The Power of One: Exploring the Number 1

Materials Needed

• Pencil and paper or a notebook
• Small objects for counting, such as buttons, blocks, coins, or cereal pieces
• Index cards or sticky notes
• Number cards from 0–10, homemade or digital
• Optional: calculator, tablet, or computer
• Optional: measuring cup, ruler, or kitchen scale

Learning Objectives

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

• Explain why 1 is called the multiplicative identity.
• Use patterns involving 1 in multiplication and division.
• Identify real-world examples in which one unit, one whole, or a single action matters.
• Create and explain a short “Power of One” challenge or example.

Success Criteria

Success looks like this:

• I can explain that multiplying a number by 1 leaves the number unchanged.
• I can solve problems such as 8 × 1 = 8 and 8 ÷ 1 = 8.
• I can give at least two real-world examples involving one.
• I can explain my thinking using words, numbers, pictures, or objects.

Introduction: The One-Object Mystery

Hook: Place one object on a table. Ask:

• “What can one object do?”
• “Can one person make a difference?”
• “What happens when we multiply a group by one?”

Invite the learner to make a prediction:

“If I have 6 blocks and make 1 group of 6 blocks, will I have more, fewer, or the same number of blocks?”

Explain the lesson goal in student-friendly language:

“Today we will investigate why the number 1 is small in size but powerful in mathematics and everyday life.”

Body: Explore, Practice, and Apply

Part 1: I Do — Modeling the Power of 1

Use blocks or other objects to model the following:

1. Make one group of 5 objects. Count the objects: 1 group of 5 = 5.
2. Make one group of 9 objects. Count the objects: 1 group of 9 = 9.
3. Connect the examples to multiplication:
   • 1 × 5 = 5
   • 1 × 9 = 9
   • 1 × 42 = 42

State the rule:

Any number multiplied by 1 remains the same. This is called the multiplicative identity property.

Model division as well:

• 5 ÷ 1 = 5
• 9 ÷ 1 = 9
• 42 ÷ 1 = 42

Explain:

“When we divide something into groups of one, the number of groups equals the original number of objects.”

Quick Check

Ask the learner to answer without using a calculator:

• 7 × 1 = ?
• 1 × 12 = ?
• 15 ÷ 1 = ?
• 100 × 1 = ?

Ask: “How did you know the answers so quickly?”

Part 2: We Do — The Number 1 Detective Game

Write the following equations on index cards or display them digitally:

• 1 × 6 = 6
• 8 × 1 = 8
• 1 × 25 = 25
• 14 ÷ 1 = 14
• 1 × 0 = 0
• 1 × 1 = 1

Work together to complete these steps:

1. Read each equation aloud.
2. Circle the number that stays the same.
3. Explain why the equation is true.
4. Represent one equation with objects, a drawing, or a number line.

Think-Pair-Share Option

If another learner or adult is available, discuss:

“Is 1 more useful in multiplication or division? Explain your answer.”

For independent homeschool learning, the learner may record a spoken answer or write three sentences in a notebook.

Part 3: We Do — Real-World Connections

Discuss how “one” is used in everyday life. Consider these examples:

• Cooking: One cup, one teaspoon, or one whole recipe.
• Time: One minute, one hour, or one day.
• Money: One dollar or one coin.
• Science: One unit of measurement or one complete object.
• Community: One helpful action can begin a larger change.
• Technology: One idea can become an invention, game, or website.

Ask the learner to choose one example and explain:

• What is the “one” unit?
• What happens when more units are added?
• Why is it helpful to begin with one?

Part 4: You Do — Create a “Power of One” Challenge

The learner chooses one of the following projects.

Option A: Math Challenge Cards

Create five challenge cards involving multiplication or division by 1. Include answers on the back.

Example: 1 × 37 = ?

Option B: One-Unit Measurement Hunt

Find five examples of one unit around the home. Record the object, the unit, and its measurement.

Example: One cup of water; one meter of string; one pound of flour.

Option C: One Action, Big Impact

Choose one helpful action to complete, such as organizing one shelf, planting one seed, or writing one thank-you note. Explain how one action could lead to more positive actions.

Option D: Design a One-Themed Poster

Create a poster titled “The Power of One.” Include:

• At least three mathematical equations using 1
• Two real-world examples
• One sentence explaining why 1 is important

Formative Assessment: Stop and Check

Ask the learner to complete the following and explain each answer:

1. 1 × 18 = _____
2. 23 × 1 = _____
3. 36 ÷ 1 = _____
4. 1 × 0 = _____
5. Which property is shown by 47 × 1 = 47?

Expected responses: 18, 23, 36, 0, and the multiplicative identity property.

Conclusion: Tell What We Learned

Review Conversation

Invite the learner to complete these statements:

• “When I multiply a number by 1, the answer is…”
• “When I divide a number by 1, the answer is…”
• “The mathematical name for this rule is…”
• “One is important in real life because…”

Summative Assessment: Teach It Back

Ask the learner to teach the lesson back to an adult, sibling, classmate, or recording device. The explanation must include:

1. One multiplication example involving 1
2. One division example involving 1
3. A visual model, such as blocks, a drawing, or a number line
4. One real-world example of the importance of one

Simple Rubric

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Use physical objects before introducing equations.
• Begin with numbers from 0–10.
• Use the sentence frame: “_____ groups of 1 contain _____.”
• Allow the learner to draw or speak answers instead of writing them.
• Practice one operation at a time.

Extensions for Advanced Learners

• Investigate why multiplying by 0 is different from multiplying by 1.
• Explore powers of 1, such as 1² = 1 and 1¹⁰⁰ = 1.
• Write a word problem involving multiplication by 1 and another involving division by 1.
• Research other mathematical identity properties, such as adding 0.
• Create a short quiz and answer key for another learner.

Optional Follow-Up Activity

For one day, keep a “One Observation Journal.” Record five times you notice the number 1, such as one item, one minute, one dollar, one step, or one complete object. At the end of the day, explain which example was most interesting and why.