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Teacher Guide: Introduction to Place Value

Learn what place value means and how each digit in a number has a specific value based on its position.

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All practice problems on paper, with a separate answer key.

Worksheet Answer key

Class quiz

10 questions on Place Value. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Identify the place value of any digit in a whole number up to the thousands
  • Determine the value of a digit based on its position
  • Write numbers in expanded form and standard form
  • Compare multi-digit numbers using place value
Prerequisites
  • • Counting from 1 to 100
  • • Recognition of the digits 0-9
  • • Basic understanding of 'greater than' and 'less than'
Discussion Starters
  • 1. The places are called ones, tens, hundreds and thousands. What do these names tell you about each place?
  • 2. If you had to explain place value to a younger student, how would you do it?
  • 3. How would numbers work if each place was only 5 times the one before it instead of 10?
  • 4. Where else in life do you see place value being used?
Common Misconceptions

The biggest digit means the biggest number

Remediation: Compare 9,000 and 8,999. Even though 8,999 has three 9s, 9,000 is bigger because of the thousands place.

Adding a zero at the end doesn't change the number

Remediation: Show that 35 and 350 are different: 35 is 3 tens + 5 ones, but 350 is 3 hundreds + 5 tens + 0 ones.

Differentiation Ideas

For Struggling Students:

  • • Use physical base-10 blocks (cubes for ones, rods for tens, flats for hundreds)
  • • Focus only on two-digit numbers before moving to three digits
  • • Color-code each place value position

For On-Level Students:

  • • Work with four-digit numbers
  • • Practice converting between expanded and standard form
  • • Compare pairs of numbers and explain which is greater

For Advanced Students:

  • • Extend to millions and beyond
  • • Explore decimal place values (tenths, hundredths)
  • • Investigate number systems with different bases (binary, base-5)
Standards Alignment
  • 2.NBT.A.1 (CCSS.MATH.CONTENT.2.NBT.A.1)

    Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones

  • 4.NBT.A.2 (CCSS.MATH.CONTENT.4.NBT.A.2)

    Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form

Lesson Resources
  • visualInteractive Place Value Chart

    Students explore how digits change value based on position

  • activityBuild the Number

    Use base-10 blocks to represent different numbers

  • worksheetExpanded Form Practice

    Convert between standard and expanded form

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Place value is the value of each digit in a number based on its position.
In our number system, each place is 10 times the value of the place to its right:
ThousandsHundredsTensOnes
1,000100101
For example, in the number 3,5273{,}527:
  • The 3 is in the thousands place, so it represents 3,0003{,}000
  • The 5 is in the hundreds place, so it represents 500500
  • The 2 is in the tens place, so it represents 2020
  • The 7 is in the ones place, so it represents 77
3,527=3,000+500+20+73{,}527 = 3{,}000 + 500 + 20 + 7

Worked Examples

What is the value of the digit 6 in the number 2,6432{,}643?
1

Find the position of 6

Reading right to left: 3 is in ones, 4 is in tens, 6 is in hundreds → 6 is in the hundreds place
2

Calculate the value

6×1006 \times 100 → 600600
3

Verify

2,643=2,000+600+40+32{,}643 = 2{,}000 + 600 + 40 + 3 → The 6 represents 600

Common Mistakes

Confusing the digit with its value (saying 5 instead of 500)

Why it's wrong: Students forget that position matters. The digit 5 in 1,523 is worth 500, not 5.

Correct: Always ask: What place is this digit in? Then multiply: digit × place value = value

Reading digits from left to right when identifying places

Why it's wrong: Place values are named from the right (ones, tens, hundreds...). Reading from the left can cause confusion.

Correct: Start from the rightmost digit (ones place) and work left: ones → tens → hundreds → thousands

Forgetting zeros in expanded form

Why it's wrong: In a number like 4,507, the 0 in the tens place is a placeholder and represents 0 × 10 = 0.

Correct: Zeros matter! 4,507 = 4,000 + 500 + 0 + 7 (though we often write 4,000 + 500 + 7)

Why It Matters

Place value is the foundation of our entire number system! Understanding it helps you:
  • Read large numbers: Know what 4,5824{,}582 means versus 5,4825{,}482
  • Add and subtract: Line up digits correctly when calculating
  • Understand money: A 10 dollar bill is worth ten 1 dollar bills
  • Measure things: 100 centimeters equals 1 meter
Without place value, we would need a different symbol for every single number. Imagine having to memorize thousands of symbols!

Real World Applications

Money and Place Value

Our money system uses place value. Bills of 1, 10 and 100 dollars match the ones, tens and hundreds places: ten of one bill make one of the next.

Example:

If you have 3 hundred-dollar bills, 4 ten-dollar bills, and 7 one-dollar bills, you have 347 dollars.

1Try It Yourself

A toy costs 285 dollars. You have 2 hundred-dollar bills, 7 ten-dollar bills, and 15 one-dollar bills.

How much money do you have in total, and is it enough for the toy?

Step 1: Write the mathematical expression

Calculate your total: 2×100+7×10+15×12 \times 100 + 7 \times 10 + 15 \times 1

Odometers in Cars

Car odometers show distance traveled using place value. Each digit represents a different unit.

Example:

If an odometer shows 12,345 km, the car has traveled 12 thousand kilometers, plus 345 more.

2Try It Yourself

A car's odometer shows 8,067 km. The owner wants to know when it will reach 9,000 km.

How many more kilometers until 9,000?

Step 1: Write the mathematical expression

Calculate: 9,000−8,0679{,}000 - 8{,}067

Key Takeaways

  • 1Place value tells us the value of each digit based on its position in a number
  • 2Each place is 10 times the value of the place to its right (ones → tens → hundreds → thousands)
  • 3The same digit can have different values: 5 in 523 is worth 500, but 5 in 352 is worth 50
  • 4Expanded form shows a number as the sum of each digit times its place value

Frequently Asked Questions

Why do we use place value instead of different symbols for each number?

Using place value with just 10 digits (0-9) lets us write any number, no matter how large! Without place value, we would need infinite symbols.

What comes after the thousands place?

After thousands comes ten thousands, then hundred thousands, then millions. Each place is still 10 times greater than the one before it.

Why is zero important in place value?

Zero acts as a placeholder. In 305, the zero shows there are no tens. Without it, we would write 35, which is a different number!

Glossary

Place value
The value of a digit based on its position in a number
Digit
The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 used to write numbers
Expanded form
Writing a number as the sum of each digit times its place value (e.g., 352=300+50+2352 = 300 + 50 + 2)
Standard form
The normal way of writing a number (e.g., 352352)

More in This Topic

Ones, Tens, and Hundreds

Elementary15 min

Expanded Form

Elementary15 min

Comparing Whole Numbers

Elementary15 min

Ordering Whole Numbers

Elementary20 min