Objectives (5 - 7 minutes)

1. Understanding the Concept of Factorization:

   • Students will learn to define factorization as the process of finding the factors of a number that can be multiplied together to give the original number.
   • Students will be able to explain why factorization is a useful tool in mathematics and real-world applications.

2. Developing Skills in Prime Factorization:

   • Students will learn to identify prime numbers and how they are used in the process of factorization.
   • Students will be able to factorize numbers into their prime factors.

3. Applying Factorization in Problem Solving:

   • Students will learn how to apply factorization to solve mathematical problems, including finding the greatest common factor and least common multiple of numbers.

Secondary Objectives:

1. Enhancing Critical Thinking and Problem-Solving Skills:

   • Through the exercises and problems presented in the lesson, students will improve their critical thinking and problem-solving skills.

2. Promoting Collaborative Learning:

   • The interactive nature of the lesson plan will encourage students to work together, promoting collaborative learning and teamwork.

Introduction (8 - 10 minutes)

1. Recall of Previous Knowledge:

   • The teacher reminds students of the basic concepts of multiplication and division, as these are fundamental to understanding factorization.
   • The teacher also reviews the concept of prime numbers and how they are different from composite numbers. This review will help students in understanding the process of factorization, which involves breaking down a number into its prime factors.

2. Problem Situations as Starters:

   • The teacher presents two problem situations to the students:
     1. "If you have a garden with 12 flowers and you want to arrange them into bouquets with the same number of flowers, what are the different possible numbers of flowers you can have in each bouquet?"
     2. "If you have 16 cookies and you want to divide them into equal bags, what are the different possible numbers of cookies in each bag?"
   • The teacher asks the students to think about how they would solve these problems, setting the stage for the introduction of the concept of factorization.

3. Real-World Contextualization:

   • The teacher explains that factorization is not just a mathematical concept, but also has real-world applications. For example, in computer science, factorization is used in cryptography, which is the practice of securing communication from adversaries.
   • The teacher can also mention how factorization is used in other fields like engineering, physics, and finance, to highlight the importance and relevance of the topic.

4. Introduction of the Topic with Curiosities:

   • The teacher introduces the topic of factorization with an interesting fact: "Did you know that every positive integer greater than 1 can be expressed uniquely as a product of prime numbers? This is called the fundamental theorem of arithmetic, and factorization is the process of breaking down a number into these prime factors."
   • The teacher can also share a curiosity about the largest number that has been factored. For example, "The largest number that has been factored so far is a number with over 230 million digits! It took a supercomputer over two years to do the calculations."

5. Topic Presentation and Objectives:

   • The teacher formally introduces the topic of the lesson: "Today, we will be learning about factorization, which is the process of breaking down a number into its prime factors."
   • The teacher presents the lesson's objectives, highlighting what the students will be able to do at the end of the lesson.