Understanding Place Value vs. Name Value
What is Name Value?
Name value is simply the digit itself – what the number is called.
Example: In the number 47
- The name value of 4 is “four”
- The name value of 7 is “seven”
Think of it like this: If you see the digit 5 all by itself, you say “five” – that’s its name!
What is Place Value?
Place value tells us how much a digit is worth based on WHERE it sits in the number.
Example: In the number 47
- The 4 is in the tens place, so its place value is 40 (4 tens = 40)
- The 7 is in the ones place, so its place value is 7 (7 ones = 7)
The Big Idea: The same digit can have different values depending on where it lives!
- In 25, the 2 means 20 (2 tens)
- In 52, the 2 means 2 (2 ones)
Understanding Expanded Form
What is Expanded Form?
Expanded form shows us how to “break apart” a number to see what each digit is worth.
Think of it like breaking a toy into pieces to see how it’s made!
The Place Value Chart (Up to 200)
Hundreds | Tens | Ones
1 | 5 | 3
This shows the number 153
How to Write Numbers in Expanded Form
For 2-Digit Numbers (up to 99)
Example 1: The number 47
- 47 = 40 + 7
- We say: “47 is 4 tens and 7 ones”
- 4 tens = 40, and 7 ones = 7
Example 2: The number 83
- 83 = 80 + 3
- We say: “83 is 8 tens and 3 ones”
For 3-Digit Numbers (100 to 200)
Example 1: The number 125
- 125 = 100 + 20 + 5
- We say: “125 is 1 hundred, 2 tens, and 5 ones”
Example 2: The number 187
- 187 = 100 + 80 + 7
- We say: “187 is 1 hundred, 8 tens, and 7 ones”
Example 3: The number 200
- 200 = 200 + 0 + 0 or just 200
- We say: “200 is 2 hundreds, 0 tens, and 0 ones”
Step-by-Step Method
The “Look, Circle, Write” Method
Let’s try with 134:
Step 1: LOOK at each digit and its place
- 1 is in the hundreds place
- 3 is in the tens place
- 4 is in the ones place
Step 2: CIRCLE and say what each digit means
- 1 hundred = 100
- 3 tens = 30
- 4 ones = 4
Step 3: WRITE it with plus signs
- 134 = 100 + 30 + 4
Tips and Tricks
Trick #1: The Zero Rule
When you see a zero, that place has no value!
- In 105: The tens place has 0, so we write 100 + 0 + 5 or just 100 + 5
- In 120: The ones place has 0, so we write 100 + 20 + 0 or just 100 + 20
Trick #2: Count the Zeros
To find place value quickly, count the zeros after the digit:
- 1 in the tens place = 10 (one zero)
- 1 in the hundreds place = 100 (two zeros)
- 3 in the tens place = 30 (one zero)
- 5 in the ones place = 5 (no zeros)
Trick #3: Use Base-10 Blocks
Visualize numbers with blocks:
- Hundreds: A big flat square (100 little squares)
- Tens: A long stick (10 little squares)
- Ones: A tiny cube (1 square)
So 143 looks like: 1 big flat + 4 sticks + 3 cubes
Trick #4: The “Building Blocks” Song
Make up a little chant:
- “What’s the place? What’s the space? How much is it worth in that place?”
Trick #5: Practice with Money
- 1 hundred = 1 dollar bill ($100)
- 1 ten = 1 dime (10¢) or think of it as $10
- 1 one = 1 penny (1¢) or $1
So $145 = one $100 bill + four $10 bills + five $1 bills
Common Mistakes to Avoid
Mistake #1: Forgetting the Zero
❌ Wrong: 150 = 15 + 0 ✓ Correct: 150 = 100 + 50 + 0 (or 100 + 50)
Mistake #2: Writing Just the Digit
❌ Wrong: 182 = 1 + 8 + 2 ✓ Correct: 182 = 100 + 80 + 2
Mistake #3: Mixing Up Places
❌ Wrong: 67 = 7 + 60 ✓ Correct: 67 = 60 + 7 (Always write hundreds first, then tens, then ones)
Quick Reference Chart
| Number | Expanded Form | How to Say It |
|---|---|---|
| 45 | 40 + 5 | 4 tens and 5 ones |
| 102 | 100 + 2 | 1 hundred and 2 ones |
| 130 | 100 + 30 | 1 hundred and 3 tens |
| 199 | 100 + 90 + 9 | 1 hundred, 9 tens, and 9 ones |
| 200 | 200 | 2 hundreds |
Remember!
🌟 Name value = What the digit is called (just the number itself)
🌟 Place value = What the digit is WORTH (depends on where it sits)
🌟 Expanded form = Breaking the number into its place value parts
Think of a number like a train: Each car (digit) carries a different amount depending on its position in the train!
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