The Mystery of One: Place Value, Patterns, and Powers of 10

Materials Needed

• Paper and pencil
• Coins, buttons, or small objects for counting
• Index cards or sticky notes
• Optional: calculator, tablet, or computer
• Optional: dice or a deck of cards

Grade Level

Grade 4 homeschool

Lesson Length

45–60 minutes, with flexible sections that may be shortened or extended

Learning Objectives

By the end of the lesson, the learner will be able to:

• Explain how the value of a digit changes according to its place.
• Use powers of 10 to describe relationships between place values.
• Read, write, compare, and expand whole numbers up to 1,000,000.
• Create and solve a real-world number puzzle.

Success Criteria

I can:

• Identify the place and value of each digit in a number.
• Explain why moving a digit one place to the left makes its value 10 times greater.
• Write a number in standard, word, and expanded form.
• Explain my thinking using words, drawings, or equations.

Introduction: The Superpower of One

Hook: Write these numbers on paper: 1, 10, 100, 1,000.

Ask:

• What changes from one number to the next?
• Why does adding a zero make the number 10 times larger?
• Is the digit 1 worth the same amount in every number?

Invite the learner to make a prediction: “What might happen if the 1 moved even farther to the left?”

Tell the learner: “Today we will investigate how the digit 1 can have different values depending on its position. We will use place value to solve puzzles and design a real-world number challenge.”

Vocabulary

• Digit: A symbol used to write numbers, such as 0 through 9.
• Place value: The value a digit has because of its position in a number.
• Standard form: A number written with digits, such as 4,205.
• Expanded form: A number written as the sum of its place values, such as 4,000 + 200 + 5.
• Power of 10: A way to describe repeated groups of 10, such as 10, 100, and 1,000.

Body: I Do

1. Model Place Value

Draw or write this place-value chart:

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
1	0	0	0	0	0	0

Explain:

• In 1, the digit 1 has a value of one.
• In 10, the digit 1 has a value of ten.
• In 100, the digit 1 has a value of one hundred.
• In 1,000, the digit 1 has a value of one thousand.

Demonstrate that each move to the left multiplies the value by 10:

1 × 10 = 10; 10 × 10 = 100; 100 × 10 = 1,000.

2. Demonstrate Expanded Form

Model the number 6,214:

6,000 + 200 + 10 + 4 = 6,214

Point out that a zero still has an important job. For example:

5,006 = 5,000 + 0 + 0 + 6

Quick Check

Ask the learner to answer verbally or on paper:

1. What is the value of the 1 in 1,000?
2. What is the value of the 1 in 10,000?
3. Which is greater: 7,000 or 700?
4. Write 3,408 in expanded form.

Body: We Do

Activity 1: Digit Detective

Write one number at a time. Work together to identify the place and value of the bold digit.

1. 4 in 4,829
2. 6,315
3. 72,104
4. 125,000
5. 908,016

For each number, use the sentence frame:

“The digit ___ is in the ___ place, so its value is ___.”

Activity 2: Build the Number

Use index cards or sticky notes labeled with digits. Give clues, and build the number together.

Example clues:

• I have six digits.
• My digit in the hundred-thousands place is 1.
• My digit in the thousands place is 4.
• My digit in the tens place is 8.
• All other digits are 0.

Answer: 104,080

Invite the learner to create a new set of clues for you to solve.

Formative Assessment: Show Me

Say a number, such as 81,305. Ask the learner to show one of the following:

• A drawing of the place-value chart
• The expanded form
• The number written in words
• An explanation of the value of one selected digit

Body: You Do

Choice Activity: Create a Number Mission

Choose one of the following missions.

Option A: Design a Theme Park

Create ticket prices, visitor numbers, or prize amounts using numbers from 1,000 to 1,000,000. Write at least three numbers in:

• Standard form
• Word form
• Expanded form

Option B: Invent a Space Mission

Plan a space mission using distances, fuel amounts, or star counts. Include at least five numbers and explain the value of the digit 1 in one of them.

Option C: Number Codebreaker

Write four clues that allow someone else to discover a secret number. Include clues about place value, comparison, or expanded form.

Independent Practice

1. Write 42,607 in expanded form.
2. Write 300,019 in words.
3. What is the value of the 1 in 71,245?
4. Compare using >, <, or =: 50,000 ___ 5,000
5. Arrange these numbers from least to greatest: 1,200; 12,000; 102; 10,200.
6. Explain why the 1 in 100 is worth more than the 1 in 10.

Real-World Connection

Discuss where large numbers appear in everyday life:

• Population counts
• Distances between places
• Money and budgets
• Sports attendance
• Views, downloads, or followers
• Measurements in science and space exploration

Ask: “Why would it be important for a scientist, business owner, engineer, or shopper to understand place value accurately?”

Differentiation and Adaptations

Support

• Work with numbers up to 10,000 before moving to larger numbers.
• Use physical objects grouped into ones, tens, hundreds, and thousands.
• Provide a completed place-value chart.
• Allow the learner to explain answers orally instead of writing every response.
• Use color-coding for each place-value column.

Extension

• Explore decimals: compare 1, 10, 100, 0.1, and 0.01.
• Write a number puzzle with multiple possible solutions.
• Investigate how multiplying or dividing by 10 changes a number.
• Create a “million-dollar” budget and explain each amount using place value.

Learning-Format Options

• Hands-on: Build numbers with cards, coins, or objects.
• Digital: Use a spreadsheet or online place-value tool.
• Verbal: Solve puzzles aloud and record explanations.
• Written: Complete the practice problems and create a number mission.

Assessment

Formative Assessment

• Listen for accurate use of place-value vocabulary.
• Check responses during “Digit Detective.”
• Ask the learner to explain how moving a digit changes its value.
• Review the expanded-form examples before independent practice.

Summative Assessment: The One Challenge

Ask the learner to complete the following independently:

Create a six-digit number containing at least one 1.

The learner must:

1. Write the number in standard form.
2. Write it in word form.
3. Write it in expanded form.
4. Identify the place and value of the digit 1.
5. Compare the number with another six-digit number.
6. Explain how the value of the 1 would change if it moved one place to the left or right.

Assessment Rubric

Skill	Achieved	Almost There	Needs Practice
Identifies place and value	Correctly identifies both	Correctly identifies one	Needs additional support
Uses standard, word, and expanded forms	All forms are accurate	One form needs correction	Two or more forms need correction
Compares numbers	Uses the correct symbol and explanation	Uses the correct symbol with limited explanation	Needs help comparing numbers
Explains reasoning	Gives a clear explanation using place-value language	Gives a partly complete explanation	Needs a model or sentence frame

Conclusion: Tell What We Learned

Ask the learner to complete these statements:

• “Today I learned that the value of a digit depends on ___.”
• “When a digit moves one place to the left, its value becomes ___ times greater.”
• “One place where I might use place value in real life is ___.”

Review the main ideas:

• A digit’s position determines its value.
• Each place to the left is 10 times greater than the place to its right.
• Numbers can be written in standard, word, and expanded forms.
• Place value helps people understand real-world quantities accurately.

Optional Follow-Up

During the week, find three large numbers in books, advertisements, websites, receipts, or sports reports. Record each number, identify the value of one digit, and write one number in expanded form.