Objectives (5 - 7 minutes)

1. Understand the concept of unequal sharing problems: Students should be able to comprehend the idea that sharing a quantity is not always equal among the involved parties, and that it is necessary to find a fair solution to the problem.

2. Apply the theory in solving practical problems: Students need to be able to apply the acquired knowledge to solve real unequal sharing problems. This will involve the ability to interpret the problem, identify the total quantity to be divided and the parties involved, and arrive at a fair solution.

3. Develop logical and mathematical reasoning skills: Solving unequal sharing problems involves the application of mathematical concepts and the development of logical reasoning. Students should be able to enhance these skills throughout the lesson.

Secondary Objectives:

• Foster active student participation: The teacher should encourage student participation throughout the lesson, whether through questions, discussions, or practical activities.

• Promote teamwork: Many unequal sharing problems involve more than one party. Therefore, it is important for students to learn to work as a team to find fair solutions.

To achieve these Objectives, the teacher should plan the lesson in a way that provides students with a clear understanding of the concept of unequal sharing and practical skills for its resolution.

Introduction (10 - 12 minutes)

1. Review of Previous Content: The teacher should start the lesson by reviewing the concepts of division and sharing that were previously studied. This can be done through targeted questions to the students, such as "What is division?" and "How can we divide something among several people or groups?" This review is important to ensure that all students are on the same page and have a solid foundation for the new content. (3 - 4 minutes)

2. Presentation of Problem Situations: To spark students' interest and demonstrate the relevance of the subject, the teacher can present two problem situations. The first one can be something simple, like dividing a cake between two people, where the cake cannot be divided into equal parts. The second situation can be more complex, such as dividing a sum of money among several people, where each person has a different percentage. These problem situations will serve as a starting point for the discussion of the concept of unequal sharing. (3 - 4 minutes)

3. Contextualization of the Subject's Importance: The teacher should explain that the ability to solve unequal sharing problems is useful in many everyday situations, such as dividing tasks among group members, distributing resources in a community, or even negotiating fair agreements. This will help students understand the relevance of the subject and engage more in the lesson. (2 - 3 minutes)

4. Introduction to the Topic: The teacher should then introduce the concept of "Unequal Sharing Problems." They can explain that, in some cases, the division of a quantity cannot be done equally and that it is necessary to find a fair solution to the problem. The teacher can also mention that there are different methods to solve these problems, which will be addressed throughout the lesson. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory Presentation (10 - 12 minutes)

   1.1. The teacher should start by explaining the concept of "Unequal Sharing Problems." They should emphasize that, in some cases, sharing a quantity cannot be done equally, which can lead to conflicts and injustices. (2 - 3 minutes)

   1.2. Next, the teacher should introduce the "Principle of Proportionality." They should explain that when sharing cannot be done equally, it is possible to find a fair solution using this principle. The teacher can give examples to illustrate this concept, such as dividing a cake between two people, where one person wants a larger slice and the other a smaller slice. In this case, the teacher should explain that it is possible to find a fair solution if the second person receives a portion that is proportional to the amount the first person wants. (3 - 4 minutes)

   1.3. The teacher should then present the "Calculation of Proportions." They should explain that, to find the fair solution, it is necessary to calculate the proportions. The teacher should give examples of how to do this, using real situations that students can relate to, such as dividing a cash prize among several players in a game. The teacher should show students how to calculate each player's proportion, according to their contribution to the prize. (3 - 4 minutes)

   1.4. Finally, the teacher should introduce the "Fair Sharing Method." They should explain that this method consists of giving each person a part of the total quantity, according to their proportion. The teacher should give examples of how to use this method to solve unequal sharing problems, such as dividing a plot of land among several heirs, where each heir is entitled to a part proportional to their degree of kinship with the owner of the plot. (2 - 3 minutes)

2. Guided Practice (10 - 12 minutes)

   2.1. The teacher should then propose some unequal sharing problems for students to solve. These problems should be varied and contextualized, so that students can see the practical application of what they are learning. The teacher should guide students to think about each problem, calculate the proportions, and use the fair sharing method to find the solution. (5 - 6 minutes)

   2.2. The teacher should closely monitor the students' work, guiding them when necessary and clarifying any doubts that may arise. It is important for students to feel comfortable asking questions and discussing solutions with their peers. (3 - 4 minutes)

3. Practical Activity (5 - 7 minutes)

   3.1. To consolidate learning, the teacher can propose a practical activity. This activity can be a board game where students need to divide resources fairly among players. The teacher should guide students to use the principle of proportionality and the fair sharing method to resolve conflicts that may arise during the game. (3 - 4 minutes)

   3.2. At the end of the activity, the teacher should lead a discussion about the strategies used by students and the difficulties encountered. The teacher should reinforce the importance of respect and justice in conflict resolution and emphasize that mathematics can be a useful tool for this purpose. (2 - 3 minutes)

Return (8 - 10 minutes)

1. Content Review (3 - 4 minutes)

   • The teacher should start the content review by questioning students about their understanding of the concepts of "Unequal Sharing Problems," "Principle of Proportionality," "Calculation of Proportions," and "Fair Sharing Method."
   • The teacher can ask students to explain in their own words what each of these concepts means.
   • The teacher should emphasize the importance of each of these concepts in solving unequal sharing problems.

2. Connection with Theory (2 - 3 minutes)

   • The teacher should then connect theory with practice, explaining how the learned concepts were applied in solving the proposed problems.
   • The teacher should highlight that understanding the theory behind unequal sharing problems is essential for the practical resolution of problems and that practice is necessary for the consolidation of theory.

3. Reflection on Learning (2 - 3 minutes)

   • The teacher should encourage students to reflect on what they have learned. They can ask questions such as: "What was the most important concept you learned today?" and "What questions have not been answered yet?"
   • The teacher should give a minute for students to think about these questions and then ask some students to share their answers.
   • The teacher should welcome students' answers, reinforcing the positive points and clarifying any remaining doubts.

4. Teacher's Feedback (1 - 2 minutes)

   • Finally, the teacher should provide overall feedback on the lesson, highlighting strengths and areas that need more practice or study.
   • The teacher can also suggest extra activities for students who wish to delve deeper into the subject.
   • The teacher should encourage students to continue practicing the resolution of unequal sharing problems, reminding them that practice is essential for improving mathematical skills.

This Return is essential for the teacher to assess the effectiveness of the lesson, identify points that need reinforcement, and plan the next lessons according to the students' needs.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should start the Conclusion by briefly summarizing the main points covered in the lesson. They should review the concepts of "Unequal Sharing Problems," "Principle of Proportionality," "Calculation of Proportions," and "Fair Sharing Method."
   • It should be highlighted how these concepts relate to each other and how they were applied in solving the problems proposed during the lesson.
   • The teacher should also emphasize the importance of understanding the theory to be able to solve problems in practice.

2. Connection between Theory and Practice (1 - 2 minutes)

   • The teacher should explain that the lesson aimed to connect theory with practice.
   • They should reinforce that by understanding the theory behind unequal sharing problems, students become able to apply this knowledge in real situations.
   • The teacher can recall how practical problems were used to illustrate the theory and how the practical activity allowed students to consolidate what they learned.

3. Additional Materials (1 - 2 minutes)

   • The teacher should suggest some additional study materials for students who wish to delve deeper into the subject.
   • These materials may include textbooks, explanatory videos, math websites, and online exercises.
   • The teacher should remind students that practice is essential for learning mathematics and that solving unequal sharing problems can be a great way to enhance their skills.

4. Importance of the Subject (1 minute)

   • Finally, the teacher should emphasize the importance of the subject addressed for everyday life.
   • They can mention some common situations where the ability to solve unequal sharing problems can be useful, such as dividing tasks, distributing resources, or negotiating fair agreements.
   • The teacher should reinforce that mathematics is not just a set of formulas and procedures, but a powerful tool for solving real-world problems in a fair and efficient manner.