Objectives (5 - 10 minutes)

1. Understanding the Concept:

   • The main objective is for students to understand what a first-degree equation is and the characteristics that define it. This includes the notion that an equation is a mathematical sentence that contains an equal sign and can have one or more unknowns.

2. Developing Problem-Solving Skills:

   • Students should be able to solve first-degree equations, that is, find the value of the unknown that makes the equation true. This involves the application of various mathematical properties and techniques.

3. Practical Application of the Concept:

   • Finally, students should be able to apply the concept of first-degree equations in real-world situations. This may include solving problems involving financial, physical, or any other area that can be modeled by a first-degree equation.

Secondary Objectives:

• Encouraging Active Participation:

  • In addition to the main objectives, it is important for students to feel motivated to actively participate in the class, asking questions, sharing their ideas, and solving problems together.

• Fostering Critical Thinking:

  • Solving first-degree equations can be an exercise in critical thinking, as students need to analyze the situation, identify the unknown, and apply the correct mathematical techniques to find the solution. Therefore, a secondary objective is to foster the development of critical thinking.

Introduction (10 - 15 minutes)

1. Review of Necessary Content:

   • The teacher should start the lesson by reviewing the concepts of basic operations with real numbers. This is fundamental because solving first-degree equations involves the application of these operations. The teacher can do this through a quick quiz or practical activity to verify if students remember these concepts.

2. Initial Problem Situations:

   • To introduce the topic and spark students' interest, the teacher can propose two problem situations:
     • The first one may involve the following situation: 'Maria has a balance of R$ 200.00 at the beginning of the month and spends R$ 50.00 per day. How many days can she spend this amount without ending up with a negative balance?'.
     • The second problem situation may involve a physics question: 'A car leaves from city A and moves at a constant speed of 60 km/h towards city B, which is 300 km away. How can we determine the time it will take for the car to reach city B?'.
   • The teacher should ask students how they would solve these situations and if they can identify any similarities between them.

3. Contextualization of the Subject:

   • The teacher should explain that the first-degree equation is an important tool for solving everyday problems, such as those presented in the problem situations. He can give examples of other situations where first-degree equations are used, such as determining the final price of a product in a discount promotion, determining the time needed to complete a task, etc.

4. Topic Introduction:

   • Finally, the teacher should introduce the topic of the lesson, explaining that the first-degree equation is a mathematical expression that has one or more unknowns and can be solved to find the value of the unknown that makes it true. He should reinforce that to solve these equations, it is necessary to apply basic operations with real numbers.
   • The teacher can share some curiosities about the history of first-degree equations, such as the fact that they were used in ancient Babylon, over 4000 years ago.

Development (20 - 25 minutes)

1. Theory Presentation (10 - 12 minutes)

   1.1. What is a First-Degree Equation:

   • The teacher should start by explaining that a first-degree equation is a mathematical expression that contains one or more unknowns and whose coefficients are real numbers.
   • He should emphasize that an equation is an equality, that is, a sentence that states that two expressions have the same value.
   • The teacher should illustrate the definition with simple examples, such as: '2x + 3 = 7' and '5y - 2 = 3y + 4'.

   1.2. Elements of a First-Degree Equation:

   • The teacher should explain that a first-degree equation has three main elements: the coefficients, the unknown, and the independent term.
   • He should describe each of these elements and show how to identify them in an equation.
   • The teacher can use the previous examples to illustrate the explanation, highlighting the coefficients (2, 3, 5, 3), the unknowns (x, y), and the independent terms (3, 7, 2, 4).

   1.3. How to Solve a First-Degree Equation:

   • The teacher should explain that to solve a first-degree equation, the goal is to isolate the unknown in one side of the equation, so that the other side is equal to zero.
   • He should explain that to do this, it is necessary to apply the inverse operations to the operations present in the equation.
   • The teacher should demonstrate the process of solving an equation step by step, using simple and complex examples.

2. Guided Practice (10 - 13 minutes)

   2.1. Solving Examples:

   • The teacher should propose the resolution of some examples of first-degree equations, starting with the simplest ones and advancing to the most complex ones.
   • He should guide the students during the resolution process, explaining each step and clarifying possible doubts.
   • The teacher should emphasize the importance of always verifying the solution found, by substituting the value of the unknown in the original equation and checking if the equality is true.

   2.2. Problem Solving:

   • After solving the examples, the teacher should propose the resolution of some problems that involve the application of first-degree equations.
   • He should guide the students in reading and interpreting the problems, in identifying the unknowns, and in modeling the situations into equations.
   • The teacher should encourage students to think critically and discuss their resolution strategies.

3. Practical Activities (5 - 10 minutes)

   3.1. Practice Exercises:

   • The teacher should propose a series of practice exercises that students must solve individually. These exercises should address different aspects of first-degree equations, such as solving equations with one or more unknowns, solving equations with fractional or decimal coefficients, etc.
   • After solving the exercises, the teacher should correct them together with the class, clarifying possible doubts and reinforcing the concepts and techniques involved.

   3.2. Challenges:

   • After correcting the exercises, the teacher can propose some challenges, which are more complex problems that require a greater mastery of first-degree equations.
   • The teacher should encourage students to think creatively, to use different resolution strategies, and to discuss their ideas with their peers.

Return (10 - 15 minutes)

1. Review and Reflection (5 - 7 minutes)

   • The teacher should start the Return stage by asking students to share their resolutions of the practice exercises and challenges proposed.
   • He should ask them to explain their strategies, justify their answers, and identify the difficulties encountered.
   • The teacher should take advantage of this discussion to review the main concepts and techniques involved in solving first-degree equations, clarifying doubts and reinforcing learning.

2. Connection with Theory (2 - 3 minutes)

   • After the review, the teacher should ask students to reflect on how the practical activities connect with the theory presented in the lesson.
   • He should ask, for example, how the identification of the elements of a first-degree equation helped in solving the problems, or how the application of inverse operations allowed to find the solutions of the equations.

3. Reflection on Learning (2 - 3 minutes)

   • The teacher should propose that students reflect on what they learned in the lesson. He can do this by asking questions like:
     1. What was the most important concept you learned today?
     2. What questions have not been answered yet?
   • The teacher should encourage students to express their opinions and share their doubts, ensuring that everyone feels comfortable to speak.

4. Teacher's Feedback (1 - 2 minutes)

   • Finally, the teacher should give overall feedback on the lesson, praising the students' efforts, highlighting strengths, and pointing out areas that can be improved.
   • He should reinforce the importance of continuous study and constant practice for mastering first-degree equations, and encourage students to keep striving.

5. Homework Assignment (1 - 2 minutes)

   • The teacher should propose a homework assignment, which can be the resolution of a set of exercises or research on a topic related to first-degree equations.
   • He should clearly explain what is expected from the students and provide guidance on how to carry out the assignment.

Conclusion (5 - 10 minutes)

1. Recap of Key Points (2 - 3 minutes)

   • The teacher should start the Conclusion of the lesson by recapping the key points covered. This includes the definition of first-degree equations, the elements that compose them, and the techniques for their resolution.
   • He can do this interactively, asking students to remember the concepts and techniques or quickly solving one or two examples of first-degree equations.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes)

   • Next, the teacher should highlight the connection between the theory presented, the practical activities performed, and the real-world applications of first-degree equations discussed in the lesson.
   • He can do this by recalling the initial problem situations and showing how they were solved using the techniques for solving first-degree equations.
   • The teacher should emphasize that the ability to solve first-degree equations is a valuable tool that can be applied in various everyday situations and in various areas of knowledge.

3. Supplementary Materials (1 - 2 minutes)

   • The teacher should suggest some supplementary study materials for students. This may include textbooks, explanatory videos, math websites, online exercises, among others.
   • He should briefly explain the content of these materials and how they can help students deepen their knowledge of first-degree equations.
   • The teacher should emphasize that autonomous study is an essential part of the learning process and that these materials can be useful for reviewing the lesson content, clarifying doubts, and deepening understanding of the topic.

4. Importance of the Subject (1 - 2 minutes)

   • Finally, the teacher should summarize the importance of the subject presented for daily life and for the academic development of students.
   • He should explain that first-degree equations are widely used in various areas, such as finance, physics, engineering, among others, and that, therefore, mastering this content is essential for solving practical problems and for the development of more advanced mathematical skills.
   • The teacher should encourage students to value the learning of mathematics, reinforcing that it is a powerful tool that can help them understand and deal with the world around them.