Learning Objectives (5-7 minutes)

1). Understanding GCF (Greatest Common Factor): Students should comprehend that the Greatest Common Factor is the largest number which divides two or more numbers leaving zero as a remainder. It is essential for problem-solving involving fraction simplification and equation-solving.

2). Learn how to calculate the GCF manually: Students should be able to calculate the Greatest Common Factor of two or more numbers by the prime factorization. It involves the skill to decompose a number into its prime factors.

3).** Applying GCF in solving real-life problems:** Students should be able to apply the concept of the Greatest Common Factor in solving real-life problems, like fraction simplification and equations solving.

Secondary learning Objectives:

• Develop Logical and analytical thinking: Problem solving involving Greatest common factor requires students' logical and analytical thinking ability.

• Enhancing calculation ability: Calculating Greatest Common Factor involves various computation and operations which could enhance students' ability to compute.

Introduction (10-15 minutes)

1. Review of prior knowledge: The teacher initiates the lesson by recalling previous knowledge, concepts which are the building block of understanding the concept of the greatest common factor like divisibility, prime factors, and factorization. These can be done by short questioning or discussion, to check the prior knowledge of students and reinforce the coherence of the concept.

2. Problem situation: Next, the teacher introduces two practical situations which can be solved utilizing the concept of Greatest Common factor.

a). The first one can be of baker who needs to distribute a number of loaves of bread in equal quantities in a number of baskets and he needs to know the maximum loaves he could put in each.

b). Another situation could a number of chairs to be arranged in rows in an organized way without leaving any empty chair and the manager wants to find out the maximum possible arrangement of chairs.

3). Contextualizing the importance of GCF: Then the teacher explains that Greatest Common factor is a very helpful mathematical tool used to solve various real-life problems and in different fields like engineering, architecture, economics, etc.

4).** Introducing the topic:** To grab students' attention, the teacher can introduce Greatest Common Factor through narrating a brief history of the evolution of an idea of division and that people were trying to develop a way of dividing the quantity equally from ancient times. Also the fact that every number's 1 is its GCF may also be shared as interesting trivia.

5). Introducing the Topic (continued): Another way of developing interest among learners can be sharing interesting real-life applications of GCF. For example GCF is used cryptography data compression, fraction simplification and equational problem solving. Therefore, knowing the technique to calculate GCF can be a useful skill to apply it to solve various problems in day to day life and in various career prospects.

By the end of this Introduction, the learners should be motivated to learn about the greatest Common Factor.

Development (20 - 25 minutes)

1). "Prime Factorization" Activity(10- 12 minutes): In this activity the students are divided into the group of 5 or less, and each group is given a large paper with colourful markers and a set numbers (for eg. 36, 48, 72, 100). Then all groups are asked to select one number from the given set and factorize that number in prime factors. This factorization has to done collaboratively on the paper provided. The instructor will be there to help them out, guiding them and solving their queries. The objective is to solidify the understanding of prime factorization which acts a stepping stone in the process of calculating the Greatest common Factor.

1. **Step 1**: Each group selects its' number from given set of number.
2.**Step2**: Students discuss among themselves, and prime- factorize their selected number on the large piece of paper using different coloured marker pens to denote different primes.
3. **Step 3:** After factorization, they check the factorization and multiply the prime factors to confirm that the multiplied value is the same as their original selected numbers.
4. **Step4**: All the groups share their prime factorization with the whole class and explain their working.

2. "The GCD Game" Activity (10 -12 minutes): Following up the prime- factorization activity, the instructor introduces the Greatest common factor game to students. In this activity, each group receives a set of playing cards. Each card contains a factorization of prime number. The goal is that by trading the card, each group will finally have a set of card which represents the GCD (greatest common divisor). The teacher observes the teamwork, providing assistance when required. This activity is designed to reinforce the concept and skills to find the GCD of different numbers.

1. **Step 1:** Each group is given a deck of cards by the teacher. Each deck has the prime factorization of numbers. 

2. **Step 2**: In their groups, the student shall find the GCD of the numbers which they get on the cards.

3. **Step 3**: The groups then gather in a big circle, and they begin trading cards with one another. The idea here is that at the conclusion, each group will be in a possession of the set cards which represents the greatest common factor of the all the numbers.

4. **Step 4**: This game ends when all groups agree that they now possess the GCD (greatest common divisor). The teacher then checks if the GCF computed by each group is correct or not.

By the conclusion of the Development students must now possess clear understanding of the Greatest Common factor, process to find GCF and its practical applications in solving real-life problems.

Debrief (8 -10 minutes)

1. Group Discussion(3-4 minutes): The educator brings together the whole class and initiates group discussion, in order to share the solution and findings of each group to one another. Each group is given up to 2 min time, and in that they have to share their finding and methods to the whole class, During the discussion the instructor should emphasize the importance and applications of GCD in simplifying fractions, solving the equations and highlight the different strategies each groups have used to find the GCD and to approach the problem.

   1.Step 1: The instructor asks a representative from each of the group to present their method and findings of the group to the whole class. 2. Step 2: The representative of the groups perform the presentation of their findings and method to the whole group.

   3.Step 3: Then, the instructor leads the discussion on the different strategies that were employed by the different groups and also on the importance of GCF in solving various equations, fraction simplifications etc.

2. Connecting Theory to Practice ( 2 - 3 minutes): Following up the group discussion, the instructor provides a short summary on the theoretical knowledge covered in this session, and relate it to how those knowledge were used during the hands on activities. The aim is to support students in connecting theory and practice, understanding how the GCD can be applied to solve problems from the real-world.

   1. Step 1: Here, the instructor reviews theoretical knowledge covered during the lesson-such as what is the greatest Common Factor, how it can be determined, and how to apply GCD when it comes to solving real-world problems.
   2. Step 2: He/she highlights how the concepts were being used during the hands on activities, as well how they can be useful to an individual in day today's life.

3.Individual reflection (2- 3 minutes): Lastly, the teacher asks students to have some quiet reflection about what was taught during the class, there can be few prompts from instructor like "what is the one most important concept you have learnt in today's class?", "what are the questions which are still unanswered?" and " how could this be applied in day-to-day life "?

1.**Step 1**: Instructor gives out few prompts to guide students through the reflection process. 

2. **Step 2**: Students take 1 minute, and think upon those questions, and try to come out with the answer. 

3. **Step 3**: Few learners share about reflections and answers with the class.

By the end of Debrief, the learners should have clear understanding on what they learned in this lesson and the real life application and the question which still need to be answered.

Conclusion ( 5-7minutes )

1. Content Review (2- 3 minutes): The teacher revisits and summarizes the major points covered in the class. The recap on concept of Greatest Common Factor, the importance of prime factorizing for finding the GCD, the practical application of the GCF in fraction simplification and in equation solving is done by teacher. The instructor may also give brief review on strategies that students have used during the hands- on activity and highlights common pitfalls to avoid.

   1. Step 1: The teacher provides a summary of major points covered during this session such as the concept of Greatest Common Factor, importance of prime factorization, and its practical application.

   2. Step 2: He/She then highlights the strategies used by the students and the common pitfalls that should have been avoided.

2.Connecting Theory and practice ( 1 - 2 minutes): The instructor discusses how the theory that has been taught in this session relates with practical activities .The instructor emphasizes on the understanding that the knowledge on Greatest Common Divisor and the skill to calculate it is very essential for problem-solving that involve simplifying the fraction and solving the equations. Furthermore, he or she also shares how practicing calculating GCD helps in enhancing analytical thinking and problem-solving skills.

1. **1 step**: Here, the teacher discusses the relation of theory to practice explaining the importance  the Greatest Common Divisor plays to solve the real world problem. 
2. **2 step**: He or she then emphasizes on how practicing the calculating the GCD helps to enhance analytical thinking skills. 

3. Suggest for further Reading ( 1- 2 minutes): The teacher suggests few additional resources through which the students can enhance and extend their knowledge on the topic of the topic of Greatest common divisor. The resources can be textbooks, mathematical websites or applications, instructive video or online practice exercise. Additionally, the instructor can recommend real world problem-solving that can involve Greatest common divisor to provide the learners with opportunities of applying their learning practically.

1.**Step 1:** The teacher recommends some additional study materials like books, websites or videos and online exercises.
2.**Step2:** He/she suggests the students try solving real world problems that involves the idea and application  Greatest common divisor as way to apply their knowledge practically. 

4. Relevancy of topic ( 1 minutes): Finally, the instructor reinforces the importance and relevance of the topic of Greatest Common Factor to learners in various professional fields and real life situations. He or she also shares that the knowledge of GCD is valuable tool to be used to solve wide array of real-life problems and having the ability to calculate GCF can be useful to overcome many challenges.

1. **1 step**: Here the instructor reinforces the significance of the Greatest common factor to real life situations and various professions. 

2. **2 step**: He or she highlights that having the skill of knowing how to calculate GCF can help an overcome various challenges.