Objectives (5 - 7 minutes)

1. Understanding of fundamental concepts: Students should be able to understand the fundamental concepts of operations with rational numbers, including addition, subtraction, multiplication, and division. This includes understanding how these operations are performed and the rules that govern them.

2. Problem-solving skills: Students should be able to apply the concepts learned in solving problems involving operations with rational numbers. This includes the ability to identify the type of problem, apply the correct operation, and arrive at a correct answer.

3. Connection of theory and practice: Students should be able to connect the theory learned in the classroom with the practice of problem-solving. This includes the ability to apply the concepts learned in practical situations and understand the relevance of these concepts.

Secondary objectives:

• Development of critical thinking: Students should be encouraged to develop critical thinking skills, which will be useful not only in mathematics but in many other areas of life. This can be done through the discussion of problem-solving strategies and reflection on the problem-solving process.

• Promotion of collaboration and communication: Students should be encouraged to work in teams, discuss their ideas, and share their solutions. This can be done through group activities and classroom discussions.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reminding students about the basic concepts of rational numbers, including what they are, how they are represented, and how they are ordered. This review can be done through direct questions to the students or through a brief presentation of slides, diagrams, or graphs. (2 - 3 minutes)

2. Initial problem situations: The teacher should then present two problem situations to the students, which will serve as starting points for the development of the theory. For example, "If I have 3/4 of a pizza and give half of it to my friend, how much pizza will I have now?" and "If I multiply 2/3 by 3/4, what will be the result?" The teacher should encourage students to discuss these situations among themselves and try to find their own solutions. (3 - 5 minutes)

3. Contextualization of the importance of the subject: The teacher should then explain the importance of operations with rational numbers, showing examples of how these concepts are used in everyday life and in other disciplines. For example, the addition and subtraction of fractions are used in the kitchen when following a recipe, and the multiplication and division of fractions are used in proportion situations, such as adjusting a recipe to make more or fewer portions. (1 - 2 minutes)

4. Introduction to the topic: To capture the students' attention, the teacher can share curiosities about the subject. For example, they can mention that fractions can be used to represent parts of a whole, such as dividing a pizza among friends, or to represent parts of a set, such as choosing a card from a deck. Additionally, they can show how fractions are used in measurements, such as measuring ingredients for a recipe. (2 - 3 minutes)

5. Engaging students' attention: To spark students' interest, the teacher can present some mathematical challenges involving operations with rational numbers. For example, "If I have a cake and divide it into 8 equal parts, and then divide each of these parts into 3 equal parts, how many parts of the cake do I have now?" and "If I have 2/3 of a pizza and 3/4 of a cake, what is the total amount of food I have?" The teacher should encourage students to try to solve these challenges, even if they have not learned the necessary operations yet. (2 - 3 minutes)

Development (20 - 25 minutes)

1. "Fraction Pizza" Activity (10 - 12 minutes): Students will be divided into groups of five, and each group will receive a sheet of paper with the representation of a pizza divided into different fractions. The teacher will provide each group with a list of problems involving the addition, subtraction, multiplication, and division of fractions. The groups should discuss and solve the problems, using the fraction pizza as a visual tool. For example, if the problem is "If I have 3/4 of a pizza and give half of it to my friend, how much pizza will I have now?", the students should color 3/4 of the pizza, then divide that part in half and color the corresponding amount. The activity will allow students to visualize operations with fractions and better understand how they work.

   1. Preparation: The teacher should prepare the sheets of paper with the fraction pizzas in advance. Each pizza should be divided into different fractions to ensure that the problems vary in difficulty. The teacher should also prepare the list of problems, ensuring that they cover all types of operations with fractions.

   2. Execution: Each group will receive a fraction pizza and a list of problems. The students should solve the problems together, using the fraction pizza to aid in visualization. The teacher should circulate around the room, monitoring the groups' progress and clarifying doubts.

2. "Cake and Pizza" Activity (10 - 12 minutes): Still in their groups, students will receive a set of cards representing different parts of a cake and a pizza. Each card will have a fraction written on it, for example, "1/4 of the cake" or "3/8 of the pizza". The teacher will read a series of problems aloud, and the students should use the cards to help solve the problems. For example, if the problem is "If I have 2/3 of a pizza and 3/4 of a cake, what is the total amount of food I have?", the students should match the corresponding cards, add the fractions, and write the answer. This activity will allow students to practice adding fractions with a fun and relevant context.

   1. Preparation: The teacher should prepare the sets of cards in advance, ensuring that there is a variety of fractions and that they can be combined to form a whole number.

   2. Execution: Each group will receive a set of cards, and the teacher will read the problems aloud. The students should use the cards to solve the problems, discussing their solutions in the group. The teacher should circulate around the room, monitoring the groups' progress and clarifying doubts.

3. Group Discussion (3 - 5 minutes): After completing the activities, the teacher should promote a group discussion with all students. Each group should share their solutions to the problems and discuss the strategies they used. The teacher should encourage students to ask questions, express their opinions, and reflect on the problem-solving process. This will help students consolidate their understanding of the topic and develop their critical thinking skills.

   1. Preparation: The teacher should prepare a series of questions to promote the discussion, focusing on key aspects of the topic, such as choosing the correct operation, visualizing fractions, and applying the concepts to real-world situations.

   2. Execution: The teacher should lead the discussion, asking the questions and ensuring that all students have the opportunity to participate. The teacher should also provide feedback and clarify any misunderstandings.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should promote a group discussion, where each team will share their solutions, strategies used, and conclusions reached. Each group will have up to 3 minutes to present. During the presentations, the teacher should encourage the groups to explain how they arrived at their answers, highlighting the concepts of operations with rationals that were applied. After each presentation, the other groups will have the opportunity to ask questions or make comments. The teacher should moderate the discussion, ensuring that all students are involved and that the focus is on mathematical concepts and processes. (3 - 4 minutes)

2. Connection with theory (2 - 3 minutes): After the presentations, the teacher should summarize the solutions presented, highlighting the main points and connecting them with the theory presented at the beginning of the lesson. For example, the teacher can reinforce the importance of understanding the concept of fractions as parts of a whole or a set when discussing the strategies used by the students. The teacher should also highlight the difficulties encountered by the students and the strategies they developed to overcome them. This will help reinforce the concepts and promote the development of students' critical thinking. (2 - 3 minutes)

3. Final Reflection (3 - 4 minutes): To conclude the lesson, the teacher should propose a moment of reflection. Students should silently think for a minute about the answers to the questions: "What was the most important concept I learned today?" and "What questions have not been answered yet?" After the minute of reflection, the teacher should ask some students to share their answers with the class. The teacher should encourage students to be honest in their answers and to express any doubts or concerns they may have. This final reflection will help students consolidate what they have learned and identify any areas that may need review or additional practice. (3 - 4 minutes)

   1. Preparation: The teacher should prepare the reflection questions in advance and think about how students' answers can be used to guide the next lesson or activity.

   2. Execution: The teacher should lead the discussion, ensuring that all students have the opportunity to participate and that the answers are respected and valued. The teacher should also provide feedback and clarify any misunderstandings. Additionally, the teacher should take note of any questions or concerns that arise during the discussion for future reference.

Conclusion (5 - 7 minutes)

1. Summary and Review (2 - 3 minutes): The teacher should recap the main points discussed during the lesson. This includes the fundamental concepts of operations with rational numbers, the rules governing these operations, and the strategies for problem-solving. The teacher should briefly recall the initial problem situations and the practical activities carried out by the students, highlighting how they helped illustrate and apply the theoretical concepts. This recap will give students the opportunity to consolidate what they have learned and identify any gaps in their understanding.

   1. Preparation: The teacher should review the lesson notes and prepare a concise summary of the main points to be addressed during the summary and review.

   2. Execution: The teacher should conduct the summary and review, ensuring that all key points are addressed and that students are following along and understanding.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should emphasize how the lesson connected theory, practice, and applications. The teacher should reinforce the importance of understanding theoretical concepts for solving practical problems and for applying these concepts in real-world situations. The teacher can use additional examples to illustrate this connection, showing how operations with rational numbers are used in different contexts and disciplines.

   1. Preparation: The teacher should prepare some additional examples that demonstrate the application of the concepts learned in the classroom in different contexts.

   2. Execution: The teacher should present the examples and explain how they illustrate the connection between theory, practice, and applications.

3. Additional Materials (1 - 2 minutes): The teacher should suggest additional study materials for students who wish to deepen their knowledge on the subject. This may include books, articles, videos, online games, and math websites. The teacher should provide a brief description of each resource and explain how it can help students consolidate what they have learned and expand their understanding.

   1. Preparation: The teacher should research and select the additional study materials in advance, ensuring that they are relevant, high-quality, and appropriate for the students' skill level.

   2. Execution: The teacher should present the additional study materials and explain how students can access and effectively use them.

4. Importance of the Subject (1 minute): To conclude the lesson, the teacher should emphasize the importance of the concepts learned for everyday life and for other disciplines. The teacher should reiterate that operations with rational numbers are used in many everyday situations, from cooking a recipe to calculating discounts in a store. The teacher should also emphasize that the critical thinking, problem-solving, and communication skills developed during the lesson are valuable and applicable in many other contexts.

   1. Preparation: The teacher should prepare some additional examples that demonstrate the application of the concepts learned in the classroom in real-world situations and in other disciplines.

   2. Execution: The teacher should present the examples and explain how they illustrate the importance of the concepts learned and the skills developed.