Lesson 3: Properties of Natural Numbers

📚 Introduction

Welcome! In this lesson, we are going to explore Natural Numbers — the very first numbers we learn as children: 1, 2, 3, 4, 5, and so on!

We will also study their important properties, which help us understand how numbers work when we add, multiply, or rearrange them.

By the end of this lesson, you will know:

• What natural numbers are
• The major properties they follow (commutative, associative, distributive, identity)
• How these properties make calculations easier

🧠 Key Concepts and Explanations

What are Natural Numbers?

Natural Numbers are the counting numbers starting from 1 and going on forever: 1, 2, 3, 4, 5, 6, …

Note: Natural numbers do not include 0 or negative numbers!

Key Properties of Natural Numbers

Visual Representation

📝 Sample Problem Walkthroughs

Example 1: Commutative Property

Question: Show that 4 + 7 = 7 + 4.

Solution: 4 + 7 = 11 and 7 + 4 = 11. They are equal!

Example 2: Associative Property

Question: Show that (1 + 2) + 5 = 1 + (2 + 5).

Solution:

• (1 + 2) + 5 = 3 + 5 = 8
• 1 + (2 + 5) = 1 + 7 = 8

Thus, both sides equal 8!

Example 3: Distributive Property

Question: Expand 3 × (5 + 2).

Solution: (3 × 5) + (3 × 2) = 15 + 6 = 21.

Example 4: Identity Property

Question: What is 12 × 1?

Solution: 12 × 1 = 12.

📝 Practice Exercises

Exercise 1:

Use the commutative property to find the missing number: 6 + ___ = ___ + 6.

Exercise 2:

Use the associative property to complete: (2 + 5) + 7 = 2 + (___ + ___).

Exercise 3:

Apply the distributive property: 4 × (3 + 2) = ?

Exercise 4:

What is 9 × 1? What is 15 + 0?

📝 Extra Challenge Problems

Challenge 1:

Explain in your own words why 0 is not a natural number but is important for identity property.

Challenge 2:

Solve and show steps: 5 × (7 + 2) = ?

🔁 Recap

In this lesson, we discovered that natural numbers start from 1 and go on endlessly.
We studied important properties like commutative, associative, distributive, and identity properties,
and saw how they help us solve problems faster and smarter.

🪞 Reflection Prompt

Think about this: Can you find real-life examples where you use the commutative or distributive property without even realizing it?