The Amazing Number 1: Math’s Unique Identity

Materials Needed

• Paper and pencil
• Index cards or small pieces of paper
• Coins, buttons, or small objects for counting
• Dice or a digital dice roller
• Optional: calculator, colored pencils, and a number line

Grade Level and Time

Grade: 4

Time: 45–60 minutes

Setting: Homeschool, classroom, or small-group learning

Learning Objectives

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

• Explain at least three special properties of the number 1.
• Use 1 as the multiplicative identity in multiplication equations.
• Identify whether a number is prime or composite and explain why 1 is neither.
• Create and solve a real-world problem involving the number 1.

Success Criteria

I can:

• Explain that multiplying a number by 1 keeps its value the same.
• Explain why 1 has exactly one factor: itself.
• Explain why mathematicians classify 1 as neither prime nor composite.
• Use examples, drawings, or equations to support my thinking.

Introduction: The Number 1 Mystery

Hook: Tell the learner: “Today we are investigating a number that looks small but has some very important jobs in mathematics. It can be a number, a multiplier, a factor, and the starting point for counting. What number could it be?”

Allow the learner to guess. Reveal that the mystery number is 1.

Ask:

• What do you already know about the number 1?
• What happens when you add 1 to a number?
• What happens when you multiply a number by 1?
• Do you think 1 is prime, composite, or something different?

Explain the lesson goal in student-friendly language: “We will discover why 1 is one of the most unusual and useful numbers in mathematics.”

Body

Part 1: I Do — What Makes 1 Special?

1. One as the Counting Unit

Place several objects on the table. Count them one at a time.

Explain: “The number 1 tells us about one single object or one equal unit. Every whole number can be built by combining groups of 1.”

Model:

• 1 + 1 = 2
• 1 + 1 + 1 = 3
• 1 + 1 + 1 + 1 = 4

Connect to real life: A recipe may call for 1 cup of flour, a team may have 1 captain, or a person may need 1 ticket to enter an event.

2. One as the Multiplicative Identity

Write the following examples:

7 × 1 = 7
1 × 12 = 12
35 × 1 = 35

Explain: “When any number is multiplied by 1, the number stays the same. This is called the multiplicative identity property. Identity means that something keeps its identity or original value.”

Use an everyday comparison: “If you have 7 groups of 1 toy, you still have 7 toys. If you have 1 group of 12 books, you still have 12 books.”

3. One as a Factor

Explain that a factor is a number multiplied by another number to make a product.

Model:

• 1 × 8 = 8, so 1 and 8 are factors of 8.
• 1 × 24 = 24, so 1 and 24 are factors of 24.

Point out that every whole number has 1 as a factor.

4. Why 1 Is Neither Prime nor Composite

Review the definitions:

• A prime number has exactly two different factors: 1 and itself.
• A composite number has more than two factors.

The number 1 has only one factor: 1. Therefore, it does not fit either definition. It is neither prime nor composite.

Compare:

• 2 has factors 1 and 2, so 2 is prime.
• 6 has factors 1, 2, 3, and 6, so 6 is composite.
• 1 has only factor 1, so it is neither.

Part 2: We Do — Investigating 1 Together

Activity A: The Always-the-Same Challenge

Roll a die three to five times. Each time, write the number rolled and multiply it by 1.

Number Rolled	Number × 1	What Do You Notice?

Discuss: “What happened every time? Why do you think multiplying by 1 works this way?”

Activity B: Factor Detective

Choose three numbers between 2 and 30. List all the factors of each number. Circle the factor 1 each time it appears.

Example:

12: 1, 2, 3, 4, 6, 12

Ask:

• Did every number have 1 as a factor?
• Which numbers had exactly two factors?
• Which numbers had more than two factors?

Activity C: Think-Pair-Share

Think about this question: Why is 1 not prime?

1. Think silently and write or draw an explanation.
2. Explain your thinking to a partner, family member, or teacher.
3. Share your explanation with the group.

Listen for the key idea: 1 has only one factor, but a prime number must have exactly two different factors.

Part 3: You Do — Choose a Number 1 Mission

Choose one of the following missions.

Mission 1: Create a Math Comic

Create a three-panel comic called “The Adventures of Number 1.” Include:

• One example of multiplying by 1
• One example showing that 1 is a factor
• A statement explaining why 1 is neither prime nor composite

Mission 2: Design a Number 1 Poster

Make a poster that includes:

• Three facts about 1
• At least three equations
• A drawing or real-life example
• The words “multiplicative identity,” “factor,” and “neither prime nor composite”

Mission 3: Write a Real-World Word Problem

Write and solve a word problem involving multiplication by 1.

Example: “A store has 1 box containing 18 pencils. How many pencils are in the box?”

Equation: 1 × 18 = 18

The learner may choose to write, draw, record an audio explanation, or present the problem orally.

Formative Assessment Checks

Ask these questions throughout the lesson:

1. What happens when 46 is multiplied by 1?
2. What is the only factor of 1?
3. Why is 1 not prime?
4. Is 15 prime or composite? How do you know?
5. Can you give a real-life example of one group containing several items?

Summative Assessment: Number 1 Exit Challenge

Complete the following independently:

1. Solve: 27 × 1 = _____
2. List all the factors of 1.
3. Is 1 prime, composite, or neither? Explain your answer.
4. Write one original equation that shows the multiplicative identity property.
5. Describe one way the number 1 is useful in everyday life.

Answer Guide

1. 27
2. 1
3. Neither; it has only one factor, while prime numbers have exactly two different factors.
4. Answers may vary, such as 9 × 1 = 9.
5. Answers may vary.

Feedback and Reflection

Give specific feedback using the following sentence starters:

• “You clearly showed that 1 is a factor when you…”
• “Your explanation of prime and composite numbers was strong because…”
• “One detail you could add is…”

Have the learner complete one of these reflections:

• “The most surprising thing about 1 is…”
• “At first I thought…, but now I know…”
• “One question I still have is…”

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Use objects to model groups of 1 before writing multiplication equations.
• Provide sentence frames such as: “One is not prime because…”
• Work with numbers from 1 to 12 before using larger numbers.
• Allow the learner to explain ideas orally or through drawings.

Extension for Advanced Learners

• Investigate what happens when a number is multiplied by 0 compared with 1.
• Explain why mathematicians call 1 the multiplicative identity.
• Explore how prime factorization changes when 1 is included or excluded.
• Create a puzzle in which another learner must identify whether numbers are prime or composite.

Flexible Learning Options

• Hands-on: Use coins, blocks, or buttons to build groups.
• Digital: Create a digital poster or record a short video explanation.
• Auditory: Explain each property aloud to a family member.
• Written: Complete the investigation table and exit challenge.
• Movement-based: Make number cards and physically sort numbers into prime, composite, and neither.

Conclusion: Tell What We Learned

Ask the learner to complete this recap aloud:

“Today I learned that the number 1 is special because…”

Review the main ideas:

• Multiplying any number by 1 leaves the number unchanged.
• Every whole number has 1 as a factor.
• The number 1 has exactly one factor: itself.
• Because it does not have exactly two factors or more than two factors, 1 is neither prime nor composite.

Final challenge: Find three examples of the number 1 being used at home today, such as 1 cup, 1 minute, 1 item, or 1 group. Explain how 1 is being used in each example.