Objectives (5 - 10 minutes)

1. Understand the concept of variables and their importance in the context of Mathematics and everyday life.

   • Identify the variables present in problem situations and recognize the need to balance them to reach a solution.

2. Learn to solve equations with one variable.

   • Apply the properties of equalities to solve simple equations, step by step.

3. Practice solving real-world problems involving the use of equations with one variable.

   • Apply the knowledge acquired in solving practical problems, developing logical reasoning skills and applying Mathematics in daily life.

Secondary Objectives:

• Stimulate active participation of students in the class, through discussions and problem solving in groups.
• Develop the ability to express mathematical concepts clearly and organized.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts:

   • The teacher starts the class by revisiting the concepts of equations, equalities, and basic operations (addition, subtraction, multiplication, and division) that were addressed in previous classes. It is important to ensure that students have a solid understanding of these concepts before moving on to the topic of variables.

2. Problem Situations:

   • The teacher presents two problem situations to arouse students' interest:
     • 'If the sum of two numbers is 10 and the difference between them is 2, what are these numbers?'
     • 'A father is three times the age of his son. The sum of their ages is 48. What is the age of each one?'

3. Contextualization:

   • The teacher explains that the presented problem situations are related to the use of variables. In everyday life, we often come across situations where we do not know a specific value, but we know how it relates to other values. The ability to work with these unknowns is fundamental in many areas, such as engineering, physics, economics, among others.

4. Introduction to the Topic:

   • The teacher introduces the concept of variables, explaining that they are symbols that represent unknown numbers or that can take on different values in an expression or equation. He emphasizes that Mathematics uses variables to express relationships and solve problems in a general way.

5. Curiosities and Applications:

   • The teacher shares two curiosities to arouse students' interest:
     • 'Did you know that the symbol 'x' is often used to represent a variable in Mathematics because it is the first letter of the word 'unknown' in Greek?'
     • 'Solving equations with one variable is one of the oldest methods in Mathematics, dating back over 4000 years, and is one of the most powerful and widely used tools in many areas of knowledge.'
   • Next, the teacher presents some practical applications of using variables, such as in solving physics problems, mathematical modeling of natural and social phenomena, and in economics, where they are used to represent quantities that can change in different situations.

Development (20 - 25 minutes)

1. Theory Presentation (10 - 15 minutes)

   • Definition of Variables: The teacher reinforces the definition of variables as symbols that can represent different values in an expression or equation. He highlights that, in Mathematics, variables are used to express relationships and solve problems.
   • Types of Variables: The teacher explains that there are different types of variables, depending on the domain of application. For example, in Mathematics, variables can be classified as dependent or independent, continuous or discrete. In social sciences, variables can be classified as qualitative or quantitative.
   • Equations with Variables: The teacher introduces the concept of equations with variables, explaining that an equation is an equality that contains one or more variables. He shows some examples of equations with variables and explains that the goal is to find the value of the variable that makes the equation true.
   • Solving Equations: The teacher proceeds to explain the process of solving equations, emphasizing that the goal is to isolate the variable on one side of the equation, maintaining equality. He demonstrates the process step by step, using simple and clear examples.
   • Properties of Equalities: The teacher reinforces the importance of the properties of equalities in solving equations. He explains that the properties of equalities allow us to perform the same operations on both sides of an equation without altering the solution.

2. Guided Practice (5 - 10 minutes)

   • Solving Equations: The teacher guides students in solving equations with one variable. He starts with simple examples and gradually increases complexity, always explaining each step of the process.

3. Problem Solving (5 - 10 minutes)

   • Application of Theory: The teacher proposes some real-world problems that involve the use of equations with one variable. He asks students to identify the variables involved, write the corresponding equation, and solve the equation to find the solution. The teacher circulates around the room, guiding students and clarifying doubts.

4. Group Discussion (5 - 10 minutes)

   • Sharing Experiences: The teacher divides the class into groups and asks them to discuss the solutions found for the proposed problems. He encourages students to explain their strategies and to help each other. The teacher circulates around the room, listening to the discussions and clarifying doubts.
   • Feedback: After the discussion, the teacher gathers the class and asks each group to share an interesting solution or strategy that emerged during the discussion. He takes this opportunity to reinforce key concepts and correct possible errors or misunderstandings.

Return (10 - 15 minutes)

1. Connection with the Real World (5 - 7 minutes)

   • The teacher proposes that students discuss and share examples of real situations where the use of variables and solving equations are useful. This may include engineering problems, physics, economics, among others.
   • The teacher may also provide some additional examples to further illustrate the practical application of the concept, such as 'How is Mathematics used to predict the weather?' or 'How is Mathematics used to determine the shortest route between two points on a map?'.
   • The teacher then guides students to reflect on how understanding and the ability to work with variables can be applied in their daily lives. For example, they can think of situations where they need to solve practical problems using logic and the ability to manipulate symbols or variables, such as planning a party, managing a budget, or solving a puzzle.

2. Concepts Review (3 - 5 minutes)

   • The teacher asks students to summarize the main concepts learned in the class. They can do this individually, writing on a piece of paper or sharing aloud with the class. The teacher should emphasize the importance of being able to explain the concepts in their own words, to ensure they have a solid understanding.
   • The teacher can ask review questions to check students' understanding. For example, 'What is a variable?' or 'How would you solve the equation x + 5 = 10?'.
   • The teacher can also ask students to identify any areas where they still feel insecure or confused, so they can be addressed in future classes.

3. Reflection and Self-assessment (2 - 3 minutes)

   • The teacher guides students to reflect on what they learned in the class and to evaluate themselves. He may ask questions like 'What was the most important concept you learned today?' or 'What questions do you still have about the topic?'.
   • The teacher may also ask students to assess how well they think they were able to apply the concepts and skills learned in solving the proposed problems. This can be done through a quick poll with response options like 'completely understood', 'somewhat understood', or 'did not understand'.

4. Feedback (1 - 2 minutes)

   • The teacher thanks the students for their participation and effort. He may provide general feedback on the class and express expectations for the next classes. The teacher may also encourage students to continue practicing and exploring the topic outside the classroom, through readings, extra exercises, or online research.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher starts the Conclusion by summarizing the main points of the class. He reviews the definition of variables, solving equations with one variable, and the importance of the properties of equalities.
   • The teacher reinforces the idea that Mathematics uses variables to express relationships and solve problems, and that the ability to work with variables is fundamental in many areas of knowledge and daily life.

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

   • The teacher highlights how the class connected theory (the concept of variables and solving equations) with practice (problem solving in groups) and applications (discussion on how these concepts are used in the real world).
   • He reinforces that practice is essential for the consolidation of learning, and that solving real-world problems helps make the content more relevant and meaningful for students.

3. Extra Materials (1 - 2 minutes)

   • The teacher suggests some extra materials for students who wish to deepen their knowledge on the topic. These may include Mathematics books, educational websites, explanatory videos, and additional exercises.
   • He may also recommend that students practice solving equations at home, using everyday problems like 'If I have R$ 100 and spend R$ 20 per day, how long will it take until I have no money left?'.

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

   • In conclusion, the teacher emphasizes the importance of the topic for students' lives. He explains that the ability to work with variables and solve equations is a fundamental skill not only in Mathematics, but in many other disciplines and in various everyday situations.
   • He encourages students to see Mathematics not only as a school subject, but as a powerful tool that can help them understand the world around them and solve problems efficiently and logically.