The Amazing Number 1: Math Patterns, Factors, and Fractions

Materials Needed

• Pencil and paper or a notebook
• Small objects for counting, such as coins, buttons, or blocks
• Index cards or slips of paper
• Optional: calculator, colored pencils, and a number line

Learning Objectives

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

• Explain why 1 is the multiplicative identity.
• Identify the factors of whole numbers and explain why 1 is a factor of every whole number.
• Describe how 1 relates to fractions, decimals, and percentages.
• Use patterns involving 1 to solve real-world math problems.

Success Criteria

The learner is successful when they can:

• Correctly solve multiplication problems involving 1.
• List the factors of at least four numbers.
• Show that equivalent forms of 1 include 1/1, 2/2, 100%, and 1.0.
• Explain their thinking using words, numbers, drawings, or objects.

Introduction: The Mystery of One

Hook

Ask:

“If you multiply any number by 1, what happens? Why do you think that happens?”

Invite the learner to test a few examples:

• 5 × 1 = ?
• 12 × 1 = ?
• 100 × 1 = ?

Explain that today’s lesson is about how the number 1 appears in multiplication, factors, fractions, decimals, percentages, and everyday life.

Learning Preview

Tell the learner:

“First, I will show you how 1 works in math. Then we will investigate its patterns together. Finally, you will create and solve your own Number 1 challenge.”

Body

Part 1: I Do — The Special Job of 1

Use small objects to demonstrate multiplication. Place one group of five objects on the table:

1 group of 5 = 5

Write:

1 × 5 = 5

Explain that multiplying by 1 means keeping the same amount. The number 1 is called the multiplicative identity because it keeps a number’s identity unchanged.

Model several examples:

• 1 × 8 = 8
• 23 × 1 = 23
• 1 × 64 = 64

Contrast this with multiplying by zero:

• 8 × 1 = 8
• 8 × 0 = 0

Explain:

“Multiplying by 1 keeps the number the same. Multiplying by 0 makes the result zero.”

Quick Check

Ask the learner to explain why each answer is correct:

• 37 × 1 = 37
• 1 × 205 = 205
• 91 × 0 = 0

Part 2: We Do — One as a Factor

Explain that a factor is a number that multiplies with another number to make a product.

Model:

3 × 4 = 12

The factors of 12 include 3 and 4. Since:

1 × 12 = 12

1 and 12 are also factors of 12.

Factor Detective Activity

Write these numbers on index cards:

6, 10, 15, 18, and 24

Work together to find factor pairs for each number. Use objects or arrays if helpful.

Number	Factor Pairs
6	1 × 6, 2 × 3
10	1 × 10, 2 × 5
15	1 × 15, 3 × 5
18	1 × 18, 2 × 9, 3 × 6
24	1 × 24, 2 × 12, 3 × 8, 4 × 6

Ask:

• What factor appears in every list?
• Why is 1 a factor of every whole number?
• Which number has the most factor pairs?

Think-Pair-Share Option

If another person is available, have the learner explain the factor rule to them. If working independently, have the learner record a short explanation or explain it aloud to a stuffed animal, family member, or imaginary student.

Part 3: We Do — One as a Whole

Draw a rectangle and divide it into four equal parts. Shade all four parts.

Discuss:

4/4 = 1 whole

Show other equivalent forms of one:

• 1/1 = 1
• 2/2 = 1
• 4/4 = 1
• 10/10 = 1
• 1.0 = 1
• 100% = 1 whole

Connect the idea to real life:

• One whole pizza can be written as 8/8 of a pizza.
• A full glass can represent 100% of the glass.
• One dollar can be written as 100 cents.
• One meter can be written as 100 centimeters.

Hands-On Challenge: Build One Whole

Ask the learner to use paper strips, blocks, or drawings to show at least three different ways to make one whole. Examples include:

• Two halves
• Four fourths
• Ten tenths
• One whole object

For each model, have the learner write the matching fraction.

Part 4: You Do — The Number 1 Challenge

Have the learner complete the following independently. They may use drawings, objects, or a number line.

1. Complete: 48 × 1 = ____.
2. Complete: 1 × 326 = ____.
3. List all the factor pairs of 20.
4. Write three fractions equal to 1.
5. Write 1 as a decimal and as a percentage.
6. Explain in your own words why 1 is called the multiplicative identity.

Creative Choice Activity

Choose one:

• Number 1 Comic: Create a short comic in which 1 helps another number solve a math problem.
• Math Advertisement: Make an advertisement explaining why 1 is useful in multiplication, fractions, or percentages.
• Real-Life Investigation: Find five examples of “one whole” at home, such as one full cup, one dollar, or one complete book. Write how each could be represented mathematically.
• Number 1 Riddle: Write three clues that help someone guess a math idea involving 1.

Formative Assessment

Pause throughout the lesson and ask:

• What happens when a number is multiplied by 1?
• Why is 1 a factor of every whole number?
• How can a fraction equal 1?
• How are 1, 1.0, and 100% related?

Look for the learner to explain ideas rather than only give answers. Offer feedback using specific language, such as:

• “Your factor pair is correct because the two numbers multiply to make the target number.”
• “Your fraction represents one whole because the numerator and denominator are equal.”
• “You explained the identity property clearly by showing that the number stays unchanged.”

Summative Assessment: Teach It Back

Ask the learner to give a two- to three-minute explanation titled “Why One Is Important in Math.” The explanation should include:

• One multiplication example involving 1
• One example showing 1 as a factor
• One fraction equal to 1
• One decimal or percentage equal to 1
• A real-world example of one whole

Evaluation Checklist

• 4 — Excellent: Gives accurate examples, explains the ideas clearly, and connects them to real life.
• 3 — Proficient: Gives mostly accurate examples and explains the main ideas.
• 2 — Developing: Understands some examples but needs help explaining the connections.
• 1 — Beginning: Needs significant support to identify how 1 works in math.

Differentiation and Adaptations

For Additional Support

• Use physical objects to model multiplication and fractions.
• Begin with smaller numbers such as 2, 3, 4, and 5.
• Provide sentence starters:
  • “Multiplying by 1 means…”
  • “One is a factor of every number because…”
  • “This fraction equals 1 because…”
• Allow the learner to answer verbally instead of writing every response.

For an Extra Challenge

• Investigate why multiplying by a fraction less than 1 makes a number smaller.
• Find all the factors of 36, 48, or 60.
• Explain why dividing a number by 1 leaves the number unchanged.
• Create a puzzle in which every answer is 1.
• Explore the pattern in powers of 1: 1¹, 1², 1³, and 1¹⁰.

Learning Format Options

• Hands-on: Use blocks, coins, paper strips, or household items.
• Digital: Use a virtual whiteboard, spreadsheet, or drawing app.
• Verbal: Discuss and explain each concept aloud.
• Written: Complete the challenges in a math journal.

Conclusion and Recap

Ask the learner to complete these statements:

• “When I multiply a number by 1, the number…”
• “One is a factor of every whole number because…”
• “A fraction can equal 1 when…”
• “One whole can also be written as…”

Review the key ideas:

• Multiplying by 1 leaves a number unchanged.
• 1 is a factor of every whole number.
• Fractions with equal numerators and denominators equal 1.
• 1 whole can be represented as 1.0 or 100%.
• Mathematical ideas about 1 appear in money, measurement, food, time, and everyday decisions.

Exit Ticket

Answer this final question:

“If you could teach one fact about the number 1 to someone else, what would you teach, and how would you prove it?”