Place Values | Second Grade
What is Place Value?
Concept: Place value tells us what each digit is worth based on its position in a number. The same digit can have different values depending on where it sits!
Two Place Value Positions:
TENS
Left position
Worth 10 times more
ONES
Right position
Individual units
Example: The Number 45
4 tens = 40 | 5 ones = 5 | Total = 45
💡 Tip: The position of a digit determines its value!
1. Place Value Models - Tens and Ones
Concept: We use visual models like base-10 blocks to show place value. Tens are long rods, ones are small cubes!
📝 Base-10 Blocks
TEN (Rod)
10 units
1 rod = 10 ones
ONE (Cube)
1 cube = 1 unit
Visual Example: 34
3 tens + 4 ones = 34
TENS
3 rods = 30
+
ONES
4 cubes = 4
30 + 4 = 34
💡 Tip: Count the rods by 10s, then add the individual cubes!
2. Value of a Digit - Tens and Ones
Concept: Each digit has a value based on its place. The tens digit is worth 10 times more than the ones digit!
Place Value Chart
| TENS | ONES |
|---|---|
| 7 | 3 |
7 in the tens place = 70
3 in the ones place = 3
Total Value = 73
Value Formula
\( \text{Value} = (\text{Tens digit} \times 10) + (\text{Ones digit} \times 1) \)
Example: 58
\( (5 \times 10) + (8 \times 1) \)
\( 50 + 8 = 58 \)
More Examples:
42
4 tens = 40
2 ones = 2
89
8 tens = 80
9 ones = 9
30
3 tens = 30
0 ones = 0
💡 Tip: Multiply the tens digit by 10 to find its value!
3. Regroup Tens and Ones
Concept: Regrouping means exchanging between place values. We can trade 10 ones for 1 ten, or break 1 ten into 10 ones!
Regrouping Rules
Ones → Tens
10 ones = 1 ten
Group 10 ones together!
Tens → Ones
1 ten = 10 ones
Break apart a ten!
📝 Example: Regroup 10 Ones
You have 2 tens and 13 ones
Before Regrouping:
2 tens + 13 ones
⬇️ Regroup 10 ones as 1 ten ⬇️
After Regrouping:
3 tens + 3 ones
Both equal 33! (20 + 13 = 33 and 30 + 3 = 33)
📝 Example: Regroup 1 Ten
You have 5 tens and 2 ones, need more ones
Before Regrouping:
5 tens + 2 ones
⬇️ Break 1 ten into 10 ones ⬇️
After Regrouping:
4 tens + 12 ones
Both equal 52! (50 + 2 = 52 and 40 + 12 = 52)
💡 Tip: Regrouping doesn't change the value - just how we show it!
4. Ways to Make a Number (Regrouping)
Concept: Any number can be shown in different ways using tens and ones. All ways equal the same value!
📝 Example: Different Ways to Make 35
3 tens + 5 ones
30 + 5 = 35
2 tens + 15 ones
20 + 15 = 35
1 ten + 25 ones
10 + 25 = 35
0 tens + 35 ones
0 + 35 = 35
All equal 35! Just shown different ways.
More Examples:
Ways to Make 47:
• 4 tens + 7 ones
• 3 tens + 17 ones
• 2 tens + 27 ones
• 1 ten + 37 ones
Ways to Make 62:
• 6 tens + 2 ones
• 5 tens + 12 ones
• 4 tens + 22 ones
• 3 tens + 32 ones
💡 Tip: As tens decrease by 1, ones increase by 10!
5. Convert To/From a Number - Tens and Ones
Concept: We can write numbers in different forms - as a single number or broken into tens and ones!
→ From Standard Form
68
⬇️ Break apart ⬇️
6 tens + 8 ones
or 60 + 8
→ To Standard Form
4 tens + 7 ones
⬇️ Combine ⬇️
47
Conversion Examples
Standard → Expanded
53 → 5 tens + 3 ones
53 = 50 + 3
Expanded → Standard
8 tens + 1 one → 81
80 + 1 = 81
Standard → Expanded
90 → 9 tens + 0 ones
90 + 0 = 90
💡 Tip: Expanded form shows the value of each digit clearly!
6. Convert Between Place Values
Concept: We can exchange between tens and ones. This is super useful for adding and subtracting!
Conversion Formulas
Ones to Tens
\( \text{Tens} = \frac{\text{Ones}}{10} \)
40 ones = 4 tens
Tens to Ones
\( \text{Ones} = \text{Tens} \times 10 \)
7 tens = 70 ones
📝 Conversion Practice
Question: How many ones in 6 tens?
Step 1: Use formula → Ones = Tens × 10
Step 2: Substitute → Ones = 6 × 10
Step 3: Calculate → Ones = 60
Answer: 60 ones
Question: How many tens in 80 ones?
Step 1: Use formula → Tens = Ones ÷ 10
Step 2: Substitute → Tens = 80 ÷ 10
Step 3: Calculate → Tens = 8
Answer: 8 tens
Quick Reference:
1 ten = 10 ones
2 tens = 20 ones
5 tens = 50 ones
9 tens = 90 ones
💡 Tip: To convert tens to ones, multiply by 10. To convert ones to tens, divide by 10!
Important Place Value Formulas
Place Value Formula
\( \text{Number} = (\text{T} \times 10) + (\text{O} \times 1) \)
T = Tens digit
O = Ones digit
Regrouping Formula
10 ones = 1 ten
1 ten = 10 ones
Exchange between
place values
Conversion Formulas
Tens → Ones:
\( \text{Ones} = \text{Tens} \times 10 \)
Ones → Tens:
\( \text{Tens} = \frac{\text{Ones}}{10} \)
🎯 Tips for Place Value Success 🎯
- ✓ Remember: Position matters! Same digit, different place, different value
- ✓ Always use base-10 blocks to visualize place values
- ✓ When regrouping, the total value never changes
- ✓ Practice converting between standard and expanded form
- ✓ Tens are always worth 10 times more than ones
- ✓ Use place value to understand how numbers work!
⭐ You're a Place Value Expert! ⭐
Incredible work mastering place value! You now understand how tens and ones work together, can read place value models, identify the value of each digit, regroup between tens and ones, show numbers in different ways, and convert between place values. Place value is the foundation of all number work - it helps you understand how our number system works and makes adding, subtracting, and comparing numbers so much easier! Understanding that the same digit has different values based on its position is one of the most important concepts in all of mathematics. You're building powerful number sense that will help you forever. Keep exploring how numbers work - you're doing absolutely phenomenal work!