Objectives (5 - 7 minutes)

Main Objectives:

1. Provide students with a clear and concise understanding of operations with rational numbers.
2. Develop students' ability to solve problems involving operations with rational numbers.
3. Encourage students to apply the concepts learned in practical everyday situations.

Secondary Objectives:

1. Stimulate students' critical thinking in solving mathematical problems.
2. Promote interaction among students through playful and collaborative activities.
3. Foster students' confidence in their mathematical abilities.

Introduction (10 - 12 minutes)

1. Review of previous content: The teacher starts the lesson by briefly reviewing the concepts of rational numbers, their properties, and the basic operations of addition, subtraction, multiplication, and division. This review can be done through a quick classroom discussion, asking students what they remember about the subject and clarifying any doubts that may arise. (3 - 4 minutes)

2. Problem situations: The teacher then proposes two problem situations involving operations with rational numbers. For example, 'If João ate 3/4 of a pizza and Maria ate 2/3 of the same pizza, how much pizza is left?' and 'If a juice box has 1/2 liter and I want to fill 3 glasses, each with 1/4 liter, how many juice boxes do I need?' These problem situations will serve as a starting point for the theoretical discussion that will follow. (3 - 4 minutes)

3. Contextualization: The teacher then contextualizes the importance of operations with rational numbers, explaining how these concepts are applied in real situations, such as dividing food, measuring liquids, and solving financial problems. This helps to arouse students' interest in the subject and understand the relevance of what they are learning. (2 - 3 minutes)

4. Topic introduction: To introduce the topic of the lesson, the teacher can share some curiosities or interesting facts about rational numbers. For example, 'Did you know that the idea of fractions dates back to antiquity, when people used stones to represent divided quantities?' or 'Did you know that rational numbers can be written as a repeating decimal or as an irreducible fraction?' These curiosities help to create an atmosphere of curiosity and discovery in the classroom. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory and Explanation (10 - 12 minutes): The teacher starts the theoretical part of the lesson by explaining what rational number operations problems are and how they can be solved. For this, the teacher can:

   • Define what rational number operations problems are, explaining that they are situations where mathematical operations with fractions, decimals, or percentages need to be performed.
   • Explain that there are different methods to solve these problems, depending on the situation. For example, adding and subtracting fractions require the denominators to be the same, while multiplying and dividing fractions can be solved by multiplying or inverting the fraction.
   • Demonstrate, step by step, how to solve the problem situations presented in the Introduction, using the appropriate methods for each operation.

2. Guided Practice (5 - 6 minutes): After the theoretical explanation, the teacher guides the students to solve other problems involving operations with rational numbers, following the same demonstrated method. The teacher should monitor the students' progress, correcting possible errors and clarifying doubts.

3. Practical Activity (5 - 7 minutes): Next, the teacher divides the class into small groups and distributes different problems involving operations with rational numbers for each group to solve. The problems should be varied, involving different operations (addition, subtraction, multiplication, and division) and types of rational numbers (fractions, decimals, and percentages). The teacher should circulate around the room, assisting the groups as needed.

4. Discussion and Correction (5 - 7 minutes): After the groups have had time to solve the problems, the teacher leads a discussion in the classroom, where each group presents one of their solutions and explains how they arrived at it. The teacher should provide constructive feedback and correct possible misunderstandings. This activity not only allows students to learn from each other but also helps reinforce the understanding of the concepts presented.

Return (8 - 10 minutes)

1. Connection with Theory (3 - 4 minutes): The teacher starts the Return phase by connecting the practice performed with the theory presented. This can be done through guiding questions, such as:

   • 'How do the problems you solved in groups relate to what we discussed in theory?'
   • 'What methods did you use to solve the problems and why? Did you need to adapt the theory in any way to solve the problems?'
   • 'What challenges did you face when solving the problems and how did you overcome them?'

2. Individual Reflection (3 - 4 minutes): The teacher then asks students to reflect individually on what they learned in the lesson. For this, the teacher can propose the following questions:

   • 'What was the most important concept you learned today?'
   • 'What questions have not been answered yet? What doubts do you still have about the topic?'
   • 'How can you apply what you learned today in everyday situations or in other subjects?'

3. Sharing (2 - 3 minutes): After individual reflection, the teacher invites students to share their answers with the class. The teacher should encourage all students to participate, ensuring that the discussion is respectful and inclusive. During the sharing, the teacher can clarify any misunderstandings, reinforce key concepts, and highlight the practical applications of problems involving operations with rational numbers.

4. Lesson Evaluation (1 minute): To conclude, the teacher can briefly evaluate the lesson by asking students what they thought of the approach used, if they felt they learned, and if they believe they are prepared to apply what they learned. This evaluation can be useful for the teacher to adjust their teaching strategies and for students to reflect on their own learning process.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes): The teacher begins the Conclusion of the lesson by summarizing the main points covered. This includes defining problems involving operations with rational numbers, the different methods to solve them, and the importance of applying these methods correctly to obtain the correct answer. The teacher can briefly recall the problem situations presented at the beginning of the lesson and how they were solved, highlighting the essential steps of each operation.

2. Theory-Practice Connection (1 - 2 minutes): Next, the teacher reinforces the connection between theory, practice, and real-life applications. The teacher can highlight how understanding theoretical concepts allowed students to solve the practical problems proposed. Additionally, the teacher should reiterate the importance of applying these concepts in real situations, such as dividing food, measuring liquids, and solving financial problems.

3. Additional Materials (1 minute): The teacher then suggests additional study materials for students who wish to deepen their understanding of operations with rational numbers. These materials may include textbooks, math websites, educational videos, and online exercises. The teacher should emphasize that practice is essential for learning mathematics, and that students should dedicate themselves to solving problems regularly to develop their skills.

4. Subject Importance (1 - 2 minutes): Finally, the teacher reinforces the importance of the subject for students' daily lives. The teacher may mention additional examples of everyday situations involving operations with rational numbers, such as solving problems related to time, distance, and speed, interpreting statistical data, and understanding financial concepts. The teacher should encourage students to observe and apply these concepts in their daily lives, thus reinforcing the relevance of what was learned.