2
Step 2 — Make groups of 10

We count out 10 marbles and put them in a small cup. Then we count 10 more and put them in another cup. We keep doing this until all marbles are in cups.

Each cup has 10 marbles
3
Step 3 — Count the cups

Now we count how many cups we have: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We have 10 cups!

10 cups with 10 marbles each
4
Step 4 — Check our work

We can check by counting by tens: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Perfect! We can also multiply: 10 cups × 10 marbles = 100 marbles.

10 × 10 = 100 ✓

This example shows us how grouping by tens makes counting easier. When we have ten groups of ten things, we always get 100!

SECTION 7

When Do We Use Ten Tens?

Understanding ten tens make 100 is helpful in many situations. Let's see when this idea is useful!

When It's Helpful	Example	Why It Works
Counting lots of things	100 stickers, 100 pennies	Groups of 10 are easier to count
Learning place value	Understanding 100, 200, 300	Shows how hundreds work
Adding and subtracting	50 + 50 = 100, 100 − 30 = 70	Makes mental math easier
Organizing collections	Baseball cards, toy cars	Easy to see how many you have

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KEY TAKEAWAY

Think of 100 like a pizza cut into 10 slices, where each slice has 10 pepperonis! When you put all the slices back together, you have 10 × 10 = 100 pepperonis total. This way of thinking helps us with bigger numbers too!

SECTION 8

Beyond 100: Building Even Bigger Numbers

Once we understand that ten tens make 100, we can learn about even bigger numbers! This idea helps us build numbers like 200, 300, and beyond.

What We Know Now	What Comes Next
10 ones = 1 ten	10 hundreds = 1 thousand
10 tens = 1 hundred (100)	10 thousands = 1 ten thousand
Count by 10s: 10, 20, 30...	Count by 100s: 100, 200, 300...
Groups help us organize small collections	Groups help us organize huge collections

The pattern we learned with ten tens making 100 continues forever! In third grade, you'll learn that ten hundreds make 1,000. This pattern helps us understand our whole number system!

SECTION 9

Practice Building 100

Now let's practice what we learned! These problems will help you understand how ten tens make 100.

Question 1: CONCEPTUAL

How many groups of 10 do you need to make 100?

Show answer

You need 10 groups of 10 to make 100. Each group has 10 things, so when you have 10 groups, you get 10 × 10 = 100. You can count by tens to check: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100!

Question 2: BASIC CALCULATION

Fill in the blank: 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = ____

Show answer

10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100. We are adding ten to itself ten times. Each 10 represents one group of ten things, and ten groups of ten equals 100.

Question 3: INTERMEDIATE

Maya has 7 boxes with 10 crayons in each box. How many more boxes does she need to have 100 crayons total?

Show answer

Maya has 7 boxes × 10 crayons = 70 crayons. She needs 100 crayons total. Since 100 = 10 boxes × 10 crayons, she needs 10 − 7 = 3 more boxes. We can check: 7 + 3 = 10 boxes, and 10 × 10 = 100 crayons.

Question 4: APPLIED

A teacher wants to give 100 stickers to her class. The stickers come in sheets of 10. How many sheets does she need? If each sheet costs 50 cents, how much will it cost?

Show answer

The teacher needs 100 ÷ 10 = 10 sheets because ten tens make 100. Each sheet costs 50 cents, so 10 sheets × 50 cents = 500 cents = $5.00 total. This shows how understanding groups of ten helps us solve real problems with money and counting!

Question 5: CRITICAL THINKING

Jake says "I can make 100 with 5 groups of 20, so ten tens isn't the only way." Is Jake right? Explain why ten tens is still special for learning about 100.

Show answer

Jake is right that 5 × 20 = 100, and there are other ways to make 100. However, ten tens is special because it shows us place value. When we write 100, the 1 represents one hundred (ten groups of ten), and the two 0s show zero leftover tens and zero leftover ones. This pattern (groups of ten) continues for all bigger numbers in our number system.

SUMMARY

Building 100 with Ten Tens

Summary

We learned that ten tens make one hundred! When we have 10 groups with 10 things in each group, we get 100 things total. This can be written as 10 × 10 = 100 or by adding ten tens: 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 100.

Understanding this idea helps us with place value, counting by tens, and organizing collections. The pattern of grouping by tens continues with bigger numbers like 200, 300, and even 1,000. This makes 100 a very important building block in our number system!