The Amazing Number 1: Patterns, Powers, and Real-World Uses

Materials Needed

• Pencil and paper or a notebook
• Small household objects, such as buttons, blocks, coins, or LEGO bricks
• Index cards or scraps of paper
• Crayons, colored pencils, or markers
• A ruler or measuring tape
• Optional: calculator, tablet, or computer

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 1 as an identity number in addition and multiplication.
• Recognize patterns involving groups of one and powers of one.
• Apply the idea of “one” to a real-world design or measurement challenge.
• Explain their thinking using words, drawings, numbers, or objects.

Success Criteria

The learner is successful when they can:

• Correctly solve at least 8 out of 10 practice problems.
• Describe what happens when 1 is added to or multiplied by a number.
• Complete the “One-of-a-Kind Design Challenge.”
• Give one real-world example of why the number 1 is useful.

Introduction: The One-Minute Mystery

Hook: Ask: “Could you live for one day without using the number 1? Think about clocks, addresses, prices, measurements, scores, and instructions.”

1. Give the learner one minute to find or name as many examples of “1” as possible.
2. Record the examples in a notebook or on a sheet of paper.
3. Discuss: “What makes 1 different from other numbers?”

Tell the learner: “Today we will investigate the number 1, discover its special math rules, and use it to create something of our own.”

Body

Part 1: I Do — Exploring One

Use objects to demonstrate the following ideas. Encourage the learner to watch, listen, and predict what will happen next.

1. One means a single unit

Place one object on the table. Explain that this is one unit or one whole object.

Then place several groups of one object together:

• 1 group of 1 = 1
• 2 groups of 1 = 2
• 5 groups of 1 = 5
• 10 groups of 1 = 10

Explain that counting by ones is the foundation of all whole-number counting.

2. Adding 1 means finding the next number

Model these examples:

• 4 + 1 = 5
• 9 + 1 = 10
• 25 + 1 = 26

Say: “When we add 1, we move one step forward on the number line.” Use a ruler or draw a number line to show the movement.

3. Multiplying by 1 keeps a number the same

Build groups with objects:

• 3 groups of 1 object = 3 objects, so 3 × 1 = 3
• 7 groups of 1 object = 7 objects, so 7 × 1 = 7

Explain the rule:

Any number multiplied by 1 stays the same.

4. Powers of 1

Write and read these examples:

• 1¹ = 1
• 1² = 1 × 1 = 1
• 1³ = 1 × 1 × 1 = 1
• 1¹⁰ = 1

Explain that multiplying 1 by itself any number of times always gives 1.

Part 2: We Do — The Number 1 Detective Game

Work together to complete the activity. If learning independently, the adult can read each card aloud or the learner can draw cards one at a time.

Preparation

1. Write the following problems on separate index cards:
2. 4 + 1
3. 12 + 1
4. 9 × 1
5. 35 × 1
6. 1⁴
7. 100 + 1
8. 17 × 1
9. 1⁸

How to Play

1. Choose one card.
2. Solve the problem.
3. Explain the rule used.
4. Earn one point for a correct answer and one bonus point for a clear explanation.

After several turns, ask:

• Which problems were easiest?
• What patterns did you notice?
• How are adding 1 and multiplying by 1 different?

Part 3: You Do — Practice Challenge

Have the learner solve the following independently. They may use objects, a number line, drawings, or mental math.

1. 7 + 1 = _____
2. 18 + 1 = _____
3. 49 + 1 = _____
4. 5 × 1 = _____
5. 21 × 1 = _____
6. 64 × 1 = _____
7. 1³ = _____
8. 1⁷ = _____
9. Explain why 92 × 1 = 92.
10. Write your own problem using the number 1 and solve it.

Feedback opportunity: Review the answers together. For each incorrect answer, ask the learner to show the problem with objects or a drawing before correcting it.

Part 4: Real-World Application — One-of-a-Kind Design Challenge

Choose one of the following challenges:

Option A: Design a One-Unit Building

Use blocks, LEGO bricks, paper, or drawing materials to design a building made from equal groups of one unit. Label the number of units used.

Option B: Create a One-Ingredient Recipe

Invent a pretend recipe that uses one main ingredient. Write how many groups of one ingredient are needed for different numbers of servings.

Option C: Make a Number 1 Poster

Create a poster showing at least five places where the number 1 appears in daily life. Include at least two equations, one drawing, and one written explanation.

Option D: Build a One-Step Number Line

Make a number line from 0 to 20. Show what happens when you add 1 to at least five different numbers.

Required explanation: The learner must explain:

• What they created
• Where the number 1 appears
• One mathematical rule involving 1
• One real-world reason the number 1 is important

Differentiation and Support

For Learners Who Need More Support

• Use physical objects and a number line for every problem.
• Practice only addition by 1 before introducing multiplication by 1.
• Provide sentence starters: “When I add 1, I _____.” and “When I multiply by 1, the number _____.”
• Reduce the independent practice to five carefully chosen problems.
• Allow oral answers, drawings, or demonstrations instead of written explanations.

For Learners Ready for Extension

• Investigate why any number divided by 1 stays the same.
• Compare 1 with 0 and explain how their multiplication rules differ.
• Find examples of the number 1 in fractions, decimals, money, time, and measurement.
• Create a puzzle containing at least five equations involving 1 for someone else to solve.
• Research the use of the number 1 in computer coding, science, or sports statistics.

Assessment

Formative Assessment

• Listen to the learner’s explanations during the Number 1 Detective Game.
• Use the quick-check questions to identify misunderstandings.
• Observe whether the learner can model equations with objects or drawings.
• Ask the learner to explain the difference between adding 1 and multiplying by 1.

Summative Assessment

Evaluate the completed practice challenge and design project using this checklist:

Conclusion and Recap

Ask the learner to complete these statements:

• “When I add 1 to a number, _____.”
• “When I multiply a number by 1, _____.”
• “Any power of 1 equals _____.”
• “One way I use the number 1 in real life is _____.”

Review the key ideas:

• Adding 1 moves a number one step forward.
• Multiplying by 1 leaves a number unchanged.
• Any positive power of 1 equals 1.
• The number 1 represents one unit and appears in many real-world situations.

Optional Follow-Up

During the next day, have the learner keep a “Number 1 Spotting Log.” They should record at least ten examples of 1 in real life, such as a number on a clock, a price, a measurement, a page number, a score, or an address. For each example, they should explain what the 1 represents.