The Power of One: A Fun Math Investigation

Materials Needed

• Pencil and paper or a notebook
• 12–20 small objects, such as coins, buttons, blocks, or cereal pieces
• Paper or index cards
• Crayons, colored pencils, or markers
• Ruler
• Optional: calculator, tablet, or computer

Learning Objectives

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

• Explain how the number 1 behaves when added to, subtracted from, multiplied by, or divided into another number.
• Identify 1 as the multiplicative identity and explain what that means.
• Use the number 1 to solve real-world problems.
• Create and explain a small “Power of One” project using words, numbers, pictures, or a combination.

Success Criteria

Success looks like:

• I can correctly solve problems involving 1.
• I can explain why multiplying a number by 1 does not change the number.
• I can give at least two real-life examples involving one.
• I can clearly explain my project to another person.

Introduction: The Mystery of One

Hook: Ask: “If you could choose only one superpower, one snack, or one place to visit, what would you choose? Why can one choice still be important?”

Explain that the number 1 may look small, but it has special powers in mathematics. It can act as a starting point, a unit of measurement, and a number that leaves other numbers unchanged when used in multiplication.

Today’s learning goal: “We will investigate the special jobs that the number 1 can do and use what we discover to solve puzzles and design a project.”

Part 1: What Does One Mean?

I Do: Teacher or Parent Modeling

Show one object, such as one block or one coin. Explain that 1 can mean one object, one group, one unit, or one whole.

Use these examples:

• One apple means a single apple.
• One meter means one unit of length.
• One dollar means one unit of money.
• One whole pizza means the entire pizza.

Point out that 1 can describe both a quantity and a measurement.

We Do: Sort and Discuss

Place several objects on a table. Ask the learner to make groups containing exactly one object. Then discuss:

• How many groups of one can you make?
• How many objects are in each group?
• What would happen if each group had two objects instead?

Quick Check: Ask the learner to name three things in the room that could be described using the word “one.”

You Do: One-Object Scavenger Hunt

Find five examples of “one” around the home. Examples might include one door, one lamp, one spoon, one book, or one pet. Record each example in a notebook or draw a picture of it.

Part 2: The Special Rules of One

I Do: Model the Math Rules

Demonstrate each rule with objects and equations.

Introduce the term multiplicative identity. Explain that this is a special number that does not change another number when multiplied by it. The multiplicative identity is 1.

Use a real-world example: If one package contains 6 pencils, then 1 package has 6 pencils. In symbols, 1 × 6 = 6.

We Do: Build the Equations

Use small objects to model the following:

1. Make 4 groups of 1 object. How many objects are there? Write an equation.
2. Make 1 group of 5 objects. How many objects are there? Write an equation.
3. Start with 9 objects and remove 1. How many remain?
4. Start with 6 objects and add 1. How many are there now?

Discuss how 4 × 1 and 1 × 4 both equal 4, even though the groups can be pictured differently.

You Do: One-Step Challenge Cards

Write these problems on separate cards. The learner solves each card and explains the answer aloud.

1. 12 + 1 = ___
2. 15 − 1 = ___
3. 8 × 1 = ___
4. 20 ÷ 1 = ___
5. 1 × 13 = ___
6. 18 ÷ 1 = ___

Formative Assessment: Ask, “Which operation involving 1 changes a number? Which operations leave a number unchanged?” Look for the learner to explain the answer rather than simply state it.

Part 3: Real-World One

Think-Pair-Share or Think-Tell-Write

Think about each situation. The learner may discuss the answer with a parent, sibling, partner, or imaginary audience before writing it down.

1. You have 10 stickers and receive 1 more. How many stickers do you have?
2. A recipe needs 1 cup of milk. How many cups are needed for one batch?
3. There are 7 boxes with 1 toy in each box. How many toys are there?
4. A 24-page book is divided into 1 equal section. How many pages are in the section?
5. You walk 1 kilometer each day for 5 days. How many kilometers do you walk?

Invite the learner to create one original word problem involving the number 1. The learner should draw a picture, write an equation, and explain the solution.

Part 4: Creative Choice Project

Choose one project option:

• One-Page Poster: Create a poster titled “The Power of One.” Include four equations, two real-world examples, and one illustration.
• Mini-Book: Make a four-page book. Each page should explain one way the number 1 is used.
• Math Comic: Create a character called “Captain One” who solves four math problems.
• Household Math Hunt: Photograph or draw five examples of one being used at home. Label each example.
• Short Presentation: Prepare a two-minute explanation of why 1 is special in multiplication.

Project requirements:

• Include at least four correct equations.
• Explain the multiplicative identity in your own words.
• Include at least two real-world examples.
• Use neat labels, drawings, writing, or spoken explanations.

Differentiation and Support

For Learners Who Need More Support

• Use physical objects to model every equation.
• Begin with numbers from 1 to 10.
• Provide sentence starters such as “When I multiply by 1, the number…”
• Allow oral answers, drawings, or pointing instead of requiring all written work.
• Use a number line to show adding and subtracting 1.

For Learners Ready for a Challenge

• Explain why 1 is called an identity number in multiplication.
• Compare the roles of 0 and 1 in addition and multiplication.
• Solve problems involving fractions, such as 1 × 3/4 or 5 ÷ 1.
• Investigate powers of 1, such as 1², 1⁵, and 1¹⁰.
• Create a puzzle that another learner must solve using the number 1.

Conclusion: Tell What You Learned

Ask the learner to complete these statements:

• “One can represent…”
• “When I add 1, I…”
• “When I subtract 1, I…”
• “When I multiply by 1, I…”
• “When I divide by 1, I…”
• “One is important in real life because…”

Review the main ideas:

• Adding 1 increases a number by one.
• Subtracting 1 decreases a number by one.
• Multiplying by 1 keeps a number the same.
• Dividing by 1 keeps a number the same.
• The number 1 is the multiplicative identity.

Summative Assessment

Give the learner this exit challenge:

1. Solve: 14 + 1, 14 − 1, 14 × 1, and 14 ÷ 1.
2. Explain in one or two sentences why 14 × 1 = 14.
3. Create a real-world situation that could be represented by 6 × 1 = 6.
4. Share the completed creative project.

Simple Scoring Guide

Optional Extension

Ask: “Is 1 the only number with a special mathematical job?” Investigate the role of zero, compare it with 1, and create a two-column poster titled “The Powers of Zero and One.”