Objectives (5 - 7 minutes)

1. Understand the concept of first-degree equations: The teacher must ensure that students have a clear understanding of what a first-degree equation is and how it differs from other types of equations, such as second-degree equations. This can be done through a quick review of equation concepts, with an emphasis on the importance of the equation's 'degree'.

2. Learn to solve problems involving first-degree equations: The main objective of this lesson is to help students gain confidence and skill in solving practical problems involving first-degree equations. This can be done through the presentation of various examples and practice exercises, where students are guided step by step in solving the problems.

3. Apply theoretical knowledge in solving practical problems: In addition to learning how to solve first-degree equations, students should be able to apply this knowledge in solving real-world problems. The teacher should therefore include examples of problems that can be solved using first-degree equations, such as problems involving speed, distance, time, etc.

Secondary objectives:

• Promote active student participation: The teacher should encourage active student participation during the lesson, whether by asking questions, solving problems in groups or individually, or sharing their own strategies for solving problems.

• Stimulate critical thinking and problem-solving: The teacher should encourage students to think critically about the problems presented and to develop their own problem-solving strategies. This can be done through questions that challenge students to think beyond the formula or algorithm and to consider the 'why' behind the solutions.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing concepts that are essential for understanding first-degree equations. These concepts may include: what an equation is, what an unknown variable is, what a coefficient is, what a term is, and what the degree of an equation is. This review can be done interactively, with the teacher asking questions to the students and encouraging them to participate actively.

2. Problem situations: The teacher should then present two problem situations that will be the starting point for the Introduction of the topic. The situations can be, for example: 'João is twice as old as Maria. If the sum of their ages is 30, what is the age of each?' and 'A bus travels a distance of 180 km in 3 hours. What is the bus's average speed?' These situations should be chosen to arouse students' interest and to show the relevance of first-degree equations in solving real-world problems.

3. Contextualization of the subject's importance: The teacher should then contextualize the importance of the subject, explaining how first-degree equations are used in various areas of life, such as physics, economics, engineering, architecture, etc. The teacher can, for example, mention that the formula for calculating average speed is a first-degree equation.

4. Introduction of the topic: Finally, the teacher should introduce the topic of the lesson, explaining that the goal is to learn how to solve first-degree equations and apply this knowledge in problem-solving. The teacher can, for example, say: 'Today, we will learn how to solve problems like the ones we just discussed, using first-degree equations. It may seem complicated, but I promise that by the end of the lesson, all of you will be able to do it!'

Development (20 - 25 minutes)

1. Theory - First-Degree Equations (5 - 7 minutes): The teacher should start the theoretical part of the lesson by explaining what first-degree equations are and how they are formed. It should be emphasized that first-degree equations are equations whose exponents are all equal to 1. The teacher can use the following equation as an example: 2x + 3 = 9. He should explain that x is the unknown variable, 2 is the coefficient of x, 3 is the independent term, and 9 is the constant term. The teacher should then explain that the goal is to isolate the unknown variable, that is, to leave x alone on one side of the equation.

2. Solving First-Degree Equations (10 - 12 minutes): The teacher should then explain the steps for solving a first-degree equation. The steps are:

   1. Simplify the equation, if necessary, by removing parentheses and combining like terms.
   2. Move all terms containing the unknown variable to one side of the equation, and all constant terms to the other side.
   3. Divide all terms by the coefficient of the unknown variable to isolate the unknown variable.

   The teacher should explain each step in detail, using concrete examples to illustrate. For example, the teacher can solve the equation 2x + 3 = 9 step by step, explaining that first we should move the 3 to the other side of the equation, resulting in 2x = 6, then we should divide both sides of the equation by 2, resulting in x = 3.

3. Application of Theoretical Knowledge (5 - 6 minutes): The teacher should then show students how to apply theoretical knowledge in solving practical problems. He should start with simple problems and gradually increase the complexity. For example, the teacher can present the problem: 'A bus travels a distance of 180 km in 3 hours. What is the bus's average speed?' The teacher should then guide the students in transforming this problem into a first-degree equation and in solving this equation. The teacher should emphasize that the key to solving problems of this type is the ability to transform the problem situation into a mathematical equation.

4. Exercise Practice (5 - 7 minutes): Finally, the teacher should give students the opportunity to practice what they have learned by solving a series of exercises. The exercises should vary in difficulty and should include real-world problems, such as those mentioned above. The teacher should circulate around the room, monitoring students' progress and providing help and feedback as needed. The teacher should encourage students to work together in groups, so they can learn from each other and develop teamwork skills.

Return (8 - 10 minutes)

1. Review of concepts and methods learned (3 - 4 minutes): The teacher should review the main concepts and methods that were learned during the lesson. He can start by asking a general question, such as: 'What are the steps to solve a first-degree equation?' The students should then respond, recalling the steps that were presented during the theoretical part of the lesson. The teacher should encourage all students to participate, whether by responding directly to the question or agreeing with a classmate's answer.

2. Connection to practice (2 - 3 minutes): The teacher should then make the connection between the presented theory and the practical examples that were discussed. He can, for example, ask: 'How do we use first-degree equations to solve the problem of the bus traveling a distance of 180 km in 3 hours?' The students should then explain that they transformed the problem into a first-degree equation, where the unknown variable was the bus's speed, and solved the equation to find the answer. The teacher should emphasize that the ability to transform real-world problems into mathematical equations is a valuable skill that can be applied in many areas of life.

3. Reflection on learning (2 - 3 minutes): The teacher should then ask students to reflect on what they learned during the lesson. He can ask questions like: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?' Students should have a minute to think about the questions and then share their answers with the class. The teacher should listen carefully to students' responses and, if there are questions that many students still do not understand, he should take the time to clarify those doubts.

4. Feedback to the teacher (1 minute): Finally, the teacher should ask for feedback from students about the lesson. He can ask: 'What did you think of today's lesson?' and 'Is there anything you would like to do differently in the next lesson?' Students' feedback can help the teacher improve his lessons in the future and adapt his teaching to students' needs and interests.

Conclusion (5 - 7 minutes)

1. Summary of key points (2 - 3 minutes): The teacher should start the Conclusion by recalling the main concepts covered during the lesson. He can, for example, recap the definition of first-degree equations, the steps for their resolution, and the importance of the skill of transforming real-world problems into mathematical equations. The teacher should ensure that all students have understood these essential concepts before moving on.

2. Connection between theory, practice, and applications (1 - 2 minutes): Next, the teacher should highlight how the lesson connected theory, practice, and applications. He can, for example, mention how the theory of first-degree equations was applied in solving practical problems, such as the problem of João and Maria's ages and the problem of the bus's average speed. The teacher should emphasize that mathematics is not just a series of formulas and algorithms, but a powerful tool for solving real-world problems.

3. Extra study materials (1 minute): The teacher should then suggest some extra materials that students can consult to deepen their understanding of the topic. These materials may include math books, educational websites, explanatory videos, math games, etc. The teacher should encourage students to explore these materials at their own pace and to bring any questions or discoveries to the next lesson.

4. Relevance of the topic (1 - 2 minutes): Finally, the teacher should emphasize the importance of the topic for everyday life. He can, for example, mention that the ability to solve first-degree equations is useful in many practical situations, such as trip planning, time management, understanding graphs and tables, etc. The teacher should reinforce that mathematics is not just an academic discipline, but an essential tool for life.

5. Closing (30 seconds): To conclude, the teacher should thank the students for their participation and effort during the lesson. He should encourage them to continue practicing and studying the topic at home and to bring their doubts to the next lesson. The teacher should then bid farewell to the students, wishing them a good day or afternoon, and reminding them to be prepared for the next lesson.