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Teacher Guide: Ones, Tens, and Hundreds

Learn how digits in different positions represent different values in our number system.

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Printable worksheet

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 ones, tens, and hundreds places in a three-digit number
  • Determine the value of each digit in a number
  • Write numbers in expanded form
  • Understand that zero can be a placeholder
Prerequisites
  • • Counting to 100
  • • Recognizing digits 0-9
  • • Basic addition
Discussion Starters
  • 1. Why do you think we use place value instead of having a different symbol for every number?
  • 2. What would happen if we forgot to use zero as a placeholder?
  • 3. Can you think of places in real life where you see three-digit numbers?
  • 4. If the 5 in 352 moved to the hundreds place, how would the number change?
Common Misconceptions

All digits have the same value regardless of position

Remediation: Use physical base-10 blocks. Show that one flat (100) is physically larger than one rod (10) which is larger than one cube (1).

Zero means nothing, so it can be removed

Remediation: Compare 503 and 53 using money. Show that removing the zero changes five 100-dollar bills to five 10-dollar bills - a huge difference!

Differentiation Ideas

For Struggling Students:

  • • Use physical base-10 blocks for every problem
  • • Start with two-digit numbers only
  • • Color-code place value positions (red for hundreds, blue for tens, green for ones)

For On-Level Students:

  • • Practice converting between standard and expanded form
  • • Compare numbers by looking at place values
  • • Use place value to add two-digit numbers mentally

For Advanced Students:

  • • Extend to thousands place
  • • Explore place value with decimals (tenths)
  • • Discover patterns: what happens when you multiply a number by 10?
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

  • 2.NBT.A.3 (CCSS.MATH.CONTENT.2.NBT.A.3)

    Read and write numbers to 1000 using base-ten numerals, number names, and expanded form

Lesson Resources
  • visualPlace Value Chart

    Interactive chart showing digit positions

  • activityBuild-a-Number Game

    Use base-10 blocks to construct 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 tells us how much a digit is worth based on its position in a number.
In our number system, each position has a value 10 times greater than the position to its right:
PositionValueExample in 253
Hundreds1002 hundreds = 2×100=2002 \times 100 = 200
Tens105 tens = 5×10=505 \times 10 = 50
Ones13 ones = 3×1=33 \times 1 = 3
So 253=200+50+3253 = 200 + 50 + 3
This is called expanded form - writing a number as the sum of the values of each digit.

Worked Examples

What is the value of each digit in 472?
1

Identify the ones digit

The rightmost digit is 2 → 2×1=22 \times 1 = 2
2

Identify the tens digit

The middle digit is 7 → 7×10=707 \times 10 = 70
3

Identify the hundreds digit

The leftmost digit is 4 → 4×100=4004 \times 100 = 400
4

Write in expanded form

Add all values together → 472=400+70+2472 = 400 + 70 + 2

Common Mistakes

Confusing the digit with its value (saying the 5 in 350 is worth 5)

Why it's wrong: The position matters! The 5 is in the tens place, so it represents 50, not 5.

Correct: Always multiply the digit by its place value: 5×10=505 \times 10 = 50

Forgetting zero as a placeholder (writing 608 as 68)

Why it's wrong: Zero holds the position. Without the 0, the 6 would move to the tens place.

Correct: 608 means 6 hundreds, 0 tens, 8 ones. The zero keeps 6 in the hundreds place.

Why It Matters

Understanding place value is the foundation of all math!
  • Reading numbers: When you see 847, you know it means "eight hundred forty-seven"
  • Adding and carrying: When adding 58 + 37, you need to know that 5 and 3 are in the tens place
  • Money: A 100 dollar bill is worth ten 10 dollar bills, which is worth one hundred 1 dollar bills
  • Measurement: 1 meter = 10 decimeters = 100 centimeters
Without place value, we would need a different symbol for every number - imagine memorizing millions of symbols!

Real World Applications

Money and Bills

Our money system uses place value! A 100 dollar bill equals ten 10 dollar bills or one hundred 1 dollar bills.

Example:

If you have 3 hundred dollar bills, 2 ten dollar bills, and 7 one dollar bills, you have 327 dollars total.

1Try It Yourself

You have 4 hundred dollar bills, 5 ten dollar bills, and 6 one dollar bills.

How much money do you have in total?

Step 1: Write the mathematical expression

Calculate the total:

Addresses and House Numbers

House numbers are written with place value too. In house number 253, the 2 means 2 hundreds, the 5 means 5 tens and the 3 means 3 ones.

Example:

Houses 253 and 235 use the same three digits, but they are different houses: in 253 the 5 is worth 50, in 235 it is worth only 5.

2Try It Yourself

A house number is 5 hundreds, 0 tens, and 9 ones.

What is the house number?

Step 1: Write the mathematical expression

Find the house number:

Key Takeaways

  • 1Each position in a number has a value: ones (1), tens (10), hundreds (100)
  • 2The value of a digit equals the digit times its place value
  • 3Expanded form shows a number as the sum of each digit's value: 253=200+50+3253 = 200 + 50 + 3
  • 4Zero is a placeholder that keeps other digits in their correct positions

Frequently Asked Questions

Why do we need zero in numbers like 305?

Zero holds the tens place. Without it, 305 would become 35, which is a completely different number! Zero tells us there are no tens, but it keeps the 3 in the hundreds position.

Why is our system called 'base 10'?

Because each place is worth 10 times more than the place to its right. We use 10 digits (0-9), and when we count past 9, we move to the next place. This is probably because humans have 10 fingers!

Glossary

Place value
The value of a digit based on its position in a number
Digit
A single symbol used to write numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Expanded form
A number written as the sum of each digit's value (e.g., 253=200+50+3253 = 200 + 50 + 3)
Placeholder
A zero that holds a position when there are no units of that value

More in This Topic

Introduction to Place Value

Elementary20 min

Expanded Form

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Comparing Whole Numbers

Elementary15 min

Ordering Whole Numbers

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