Objectives (5 - 10 minutes)

1. Understanding the concept of inverse relationships: Students should be able to understand that the mathematical operations of addition and subtraction, and multiplication and division are inversely related to each other. They should understand that addition undoes subtraction and multiplication undoes division, and vice versa.

2. Applying inverse relationships: Students should be able to use the inverse relationships of mathematical operations to solve problems. They should be able to identify the necessary inverse operation to solve a specific problem. For example, if they need to find out which number was subtracted from 10 to get 6, they should be able to use the inverse operation, addition, to solve the problem.

3. Solving problems creatively: In addition to understanding the inverse relationships of operations, students should be encouraged to solve the proposed problems in a creative way. They should be encouraged to use different strategies and methods to reach solutions, thus promoting critical thinking and problem-solving in an autonomous way.

Introduction (10 - 15 minutes)

1. Recalling Previous Concepts: The teacher should start the lesson by reminding students about the basic concepts of addition, subtraction, multiplication, and division. This can be done through simple and quick questions, such as "What is addition?" or "How do we do a subtraction?" This is an important step to ensure that all students have a solid foundation to understand the inverse relationships of operations.

2. Problem Situation 1: The teacher can then present the first problem situation: "Imagine that you are playing with your friends and decide to hide some toys. You remember how many toys were hidden, but you can't remember how many toys each one hid. How can you use addition and subtraction to solve this problem?".

3. Problem Situation 2: Next, the teacher can present the second problem situation: "Now, imagine that you are dividing a pack of cookies with your friends. You know how many cookies each one received, but you can't remember how many cookies were in the pack. How can you use multiplication and division to solve this problem?".

4. Contextualization: The teacher should explain that the presented problem situations are examples of how we use the inverse relationships of operations in our daily lives. For example, in the first problem situation, we use subtraction (the inverse operation of addition) to find the unknown number. In the second problem situation, we use division (the inverse operation of multiplication) to solve the problem.

5. Capturing Students' Attention: To capture students' attention, the teacher can share some curiosities related to the topic. For example, they can mention that the idea of inverse relationships of operations was developed by ancient Greek mathematicians, and that the study of inverse operations is very important in modern mathematics. Additionally, the teacher can highlight that understanding the inverse relationships of operations can greatly facilitate the resolution of mathematical problems.

Development (20 - 25 minutes)

In this stage, the teacher should propose practical activities that allow students to explore and apply the concepts of inverse relationships of operations. The teacher can choose one or more of the following activities to carry out with the class:

1. Inverse Relationships Bingo Game: The teacher can create bingo cards with simple mathematical problems involving the four operations (addition, subtraction, multiplication, and division). Students, in groups, must solve the problems and mark the corresponding result on the card. The teacher will then draw the problems to solve them on the board, reinforcing the idea of inverse relationships. The first group to complete the card wins the game.

2. Math Treasure Hunt: The teacher can hide cards with mathematical problems around the classroom. The problems should be created in a way that students need to use inverse operations to solve them. Each group of students must search for the cards and solve the problems. When all cards are found and the problems are solved, the group that finishes first wins. The teacher can then choose some cards to discuss the solutions with the class, emphasizing the use of inverse operations.

3. Creation of Mathematical Stories: The teacher can suggest that students, in groups, create their own mathematical stories. Each story should involve solving a mathematical problem that requires the use of inverse operations. Students should then write the story and the problems on pieces of paper. The teacher collects the papers and distributes them to other groups to solve the problems. Then, the solutions are discussed in class, reinforcing the concepts learned.

4. Inverse Operations Puzzle: The teacher can create a puzzle where students need to match mathematical operations with their correct inverses. For example, a puzzle piece may contain the addition operation and its inverse, subtraction. Students must then correctly match the puzzle pieces, reinforcing the idea of inverse operations.

In all of these activities, the teacher should circulate around the classroom, assisting students as needed and observing the progress of each one. After completing the activities, the teacher should set aside time to discuss the solutions with the class, emphasizing the strategies used and the importance of inverse operations. These playful and interactive activities allow students to experience and internalize the concepts in a meaningful and fun way.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): After completing the practical activities, the teacher should gather all students in a large circle for a group discussion. Each group will have the opportunity to share their solutions and strategies for solving the problems. The teacher should encourage students to explain how they used inverse operations to arrive at their answers. During the discussion, the teacher should ask questions to verify students' understanding, such as "Why did you choose this operation to solve this problem?" or "How do you know that the operation you used is the inverse of the original operation?" This is an opportunity for students to learn from each other and for the teacher to assess each student's understanding of the concept.

2. Connection to Theory (3 - 5 minutes): After the group discussion, the teacher should revisit the theoretical concepts discussed at the beginning of the lesson and make connections with the solutions and strategies presented by the students. For example, the teacher can demonstrate how addition is the inverse operation of subtraction, and how multiplication is the inverse operation of division, using the examples presented by the students. The teacher should emphasize that by using inverse operations, students are verifying the validity of their solutions, which is an important aspect of mathematics.

3. Individual Reflection (2 - 3 minutes): Finally, the teacher should propose that students reflect individually on what they learned in the lesson. The teacher can ask two simple questions to guide students' reflection:

   a) "How do you feel now about using inverse operations to solve mathematical problems?" b) "How can you use what you learned today in real-life situations outside the classroom?"

   The teacher should give a minute for students to think about the answers before sharing them with the class. This is an important moment for students to consolidate their learning and for the teacher to assess the effectiveness of the lesson.

4. Teacher Feedback (1 minute): The teacher should end the lesson with positive feedback, reinforcing the strengths of the students and the progress they have made. The teacher can also identify any areas that need more practice and suggest review activities for home. This feedback is essential to motivate students and encourage them to continue learning.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the conclusion by recalling the main concepts covered during the lesson. They should emphasize that the mathematical operations of addition and subtraction, and multiplication and division are inversely related to each other. The teacher can briefly recap the problem-solving strategies discussed, highlighting the importance of using inverse operations to verify the validity of solutions.

2. Connection between Theory and Practice (1 - 2 minutes): Next, the teacher should highlight how the lesson connected theory and practice. They should explain that through practical activities, students were able to experience in practice how mathematical operations and their inverses are related. This allows students not only to understand the concept theoretically but also to become familiar with its practical application.

3. Extra Materials (1 - 2 minutes): The teacher can then suggest some extra materials for students who wish to deepen their knowledge on the topic. This may include educational websites with interactive games and exercises on inverse operations, mathematics books with chapters dedicated to the subject, or explanatory videos available online. The teacher should emphasize that these materials are optional and intended to complement learning in the classroom.

4. Importance of the Subject (1 minute): Finally, the teacher should briefly explain the importance of inverse relationships of operations in everyday life. They can mention that these concepts are fundamental for solving mathematical problems and can greatly simplify the resolution process. Additionally, they can highlight that understanding inverse operations allows students to verify the validity of their solutions, which is an essential skill in mathematics.

5. Closure (1 minute): The teacher should end the lesson by thanking the participation and effort of all students. They can encourage them to continue exploring the wonderful world of mathematics and to apply what they have learned in everyday situations. The teacher should remind students that practice is essential for the development of their mathematical skills and that they should feel confident to use inverse operations in their future studies.