The Amazing Number 1: The Number That Changes Everything

Materials Needed

• Pencil and paper or a notebook
• Small household objects for counting, such as coins, blocks, buttons, or cereal pieces
• Index cards or small slips of paper
• Optional: calculator, tablet, or computer
• Optional: measuring cup, ruler, or kitchen scale

Lesson Overview

Recommended level: Grade 4

Time: Approximately 40 minutes

Topic: The role of 1 in whole numbers, multiplication, fractions, measurement, and everyday life

Learning Objectives

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

• Explain why 1 is called the multiplicative identity.
• Use the number 1 to compare whole numbers and fractions.
• Identify real-life examples in which “one” represents a complete unit.
• Create and explain a simple real-world problem involving the number 1.

Success Criteria

The learner is successful when they can:

• Correctly explain that multiplying a number by 1 leaves the number unchanged.
• Correctly identify 1 whole, such as 1/1, 2/2, or 4/4.
• Complete at least 4 out of 5 practice questions correctly.
• Give a clear real-life example of how the number 1 is used.

Introduction: The One Mystery Hook — 5 Minutes

Place one object on the table. Ask:

• “What makes this group different from a group of zero objects or a group of ten objects?”
• “Is one small or large? Can it be both?”
• “What would happen if we multiplied 7 by 1?”

Invite the learner to predict the answer before calculating. Explain:

“Today we are investigating the number 1. It may look simple, but it has an important job in mathematics. We will discover how 1 works with multiplication, fractions, measurement, and real-life situations.”

Learning Preview

Tell the learner:

1. First, you will see how 1 behaves in multiplication.
2. Next, you will explore how 1 represents a whole.
3. Then, you will solve practical problems using the number 1.
4. Finally, you will invent your own “number 1” challenge.

Body: Explore and Practice

Part 1 — I Do: The Multiplication Identity — 7 Minutes

Write the following examples:

• 5 × 1 = 5
• 12 × 1 = 12
• 100 × 1 = 100

Think aloud:

“Multiplication can mean equal groups. Five groups of one make five. Twelve groups of one make twelve. When any number is multiplied by 1, the number stays the same. This is called the multiplicative identity property.”

Explain the vocabulary:

• Identity: Something that keeps another number unchanged.
• Multiplicative identity: The number 1, because multiplying by 1 does not change a number.

Demonstrate using objects. Make three groups with four objects in each group, or one group of three objects. Then show that multiplying by one preserves the number:

3 × 1 = 3

Quick Check

Ask the learner to answer without using a calculator:

• 8 × 1 = ?
• 24 × 1 = ?
• 1 × 63 = ?

Ask: “How did you know the answer so quickly?” Listen for the idea that multiplying by 1 keeps the other number unchanged.

Part 2 — We Do: One Whole and Fractions — 8 Minutes

Explain that 1 can represent one complete whole.

Write these examples:

• 1/1 = 1
• 2/2 = 1
• 3/3 = 1
• 4/4 = 1

Explain:

“A fraction represents one whole when the numerator and denominator are equal. For example, 4/4 means four out of four equal parts. All the parts together make one complete whole.”

Use a household object or draw a rectangle. Divide it into four equal sections and shade all four sections. Label the picture 4/4 = 1 whole.

Work together to decide whether each fraction equals one:

• 5/5
• 3/4
• 7/7
• 2/3
• 10/10

Think-Pair-Share Adaptation

For a homeschool setting, the learner can:

1. Think silently about the answer.
2. Explain the answer to a parent, sibling, stuffed animal, or imaginary classmate.
3. Write one sentence explaining why 7/7 equals 1.

Part 3 — We Do: The Number 1 in Real Life — 7 Minutes

Discuss examples of “one” in everyday situations:

• One dollar is a complete dollar unit.
• One meter is a complete measurement unit.
• One hour is a complete hour.
• One kilogram is a complete kilogram.
• One whole pizza is a complete pizza.
• One person can complete a task independently.

Ask the learner to choose one example and explain what makes it a complete unit.

Work through this problem together:

“A recipe needs 1 cup of flour. You add 1 cup. How much flour did you add?”

Answer: 1 cup, or one complete cup.

Then try:

“A ribbon is 1 meter long. You cut it into 4 equal pieces. What fraction of the original ribbon is each piece?”

Answer: Each piece is 1/4 of the original ribbon.

Part 4 — You Do: Number 1 Challenge Stations — 8 Minutes

Complete the following challenges. The learner may write, draw, use objects, or use a calculator after making a prediction.

1. Multiplication Challenge: Complete: 9 × 1 = ___, 1 × 45 = ___, and 72 × 1 = ___.
2. Fraction Challenge: Circle the fractions equal to 1: 6/6, 4/5, 8/8, 1/2.
3. Measurement Challenge: Find one item in the home that could be measured in approximately 1 centimeter, 1 meter, or 1 kilogram. Explain your choice.
4. Object Challenge: Make one group of objects. Write a multiplication equation that represents it.
5. Explain It: Complete the sentence: “Multiplying a number by 1 does not change it because…”

Creative Application — Invent a “One” Problem — 3 Minutes

The learner creates one original problem involving the number 1. They may choose one of these formats:

• A cooking problem involving 1 cup or 1 teaspoon
• A money problem involving $1
• A fraction problem involving one whole
• A multiplication problem involving ×1
• A measurement problem involving 1 meter, liter, or kilogram

Example: “I have 1 whole chocolate bar. I divide it into 3 equal pieces. What fraction is each piece?”

Have the learner solve the problem and explain the reasoning aloud.

Assessment

Formative Assessment

• Listen to the learner’s predictions during the opening hook.
• Check whether the learner explains why a number multiplied by 1 stays the same.
• Ask the learner to justify why fractions such as 5/5 equal 1.
• Review the completed Number 1 Challenge Stations.

Summative Assessment: Exit Ticket

Ask the learner to answer the following independently:

1. What is 36 × 1?
2. Does 9/9 equal 1? Explain why.
3. Give one real-life example of a complete unit.
4. Write one sentence explaining the multiplicative identity property.

Suggested Scoring Guide

• 4 — Excellent: All answers are correct, explanations are clear, and the real-life example is appropriate.
• 3 — Successful: Most answers are correct, with only minor errors or incomplete explanations.
• 2 — Developing: The learner understands some ideas but needs additional practice with fractions or multiplication by 1.
• 1 — Beginning: The learner needs direct support and concrete examples to explain the role of 1.

Differentiation and Adaptations

Support for Learners Who Need More Practice

• Use physical objects to show groups of one.
• Begin with smaller numbers, such as 2 × 1, 3 × 1, and 4 × 1.
• Draw fraction models before writing fraction equations.
• Use the sentence frame: “___ × 1 = ___ because multiplying by 1 keeps the number ___.”
• Complete the problems orally before asking the learner to write them.

Extension for Advanced Learners

• Investigate why dividing a number by 1 also leaves it unchanged.
• Compare the multiplicative identity property with the additive identity property: adding 0.
• Find three different fractions that equal 1 and prove each one with a drawing.
• Create a real-life math puzzle involving multiplication, fractions, and measurement.
• Research how the number 1 is used in computer science, science, or coding.

Conclusion and Recap — 2 Minutes

Ask the learner to complete these statements:

• “When I multiply a number by 1, the answer is…”
• “A fraction equals 1 when…”
• “One real-life example of a complete unit is…”

Review the main ideas:

• One is the multiplicative identity: multiplying by 1 does not change a number.
• Fractions with equal numerators and denominators represent one whole.
• The number 1 is used to describe complete units in money, measurement, cooking, and everyday life.

Final takeaway: “The number 1 may be small, but it has a very important job: it helps numbers stay themselves and helps us describe complete units.”

Optional Follow-Up Activity

Take a “One Hunt” around the home. Find and record five examples of the number 1, such as one book, one cup, one meter, one dollar, or one complete object. For each example, explain what makes it one complete unit.