The Amazing Number 1: Patterns, Multiplication, and Real-Life Math
Materials Needed
- Paper and pencil
- Colored pencils or crayons
- Small objects for counting, such as blocks, coins, or buttons
- Index cards or small pieces of paper
- A ruler
- Optional: calculator or digital whiteboard
Grade Level and Time
Grade: 4
Time: 45–60 minutes
Setting: Homeschool, classroom, or small-group instruction
Learning Objectives
By the end of the lesson, the learner will be able to:
- Explain why multiplying a number by 1 keeps the number the same.
- Identify patterns involving the number 1 in multiplication and division.
- Use the number 1 to solve real-world problems.
- Create and explain a short number pattern or math puzzle.
Success Criteria
I can:
- Accurately solve multiplication problems involving 1.
- Explain the rule: Any number multiplied by 1 equals that same number.
- Use examples, words, pictures, or objects to explain my thinking.
- Create a correct puzzle or pattern using the number 1.
Introduction: The Mystery of Number 1
Hook
Show the learner one block, one coin, or one button. Ask:
“What happens when I have 7 groups of 1 object? What happens when I have 1 group of 7 objects? Are the answers the same?”
Let the learner build both examples with objects:
- 7 groups of 1: 1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
- 1 group of 7: 7 = 7
Explain that today the learner will investigate why the number 1 has a special job in multiplication and division.
Tell the Learner What They Will Learn
Say:
“Today we will discover how the number 1 works in multiplication, look for number patterns, and use those patterns to solve real-life challenges.”
Body: Explore and Practice
Part 1: I Do — Modeling the Rule
Write the following equations:
| Equation | Repeated Addition | Answer |
|---|---|---|
| 1 × 4 | One group of 4 | 4 |
| 4 × 1 | Four groups of 1 | 4 |
| 1 × 9 | One group of 9 | 9 |
| 9 × 1 | Nine groups of 1 | 9 |
Think aloud:
“When I multiply a number by 1, I have only one group of that number, so the amount does not change. When I multiply 1 by a number, I am making that many groups of 1. The total is still the original number.”
Introduce the rule:
Identity Property of Multiplication: Any number multiplied by 1 equals that same number.
Examples:
- 1 × 12 = 12
- 12 × 1 = 12
- 1 × 100 = 100
- 100 × 1 = 100
Quick Check
Ask the learner to answer without writing:
- What is 1 × 8?
- What is 15 × 1?
- What is 1 × 43?
Ask:
“How did you know the answers so quickly?”
Part 2: We Do — Number 1 Investigation
Work together to complete the table. The learner may use objects, drawings, or mental math.
| Number | Number × 1 | 1 × Number | What do you notice? |
|---|---|---|---|
| 3 | 3 × 1 = ___ | 1 × 3 = ___ | |
| 7 | 7 × 1 = ___ | 1 × 7 = ___ | |
| 10 | 10 × 1 = ___ | 1 × 10 = ___ | |
| 25 | 25 × 1 = ___ | 1 × 25 = ___ |
Think-Pair-Share or Think-and-Tell
If working with a partner, have the learner discuss the question. If working independently, have the learner explain the answer aloud or record it.
Question: Why do both 7 × 1 and 1 × 7 equal 7, even though the order of the factors is different?
Look for an explanation involving groups:
- 7 × 1 means 7 groups of 1.
- 1 × 7 means 1 group of 7.
- Both situations contain 7 objects altogether.
Part 3: We Do — Division and the Number 1
Explain that division can also involve the number 1.
Model:
- 8 ÷ 1 = 8 because dividing 8 objects into groups of 1 creates 8 groups.
- 8 ÷ 8 = 1 because 8 can be placed into 1 equal group of 8.
Work through these examples together:
- 14 ÷ 1 = ___
- 1 ÷ 1 = ___
- 20 ÷ 20 = ___
- 36 ÷ 1 = ___
Ask the learner to explain one answer using words or a drawing.
Part 4: You Do — Number 1 Challenge Cards
Write the following problems on index cards or display them one at a time. The learner solves each problem and explains the rule used.
- 1 × 18 = ___
- 32 × 1 = ___
- 1 × 75 = ___
- 49 ÷ 1 = ___
- 9 ÷ 9 = ___
- Which is greater: 27 or 27 × 1?
- Fill in the blank: ___ × 1 = 64
- Fill in the blank: 1 × ___ = 91
For each correct answer, the learner earns one point, sticker, or tally mark. Award an additional point for a clear explanation.
Part 5: Real-World Application — The One-Item Store
Imagine a store where each package contains exactly one item. The learner must calculate how many items are in different numbers of packages.
| Situation | Equation | Answer |
|---|---|---|
| 6 packages with 1 pencil in each | 6 × 1 | ___ pencils |
| 12 bags with 1 apple in each | 12 × 1 | ___ apples |
| 1 box containing 24 crayons | 1 × 24 | ___ crayons |
| 30 stickers divided into groups of 1 | 30 ÷ 1 | ___ groups |
Invite the learner to create a new one-item store problem and solve it.
Part 6: Creative Choice Activity
Choose one activity:
Option A: Make a Number 1 Poster
Create a colorful poster showing at least six equations involving 1. Include the identity property in your own words.
Option B: Design a Math Riddle
Write a riddle such as:
“I am a number. When you multiply me by 1, I stay exactly the same. What number could I be?”
Make the riddle more challenging by using a two-digit or three-digit number.
Option C: Build It with Objects
Use blocks, coins, or buttons to show the difference between 1 × 6 and 6 × 1. Explain why both have the same total.
Option D: Create a Number Pattern
Write a pattern such as:
1 × 5 = 5, 2 × 5 = 10, 3 × 5 = 15, 4 × 5 = 20
Circle the factor that changes and underline the factor that stays the same. Explain what happens when the other factor is 1.
Formative Assessment
- Observe whether the learner models multiplication correctly with objects or drawings.
- Ask the learner to explain why multiplying by 1 does not change a number.
- Listen for accurate use of terms such as factor, product, group, and quotient.
- Use the challenge cards to check accuracy and reasoning.
- Ask the learner to identify and correct one intentionally incorrect equation, such as 1 × 36 = 37.
Summative Assessment: The Number 1 Exit Challenge
Have the learner complete the following independently:
- Solve: 1 × 47 = ___
- Solve: 63 × 1 = ___
- Solve: 81 ÷ 1 = ___
- Explain in one or two sentences why 29 × 1 = 29.
- Create one real-life problem involving multiplication or division by 1, then solve it.
Assessment Rubric
| Skill | Beginning | Developing | Successful |
|---|---|---|---|
| Solves equations involving 1 | Needs substantial help | Solves some correctly | Solves nearly all correctly |
| Explains the rule | Explanation is unclear | Gives a partial explanation | Clearly explains why the number stays the same |
| Applies learning | Needs help creating a problem | Creates a problem with minor errors | Creates and solves a realistic problem correctly |
Differentiation and Adaptations
Support for Learners Who Need More Help
- Use physical objects to represent every multiplication problem.
- Begin with numbers from 1 to 10 before using larger numbers.
- Provide the sentence frame: “___ groups of 1 equals ___.”
- Use a multiplication chart and highlight the row and column for 1.
- Allow the learner to answer orally, by drawing, or by pointing to a choice.
Extension for Advanced Learners
- Compare the identity property of multiplication with the identity property of addition: adding 0 keeps a number the same.
- Investigate why multiplying by 0 has a different result from multiplying by 1.
- Create a puzzle with missing factors, such as ___ × 1 = 3,482.
- Explain why 1 is neither prime nor composite.
- Write a short explanation comparing 1 × 24, 2 × 24, and 0 × 24.
Digital or Group Adaptations
- Use a digital whiteboard for equations and learner explanations.
- Play a quick “true or false” game using statements such as 1 × 56 = 57.
- In a group, assign roles such as solver, checker, explainer, and recorder.
- Use an online spreadsheet to record multiplication patterns.
Conclusion: Tell What Was Learned
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 ______.”
- “One real-life example of using 1 is ______.”
Review the key ideas:
- Multiplying by 1 leaves a number unchanged.
- Dividing by 1 also leaves a number unchanged.
- The number 1 represents one group or one item in each group.
- Math properties help us solve problems quickly and explain why our answers work.
Reflection
Have the learner answer:
“What is one thing you understand better about the number 1 now? What is one question you still have?”
Optional Follow-Up Activity
During the next day, ask the learner to find three examples of “one” in real life, such as one item in a package, one person in a group, or one unit of measurement. For each example, write a matching multiplication or division equation.