Math Adventure: The Amazing Number 1
Materials Needed
- Pencil and paper or a whiteboard
- Small objects for counting, such as buttons, blocks, coins, or cereal pieces
- Index cards or scraps of paper
- Optional: calculator, spreadsheet, or math app
- Optional challenge materials: measuring tape, ruler, or playing cards
Learning Objectives
By the end of the lesson, the learner will be able to:
- Explain at least three important properties of the number 1.
- Use the identity property of multiplication to solve equations such as 27 × 1 = 27.
- Identify whether 1 is even, odd, prime, or composite, and explain the reasoning.
- Apply the number 1 to fractions, measurement, patterns, and real-world situations.
- Create and explain a short “Number 1” math challenge.
Success Criteria
Success looks like this:
- I can explain why multiplying a number by 1 does not change the number.
- I can explain why 1 is odd and why it is neither prime nor composite.
- I can recognize 1 whole in fractions and measurements.
- I can solve and explain problems involving the number 1.
Lesson Overview
Recommended time: 45–60 minutes
Setting: Homeschool, one-on-one tutoring, small group, or classroom
Introduction: The Number 1 Mystery
Hook: Ask, “What makes the number 1 special? Is it just the smallest counting number, or does it have secret powers in mathematics?”
Give the learner a minute to write or say as many facts about 1 as possible. Encourage unusual ideas, such as:
- There is one Sun in our solar system.
- A whole pizza can be written as 1 or 1/1.
- One is the multiplicative identity.
- One is odd but is not prime.
Tell the learner: “Today we will investigate the number 1 and discover why this small number is important in arithmetic, fractions, patterns, and everyday life.”
Body
Part 1: I Do — Discovering the Properties of 1
Model each idea clearly. Use objects, drawings, or written equations as you explain.
1. One Means a Single Unit
Place one object on the table and say, “This is one object.” Add another object and ask, “How many objects are there now?” Continue briefly to show that 1 is the starting point for counting groups of objects.
2. Multiplying by 1
Show one group of 5 objects:
1 × 5 = 5
Explain that multiplying by 1 means having one group of the number. Therefore:
- 1 × 8 = 8
- 14 × 1 = 14
- 103 × 1 = 103
This is called the identity property of multiplication. The word “identity” means that the number keeps its identity or original value.
3. One and Addition
Explain that adding 1 means finding the next counting number:
- 6 + 1 = 7
- 25 + 1 = 26
Subtracting 1 means finding the number immediately before it:
- 9 − 1 = 8
- 40 − 1 = 39
4. Is 1 Prime, Composite, or Neither?
Review the terms:
- A prime number has exactly two factors: 1 and itself.
- A composite number has more than two factors.
The number 1 has only one factor: 1. It does not have exactly two factors and does not have more than two factors. Therefore, 1 is neither prime nor composite.
5. Is 1 Even or Odd?
Explain that an even number can be split into pairs with none left over. One object cannot make a complete pair, so 1 is odd.
Quick Check
Ask the learner to answer verbally or on paper:
- What is 37 × 1?
- Is 1 even or odd?
- Is 1 prime, composite, or neither?
- What number comes immediately after 99?
Expected answers: 37, odd, neither, and 100.
Part 2: We Do — The Number 1 Investigation
Work through the following activities together. Ask the learner to explain the reasoning rather than only state the answer.
Investigation A: Multiplication Machine
Write the following equations on cards or read them aloud:
- 7 × 1 = ___
- 1 × 32 = ___
- 86 × 1 = ___
- 1 × 405 = ___
- 1 × 1,000 = ___
After solving, ask: “What pattern do you notice?” Guide the learner to explain that multiplying any number by 1 leaves the number unchanged.
Investigation B: Fraction Detective
Discuss the following examples:
- 1/1 means one whole divided into one equal part, so it equals 1 whole.
- 2/2, 3/3, and 10/10 also equal 1 whole.
- 4/5 is less than 1 because four out of five equal parts are being used.
- 6/5 is greater than 1 because there are more than five fifths.
Ask the learner to sort these fractions into groups: equal to 1, less than 1, or greater than 1:
3/3, 2/7, 8/8, 9/4, 5/6, 12/12
Investigation C: One-Unit Measurement
Choose a unit of measurement, such as one inch, one foot, one centimeter, or one cup. Find examples of objects or quantities that could be described using 1 unit.
Possible examples:
- One cup of water
- One meter of string
- One inch of pencil length
- One kilogram of rice
Discuss how changing the unit changes the way a measurement is described, even though the amount may stay the same.
Part 3: You Do — Number 1 Challenge Quest
Invite the learner to complete the challenges independently. The learner may write answers, explain them aloud, or use objects to model them.
Challenge 1: Solve and Explain
- 1 × 24 = ___
- 58 × 1 = ___
- 1,000 − 1 = ___
- 349 + 1 = ___
- Is 1 prime? Explain why or why not.
Challenge 2: Fraction Decisions
Label each fraction as less than 1, equal to 1, or greater than 1:
- 7/7
- 3/8
- 11/10
- 5/5
- 2/3
Challenge 3: Create a Real-World Problem
Create a short story problem using the number 1. Choose one of these settings:
- Shopping
- Cooking
- Sports
- Animals
- Travel
- Building or crafting
Example: “A recipe needs 1 cup of flour for each batch. How many cups are needed for one batch?”
The learner should write the problem, solve it, and explain how the number 1 is used.
Choice Activity: Select One
- Number 1 Poster: Create a mini-poster showing five facts about 1.
- Number 1 Comic: Draw a comic in which the number 1 uses its “multiplication identity power.”
- Number 1 Scavenger Hunt: Find ten examples of 1 in the home, such as one clock, one cup, or 1/1 on a measuring tool.
- Number Pattern Challenge: Create a pattern that uses adding 1, subtracting 1, or multiplying by 1.
Formative Assessment and Feedback
During the lesson, check understanding by asking:
- “How do you know that 1 is odd?”
- “Why does multiplying by 1 leave a number unchanged?”
- “How can you tell whether a fraction is equal to 1?”
- “What is the difference between prime and composite numbers?”
Give specific feedback using statements such as:
- “You correctly used the identity property because the original number stayed the same.”
- “Your explanation shows that you understand why 1 is neither prime nor composite.”
- “Check the numerator and denominator. When they are equal, the fraction represents one whole.”
Summative Assessment: Explain the Amazing Number 1
Ask the learner to complete the following independently:
- Explain in their own words what happens when a number is multiplied by 1.
- Solve: 76 × 1.
- State whether 1 is even or odd and explain why.
- State whether 1 is prime or composite and explain why.
- Write one fraction equal to 1.
- Give one real-world example involving the number 1.
Suggested Scoring Guide
- 6 points: Complete understanding; explanations are accurate and clear.
- 4–5 points: Good understanding; one or two ideas need clarification.
- 2–3 points: Partial understanding; provide additional modeling and practice.
- 0–1 point: Review the concepts using objects, drawings, and simpler examples.
Differentiation and Adaptations
Support for Learners Who Need More Practice
- Use physical objects to model one group, one pair, and one whole.
- Begin with smaller numbers before using numbers greater than 100.
- Use sentence starters: “One is odd because…” and “Multiplying by one means…”
- Allow the learner to explain answers orally instead of writing every response.
- Represent fractions with paper strips, measuring cups, or drawn shapes.
Extensions for Advanced Learners
- Investigate why any nonzero number raised to the power of 0 equals 1.
- Explore why 1 is called the multiplicative identity while 0 is called the additive identity.
- Research the role of 1 in binary computer code.
- Write a proof explaining why 1 is neither prime nor composite.
- Create a puzzle involving multiplication, fractions, and the number 1.
Conclusion and Recap
Ask the learner to complete these statements:
- “Multiplying a number by 1…”
- “The number 1 is odd because…”
- “The number 1 is neither prime nor composite because…”
- “A fraction equal to 1 could be…”
- “One real-life use of 1 is…”
Finish with this recap:
The number 1 is more than the first counting number. It represents one unit, multiplying by 1 keeps a number unchanged, it is odd, it is neither prime nor composite, and it represents one whole in fractions and measurements.
Optional Follow-Up
For the next few days, invite the learner to record one example of the number 1 from everyday life and explain its mathematical meaning. Examples might include a single object, one whole, a measurement of one unit, or a calculation involving multiplication by 1.