The Amazing Number 1: The Identity Hero of Math

Materials Needed

• Pencil and paper or a math notebook
• 12 small objects, such as coins, blocks, buttons, or cereal pieces
• Index cards or small slips of paper
• Markers or colored pencils
• Optional: calculator, dice, or digital whiteboard

Learning Objectives

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

• Explain why multiplying a number by 1 leaves the number unchanged.
• Explain why dividing a number by 1 leaves the number unchanged.
• Identify 1 as a factor of every whole number.
• Use the number 1 to solve real-world math problems.
• Describe how 1 is different from 0 in multiplication and division.

Success Criteria

I can:

• Complete multiplication and division equations involving 1.
• Explain my answers using words, pictures, or objects.
• Correctly solve at least 8 out of 10 review problems.
• Give an example of how multiplying by 1 is useful in real life.

Introduction: Meet the Identity Hero

Hook: Imagine a superhero who can enter a number’s world without changing anything about it. If the hero visits 7, it remains 7. If the hero visits 1,000, it remains 1,000. Who is this mysterious hero?

Today, we will investigate the number 1 and discover why it is called the multiplicative identity. “Identity” means that a number keeps its identity or value when it is multiplied by 1.

Tell the learner: “First, we will explore what happens when we multiply and divide by 1. Then we will practice together. Finally, you will create and solve your own number puzzles.”

Body

Part 1: I Do — Teacher or Parent Demonstration

Use objects to demonstrate multiplication by 1.

1. Place 5 objects in one group.
2. Ask: “How many objects are in 1 group of 5?”
3. Write: 1 × 5 = 5.
4. Repeat with 1 group of 3, 8, and 12 objects.

Explain:

Multiplying by 1 means having one group of the number. Therefore:

• 1 × 3 = 3
• 1 × 8 = 8
• 1 × 12 = 12

Now demonstrate the commutative property of multiplication:

• 1 × 7 = 7
• 7 × 1 = 7

Explain that both equations have the same answer because multiplication can be written in either order.

Quick Check

Ask the learner:

• What is 1 × 9?
• What is 6 × 1?
• Why does the answer stay the same?

Part 2: I Do — Division by 1

Use 8 objects to model division.

1. Place all 8 objects into one group.
2. Ask: “How many objects are in the one group?”
3. Write: 8 ÷ 1 = 8.

Explain:

Dividing by 1 means putting the number into one equal group. The one group contains the entire amount.

• 4 ÷ 1 = 4
• 10 ÷ 1 = 10
• 25 ÷ 1 = 25

Important comparison:

• 12 × 1 = 12
• 12 ÷ 1 = 12
• 12 × 0 = 0

Multiplying by 1 keeps a number the same, while multiplying by 0 makes the answer 0.

Part 3: We Do — Number 1 Investigation

Work together to complete the table. The learner should look for a pattern and explain it.

Think-Pair-Share or Talk-It-Out

Ask the learner to think quietly, explain the answer aloud, and then write a response:

Why is 1 called the “identity” number for multiplication?

A strong response might be: “One is called the identity number because multiplying any number by 1 keeps the number’s value the same.”

Part 4: We Do — Real-World Math Mission

Read each situation aloud. The learner should write an equation and solve it.

1. You have 6 boxes with 1 sticker in each box. How many stickers do you have? 6 × 1 = 6
2. A recipe needs 24 ounces of flour. You divide the flour into 1 container. How many ounces go into the container? 24 ÷ 1 = 24
3. A runner completes 1 lap that is 400 meters long. How far does the runner travel? 1 × 400 = 400 meters
4. You have 15 pencils and place them into 1 cup. How many pencils are in the cup? 15 ÷ 1 = 15

Feedback prompt: After each problem, ask, “How did the 1 affect the answer?” Encourage the learner to explain rather than only state the answer.

Part 5: You Do — The Number 1 Challenge

Complete the following independently. Show work or explain the strategy.

1. 1 × 14 = ______
2. 19 × 1 = ______
3. 1 × 32 = ______
4. 7 ÷ 1 = ______
5. 48 ÷ 1 = ______
6. 100 × 1 = ______
7. 1,000 ÷ 1 = ______
8. Which is greater: 23 × 1 or 23 × 0?
9. Write a multiplication equation with an answer of 17 that uses 1.
10. Write a division equation with an answer of 36 that uses 1.

Part 6: You Do — Create a Number 1 Puzzle

Choose one of the following creative options:

• Comic strip: Draw the number 1 as a superhero explaining its power.
• Riddle: Write a riddle whose answer is 1.
• Real-life problem: Create a shopping, cooking, sports, or travel problem using multiplication or division by 1.
• Number card game: Make five cards with numbers and five cards with equations involving 1. Mix them up and match each equation to its answer.

The learner should share the creation and explain why the answer is correct.

Formative Assessment

• Listen for accurate explanations during object demonstrations.
• Check whether the learner notices that multiplying or dividing by 1 keeps a number unchanged.
• Ask the learner to explain the difference between multiplying by 1 and multiplying by 0.
• Use thumbs-up, thumbs-down, or written responses for quick checks.

Summative Assessment

Use the following short exit ticket. The learner should answer at least 8 of the 10 questions correctly and explain one answer clearly.

1. 1 × 16 = ______
2. 16 × 1 = ______
3. 1 × 45 = ______
4. 45 ÷ 1 = ______
5. 72 ÷ 1 = ______
6. What is 8 × 0?
7. What is 8 × 1?
8. Explain how 8 × 0 and 8 × 1 are different.
9. Write one real-world example of multiplying by 1.
10. Write one real-world example of dividing by 1.

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Use objects or drawings to represent every equation.
• Begin with numbers from 1 to 10 before using larger numbers.
• Provide sentence starters such as, “When I multiply by 1, the number…”
• Use a completed example beside each new problem.
• Practice orally before requiring written answers.

Extensions for Learners Ready for More Challenge

• Investigate why 1 is not considered a prime number.
• Explore powers of 1, such as 1², 1³, and 1¹⁰.
• Find examples of fractions multiplied by 1, such as ³/₄ × 1.
• Write a two-step word problem that uses both multiplication by 1 and multiplication by 0.
• Research other mathematical identity properties, such as adding 0.

Flexible Learning Formats

• For a hands-on lesson, use objects, movement, and sorting.
• For a digital lesson, use a virtual whiteboard or an online quiz tool.
• For a classroom, have learners work in pairs and compare explanations.
• For homeschool learning, connect the examples to cooking, shopping, sports, or household organization.

Conclusion: Tell What We Learned

Ask the learner to complete these statements:

• Multiplying a number by 1 gives me ______.
• Dividing a number by 1 gives me ______.
• The number 1 is called the multiplicative identity because ______.
• Multiplying by 0 is different because ______.

Final recap: When a number is multiplied by 1, its value stays the same. When a number is divided by 1, its value also stays the same. The number 1 is a mathematical “identity hero” because it does not change the number it works with.

Optional Follow-Up Activity

During the day, look for three real-world examples involving the number 1. Examples might include one item in a package, one lap around a track, one serving of food, or one group of objects. Write an equation for each example and explain how the number 1 affects the answer.