Math Detectives: Why Is the Number 1 Special?

Materials Needed

• Paper or a notebook
• Pencil and colored pencils
• Small objects for counting, such as coins, buttons, or blocks
• Number cards labeled 1–20, made from scraps of paper
• Optional: calculator or digital whiteboard

Learning Objectives

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

• Explain why the number 1 is neither prime nor composite.
• Identify factors and multiples of whole numbers.
• Use the number 1 to solve multiplication and division problems.
• Explain how the number 1 appears in real-life situations.

Success Criteria

I can:

• Tell what makes a number prime or composite.
• Explain why 1 is different from other numbers.
• Find the factors of numbers from 1 to 20.
• Use examples to show that multiplying by 1 does not change a number.

Introduction: The Number 1 Mystery

Hook: Imagine that every number is a member of a secret math club. The number 1 wants to join two clubs: the Prime Club and the Composite Club. Should it be allowed into either club?

Show the learner the number cards from 1 to 20. Ask:

• What makes the number 1 different from the other numbers?
• How many objects are in a group of 1?
• What happens when you multiply a number by 1?

Share the lesson goal: “Today we will investigate the number 1, learn about factors and multiples, and discover why 1 has a special role in mathematics.”

Body: Explore and Learn

Part 1: I Do—Modeling Factors

Explain that a factor is a whole number that divides another number evenly. Factors can also be multiplied together to make a number.

Use objects to demonstrate:

• Arrange 6 objects in 1 equal row of 6: 1 × 6 = 6.
• Arrange 6 objects in 2 equal rows of 3: 2 × 3 = 6.

Therefore, the factors of 6 are 1, 2, 3, and 6.

Point out that 1 is a factor of every whole number because any whole number can be written as 1 times that number:

• 1 × 4 = 4
• 1 × 9 = 9
• 1 × 15 = 15

Part 2: I Do—Prime, Composite, and the Special Case of 1

Explain the vocabulary:

• A prime number has exactly two factors: 1 and itself. Examples include 2, 3, 5, and 7.
• A composite number has more than two factors. Examples include 4, 6, 8, and 9.
• The number 1 has exactly one factor: itself.

Therefore, 1 is neither prime nor composite. It does not have two factors, so it is not prime. It does not have more than two factors, so it is not composite.

Quick Check: Ask the learner to explain why 1 cannot be called prime or composite. Listen for the idea that it has only one factor.

Part 3: We Do—Factor Detective Game

Choose a number card from 1 to 20. Work together to find all of its factor pairs.

Use this process:

1. Start with 1 and ask, “Does 1 divide evenly into the number?”
2. Try 2, 3, 4, and so on.
3. Write each multiplication fact that makes the number.
4. List all the factors.
5. Decide whether the number is prime or composite.

Example: For 12:

• 1 × 12 = 12
• 2 × 6 = 12
• 3 × 4 = 12

The factors are 1, 2, 3, 4, 6, and 12. Since 12 has more than two factors, it is composite.

Think-Pair-Share Alternative: If learning with a partner or group, one person chooses a number, one finds factor pairs, and one explains whether the number is prime or composite. For homeschool learning, the learner can explain the answer aloud to a parent, stuffed animal, or recording device.

Part 4: We Do—The Identity Magic Trick

Write several equations and ask the learner to predict the answer:

• 7 × 1 = ?
• 1 × 13 = ?
• 25 ÷ 1 = ?
• 1 ÷ 1 = ?

Discuss the rule:

Multiplying or dividing a number by 1 leaves the number unchanged.

Invite the learner to create three “magic number” equations using 1. For example:

• 42 × 1 = 42
• 18 ÷ 1 = 18
• 1 × 100 = 100

Part 5: You Do—Number 1 Challenge

Complete the following independently. The learner may use objects, drawings, or equations.

1. List the factors of 1.
2. Is 1 prime, composite, or neither? Explain your answer.
3. List all the factors of 10.
4. Is 10 prime or composite? Explain your answer.
5. Complete: 16 × 1 = ____.
6. Complete: 1 × 23 = ____.
7. Complete: 35 ÷ 1 = ____.
8. Write two different multiplication equations that equal 8.
9. Find a number between 1 and 20 that has exactly two factors.
10. Find a number between 1 and 20 that has more than two factors.

Creative Application: Design a Math Detective Badge

Ask the learner to design a badge or mini-poster titled “The Case of the Special Number 1.” It should include:

• One reason 1 is a factor of every whole number
• One example showing that 1 is neither prime nor composite
• One multiplication fact using 1
• One division fact using 1
• A drawing or symbol representing the number 1

Choice: The learner may create the badge on paper, with craft materials, or as a digital slide.

Assessment

Formative Assessment

• Ask the learner to define “factor” in their own words.
• Give the learner the number 9 and ask for its factor pairs.
• Ask, “Why is 1 not prime?”
• Ask the learner to predict the result of 56 × 1 without calculating.

Summative Assessment: Explain the Mystery

Ask the learner to give a short spoken or written explanation answering this question:

Why is the number 1 special when we talk about factors, prime numbers, composite numbers, multiplication, and division?

A successful response should include:

• 1 has exactly one factor: 1.
• 1 is neither prime nor composite.
• 1 is a factor of every whole number.
• Multiplying or dividing by 1 leaves a number unchanged.

Differentiation and Support

For Learners Who Need More Support

• Use physical objects to build equal groups.
• Begin with numbers from 1 to 10 instead of 1 to 20.
• Provide a factor-pair template: ___ × ___ = ___.
• Use the sentence frame: “The number 1 is neither prime nor composite because it has ___ factor.”
• Allow answers to be spoken, drawn, or demonstrated with objects.

For Learners Ready for More Challenge

• Investigate why multiplying by 0 is different from multiplying by 1.
• Find all prime numbers between 1 and 50.
• Explain why 2 is the only even prime number.
• Create a number riddle using factors and multiples.
• Research how the number 1 is used in computer science, measurement, or coding.

Conclusion: Recap and Reflection

Ask the learner to complete these statements:

• “A factor is...”
• “The number 1 is neither prime nor composite because...”
• “When I multiply a number by 1...”
• “One real-life example of 1 is...”

Finish with the key takeaway:

The number 1 is a factor of every whole number, has exactly one factor, is neither prime nor composite, and acts as the identity number in multiplication and division.

Optional Real-World Connection

Invite the learner to find examples of “one” at home, such as one household, one dollar, one liter, one item in a package, or one person completing a task. Have the learner explain how the meaning of 1 changes depending on the situation while still representing a single unit.