The Amazing Number 1: Multiplication and Division Patterns

Materials Needed

• Pencil and paper or a whiteboard
• Small objects for counting, such as buttons, blocks, or coins
• Number cards from 1–12, optional
• Dice, optional
• Crayons or colored pencils
• Exit ticket worksheet or a blank sheet of paper

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.
• Solve multiplication and division problems involving 1 with at least 80% accuracy.
• Use examples from everyday life to describe the identity property of 1.

Success Criteria

I can say, show, and use these rules:

• Any number multiplied by 1 equals that same number. For example, 8 × 1 = 8.
• Any number divided by 1 equals that same number. For example, 8 ÷ 1 = 8.
• I can explain my answer with words, objects, pictures, or equations.

Introduction: The One-of-a-Kind Number

Hook: Imagine you are ordering one pizza with 8 slices. How many slices do you have? Now imagine you have 8 pizzas with one slice each. How many slices do you have?

Invite the learner to answer using objects or drawings. Explain that the number 1 is special because it does not change a number when we multiply or divide by it.

Today We Will...

• Discover what happens when numbers meet 1.
• Practice multiplying and dividing by 1.
• Use a real-world challenge to prove our thinking.

Body

Part 1: Explore with Objects

Place 5 objects in front of the learner.

1. Ask: “How many groups of 1 can we make using 5 objects?”
2. Have the learner make five groups, with one object in each group.
3. Write the matching division equation: 5 ÷ 1 = 5.
4. Combine the five groups into one group of five and write: 1 × 5 = 5.

Repeat with 3, 7, and 10 objects. Ask the learner what pattern they notice.

Formative Check

Ask:

• What happens to a number when we multiply it by 1?
• What happens to a number when we divide it by 1?
• Can you give an example using a number of your choice?

Part 2: I Do — Teacher or Parent Modeling

Explain that multiplication can be understood as equal groups.

For example:

4 × 1 means 4 groups of 1.

That gives us 1 + 1 + 1 + 1 = 4, so 4 × 1 = 4.

Then model division:

4 ÷ 1 asks, “How many groups of 1 can be made from 4?” The answer is 4, so 4 ÷ 1 = 4.

Show several examples:

• 9 × 1 = 9
• 12 × 1 = 12
• 6 ÷ 1 = 6
• 11 ÷ 1 = 11

Introduce the term identity property of multiplication. Explain that multiplying by 1 keeps a number’s identity—it stays the same.

Part 3: We Do — Pattern Detective

Work through the following problems together. Encourage the learner to explain the pattern before writing the answer.

1. 2 × 1 = ___
2. 1 × 10 = ___
3. 7 ÷ 1 = ___
4. 15 × 1 = ___
5. 20 ÷ 1 = ___

After each problem, ask the learner to explain the answer using one of these sentence starters:

• “I know the answer is ___ because multiplying by 1...”
• “I know the answer is ___ because dividing by 1...”
• “The number stays the same because...”

Part 4: Fun Activity — One-Item Shop

Set up an imaginary shop. The learner may choose a theme, such as a toy shop, bakery, pet store, or space station.

1. Choose 5–8 products and give each product a price.
2. Write shopping challenges involving multiplication or division by 1.
3. Have the learner solve the challenges and explain each answer.

Examples:

• One robot costs $14. How much do 1 × 14 robots cost? $14
• You have 9 stickers and place them into groups of 1. How many groups are there? 9 groups
• One space helmet weighs 6 pounds. How much do 1 × 6 helmets weigh? 6 pounds

Part 5: You Do — Independent Practice

Have the learner solve the problems independently. The learner may use objects, drawings, or equations.

1. 3 × 1 = ___
2. 1 × 8 = ___
3. 13 ÷ 1 = ___
4. 1 × 16 = ___
5. 19 ÷ 1 = ___
6. 25 × 1 = ___
7. 30 ÷ 1 = ___
8. Explain why 42 × 1 = 42.

Optional Game: Roll, Multiply, and Explain

Use a die or number cards.

1. Choose or roll a number.
2. Multiply it by 1.
3. State the answer and explain why it stays the same.
4. For an extra challenge, divide the number by 1.

For example: “I rolled 6. Six times one is six, and six divided by one is six.”

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Use physical objects to create groups of one.
• Begin with numbers from 1–10 before using larger numbers.
• Provide the sentence frame: “When I multiply or divide by 1, the number stays ___.”
• Allow the learner to draw groups before writing an equation.

Extensions for Learners Ready for a Challenge

• Compare multiplying by 1 with multiplying by 0, 2, or 10.
• Create a short comic explaining why 1 is called the multiplicative identity.
• Write and solve a real-world word problem involving multiplication and division by 1.
• Investigate whether the same identity idea works for addition and subtraction.

Flexible Learning Formats

• Hands-on: Use blocks, coins, or snacks to make groups.
• Visual: Draw arrays and groups of one.
• Verbal: Explain the rules aloud or record an audio explanation.
• Digital: Create a simple slide, digital poster, or recorded presentation.

Assessment

Formative Assessment

• Listen for accurate explanations during object exploration.
• Check answers during the Pattern Detective activity.
• Ask the learner to predict answers before solving.
• Use thumbs-up, thumbs-down, or verbal responses for quick checks.

Summative Assessment: The Number 1 Challenge

Ask the learner to complete the following:

1. Solve: 18 × 1 = ___.
2. Solve: 18 ÷ 1 = ___.
3. Draw a picture showing one of the equations.
4. Explain in two or three sentences why the answer stays the same.
5. Create one original word problem involving multiplying or dividing by 1.

Assessment Guide

• Beginning: Needs help solving problems and explaining the pattern.
• Developing: Solves some problems correctly and gives a partial explanation.
• Proficient: Solves at least 80% correctly and clearly explains the identity property.
• Advanced: Applies the idea to an original word problem and compares it with another operation.

Conclusion and Recap

Ask the learner to complete these statements:

• “When I multiply a number by 1, the answer is...”
• “When I divide a number by 1, the answer is...”
• “The special name for multiplying by 1 is...”
• “One real-life example is...”

Review the key idea: Multiplying or dividing a number by 1 does not change the number. The learner can demonstrate understanding by solving a final problem of choice and explaining the answer using words, objects, or a drawing.

Optional Follow-Up

Invite the learner to make a “Number 1” poster with three examples, one drawing, and a memorable slogan such as: “One keeps numbers the same!”