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Expand Your Numbers!

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Lesson Plan

Expand Your Numbers!

Students will be able to write numbers up to the hundred thousands in expanded form by identifying the value of each digit.

Understanding expanded form strengthens students' grasp of place value, which is fundamental for understanding larger numbers, performing multi-digit arithmetic, and building a strong foundation for future math concepts.

Audience

3rd Grade Students

Time

30 minutes

Approach

Hands-on practice and interactive discussion.

Materials

Smartboard or Projector, Slide Deck: Expand Your Numbers!, Worksheet: Expanded Form Fun, and Answer Key: Expanded Form Fun

Prep

Teacher Preparation

10 minutes

Step 1

Warm-Up: Place Value Ponderings

5 minutes

  • Display a number like 4,287 on the board.
    - Ask students: "What is the value of the '2' in this number? What about the '4'?"
    - Briefly review place values (ones, tens, hundreds, thousands).

Step 2

Introduction to Expanded Form

10 minutes

  • Use the Slide Deck: Expand Your Numbers! to introduce expanded form.
    - Explain that expanded form is a way to break down a number to show the value of each digit.
    - Go through examples together, starting with smaller numbers (hundreds, thousands) and progressing to ten thousands and hundred thousands.
    - Emphasize the use of addition signs to combine the values.
    - Key phrases to use: "What is the value of this digit?", "How many hundreds are there?", "Let's add the value of each part together."

Step 3

Guided Practice: Worksheet Time!

10 minutes

  • Distribute the Worksheet: Expanded Form Fun.
    - Work through the first few problems together as a class, using the slides for guidance if needed.
    - Circulate around the room to provide individual support and answer questions.
    - Encourage students to explain their thinking to a partner if they finish early.

Step 4

Wrap-Up: Quick Check

5 minutes

  • Ask students to share one thing they learned about expanded form.
    - Present one final number (e.g., 70,500) and ask students to write it in expanded form on a scratch piece of paper or mini-whiteboard.
    - Collect the Worksheet: Expanded Form Fun to assess understanding.
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Slide Deck

Expand Your Numbers!

Understanding Place Value to the Hundred Thousands!

Welcome students and introduce the exciting journey of breaking down big numbers!

What is Expanded Form?

Expanded form is a way to show the value of each digit in a number.

Example:

245 = 200 + 40 + 5

What is the value of the 2? 200
What is the value of the 4? 40
What is the value of the 5? 5

Explain that expanded form shows the value of each digit. Start with a simple example.

Let's Go Bigger!

How would we expand a number like 1,368?

1,368 = 1,000 + 300 + 60 + 8

  • 1 in the thousands place is 1,000
  • 3 in the hundreds place is 300
  • 6 in the tens place is 60
  • 8 in the ones place is 8

Move to a thousands example, emphasizing the role of zeroes for place value holders.

Even Bigger: Ten Thousands!

What about 27,419?

27,419 = 20,000 + 7,000 + 400 + 10 + 9

  • 2 in the ten thousands place is 20,000
  • 7 in the thousands place is 7,000
  • 4 in the hundreds place is 400
  • 1 in the tens place is 10
  • 9 in the ones place is 9

Introduce a ten thousands example. Reinforce the pattern of place values.

The Biggest Yet: Hundred Thousands!

Let's try 350,206!

350,206 = 300,000 + 50,000 + 0 + 200 + 0 + 6

  • 3 in the hundred thousands place is 300,000
  • 5 in the ten thousands place is 50,000
  • 0 in the thousands place is 0 (we don't need to write it!)
  • 2 in the hundreds place is 200
  • 0 in the tens place is 0 (we don't need to write it!)
  • 6 in the ones place is 6

So, 350,206 = 300,000 + 50,000 + 200 + 6

Challenge students with a hundred thousands example. Discuss numbers with zeros in certain place values.

Time to Practice!

Now it's your turn to expand some numbers!

Complete the Worksheet: Expanded Form Fun.

Remember to show the value of each digit!

Transition to the worksheet for independent practice. Encourage students to apply what they've learned.

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Worksheet

Expanded Form Fun!

Instructions: Write each number in expanded form.

  1. 452



  2. 1,739



  3. 9,081



  4. 15,207



  5. 63,450



  6. 200,814



  7. 571,030



  8. 805,002



Challenge Question!

  1. What is the number if its expanded form is 70,000 + 5,000 + 900 + 20 + 1?



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Answer Key

Expanded Form Fun Answer Key

Instructions: Write each number in expanded form.

  1. 452

    • Thought Process: The 4 is in the hundreds place (400), the 5 in the tens place (50), and the 2 in the ones place (2).
    • Answer: 400 + 50 + 2

  2. 1,739

    • Thought Process: The 1 is in the thousands place (1,000), 7 in the hundreds (700), 3 in the tens (30), 9 in the ones (9).
    • Answer: 1,000 + 700 + 30 + 9

  3. 9,081

    • Thought Process: The 9 is in the thousands place (9,000), 0 in the hundreds (0), 8 in the tens (80), 1 in the ones (1).
    • Answer: 9,000 + 80 + 1

  4. 15,207

    • Thought Process: The 1 is in the ten thousands place (10,000), 5 in the thousands (5,000), 2 in the hundreds (200), 0 in the tens (0), 7 in the ones (7).
    • Answer: 10,000 + 5,000 + 200 + 7

  5. 63,450

    • Thought Process: The 6 is in the ten thousands place (60,000), 3 in the thousands (3,000), 4 in the hundreds (400), 5 in the tens (50), 0 in the ones (0).
    • Answer: 60,000 + 3,000 + 400 + 50

  6. 200,814

    • Thought Process: The 2 is in the hundred thousands place (200,000), 0 in the ten thousands (0), 0 in the thousands (0), 8 in the hundreds (800), 1 in the tens (10), 4 in the ones (4).
    • Answer: 200,000 + 800 + 10 + 4

  7. 571,030

    • Thought Process: The 5 is in the hundred thousands place (500,000), 7 in the ten thousands (70,000), 1 in the thousands (1,000), 0 in the hundreds (0), 3 in the tens (30), 0 in the ones (0).
    • Answer: 500,000 + 70,000 + 1,000 + 30

  8. 805,002

    • Thought Process: The 8 is in the hundred thousands place (800,000), 0 in the ten thousands (0), 5 in the thousands (5,000), 0 in the hundreds (0), 0 in the tens (0), 2 in the ones (2).
    • Answer: 800,000 + 5,000 + 2

Challenge Question!

  1. What is the number if its expanded form is 70,000 + 5,000 + 900 + 20 + 1?
    • Thought Process: Combine the values of each digit according to their place value.
    • Answer: 75,921
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Expand Your Numbers! • Lenny Learning