Why Place Value Is the Foundation of All Math
What Is Place Value?
Place value is the idea that a digit's position determines its value.
In the number 352:
- 3 is in the hundreds place = 300
- 5 is in the tens place = 50
- 2 is in the ones place = 2
The 3 isn't just "three" — it's "three hundred."
Why It Matters So Much
Place value is the foundation for:
- Multi-digit addition and subtraction
- Multiplication and division
- Understanding decimals
- Reading large numbers
- Rounding and estimation
Without strong place value understanding, kids struggle with almost everything in math.
Concrete First: Base-10 Blocks
Use physical manipulatives:
- Unit cubes = ones
- Rods (10 units) = tens
- Flats (10 rods) = hundreds
- Large cube (10 flats) = thousands
Build numbers physically. Trade 10 ones for 1 ten. This is the foundation of regrouping.
Teaching Activities
Build It: "Show me 47 with blocks"
- 4 tens and 7 ones
What's the Value?: Point to a digit and ask its value
- In 582, what is the 8 worth? (80)
Expanded Form: Write numbers as sums
- 352 = 300 + 50 + 2
Comparing: Which is greater?
- 47 or 74? Why?
Common Misconceptions
Digit vs. Value: Kids confuse the digit (5) with its value (50 or 500)
Zero confusion: In 502, the 0 is a placeholder. It doesn't mean "nothing."
Reading large numbers: 1,234 is "one thousand two hundred thirty-four" not "one-two-three-four"
Extending to Decimals
Place value extends right of the decimal:
- Tenths (0.1) = 1/10
- Hundredths (0.01) = 1/100
The pattern continues: each place is 10× the place to its right.
Practice Resources
Build place value understanding: