The Power of One: A Grade 4 Math Adventure

Materials Needed

• Paper or a math notebook
• Pencil, colored pencils, or markers
• Coins or small objects for counting
• Index cards or small slips of paper
• Optional: calculator, spreadsheet, or digital drawing tool

Learning Objectives

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

• Explain how the number 1 changes the value of a number in multiplication and place value.
• Identify patterns involving multiples of 1, 10, and 100.
• Use multiplication and division to solve a real-world problem.
• Create and explain a “Power of One” number puzzle.

Success Criteria

I can:

• Explain why multiplying a number by 1 keeps it the same.
• Explain how placing 1 in different positions changes a number’s value.
• Show my mathematical thinking with numbers, words, pictures, or objects.
• Check whether my answer makes sense.

Introduction: The One-Minute Mystery

Hook: Ask the learner:

“Is 1 a small number, or can it have a huge effect? How could adding or moving just one digit change a number?”

Give the learner one minute to write or say as many ways as possible that the number 1 is used in everyday life. Possible ideas include one dollar, first place, one whole pizza, 1:00 on a clock, one point, or one person making a difference.

Tell the learner:

“Today we will investigate how the number 1 works in multiplication, place value, and real-life problems. Then you will create your own number challenge.”

Body: Learn, Practice, and Apply

Part 1: I Do — Multiplying by One

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

1 × 4 = 4

There is one group of four, so there are four objects altogether. Repeat with two or three other examples:

• 1 × 7 = 7
• 1 × 12 = 12
• 1 × 25 = 25

Explain the rule:

Any number multiplied by 1 stays the same because there is only one group of that number.

Also model the related division fact:

• 7 ÷ 1 = 7
• 12 ÷ 1 = 12
• 25 ÷ 1 = 25

Quick Check: Ask, “What is 1 × 38? How do you know?” Look for an explanation, not just the answer.

Part 2: We Do — The Place-Value Power of 1

Write the number 1 on a card. Ask the learner what the digit is worth when it is in different places:

Discuss how the digit stays the same but its position changes its value. Use coins, blocks, drawings, or place-value charts if helpful.

Think-Pair-Share:

1. Think: Which is greater, 1,000 or 100? By how much?
2. Pair: Explain how the position of the 1 affects its value.
3. Share: Give an example of a number in which the digit 1 is worth 10 or more.

Part 3: We Do — Pattern Detective

Complete the patterns together. Ask the learner to describe the rule in words.

1. 1, 10, 100, 1,000, _____
2. 1, 2, 3, 4, _____, _____
3. 5 × 1 = 5, 5 × 10 = 50, 5 × 100 = _____
4. 9 ÷ 1 = 9, 90 ÷ 1 = _____, 900 ÷ 1 = _____

Discuss the difference between multiplying by 1 and multiplying by 10 or 100. Emphasize that multiplying by 1 keeps a number the same, while multiplying by 10 or 100 changes its place-value position.

Formative Assessment: Ask the learner to explain why 34 × 1 = 34 but 34 × 10 = 340.

Part 4: You Do — One Person, One Plan

Present this real-world challenge:

You are planning a one-day neighborhood clean-up. One volunteer can collect 12 pieces of litter in 30 minutes.

Have the learner answer:

1. How many pieces of litter could one volunteer collect in 30 minutes?
2. How many pieces could 5 volunteers collect if each person works at the same rate?
3. How many pieces could 10 volunteers collect?
4. How many pieces could one volunteer collect in 2 hours?

Encourage the learner to use drawings, repeated addition, multiplication, or a table.

Possible answers:

• One volunteer in 30 minutes: 12 pieces
• Five volunteers: 5 × 12 = 60 pieces
• Ten volunteers: 10 × 12 = 120 pieces
• One volunteer in 2 hours: Four 30-minute periods, so 4 × 12 = 48 pieces

Ask: “Which part of the problem used the idea of one? Which part used groups of 5 or 10?”

Part 5: Creative Choice Activity

Choose one project:

Option A: Create a Number Puzzle

Make a puzzle using the digit 1. For example:

• “I am a four-digit number. The digit 1 is worth 100. What could I be?”
• “What number multiplied by 1 equals 246?”
• “Use 1, 2, 3, and 4 to make the greatest possible number.”

Option B: Design a “Power of One” Poster

Include:

• One multiplication fact involving 1
• One division fact involving 1
• One place-value example
• One real-world example of how one person, object, or action can make a difference

Option C: Build a Mini Math Story

Write a short story involving one person or one object. Include at least three multiplication or division equations and explain how you solved them.

Assessment

Formative Assessment

• Listen to explanations during the object demonstration.
• Check answers during the pattern activity.
• Ask the learner to explain the difference between multiplying by 1 and multiplying by 10.
• Review the learner’s strategy for solving the clean-up challenge.

Summative Assessment: Exit Challenge

Ask the learner to complete the following independently:

1. Complete: 1 × 47 = _____
2. Complete: 47 ÷ 1 = _____
3. In the number 3,105, what is the value of the digit 1?
4. Explain why 62 × 1 is not the same as 62 × 10.
5. Create a real-world problem involving the number 1 and solve it.

Suggested Scoring Guide

• 4 — Excellent: Answers are accurate, explanations are clear, and the real-world problem includes a correct solution.
• 3 — Ready: Most answers are accurate, with a mostly clear explanation.
• 2 — Developing: Some answers are correct, but the learner needs support explaining the rules.
• 1 — Beginning: The learner needs significant practice with multiplication by 1 and place value.

Differentiation and Support

For Learners Needing More Support

• Use objects, drawings, or a place-value chart before using only numerals.
• Practice with smaller numbers first.
• Provide sentence frames such as: “When I multiply by 1, the answer stays the same because _____.”
• Work through one example at a time and allow oral answers.

For Advanced Learners

• Investigate why any number multiplied by 1 remains unchanged.
• Compare the effects of multiplying by 1, 10, 100, and 1,000.
• Create a puzzle with more than one possible answer.
• Explore the role of 1 in fractions, such as why multiplying by 1/1 keeps a fraction equivalent.

Conclusion: Tell What You Learned

Ask the learner to complete these statements:

• “When I multiply a number by 1, _____.”
• “The value of the digit 1 changes when _____.”
• “One way math helps in real life is _____.”
• “The most surprising thing about 1 is _____.”

Recap the key ideas:

• Multiplying or dividing a number by 1 leaves the number unchanged.
• The position of a digit determines its place value.
• Multiplying by 10, 100, or 1,000 changes a number by moving its digits into greater place values.
• Even one person or one action can contribute to a much larger result.

Optional Follow-Up

Have the learner look for examples of the number 1 during the day—on clocks, prices, addresses, scores, books, or signs—and record five examples. For each example, explain what the 1 means and what its value is.