How to Explain Place Value to Fourth Graders

"How big is a million?"

This question stumps most adults, let alone fourth graders. Yet fourth grade is when students must master place value up to the millions—numbers so large they're impossible to truly visualize.

The good news? You don't need to count to a million. You need to understand the pattern that makes our number system work.

Why Place Value to Millions Matters

Fourth grade is a turning point. Students move from "comfortable" numbers (ones, tens, hundreds, thousands) to numbers that describe populations, distances, and scientific measurements. This understanding is essential for:

• Reading and interpreting real-world data
• Performing multi-digit multiplication and division
• Understanding decimals (which extend place value the other direction)
• Developing number sense for estimation and reasonableness

Without solid place value understanding, students will struggle with every math concept that follows.

The Big Idea: The 10-Times Pattern

Here's the key concept that makes our entire number system work:

Each place is worth 10 times the place to its right.

Ones        →  1
Tens        →  10         (10 × 1)
Hundreds    →  100        (10 × 10)
Thousands   →  1,000      (10 × 100)
Ten-thousands → 10,000    (10 × 1,000)
Hundred-thousands → 100,000 (10 × 10,000)
Millions    →  1,000,000  (10 × 100,000)

This pattern is the same whether you're going from ones to tens or from hundred-thousands to millions. Once students truly understand this, large numbers become manageable.

Building Understanding Step by Step

Step 1: Review What They Know

Start with thousands—numbers students already understand:

In 3,456:

• 3 is in the thousands place = 3,000
• 4 is in the hundreds place = 400
• 5 is in the tens place = 50
• 6 is in the ones place = 6

Expanded form: 3,000 + 400 + 50 + 6 = 3,456

Step 2: Introduce Ten-Thousands

Now extend the pattern:

"If we have 10 groups of 1,000, what do we get?"

10 × 1,000 = 10,000 (ten thousand)

In 45,678:

• 4 is in the ten-thousands place = 40,000
• 5 is in the thousands place = 5,000
• 6 is in the hundreds place = 600
• 7 is in the tens place = 70
• 8 is in the ones place = 8

Step 3: Hundred-Thousands

Continue the pattern:

"If we have 10 groups of 10,000, what do we get?"

10 × 10,000 = 100,000 (one hundred thousand)

In 345,678:

• 3 is in the hundred-thousands place = 300,000
• 4 is in the ten-thousands place = 40,000
• 5 is in the thousands place = 5,000
• And so on...

Step 4: Millions

One more step:

"If we have 10 groups of 100,000, what do we get?"

10 × 100,000 = 1,000,000 (one million)

Now students can read numbers like 2,456,789:

• 2 millions = 2,000,000
• 4 hundred-thousands = 400,000
• 5 ten-thousands = 50,000
• 6 thousands = 6,000
• 7 hundreds = 700
• 8 tens = 80
• 9 ones = 9

The Place Value Chart

A visual chart is invaluable for fourth graders:

Millions | Hundred-Thousands | Ten-Thousands | Thousands | Hundreds | Tens | Ones
    2    |        4          |       5       |     6     |    7     |  8   |  9

Group by periods: Numbers are grouped in threes, separated by commas:

• Ones period: ones, tens, hundreds
• Thousands period: thousands, ten-thousands, hundred-thousands
• Millions period: millions, ten-millions, hundred-millions

This grouping makes large numbers easier to read and write.

Reading Large Numbers: The Comma Method

Teach students to use commas as guides:

For 2,456,789:

1. Start from the left
2. Read each group as a number
3. Say the period name after each group

"Two million, four hundred fifty-six thousand, seven hundred eighty-nine"

Practice with:

• 1,234,567 → "One million, two hundred thirty-four thousand, five hundred sixty-seven"
• 5,008,020 → "Five million, eight thousand, twenty"

Making Millions Concrete

Real-World Contexts

Connect large numbers to things students care about:

Populations:

• Your school might have 500 students
• Your city might have 100,000 people
• Your state might have 5,000,000 people

Distances:

• The moon is about 240,000 miles away
• The sun is about 93,000,000 miles away

Time:

• There are 525,600 minutes in a year
• You've been alive for about 4,000,000 minutes (if you're 8 years old)

The Million Visualization

Help students grasp a million with this progression:

• 1 second feels like almost nothing
• 1,000 seconds = about 17 minutes
• 1,000,000 seconds = about 11.5 days!

Or with distance:

• 1 step = about 2 feet
• 1,000 steps = about 1/3 mile
• 1,000,000 steps = about 380 miles (Chicago to Nashville!)

Comparing and Ordering Large Numbers

The Left-to-Right Rule

When comparing multi-digit numbers:

1. Start from the leftmost digit
2. Compare digit by digit until you find a difference
3. The larger digit means the larger number

Compare 456,789 and 465,123:

• Both have 4 hundred-thousands (equal so far)
• Compare ten-thousands: 5 vs 6
• 5 < 6, so 456,789 < 465,123

When Numbers Have Different Lengths

The number with more digits is larger:

• 99,999 < 100,000 (five digits vs six digits)
• 999,999 < 1,000,000 (six digits vs seven digits)

Rounding Large Numbers

Fourth graders learn to round to any place value.

The Rounding Process

Round 4,567,890 to the nearest hundred-thousand:

1. Find the hundred-thousands place: 4,567,890
2. Look at the digit to its right (ten-thousands): 6
3. Is it 5 or more? Yes!
4. Round up: 4,600,000

Round 4,567,890 to the nearest million:

1. Find the millions place: 4,567,890
2. Look at the digit to its right (hundred-thousands): 5
3. Is it 5 or more? Yes!
4. Round up: 5,000,000

The Rounding Rhyme

"5 or more, let it soar. 4 or less, let it rest."

Hands-On Activities

Place Value Disks

Use or make disks labeled with place values:

• 1, 10, 100, 1,000, 10,000, 100,000, 1,000,000

Have students:

• Build numbers using disks
• Trade 10 of one value for 1 of the next (e.g., 10 hundreds for 1 thousand)
• Compare who has the larger number

Secret Number Game

One person thinks of a number up to 1,000,000. The other asks yes/no questions:

• "Is it greater than 500,000?"
• "Is the digit in the ten-thousands place greater than 5?"

This builds place value vocabulary and comparison skills.

Number Expansion Race

Write a number on the board. Students race to write it in expanded form:

2,345,678 = 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8

Real-World Research

Have students find large numbers in:

• Newspaper articles
• Sports statistics
• Population data
• Science facts

Then practice reading, comparing, and rounding these numbers.

Common Mistakes and How to Fix Them

Mistake 1: Misreading Zeros

Wrong: Reading 3,045,000 as "three million forty-five"

Fix: Emphasize that zeros are placeholders. Read each period:

• 3 million
• 45 thousand
• 0 (ones period—don't say anything)

"Three million, forty-five thousand"

Mistake 2: Wrong Period Names

Wrong: Saying "three thousand million" for 3,000,000

Fix: Practice the period sequence: ones → thousands → millions. Use the comma as a guide—after the first comma (from right), say "thousand." After the second comma, say "million."

Mistake 3: Comparing by Digit Size, Not Position

Wrong: Thinking 900,000 > 1,000,000 because 9 > 1

Fix: Always count digits first. More digits = larger number. Then compare from left to right.

Mistake 4: Rounding Errors with Zeros

Wrong: Rounding 4,950,000 to the nearest million as 4,000,000

Fix: Walk through carefully:

• Millions digit: 4
• Next digit (hundred-thousands): 9
• 9 ≥ 5, so round up
• Answer: 5,000,000

Connecting to Future Concepts

Place value to millions prepares students for:

Decimals (Fifth Grade)

The same pattern extends right of the decimal point—tenths, hundredths, thousandths are 10 times smaller each step.

Scientific Notation (Middle School)

Writing 3,400,000 as 3.4 × 10⁶ relies on understanding place value deeply.

Operations with Large Numbers

Multi-digit multiplication and division require knowing what each digit represents.

Practice Ideas for Home

Daily Number Encounters

When you see large numbers in daily life, ask:

• "What digit is in the hundred-thousands place?"
• "Round that to the nearest million."
• "Is that more or less than a million?"

Build Numbers from Clues

"I'm thinking of a number with:

• 5 in the millions place
• 0 in the hundred-thousands place
• 3 in the ten-thousands place
• 2 in the thousands place
• The rest are zeros"

What's the number? (5,032,000)

Comparison Challenges

"Which is greater: 4,567,890 or 4,576,890?"
Work through the comparison process together.

Estimation Practice

"About how many people live in our city?"
"About how far is it to grandma's house in feet?"

Building estimation skills with large numbers develops practical number sense.

The Bottom Line

Place value to millions isn't about memorizing positions—it's about understanding that our number system is built on a beautiful, consistent pattern. Each place is 10 times the one to its right, whether we're talking about ones and tens or hundred-thousands and millions.

When your fourth grader sees 2,456,789 and instinctively knows that the 4 represents four hundred thousand, they have a mental framework that will serve them through algebra, science, and beyond.

The pattern is the power. Help them see it, and large numbers lose their intimidation.