The Power of One: Exploring the Number 1

Materials Needed

• Paper or a notebook
• Pencil and colored pencils or markers
• 10–20 small objects, such as buttons, coins, blocks, or cereal pieces
• Index cards or small slips of paper
• A ruler
• Optional: calculator, tablet, or computer

Lesson Overview

Suggested age: Grade 4

Suggested time: 45–60 minutes

Big idea: The number 1 may be small, but it has an important role in counting, multiplication, fractions, measurement, patterns, and everyday life.

Learning Objectives

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

1. Explain at least three important jobs the number 1 performs in mathematics.
2. Use the identity property of multiplication: any number multiplied by 1 equals that number.
3. Recognize 1 as a whole and connect it to fractions, decimals, and percentages.
4. Apply the number 1 to solve a real-world problem.
5. Create and explain an original “Power of One” example.

Success Criteria

The learner is successful when they can:

• Correctly solve at least 4 out of 5 practice problems.
• Give a clear example of 1 as a unit, a whole, and a multiplier.
• Explain their thinking using words, numbers, drawings, or objects.
• Complete the final challenge and explain why the answer makes sense.

Introduction: The Mystery of One

Hook: “What Can One Do?”

Place one object on the table. Ask:

• “What can this one object represent?”
• “Can one be a whole?”
• “What happens when we multiply a number by 1?”
• “Can one help us measure something?”

Invite the learner to make predictions. Do not correct every answer immediately. Tell them:

Today we will investigate the number 1 and discover why mathematicians consider it one of the most useful numbers.

Student-Friendly Objectives

Say:

By the end of this lesson, you will be able to explain several jobs that the number 1 does, use it to solve math problems, and create your own real-life example.

Body: Explore and Practice

Talking Point 1: One Means a Single Unit

I Do: Model

Show one object and explain:

One can mean a single item. It can also be a unit used to count or measure. For example, one apple is one item, one meter is one unit of length, and one minute is one unit of time.

Draw a line that is one ruler length. Label it 1 unit. Explain that units help us describe how much, how long, or how many.

We Do: Investigate

Ask the learner to choose three objects or measurements and describe each using one unit.

Example	What is one unit?
A pencil	One pencil
A ruler	One centimeter or one inch
A clock	One minute or one hour

You Do: Unit Hunt

Find five objects or ideas around the home that can be described using “one.” Examples include one book, one cup, one kilogram, one minute, or one dollar.

Quick check: Ask, “Why is a unit useful?” Look for an answer such as, “It gives us a standard way to describe or compare things.”

Talking Point 2: One as a Whole

I Do: Model

Draw a rectangle and shade the entire shape. Label it:

1 whole = 1

Explain that the same whole can be written in different ways:

• 1
• 1/1
• 100%
• 1.0

Explain:

When we have all of something, we have one whole. One whole pizza, one whole dollar, or 100% of a completed project all represent the same amount: everything.

We Do: Fraction Connections

Use the objects or draw shapes. Ask the learner to decide whether each situation represents less than one, exactly one, or more than one.

1. Eight out of eight slices of pizza: 1 whole
2. Three out of four parts of a sandwich: less than 1
3. Five out of five tasks completed: 1 whole
4. Six out of four equal parts: more than 1

You Do: “Show Me One”

Choose one of the following ways to show 1:

• Draw a shape and shade one whole.
• Write three fractions equal to 1.
• Show 1 using objects.
• Show 1 as a decimal and a percentage.

Possible answers: 2/2, 4/4, 10/10, 1.0, and 100%.

Talking Point 3: One in Multiplication

I Do: Model

Arrange objects into groups:

• 3 groups of 1 = 3
• 7 groups of 1 = 7
• 25 groups of 1 = 25

Write the equations:

3 × 1 = 3

7 × 1 = 7

25 × 1 = 25

Explain the identity property of multiplication:

Multiplying any number by 1 leaves the number unchanged.

We Do: Pattern Discovery

Complete the pattern together:

Expression	Answer
4 × 1	4
9 × 1	9
12 × 1	12
100 × 1	100

Ask, “What stayed the same in every problem?”

You Do: Multiplication Challenge

Solve the following:

1. 8 × 1 = _____
2. 15 × 1 = _____
3. 1 × 36 = _____
4. 1 × 207 = _____
5. 1 × 1,000 = _____

Answers: 8, 15, 36, 207, and 1,000.

Talking Point 4: One in Real Life

I Do: Model a Real-World Problem

Read this situation:

Maya practices the piano for 1 hour each day. How many hours does she practice in 7 days?

Model the solution:

7 days × 1 hour per day = 7 hours

Explain that “one” can describe a rate, such as one hour per day, one dollar per item, or one kilometer per minute.

We Do: Solve Together

Work through these problems:

1. A notebook costs $1. How much do 9 notebooks cost?
2. A runner travels 1 kilometer each lap. How far does the runner travel in 6 laps?
3. A recipe needs 1 cup of rice for each batch. How many cups are needed for 4 batches?

Answers: $9, 6 kilometers, and 4 cups.

You Do: Choose Your Own Challenge

Choose one option:

• Home option: Create a budget using items that cost $1 each.
• Movement option: Design a workout using one movement per round.
• Cooking option: Create a recipe in which each serving uses one unit of an ingredient.
• Creative option: Write a short story titled “The Day One Saved the Day.” Include at least five mathematical uses of 1.

Hands-On Game: The Power of One Cards

Write the following numbers on separate cards: 1, 2, 3, 5, 10, 25, and 100. Make another set of cards with the words or symbols:

• one whole
• 100%
• 1 ×
• one unit
• one group
• one dollar

Mix the cards. Match each number or symbol to a situation in which it makes sense. For example:

• 100% matches “one whole.”
• 1 × 25 matches “25.”
• One dollar matches “$1.”

For an extra challenge, create three new cards and explain the matches.

Formative Assessment Checks

• Ask the learner to explain the identity property in their own words.
• Ask, “How can 1 be written as a fraction, decimal, and percentage?”
• Ask the learner to create an equation involving 1 that equals 18.
• Ask, “When might one represent a unit rather than a single object?”

Summative Assessment: The Power of One Poster or Presentation

Create a one-page poster, digital slide, or short presentation called “The Power of One.” It must include:

1. One example of 1 as a unit.
2. One example of 1 as a whole, fraction, decimal, or percentage.
3. One multiplication equation using 1.
4. One real-life problem involving 1, with the solution shown.
5. A short explanation of why the number 1 is important.

Assessment Rubric

Criteria	Excellent	Developing	Needs Practice
Math accuracy	All examples are correct.	Most examples are correct.	Several examples need correction.
Explanation	Clearly explains three or more uses of 1.	Explains one or two uses.	Explanation is incomplete.
Real-world connection	Includes a realistic problem and clear solution.	Includes a problem with some explanation.	Connection is unclear or missing.
Creativity	Uses original examples, drawings, or design.	Includes some original work.	Includes few personal details.

Differentiation and Support

For Learners Who Need More Support

• Use physical objects before moving to written equations.
• Provide sentence starters such as, “One is important because _____.”
• Use smaller numbers first, such as 2 × 1, 3 × 1, and 5 × 1.
• Allow the learner to explain answers orally or with drawings.
• Work through one example at a time and check understanding frequently.

For Learners Ready for Extension

• Investigate why multiplying by 1 is different from multiplying by 0.
• Explore how dividing a number by 1 keeps the number unchanged.
• Find examples of 1 in science, money, measurement, music, or technology.
• Create a multi-step problem involving unit rates and the number 1.
• Explain why 1 is neither prime nor composite.

Conclusion: Recap and Reflection

Ask the learner to complete these statements:

• “One can represent _____.”
• “When I multiply a number by 1, _____.”
• “One whole is the same as _____%, _____ decimal, and a fraction such as _____.”
• “I use the number 1 in real life when _____.”

Review the key ideas:

• 1 can represent a single item or a standard unit.
• 1 can represent one complete whole.
• Multiplying any number by 1 leaves that number unchanged.
• One whole can be written as 1, 1.0, 100%, or a fraction with equal numerator and denominator.
• The number 1 helps us describe real-life rates, measurements, prices, and quantities.

Exit Ticket

Answer this question in writing or aloud:

If the number 1 disappeared from mathematics, what would become difficult or confusing? Give two examples.

Optional Follow-Up Activity

Spend one day recording five ways the number 1 appears in everyday life. Examples might include one serving, one mile, one dollar, 100%, or one hour. At the end of the day, explain which example was the most useful and why.