Objectives (5 - 7 minutes)

1. Understanding the Concept of Operations with Rationals: Students should be able to understand the definition and concept of operations with rational numbers. This includes the ability to identify different types of rational numbers (fractions, decimals, percentages) and understand how they are used in operations such as addition, subtraction, multiplication, and division.

2. Calculation Skills of Operations with Rationals: Students should be able to perform calculations involving operations with rational numbers. This includes the ability to solve problems involving the addition, subtraction, multiplication, and division of rational numbers.

3. Problem Solving with Rational Operations: Students should be able to apply their skills in operations with rationals to solve real-world problems. This includes the ability to interpret the problem, identify the necessary operation, and solve the problem effectively.

Secondary Objectives:

• Development of Critical Thinking: Through problem-solving with rational operations, students will be encouraged to develop critical and analytical thinking skills.

• Improvement of Mathematical Reasoning Skills: Practicing operations with rationals will help students improve their mathematical reasoning skills, making them more efficient in other areas of mathematics.

Introduction (10 - 15 minutes)

1. Review of Fundamental Concepts: The teacher should start the lesson by reviewing the fundamental concepts that are essential for understanding the topic of operations with rational numbers. This includes the definition of rational numbers, the difference between integers and rationals, and the representation of rational numbers in the form of fractions, decimals, and percentages. This step is crucial to ensure that all students have the necessary foundation to understand the new content.

2. Problem Situations: The teacher should then present two problem situations involving operations with rationals. For example, the first situation could be dividing a pizza among a certain number of people, and the second situation could involve subtracting a percentage from the price of a product to calculate a discount. These problem situations will serve as a starting point for the discussion of the new content and for introducing the topic in a practical and contextualized way.

3. Contextualization of the Topic's Importance: The teacher should emphasize the importance of the topic of operations with rationals, explaining how this concept is used in everyday life. For example, the teacher can explain that the ability to calculate discounts, percentages, and divide objects into equal parts are essential skills for daily life. Additionally, the teacher can mention that understanding operations with rationals is crucial for future math topics, such as algebra and geometry.

4. Introduction of the Topic in an Engaging Way: To capture the students' attention, the teacher can share some curiosities or interesting facts about the topic. For example, the teacher can mention that the word 'rational' in English comes from the Latin 'ratio', which means 'reason' or 'quotient', directly related to operations with rationals. Furthermore, the teacher can mention that operations with rationals are used in many areas beyond mathematics, such as economics, physics, and computer science.

Development (20 - 25 minutes)

1. Modeling Activity with Manipulative Materials (10 - 12 minutes):

   • The teacher should divide the class into groups of up to 5 students and provide each group with manipulative materials, such as puzzle pieces, building blocks, or coins.
   • Next, the teacher should present two problem situations to the students involving sharing an object (e.g., a pizza or a cake) and applying a discount to a price.
   • Each group should solve the problem situations using the manipulative materials to represent the objects to be shared and the discounts to be applied.
   • After solving the problem situations, each group should present their solutions to the class, explaining the reasoning process used to arrive at the answer.
   • The teacher should then lead a class discussion, highlighting the strategies used by different groups and connecting them to the concepts of operations with rationals.

2. Board Game Activity (10 - 12 minutes):

   • The teacher should provide each group with a set of game cards, with each card containing a problem of operations with rationals. The problems should be varied, involving different operations (addition, subtraction, multiplication, division) and different types of rational numbers (fractions, decimals, percentages).
   • The teacher should explain the rules of the game: each group should take turns, with one group member playing at a time. When it's a member's turn to play, they should draw a card and solve the problem. If they solve it correctly, they advance on the board. If they solve it incorrectly, they stay in the same place. The goal of the game is to reach the end of the board as quickly as possible.
   • The teacher should start the game, monitoring the progress of the groups and providing feedback and guidance as needed. The game will continue until all groups have reached the end of the board.

3. Topic Application Activity (5 - 8 minutes):

   • The teacher should provide the students with an activity sheet containing problems of operations with rationals. The problems should be contextualized, involving everyday situations or other disciplines.
   • Students will have a set time to solve the problems individually. The teacher should circulate around the room, providing support and guidance as needed.
   • After the set time, the teacher should review the answers with the class, highlighting the resolution strategies and connecting them to the concepts of operations with rationals.

These activities allow students to experience and apply the concepts of operations with rationals in a practical and interactive way, reinforcing the understanding of the topic and developing critical thinking and problem-solving skills.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • The teacher should gather all students for a group discussion. Each group will have a maximum of 3 minutes to share the solutions or conclusions obtained during the activities.
   • During the presentations, students should explain the process they used to reach the solution, the strategies they applied, and the difficulties they encountered.
   • The teacher should encourage other students to ask questions and share their own perspectives or approaches to the problem.
   • This step allows students to learn from each other, strengthening the understanding of the topic and promoting collaboration and respect for others' ideas.

2. Connection to Theory (3 - 5 minutes):

   • After the presentations, the teacher should review the theoretical concepts presented at the beginning of the lesson, connecting them with the practical activities carried out.
   • The teacher should highlight how the theoretical concepts were applied in the practical activities and how practice helped reinforce the understanding of the theoretical concepts.
   • The teacher should also review the problem-solving strategies that were discussed during the lesson, reinforcing the importance of thinking critically and creatively when solving mathematical problems.

3. Final Reflection (2 - 3 minutes):

   • To conclude the lesson, the teacher should propose that students reflect individually for a minute on the following questions:
     1. What was the most important concept you learned today?
     2. What questions have not been answered yet?
   • After a minute of reflection, the teacher should ask some students to share their answers with the class.
   • The teacher should listen carefully to the students' answers, as they can provide valuable feedback on the effectiveness of the lesson and on any concepts that may need further clarification.

The Return is an essential stage of the lesson plan, as it allows the teacher to assess students' understanding, reinforce key concepts, and identify any areas that may need review in future lessons. Additionally, the Return gives students the opportunity to reflect on what they have learned, consolidating their understanding of the topic.

Conclusion (5 - 7 minutes)

1. Lesson Summary (1 - 2 minutes):

   • The teacher should start the Conclusion by summarizing the main points covered during the lesson. This may include the definition of operations with rationals, the identification of different types of rational numbers, and the application of rational operations to solve real-world problems.
   • The teacher should refer to the different practical activities carried out and how they helped reinforce the understanding of theoretical concepts.
   • The teacher should also recall the problem-solving strategies discussed and the importance of critical and analytical thinking in mathematics.

2. Connection to the Real World (1 - 2 minutes):

   • The teacher should then explain how the lesson's topic connects to the real world. This may include examples of everyday situations where operations with rationals are used, such as calculating discounts on purchases, dividing food among a group of people, or calculating the percentage of profit in a business.
   • The teacher should emphasize that the ability to operate with rationals is an important tool that students will be able to use throughout their lives, not only in mathematics but also in many other areas.

3. Extra Materials (1 - 2 minutes):

   • The teacher should suggest additional materials for students who wish to deepen their understanding of the topic. This may include reference books, math websites, educational videos, or online games involving operations with rationals.
   • The teacher may also suggest additional practice exercises for students who wish to reinforce their calculation and problem-solving skills.

4. Topic Importance (1 minute):

   • Finally, the teacher should summarize the importance of the lesson's topic and how it connects with other math topics.
   • The teacher should reinforce that understanding and the ability to operate with rationals are fundamental for success in many other math topics, and that practicing these skills is essential for improving mathematical reasoning.

The Conclusion of the lesson is an opportunity for the teacher to reinforce the concepts learned, connect theory with practice and the real world, and encourage students to continue exploring and practicing the topic. In doing so, the teacher helps consolidate students' learning and motivates them for future math lessons.