The Power of One: A Grade 4 Math Adventure

Materials Needed

• Paper and pencil
• Index cards or small slips of paper
• 20–30 small objects for counting, such as coins, buttons, blocks, or cereal pieces
• Dice or a random-number generator
• Optional: graph paper, colored pencils, and a calculator

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.
• Use the identity property of multiplication to solve problems.
• Recognize that 1 is a factor of every whole number.
• Apply the idea of “one” to real-life situations and explain their thinking.

Success Criteria

I can:

• Complete multiplication equations involving 1 correctly.
• Explain, using words, pictures, or objects, why a number multiplied by 1 stays the same.
• Identify 1 as a factor of any whole number.
• Create and solve a real-world problem involving multiplication by 1.

Introduction: The Mystery of One

Hook: Ask, “If you have 7 treasure chests and each chest contains exactly 1 gold coin, how many gold coins do you have?”

Allow the learner to answer, then ask:

• What happens when we multiply a number by 1?
• Why do you think the number stays the same?
• Can you think of something in real life that comes in groups of one?

Tell the learner: “Today we are going to investigate the special power of the number 1. We will discover why multiplying by 1 does not change a number and how this idea helps us solve real-world problems.”

Body

Part 1: I Do — Teacher or Parent Modeling

Activity: Build Groups of One

1. Place 5 objects in a row.
2. Explain that this represents 1 group of 5: 1 × 5 = 5.
3. Now make 5 groups with 1 object in each group.
4. Count the objects: there are still 5 objects.
5. Write: 5 × 1 = 5.

Explain:

Multiplying a number by 1 means having one group of that number, or having that number of groups with one item in each. Either way, the total remains the same.

Introduce the term identity property of multiplication:

Any number multiplied by 1 equals that same number.

Write several examples:

• 1 × 8 = 8
• 8 × 1 = 8
• 1 × 25 = 25
• 63 × 1 = 63

Quick Check: Ask, “Without calculating, what is 1 × 47? How do you know?”

Part 2: We Do — Guided Practice

Activity: One-Card Challenge

1. Write the numbers 2 through 12 on separate index cards.
2. Have the learner draw one card.
3. The learner creates two multiplication equations using the number and 1.
4. The learner reads both equations aloud and explains why they have the same answer as the drawn number.

Example: If the learner draws 9:

• 1 × 9 = 9
• 9 × 1 = 9

Complete these problems together:

1. 1 × 6 = _____
2. 12 × 1 = _____
3. 1 × 34 = _____
4. 75 × 1 = _____
5. 1 × 100 = _____

After each answer, ask the learner to explain the rule rather than simply stating the answer.

Real-World Connection

Discuss examples such as:

• One sticker on each of 8 notebooks: 8 × 1 = 8 stickers.
• One ticket for each of 6 people: 6 × 1 = 6 tickets.
• One plant in each of 10 pots: 10 × 1 = 10 plants.

Invite the learner to create one example from home, a hobby, a sport, or a favorite game.

Part 3: You Do — Independent Practice

Activity: The One-Point Game

1. Roll a die or choose a random number from 1 to 20.
2. Write the number in a multiplication equation with 1.
3. Write or draw a quick explanation of why the answer stays the same.
4. Earn 1 point for a correct equation and 1 bonus point for a clear explanation.
5. Continue for five rounds.

Example: Roll a 7.

Equation: 7 × 1 = 7

Explanation: “There are 7 groups of 1, so there are 7 objects altogether.”

Independent Practice Problems

1. 1 × 15 = _____
2. 28 × 1 = _____
3. 1 × 46 = _____
4. 91 × 1 = _____
5. 1 × 300 = _____

Creative Challenge: Design a One-Rule Problem

Ask the learner to create a short word problem involving multiplication by 1. The problem should include:

• A real-life setting
• A multiplication equation
• The correct answer
• A sentence explaining why multiplying by 1 keeps the number the same

Example: “There are 14 bicycles, and each bicycle has 1 bell. How many bells are there? 14 × 1 = 14 bells.”

Formative Assessment

• Listen for whether the learner can explain the identity property in their own words.
• Ask the learner to solve 1 × 39 without writing it down.
• Show the equation 52 × 1 = 52 and ask, “Is this always true? Why?”
• Ask the learner to represent 6 × 1 with objects or a drawing.

Summative Assessment: The Power of One Exit Challenge

Ask the learner to complete the following independently:

1. Solve: 1 × 83 = _____
2. Solve: 64 × 1 = _____
3. Draw a picture showing 4 × 1.
4. Write one sentence explaining the identity property of multiplication.
5. Create a real-world multiplication-by-1 problem and solve it.

Evaluation Guide

• 4 — Excellent: All equations are correct, the drawing is accurate, and the explanation clearly describes the rule.
• 3 — Proficient: Most answers are correct, with a mostly clear explanation.
• 2 — Developing: Some answers are correct, but the explanation or model needs support.
• 1 — Beginning: The learner needs additional modeling and practice with multiplication by 1.

Differentiation and Adaptations

For Additional Support

• Use physical objects to build groups before writing equations.
• Practice with numbers from 1 to 10 before using larger numbers.
• Provide the sentence frame: “_____ × 1 = _____ because multiplying by 1 means _____.”
• Allow the learner to explain answers verbally instead of writing full explanations.

For an Extra Challenge

• Compare multiplication by 1 with addition of 1. Ask how 8 × 1 differs from 8 + 1.
• Investigate the identity property of addition: What happens when a number is added to 0?
• Find examples of multiplication by 1 in a recipe, sports statistics, shopping list, or game.
• Explain why both 1 × 24 and 24 × 1 equal 24 using the commutative property of multiplication.

Flexible Learning Options

• Hands-on: Use blocks, coins, or toys to build groups of one.
• Visual: Draw arrays and color the groups.
• Auditory: Explain the rule aloud or record a short math explanation.
• Digital: Create a slide, digital drawing, or short quiz about the power of one.
• Movement-based: Place number cards around the room and walk to the answer that matches each multiplication problem.

Conclusion: Tell What You Learned

Ask the learner to complete these statements:

• “When I multiply a number by 1, the answer is _____.”
• “This is called the _____ property of multiplication.”
• “One real-life example is _____.”

Review the key idea:

The identity property of multiplication tells us that any number multiplied by 1 remains the same: n × 1 = n and 1 × n = n.

Optional Follow-Up Activity

During the day, ask the learner to find three examples of “one” in everyday life. They might notice one item in a package, one point in a game, one object in a group, or one unit of measurement. For each example, the learner should write a multiplication equation involving 1.