The Power of One: A Fourth-Grade Math Adventure

Materials Needed

• Paper and pencil
• Colored pencils or crayons
• Index cards or small slips of paper
• Coins or play money
• Dice
• Measuring cup or ruler
• Optional: calculator, computer, or tablet

Lesson Overview

Grade: 4

Time: 45–60 minutes

Topic: Place value, fractions, decimals, and real-world problem solving

Essential Question: How can the number 1 change meaning depending on where it appears?

Learning Objectives

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

• Explain how the value of 1 changes according to its place in a number.
• Represent 1 as a whole number, fraction, decimal, and percent.
• Compare examples such as 1, 0.1, 0.01, ¹/₁₀, and 1%.
• Use place value and fractions to solve a real-world problem.
• Create and explain a short “Power of One” challenge.

Success Criteria

The learner is successful when they can:

• Correctly identify the value of the digit 1 in at least four numbers.
• Match common equivalent forms of 1, such as 1 = 10/10 = 100%.
• Explain why 0.1 is smaller than 1.
• Solve the final challenge and explain the reasoning clearly.

Introduction: The Mystery of One

Hook

Write these numbers on separate cards:

1, 10, 100, 0.1, 0.01, 1/10, 1%

Ask:

• “What do all of these numbers have in common?”
• “Does the 1 always have the same value?”
• “Which is greatest? Which is least?”

Invite the learner to make a quick prediction. Explain that today they will investigate how the location and form of 1 affect its value.

Student-Friendly Objectives

Say: “Today you will discover the many forms of 1, investigate place value, and use your knowledge to solve a real-life shopping and measurement challenge.”

Body

Part 1: I Do—How Place Changes Value

Write the number 11,111. Point to each digit 1 and discuss its value:

Digit	Place	Value
1	Ten-thousands	10,000
1	Thousands	1,000
1	Hundreds	100
1	Tens	10
1	Ones	1

Explain: “The digit is still 1, but its value changes because of its position. A digit’s place tells us how many groups of ten it represents.”

Next, connect this idea to decimals:

• 1 = one whole
• 0.1 = one tenth
• 0.01 = one hundredth

Use a dollar or measuring cup as a real-world example:

• $1.00 is one whole dollar.
• $0.10 is one tenth of a dollar.
• $0.01 is one hundredth of a dollar.

Quick Check

Ask the learner to explain the value of the bold digit in each number:

1. 1,234
2. 6,100
3. 45.12
4. 0.15

Correct answers: 1,000; 100; one tenth; one tenth.

Part 2: We Do—Matching the Many Forms of One

Create or write the following cards:

• 1 whole
• 10/10
• 100/100
• 1.0
• 100%
• One complete sandwich
• One full cup

Work together to match cards that represent the same amount. Discuss why each match works.

Then complete the table:

Form	Equivalent Representation
1 whole	10/10, 100/100, 1.0, or 100%
1/10	0.1 or 10%
1/100	0.01 or 1%

Think-Pair-Share

If working with a sibling, partner, or group, ask:

“Is 1/10 greater than or less than 1/100? How do you know?”

If working independently, have the learner explain the answer aloud or write a two-sentence explanation.

Part 3: We Do—The One-Dollar Investigation

Give the learner 100 cents, play money, or a drawing of a dollar divided into 100 equal parts.

Ask the learner to show:

• One whole dollar
• One half-dollar
• One tenth of a dollar
• One hundredth of a dollar

Discuss the connections:

• $1.00 = 100 cents = 100%
• $0.50 = 50 cents = 50%
• $0.10 = 10 cents = 10%
• $0.01 = 1 cent = 1%

Formative Assessment

Ask the learner to answer without using a calculator:

1. How many tenths are in one whole?
2. How many hundredths are in one whole?
3. Which is greater: 0.1 or 0.01?
4. What percent is 0.1?

Part 4: You Do—The One-Unit Challenge

Choose one of the following real-world activities.

Option A: Snack Mix

Plan one cup of snack mix using fractions. The recipe must include:

• At least three ingredients
• Fractions that add up to 1 whole cup
• A written explanation of how the fractions make one whole

Example: 1/2 cup cereal + 1/4 cup raisins + 1/4 cup pretzels = 1 whole cup.

Option B: One-Dollar Shopping Trip

Create a shopping list that totals exactly $1.00. Use at least four items or prices. The learner must write the addition equation using decimals.

Example: $0.25 + $0.20 + $0.15 + $0.40 = $1.00.

Option C: One-Minute Data Study

Choose an activity, such as jumping jacks, reading pages, or collecting objects. Predict how many can be completed in one minute. Record the result, then compare the result with the prediction.

The learner should present the result using at least two forms, such as:

• A number and a short sentence
• A fraction and decimal
• A table and a bar graph

Creative Challenge: Invent a “Power of One” Puzzle

Create a puzzle for someone else to solve. It must include:

• At least three numbers containing the digit 1
• One fraction, decimal, or percent
• One comparison using <, >, or =
• An answer key with an explanation

Example: “Which is greater: 1/10 or 1%? Explain how you know.”

Differentiation and Support

Scaffolding for Learners Who Need More Support

• Use coins, measuring cups, fraction strips, or drawn models.
• Limit the initial examples to whole numbers, tenths, and hundredths.
• Provide sentence frames:
  • “The digit 1 is in the ______ place, so its value is ______.”
  • “I know ______ is greater because ______.”
  • “One whole is equal to ______ tenths.”
• Complete the first problem together before assigning independent work.

Extensions for Learners Ready for More Challenge

• Include thousandths, such as 0.001.
• Explain why 1.0 and 1.00 have the same value.
• Design a budget that totals exactly $10.00 using prices with tenths and hundredths.
• Investigate whether 1/3 can be written as a terminating decimal.

Flexible Learning Formats

• Hands-on: Use coins, food portions, measuring tools, or paper models.
• Digital: Use a spreadsheet, digital drawing tool, or calculator to create a table and graph.
• Verbal: Explain each answer aloud and record the explanation.
• Written: Complete the tables and write a short reflection.

Assessment

Formative Assessment

• Observe explanations during the place-value activity.
• Check matching cards for equivalent forms.
• Use the quick-check questions after each section.
• Ask the learner to explain one answer using a model, drawing, or words.

Summative Assessment: Exit Ticket

Ask the learner to complete the following independently:

1. What is the value of the 1 in 7,142?
2. Write one whole as a fraction, decimal, and percent.
3. Which is greater: 0.1 or 0.01? Explain.
4. Write an addition equation that equals 1.00.
5. In one or two sentences, explain how the position of a digit changes its value.

Simple Rubric

Skill	Excellent	Developing	Needs Practice
Place value	Identifies values accurately and explains why.	Identifies most values accurately.	Needs help identifying place values.
Equivalent forms	Correctly connects fractions, decimals, and percents.	Correctly connects some forms.	Needs additional models and examples.
Problem solving	Solves the challenge and clearly explains the reasoning.	Solves the challenge with minor errors.	Needs support choosing operations or explaining steps.
Communication	Uses precise mathematical language.	Explains the main idea.	Needs sentence frames or verbal support.

Conclusion and Reflection

Ask the learner to complete these prompts:

• “One new thing I learned about 1 is…”
• “The most surprising example was…”
• “I can use this skill in real life when…”

Recap together:

• The value of a digit depends on its place.
• One whole can be represented in many equivalent ways.
• One tenth is greater than one hundredth.
• Fractions, decimals, and percents help describe real-world amounts.

Finish by asking: “Where can you find the power of one in your home today?”