Objectives (5 - 7 minutes)

The teacher will:

1. Introduce the concept of the Greatest Common Factor (GCF) as the largest number that divides evenly into two or more numbers.

2. State the learning objectives for the lesson:

   • Understand and define what the Greatest Common Factor (GCF) is.
   • Learn to find the GCF of two or more numbers using different methods.
   • Apply the concept of GCF to solve mathematical problems and real-world situations.

3. Briefly explain the importance of understanding GCF, such as simplifying fractions, finding common denominators, and factoring polynomials.

4. Set the stage for the hands-on activities that will follow, ensuring that the students understand the relevance of the activities to the lesson's objectives.

5. Encourage students to actively participate in the lesson by asking questions, making predictions, and sharing their thoughts.

Introduction (10 - 12 minutes)

The teacher will:

1. Review prerequisite knowledge by reminding students of the concept of factors and multiples. The teacher will ask students to recall the definition of these terms and provide examples.

2. Present two problem situations to pique students' interest and serve as a starting point for the lesson:

   • The teacher could ask, "If you have 12 cookies and 8 friends, what is the largest number of cookies each friend can have without any leftovers?"
   • Another problem could involve a school setting: "If we have 30 students and we want to distribute them evenly into the least number of 5-person groups for a project, how many groups can we form?"

3. Contextualize the importance of the Greatest Common Factor (GCF) with two real-world applications:

   • The teacher could explain how knowing the GCF can help in simplifying recipes, ensuring the right proportions of ingredients.
   • Another example could involve understanding the GCF to simplify carpooling, making sure everyone gets an equal number of turns driving.

4. Grab the students' attention by sharing two interesting facts or stories related to the GCF:

   • The teacher could mention that ancient Egyptians used the concept of GCF in their construction works, ensuring the perfect alignment of columns and beams.
   • Another fun fact could be that the concept of GCF is used in computer algorithms for tasks like reducing fractions, breaking codes, and optimizing operations.

5. Introduce the topic of the lesson: The teacher will write the term "Greatest Common Factor" on the board and ask students if they have heard of it before. If some students have, the teacher will ask them to explain what they understand by the term. If none of the students have heard of it, the teacher will provide a brief definition to spark their curiosity.

Development (25 - 30 minutes)

This hands-on activity will give students a practical understanding of how to find the Greatest Common Factor (GCF) of two or more numbers.

The teacher will:

1. Divide the class into small groups of 3-4 students and provide each group with a "GCF Detective Kit" which contains:

   • A set of number cards (with different numbers on each card)
   • A "GCF Detective Manual" (a step-by-step guide on how to find the GCF using different methods)
   • A "GCF Detective Badge" (a fun visual to engage students and make the activity more enjoyable)

2. Explain the activity to the students: They are now detectives with the task of finding the GCF of different pairs of numbers. Each group will receive a case file containing a number of problems to solve. The group that solves the most cases correctly within the given time frame will be awarded the title of "Master GCF Detectives".

3. Demonstrate the usage of the "GCF Detective Manual" by solving a simple problem on the board. The teacher will explain each step clearly, making sure the students understand the process.

4. Ask the students to open their "GCF Detective Manuals" and start working on their cases. Remind them that they can use any method described in the manual to solve the problems. Encourage active collaboration within the groups.

5. Circulate around the room, observing the students at work, and providing assistance as needed. During this time, the teacher will also ask probing questions to stimulate critical thinking and discussion within the groups.

6. Once the groups have solved the problems, the teacher will lead a class discussion to review the solutions. The teacher will ask each group to present one of their solved cases, explaining their method and the answer they obtained.

7. After all groups have presented, the teacher will summarize the different methods used, highlighting the similarities and differences in the approaches. The teacher will also clarify any misconceptions that may have arisen during the activity.

8. Finally, the teacher will award the "Master GCF Detective" title to the group that solved the most cases correctly. This will serve as a fun and motivating way to end the activity.

This hands-on activity will help students develop a deep understanding of the concept of GCF by applying it to real-world scenarios. It will also promote teamwork and communication skills among the students.

Feedback (10 - 12 minutes)

The teacher will:

1. Initiate a group discussion by asking each group to share their experience during the hands-on activity. Each group will have up to 3 minutes to present their findings. They should explain the methods they used, any obstacles they encountered, and how they overcame them.

2. Facilitate a connection between the hands-on activity and the theory by guiding the discussion towards the methods used to find the Greatest Common Factor (GCF). The teacher will ask each group to explain the steps they took to find the GCF. This will allow the teacher to assess the students' understanding of the concept and determine if any misconceptions need to be addressed.

3. Encourage the students to reflect on the learning process by asking questions such as:

   • "What was the most challenging part of the activity?"
   • "Which method did you find the most effective in finding the GCF?"
   • "Can you think of any real-world situations where knowing the GCF would be useful?"

4. Give the students a few minutes to discuss these questions within their groups and then ask for volunteers to share their thoughts with the class. This will foster a collaborative learning environment where students can learn from each other's experiences and perspectives.

5. Use the students' responses to gauge their understanding and to identify areas that may need further clarification or reinforcement in future lessons.

6. Conclude the feedback session by summarizing the key points of the lesson, emphasizing the importance of the GCF in simplifying fractions, finding common denominators, and factoring polynomials.

7. Lastly, the teacher will assign a short homework task where students are asked to find the GCF of several numbers at home and be prepared to share their findings in the next class. This will provide an opportunity for students to further practice the concept and for the teacher to assess their individual understanding.

This feedback stage will not only help the teacher assess the students' learning but also allow the students to reflect on their learning process, reinforcing the concepts learned, and preparing them for future lessons.

Conclusion (5 - 7 minutes)

The teacher will:

1. Summarize and restate the main points of the lesson, reinforcing the definition of the Greatest Common Factor (GCF) as the largest number that divides evenly into two or more numbers. The teacher will also recap the different methods used to find the GCF, highlighting the similarities and differences between them.

2. Recap the hands-on activity and the group discussions, emphasizing how the students were able to apply the theoretical knowledge of GCF to practical problem-solving. The teacher will highlight the importance of the GCF in simplifying fractions, finding common denominators, and factoring polynomials, linking theory to real-world applications.

3. Suggest additional resources for students to further enhance their understanding of the GCF. This can include textbooks, online tutorials, educational games, and worksheets. The teacher will also recommend a few practice problems for students to work on at home.

4. Propose a reflection for the students to consider before the next class. The teacher will ask the students to think about how the concept of GCF can be applied in their everyday lives. This could involve tasks such as simplifying recipes, organizing items into groups, or finding common factors in their schoolwork. The students will be encouraged to share their reflections in the next class.

5. Finally, the teacher will remind the students that understanding the concept of GCF is not only important for their math class but also for various real-world applications. The teacher will highlight the importance of being able to work with others, communicate their ideas effectively, and apply their mathematical knowledge in practical situations.

This conclusion stage will help the students consolidate their learning, understand the relevance of the GCF in their everyday lives, and prepare them for future lessons.