The Amazing Number 1: Math’s Identity Hero

Materials Needed

• Pencil and paper or a whiteboard
• Small objects for counting, such as buttons, blocks, or coins
• Index cards or slips of paper
• Optional: dice, playing cards, and a calculator

Learning Objectives

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

• Explain that multiplying a number by 1 keeps the number unchanged.
• Explain that dividing a number by 1 keeps the number unchanged.
• Use the number 1 to solve real-world multiplication and division problems.
• Identify patterns involving 1 and explain why those patterns work.

Success Criteria

I can:

• Solve multiplication and division equations involving 1 with at least 80% accuracy.
• Explain in my own words why 7 × 1 = 7 and 7 ÷ 1 = 7.
• Create and solve a real-life problem involving multiplying or dividing by 1.

Introduction: The Mystery of the Unchanging Number

Hook: Imagine you have one magic box. Whenever you put a number into the box, the number comes back exactly the same. What number could be inside the box?

Write or display these equations:

• 5 × 1 = 5
• 12 × 1 = 12
• 36 ÷ 1 = 36

Ask:

• What pattern do you notice?
• What happens to a number when we multiply it by 1?
• What happens when we divide it by 1?

Tell the learner: “Today we will discover why 1 is called the multiplicative identity. Identity means that something stays the same. The number 1 has a special job in multiplication and division because it does not change the other number.”

Body

Part 1: I Do — Modeling the Idea

Multiplying by 1

Use small objects to model multiplication. Place 4 objects in one group.

Explain:

1 × 4 means “one group of four.” There are 4 objects altogether.

Now model:

• 1 × 3 = 3
• 1 × 8 = 8
• 1 × 15 = 15

Show that switching the factors gives the same result:

• 4 × 1 = 4
• 3 × 1 = 3
• 8 × 1 = 8

Explain that multiplying by 1 means there is only one group, so the amount does not change.

Dividing by 1

Place 12 objects in a group. Explain that 12 ÷ 1 means “split 12 objects into 1 equal group.” Since there is only one group, all 12 objects stay together.

Model:

• 6 ÷ 1 = 6
• 10 ÷ 1 = 10
• 24 ÷ 1 = 24

State the rule:

Any number multiplied by 1 or divided by 1 stays the same.

Quick Check

Ask the learner to answer without using a calculator:

1. 9 × 1 = ?
2. 1 × 14 = ?
3. 25 ÷ 1 = ?
4. 1 × 100 = ?

Ask the learner to explain one answer using words or objects. Listen for an explanation that mentions one group or one equal group.

Part 2: We Do — Pattern Detective

Write the following equations on index cards or read them aloud:

• 7 × 1 = 7
• 1 × 19 = 19
• 32 ÷ 1 = 32
• 45 × 1 = 45
• 18 ÷ 1 = 18
• 1 × 63 = 63

Work together to sort the cards into two groups:

• Multiplying by 1
• Dividing by 1

For each card, the learner should:

1. Read the equation aloud.
2. Identify whether it shows multiplication or division.
3. Explain why the answer stays the same.

Think-Pair-Share Alternative

If learning with a partner, each person solves one equation silently. Share the answer and explanation with the partner. If working independently, the learner can explain the answer aloud to a parent, stuffed animal, or imaginary class.

Part 3: We Do — Real-Life Math Situations

Read each situation and solve it together.

1. You buy one notebook with 24 pages. How many pages do you have?

   Equation: 1 × 24 = 24

2. You have 15 strawberries and place them in one bowl. How many strawberries are in the bowl?

   Equation: 15 ÷ 1 = 15

3. A game awards 1 point for each of 32 stars collected. If you collect 1 group of 32 stars, how many stars do you have?

   Equation: 1 × 32 = 32

After each problem, ask: “What does the 1 represent in this situation?”

Part 4: You Do — The Number 1 Challenge

Complete the following independently. Show work with drawings, objects, equations, or written explanations.

Challenge A: Solve

1. 1 × 11 = _____
2. 23 × 1 = _____
3. 1 × 48 = _____
4. 17 ÷ 1 = _____
5. 90 ÷ 1 = _____
6. 1,000 × 1 = _____

Challenge B: Find the Mistake

A student says:

42 × 1 = 43

Is the student correct? Explain the mistake and write the correct answer.

Challenge C: Create Your Own Problem

Create one real-life story problem that uses either multiplication by 1 or division by 1. Include:

• A short story
• A number sentence
• The answer
• An explanation of why the answer stays the same

Optional Game: Roll, Multiply, and Explain

1. Roll a die twice or choose two number cards.
2. Choose one number to multiply by 1.
3. Write the equation and solve it.
4. Explain what happened to the number.

Example: If the number is 6, write 6 × 1 = 6.

For an extra challenge, use larger numbers or write a division equation with the same number.

Assessment

Formative Assessment

• Listen to the learner’s explanation during the object demonstration.
• Check answers during the Pattern Detective activity.
• Ask the learner to explain the difference between “one group of a number” and “a number divided into one group.”
• Use thumbs up, thumbs down, or written responses for quick equations.

Summative Assessment: The 1-Minute Math Mission

Ask the learner to complete the following without help:

1. 36 × 1 = _____
2. 1 × 72 = _____
3. 84 ÷ 1 = _____
4. Explain why 29 × 1 = 29.
5. Write one real-world example of dividing by 1.

Suggested mastery: The learner correctly solves at least 4 of 5 tasks and gives a clear explanation for at least one equation.

Differentiation and Support

For Learners Who Need Extra Support

• Use physical objects to show one group or one equal group.
• Begin with numbers from 1 to 10 before using larger numbers.
• Provide sentence frames such as: “When I multiply by 1, the number stays the same because _____.”
• Allow the learner to draw groups instead of writing every equation.
• Practice multiplication and division separately before mixing them.

For Learners Ready for an Extension

• Explain why 1 is called the multiplicative identity.
• Compare the rules for adding 1, multiplying by 1, and dividing by 1.
• Investigate what happens when a number is multiplied by 0.
• Create a mini-poster titled “The Rules of 1” with examples and explanations.
• Write a puzzle in which a missing number must be found: _____ × 1 = 56.

Conclusion: Tell What You Learned

Ask the learner to complete these statements:

• When I multiply a number by 1, _____.
• When I divide a number by 1, _____.
• The number 1 is special because _____.

Review the main ideas:

• Multiplying by 1 does not change a number.
• Dividing by 1 does not change a number.
• The number 1 is called the multiplicative identity.
• Math rules can help us solve real-life problems quickly and accurately.

Reflection

Have the learner answer one or more questions:

• What was surprising about the number 1?
• Which activity helped you understand the idea best?
• Where might you use multiplication or division by 1 in real life?

Optional Follow-Up Activity

Invite the learner to find three examples of the number 1 during the day—for example, one book, one snack package, or one group of objects. For each example, write a multiplication or division equation involving 1.