How to Explain Place Value to Third Graders

"What's the 4 worth in 347?"

If your third grader answers "4," they're reading digits. If they answer "40" or "4 tens," they understand place value.

This distinction matters enormously. Place value isn't just about knowing where numbers sit—it's about understanding what numbers mean. And in third grade, this foundation becomes critical.

Why Place Value Matters in Third Grade

Third grade is when math gets serious about bigger numbers. Your child will:

• Work with numbers up to 1,000 (and sometimes beyond)
• Add and subtract with regrouping
• Start multiplication and division
• Round numbers to estimate

Every single one of these skills depends on understanding place value. A child who sees 347 as just "three four seven" will struggle. A child who sees it as "300 + 40 + 7" has a foundation for everything.

The Building Blocks: Ones, Tens, Hundreds

Start with What They Know

Third graders already understand ones and tens from earlier grades. Build on this:

Ones are single items. One apple. One block. One anything.

Tens are groups of 10 ones bundled together. This is where it helps to use physical objects—10 pennies become a dime, 10 small cubes become a rod.

Hundreds are 10 tens bundled together. Now you have 100 ones, but organized into a flat square of 10 rods.

The "Hotel" Analogy

Think of a number as a hotel with different floors:

• Ground floor (ones): Individual guests, 0-9 at a time
• Second floor (tens): Groups of 10, can hold 0-9 groups
• Third floor (hundreds): Groups of 100, can hold 0-9 groups

When 10 guests gather on any floor, they move up to the next floor as one group. This is regrouping!

Hands-On Activities That Work

Base-10 Blocks

If you don't have these, you can make them:

• Ones: Small squares (cut from cardstock)
• Tens: Strips of 10 squares connected
• Hundreds: 10 strips arranged as a 10×10 square

Have your child build numbers: "Show me 234." They should grab 2 hundred-squares, 3 ten-strips, and 4 ones.

Then ask: "What if we add 10 more?" Watch them add a ten-strip. "What's the number now?"

Money as Place Value

Money is a natural place value model:

• Pennies = ones
• Dimes = tens
• Dollar bills = hundreds

"You have $2.47. How many dollars? How many dimes? How many pennies?"

This connects abstract math to something real and motivating.

The Place Value Chart

Create a simple chart with three columns: Hundreds | Tens | Ones

Write numbers and have your child place digits in the correct columns. Then ask:

• "What's the value of the digit in the tens place?"
• "Which digit shows how many hundreds?"
• "What would happen if we switched the 3 and the 7?"

Teaching Comparing and Ordering

The "Left to Right" Rule

When comparing numbers, start from the left:

Compare 472 and 468:

1. Both have 4 hundreds (equal so far)
2. Compare tens: 7 vs 6
3. 7 > 6, so 472 > 468

No need to look at ones—the tens already decided it.

Number Lines Help

Draw a number line from 400 to 500. Mark where 472 and 468 fall. Visually, 472 is to the right (greater).

This builds intuition for number relationships.

Rounding: The "Nearest Neighbor" Approach

Third graders learn to round to the nearest 10 and 100. Here's a concrete way to explain it:

Rounding to the Nearest 10

For 347:

• Look at the ones digit (7)
• Is 347 closer to 340 or 350?
• Draw a mini number line: 340...347...350
• 347 is closer to 350

The rule: If the ones digit is 5 or more, round up. If it's 4 or less, round down.

Rounding to the Nearest 100

For 347:

• Look at the tens digit (4)
• Is 347 closer to 300 or 400?
• 347 is closer to 300

The rule: If the tens digit is 5 or more, round up to the next hundred.

Why We Round

Connect rounding to real life:

• "About how many students in our school?"
• "Roughly how many pages in this book?"
• "Approximately how much does this cost?"

Estimation is a practical skill, not just a math exercise.

Common Mistakes (And How to Fix Them)

Mistake 1: Reading Digits, Not Values

Wrong thinking: 347 is "three, four, seven"

Fix: Always ask "What is this digit worth?" Practice expanded form: 347 = 300 + 40 + 7

Mistake 2: Confusing Place with Value

Wrong thinking: "The 4 is in the second place"

Fix: Use consistent language. "The 4 is in the tens place, and it's worth 40."

Mistake 3: Zero Confusion

Wrong thinking: 307 and 370 are the same

Fix: Zero is a placeholder! Use base-10 blocks: 307 has 3 hundreds, 0 tens, 7 ones. 370 has 3 hundreds, 7 tens, 0 ones. Very different amounts.

Mistake 4: Rounding Errors

Wrong thinking: Round 350 down to 300 (because 5 could go either way)

Fix: Teach the convention: 5 always rounds up. 350 rounds to 400. Consistency prevents confusion.

Building Toward Bigger Concepts

Place value directly supports:

Addition with Regrouping

347 + 265: When ones add to more than 9, regroup to tens. When tens add to more than 9, regroup to hundreds.

Subtraction with Regrouping

500 - 247: Need to "borrow" from hundreds to tens to ones. Only makes sense with place value understanding.

Multiplication

3 × 40 = 3 × 4 tens = 12 tens = 120. Place value makes this logical.

Division

How many tens in 120? Place value helps students see that 120 ÷ 10 = 12.

Practice Ideas for Home

Daily Number Talks

Pick a number each day. Ask:

• "What's the digit in the tens place?"
• "What's that digit worth?"
• "Round this to the nearest ten."
• "Round this to the nearest hundred."
• "Write this in expanded form."

License Plate Math

On car rides, look at license plate numbers. "Which plate has the bigger number? How do you know?"

Grocery Store Rounding

"This costs $3.47. If we round to the nearest dollar, about how much is it?"

Building Numbers Game

Give digits (say, 5, 8, 2) and ask:

• "What's the largest number you can make?"
• "What's the smallest?"
• "Make a number between 500 and 600."

The Bottom Line

Place value is not just one unit to get through—it's the lens through which your child will see all numbers going forward. Invest time here, and every math concept that follows becomes clearer.

When your third grader looks at 347 and instinctively knows it means "three hundreds, four tens, and seven ones," they have a foundation that will serve them for years.