The Power of One: A Number-One Math Adventure
Materials Needed
- Paper or a notebook
- Pencil and colored pencils
- 10–20 small objects, such as buttons, coins, blocks, or cereal pieces
- Index cards or scraps of paper
- A ruler
- Optional: calculator, tablet, or computer
Grade Level
Grade 4 homeschool
Time
45–60 minutes, with activities that can be shortened or extended
Learning Objectives
By the end of the lesson, the learner will be able to:
- Explain why the number 1 is the identity number for multiplication.
- Use multiplication facts involving 1 to solve real-world problems.
- Recognize patterns in multiples of 1 and other numbers.
- Create and explain a real-life “one” math situation.
Success Criteria
I can:
- Explain why any number multiplied by 1 stays the same.
- Solve at least 4 out of 5 multiplication problems correctly.
- Show my thinking with objects, drawings, numbers, or words.
- Invent a practical example using multiplication by 1.
Introduction: The Mystery of One
Hook
Place 5 objects in front of the learner. Ask:
“If I have one group of 5 objects, how many objects do I have? What happens if I have one group of 27 objects?”
Invite the learner to make predictions using the objects. Then explain:
Today we will investigate why multiplying by 1 does not change a number and how this idea helps us solve everyday problems.
Quick Conversation
Ask the learner:
- Where do you see the number 1 in everyday life?
- What does “one group of” mean?
- Is having one of something always the same as having only one object?
Body: Explore, Model, and Practice
Part 1: I Do — Modeling the Idea
Use objects to demonstrate:
- 1 group of 3 = 3, so 1 × 3 = 3
- 1 group of 8 = 8, so 1 × 8 = 8
- 1 group of 25 = 25, so 1 × 25 = 25
Explain in student-friendly language:
When we multiply a number by 1, we have one group of that number. The amount does not change.
Write the rule:
1 × any number = that number
Show that multiplication works in either order:
- 1 × 6 = 6
- 6 × 1 = 6
Explain that both expressions equal 6, although they can describe groups in different ways.
Formative Check
Ask the learner to answer without a calculator:
- 1 × 9 = ?
- 1 × 42 = ?
- 17 × 1 = ?
Ask: “How did you know the answer so quickly?”
Part 2: We Do — One-Group Investigation
Work together to complete the table. The learner may use objects, drawings, or mental math.
| Expression | Meaning | Answer |
|---|---|---|
| 1 × 4 | One group of 4 | _____ |
| 1 × 12 | One group of 12 | _____ |
| 1 × 36 | One group of 36 | _____ |
| 19 × 1 | _____ | _____ |
Think-Pair-Share Alternative
If another person is available, the learner explains one answer to a partner. In a homeschool setting, the partner may be a parent, sibling, stuffed animal, or imaginary “math reporter.”
Discuss:
- What pattern do you notice?
- Does the answer ever become larger when multiplying by 1?
- How is multiplying by 1 different from adding 1?
Part 3: You Do — Real-Life Math Missions
Have the learner solve each problem and explain the meaning of the multiplication sentence.
- You have 1 backpack with 7 books inside. How many books are there? Write a multiplication sentence.
- A recipe needs 1 package containing 24 crackers. How many crackers are in the package?
- You walk 1 lap around a track that is 400 meters long. How far do you walk?
- A store sells 1 box with 18 crayons. How many crayons are in the box?
- You earn $1 for each of 15 completed chores. How much money do you earn?
Challenge: Write a matching multiplication sentence for each answer. For example, 1 × 24 = 24.
Hands-On Activity: Build a “One” Display
Ask the learner to choose one of the following creative options:
- Object model: Use objects to show “one group of” a number.
- Drawing: Draw one group containing a chosen number of items.
- Comic strip: Create a short story in which a character uses multiplication by 1.
- Mini-poster: Write the rule, draw an example, and add a real-life use.
- Digital version: Create one slide or a short recording explaining the rule.
The project must include:
- One multiplication sentence
- A picture, object model, or diagram
- A sentence explaining why the answer stays the same
Movement Break: Human Multiplication
Call out a number, such as 6, 10, or 15. The learner acts out “one group of that number” by making one group of objects, clapping that many times, or taking that many steps.
After each example, the learner says:
“One group of _____ is _____, so 1 × _____ = _____.”
Assessment
Formative Assessment Throughout the Lesson
- Observe whether the learner can model one group using objects.
- Ask the learner to explain why 1 × 18 equals 18.
- Listen for accurate use of the words factor, product, and group.
- Check answers during the table and real-life missions.
Summative Exit Challenge
Ask the learner to complete the following independently:
- Find the answer: 1 × 73 = _____.
- Find the answer: 28 × 1 = _____.
- Draw a picture showing 1 × 9.
- Write a real-life problem that can be solved with 1 × 16.
- Explain in one or two sentences why multiplying by 1 leaves a number unchanged.
Suggested Rubric
| Skill | Achieved | Developing |
|---|---|---|
| Solves multiplication-by-1 facts | Correctly solves 4–5 problems | Needs reminders or support |
| Explains the rule | Clearly explains “one group of” | Gives a partial explanation |
| Applies the skill | Creates an accurate real-life example | Needs help connecting the example to multiplication |
| Shows thinking | Uses numbers, words, objects, or drawings effectively | Shows limited or unclear work |
Differentiation and Adaptations
Support for Learners Who Need More Help
- Use small groups of objects and physically build each example.
- Provide the sentence frame: “One group of _____ is _____.”
- Begin with numbers from 1–10 before using larger numbers.
- Allow oral answers, drawings, or manipulatives instead of written explanations.
Extension for Advanced Learners
- Compare multiplication by 1 with multiplication by 0, 2, and 10.
- Investigate why 1 is called the multiplicative identity.
- Write a word problem that could be represented by both 1 × 24 and 24 × 1.
- Find examples of the number 1 in fractions, measurement, money, or science.
Conclusion: Tell What We Learned
Ask the learner to complete these statements:
- “Today I learned that multiplying by 1…”
- “One real-life example is…”
- “A strategy that helped me was…”
Review the key idea:
Multiplying by 1 means having one group of a number. Because there is only one group, the total stays the same. Therefore, 1 × any number and any number × 1 equal that number.
Optional Follow-Up
During the day, invite the learner to find three examples of “one group of” something—such as one bag of groceries, one page of a book, or one cup of water—and write a multiplication sentence for each example.