Understanding Three-Digit Numbers

In this lesson:

• Discover that 10 tens make 1 hundred
• Build three-digit numbers using hundreds, tens, and ones
• Understand what each digit represents based on its position

Learning Objectives

By the end of this lesson, you should be able to:

1. Explain that each digit in a three-digit number tells how many hundreds, tens, or ones, based on its position
2. Represent a three-digit number using base-ten blocks on a place value mat and write expanded form
3. Demonstrate that 100 is the same as a bundle of ten tens and explain why this "unitizing" works
4. Identify multiples of 100 and explain the role of the two zeros
5. Read a three-digit number and explain the value of each digit, including numbers with zero in the tens or ones place

Quick Review

Do you remember from Grade 1?

• 10 ones can be grouped into 1 ten
• The number 35 means 3 tens and 5 ones
• Position matters: 35 is different from 53

Today: We're doing the same thing - one level up!

Review: Our Base-Ten Blocks

• Unit cube = 1 one
• Ten-stick = 1 ten = 10 ones
• Hundred-flat = 1 hundred = 10 tens = 100 ones

Building to One Hundred

Count by tens: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Ten Tens Become One Hundred

10 tens = 1 hundred

Just like 10 ones = 1 ten!

The Pattern Continues

Grade 1: 10 ones = 1 ten

Grade 2: 10 tens = 1 hundred

This is called unitizing - we group things into bigger units

Quick Check

Question: If 100 is the same as 10 tens, how many tens are in 200?

Think for a moment before the next slide...

Quick Check - Answer

Question: How many tens are in 200?

Answer: 20 tens

• 1 hundred = 10 tens
• 2 hundreds = 20 tens

The Three-Column Place Value Mat

• Left column: Hundreds (hundred-flats go here)
• Middle column: Tens (ten-sticks go here)
• Right column: Ones (unit cubes go here)

Build the Number 253

Step 1: Place 2 hundred-flats in the hundreds column
Step 2: Place 5 ten-sticks in the tens column
Step 3: Place 3 unit cubes in the ones column

Count: 100, 200 ... 210, 220, 230, 240, 250 ... 251, 252, 253

What Each Digit Means in 253

• The 2 means 2 hundreds - that's 200, not just 2
• The 5 means 5 tens - that's 50, not just 5
• The 3 means 3 ones - that's 3

Position determines value!

Build the Number 471

On the mat: 4 hundreds, 7 tens, 1 one

Expanded form:

• 4 in the hundreds place = 400
• 7 in the tens place = 70
• 1 in the ones place = 1

Your Turn: Build 362

Think: How many hundreds do you need? ____
Think: How many tens do you need? ____
Think: How many ones do you need? ____

Expanded form:

Pause and try before the next slide

Your Turn: Build 362 - Answer

Answer: 3 hundreds, 6 tens, 2 ones

Expanded form:

Quick Check

Question: What does the 5 mean in the number 529?

A) Five
B) Fifty
C) Five hundred

Think about which column it's in...

Quick Check - Answer

Question: What does the 5 mean in 529?

Answer: C) Five hundred

• The 5 is in the hundreds place
• It means 5 hundreds = 500

Same Digits, Different Positions

347 = 300 + 40 + 7
743 = 700 + 40 + 3

Both use 3, 4, and 7 - but they're very different numbers!

Special Numbers: Multiples of 100

100 = 1 hundred, 0 tens, 0 ones
200 = 2 hundreds, 0 tens, 0 ones
300 = 3 hundreds, 0 tens, 0 ones
...
900 = 9 hundreds, 0 tens, 0 ones

These numbers have only hundreds - no tens and no ones

The Power of Position: 4 vs 40 vs 400

Same digit - three very different amounts!

Why Does 500 Have Two Zeros?

500 = 5 hundreds, 0 tens, 0 ones

• The 5 tells us how many hundreds
• The first 0 tells us there are no tens
• The second 0 tells us there are no ones

Without the zeros: 5 could mean five ones, or 50 could mean five tens!

Build the Number 706

7 hundreds, 0 tens, 6 ones

The tens column is empty - that's what the zero means!

Small Changes, Big Differences

706 = 7 hundreds, 0 tens, 6 ones
760 = 7 hundreds, 6 tens, 0 ones
76 = 0 hundreds, 7 tens, 6 ones

All three use the digits 7 and 6 - but look how different they are!

Your Turn: Build 408

Think:

• How many hundreds? ____
• How many tens? ____
• How many ones? ____

Which column will be empty?

Pause and build it on your mat

Your Turn: Build 408 - Answer

Answer: 4 hundreds, 0 tens, 8 ones

The tens column is empty - so we write a 0 there: 408

Quick Check

Question: Write the numeral for this number:

5 hundreds, 0 tens, 8 ones

What numeral do you write?

Quick Check - Answer

Answer: 508

• 5 in the hundreds place
• 0 in the tens place
• 8 in the ones place

Key Takeaways

✓ 10 tens = 1 hundred (just like 10 ones = 1 ten)
✓ Position determines value - same digit, different place, different amount
✓ Three-digit numbers = hundreds + tens + ones
✓ Expanded form shows the value of each digit (e.g., 347 = 300 + 40 + 7)

Watch out: The 3 in 347 means 300, not 3
Watch out: Zero is a placeholder - 706 ≠ 76
Watch out: Always check which column you're using

Next Lesson

Coming up next: Skip-counting by 5s, 10s, and 100s (2.NBT.A.2)

• Count up by hundreds: 100, 200, 300...
• Count up by tens: 120, 130, 140...
• Use patterns to count quickly

You're ready!