The Mystery of Number 1: Multiplication, Factors, and Patterns
Materials Needed
- Paper and pencil
- Small objects for counting, such as buttons, coins, or blocks
- Number cards from 1–20, handwritten or printed
- Optional: calculator, whiteboard, or math app
- Optional challenge materials: graph paper and colored pencils
Learning Objectives
By the end of the lesson, the learner will be able to:
- Explain what happens when a number is multiplied by 1.
- Identify 1 as a factor of every whole number.
- Recognize that 1 is neither prime nor composite.
- Use patterns involving 1 to solve and create real-world math problems.
Success Criteria
I can:
- Explain why 1 × any number = that number.
- Find the factors of a number and include 1.
- Explain why 1 is different from prime and composite numbers.
- Create and solve a multiplication problem involving 1.
Introduction: The Number 1 Mystery
Hook
Show the learner one object, such as one coin. Ask:
“If I have one group of 7 coins, how many coins do I have? What about two groups of 7 coins? What does multiplying by 1 do?”
Invite the learner to make a prediction before explaining the answer. Tell the learner:
“Today we are going to investigate why the number 1 is small but very important in mathematics.”
Today’s Plan
Say:
- “First, I will show you how 1 behaves in multiplication.”
- “Next, we will investigate factors and prime numbers together.”
- “Finally, you will solve a number mystery and create your own challenge.”
Body: Learn and Practice
Part 1: I Do — Multiplying by 1
Use objects to model the following:
- 1 group of 3 objects = 3 objects
- 1 group of 6 objects = 6 objects
- 1 group of 10 objects = 10 objects
Write the matching equations:
- 1 × 3 = 3
- 1 × 6 = 6
- 1 × 10 = 10
Explain:
“Multiplying by 1 does not change a number. The number keeps its identity, so this is called the identity property of multiplication.”
Model the rule:
1 × n = n
Explain that the order can be switched:
- 1 × 8 = 8
- 8 × 1 = 8
Connect to real life:
“If one notebook costs 4 dollars, then the cost of 1 notebook is 1 × 4, or 4 dollars.”
Quick Check
Ask the learner to answer mentally:
- 1 × 9 = ?
- 1 × 25 = ?
- 48 × 1 = ?
Ask: “How did you know the answers so quickly?”
Part 2: We Do — Finding Factors
Explain that a factor is a number that multiplies with another number to make a product.
Model the factors of 12:
- 1 × 12 = 12
- 2 × 6 = 12
- 3 × 4 = 12
Therefore, the factors of 12 are:
1, 2, 3, 4, 6, and 12
Ask the learner:
- “Is 1 a factor of 12?”
- “Why is 12 always a factor of 12?”
- “Can you find another pair of factors?”
Work together to find the factor pairs for 18:
- 1 × 18 = 18
- 2 × 9 = 18
- 3 × 6 = 18
Have the learner list all the factors of 18:
1, 2, 3, 6, 9, and 18
Think-Pair-Share Alternative
If another person is available, have the learner explain the steps to a partner. If working alone, have the learner explain the steps aloud to a stuffed animal, toy, or imaginary student.
Part 3: I Do and We Do — Prime, Composite, and the Special Number 1
Explain:
- A prime number has exactly two factors: 1 and itself.
- A composite number has more than two factors.
- The number 1 has exactly one factor: 1.
Therefore, 1 is neither prime nor composite.
Compare these numbers:
| Number | Factors | Classification |
|---|---|---|
| 1 | 1 | Neither prime nor composite |
| 2 | 1, 2 | Prime |
| 4 | 1, 2, 4 | Composite |
| 7 | 1, 7 | Prime |
| 9 | 1, 3, 9 | Composite |
Part 4: You Do — Number Detective Challenge
Give the learner the following mystery:
“I am a number between 1 and 20. I have exactly two factors. One of my factors is 1, and the other is myself. I am an odd number. What numbers could I be?”
Have the learner show the evidence using factor pairs. Possible answers include:
3, 5, 7, 11, 13, 17, and 19
Next, give this challenge:
“I am a number between 1 and 20. I have more than two factors. One of my factors is 1, and another factor is 2. What numbers could I be?”
Possible answers include:
4, 6, 8, 10, 12, 14, 16, 18, and 20
Part 5: Real-World Application — Design a Mini Shop
Invite the learner to create a small pretend shop. The shop may sell toys, snacks, books, art supplies, or another chosen item.
Instructions:
- Choose one item to sell.
- Choose a price, such as $3, $5, or $8.
- Write a multiplication equation for buying exactly one item.
- Write a second equation for buying more than one item.
- Explain how multiplying by 1 helps find the cost of one item.
Example:
- One notebook costs $4.
- 1 × 4 = 4
- Three notebooks cost 3 × 4 = 12.
Formative Assessment
Check understanding during the lesson by asking the learner to explain:
- What happens when a number is multiplied by 1?
- Why is 1 a factor of every whole number?
- What makes a number prime?
- Why is 1 neither prime nor composite?
Practice Questions
- 1 × 17 = _____
- 29 × 1 = _____
- List all the factors of 10.
- Is 13 prime or composite? Explain.
- Is 15 prime or composite? Explain.
- Why is 1 special when classifying numbers?
Answer Key
- 17
- 29
- 1, 2, 5, and 10
- Prime; its only factors are 1 and 13.
- Composite; its factors are 1, 3, 5, and 15.
- It has only one factor, so it is neither prime nor composite.
Summative Assessment: Create a Number 1 Poster
Have the learner create a one-page “Number 1 Expert” poster. It must include:
- The rule 1 × any number = that number.
- Two examples of multiplying by 1.
- A number and all of its factors.
- An explanation of why 1 is neither prime nor composite.
- One real-world multiplication problem involving 1.
- A drawing, pattern, comic, or symbol showing why 1 is important.
Poster Success Rubric
| Criteria | Successful Work Includes |
|---|---|
| Multiplication rule | Correctly explains that multiplying by 1 leaves a number unchanged. |
| Factors | Lists all factors for one selected number. |
| Number classification | Correctly explains why 1 is neither prime nor composite. |
| Application | Creates and solves a realistic multiplication problem. |
| Communication | Uses clear writing, labeled examples, and an original visual. |
Differentiation and Adaptations
Support for Learners Who Need More Help
- Use physical objects to build groups before writing equations.
- Provide a multiplication chart for reference.
- Start with numbers from 1–10 before using larger numbers.
- Use sentence frames such as: “The factors of ___ are ___ because ___.”
- Complete one example together before asking the learner to work independently.
Extensions for Learners Ready for More Challenge
- Find the factors of numbers from 21–50.
- Explain why multiplying by 1 and adding 1 are different operations.
- Investigate what happens when a number is multiplied by 0.
- Create a number riddle with at least three clues.
- Research why mathematicians changed the way they classified the number 1.
Learning Format Options
- Hands-on: Build groups with blocks, coins, or snacks.
- Digital: Use a calculator or digital whiteboard to test equations.
- Verbal: Explain factor pairs aloud and record the explanation.
- Written: Complete the practice questions and poster.
- Movement-based: Place number cards on the floor and step to numbers that are factors.
Conclusion: Tell What You Learned
Ask the learner to complete these statements:
- “When I multiply a number by 1, _____.”
- “The number 1 is a factor of every whole number because _____.”
- “A prime number has _____ factors.”
- “The number 1 is neither prime nor composite because _____.”
- “One way I might use this math in real life is _____.”
Finish with this recap:
“Today we learned that 1 is the identity number for multiplication: it keeps a number the same. We also learned that 1 is a factor of every whole number, but it is neither prime nor composite because it has only one factor.”
Reflection
Have the learner rate their confidence from 1 to 5 and answer:
- What was easiest?
- What was most surprising?
- What question do you still have about factors or prime numbers?