Objectives (5 - 7 minutes)

1. Understand the concept of first-degree equations: Students should be able to understand what a first-degree equation is, identify its elements (unknown, coefficients, constant terms), and recognize its general form (ax + b = 0).

2. Learn to solve first-degree equations: Students should acquire skills to solve first-degree equations efficiently and accurately, following the correct steps (isolate the unknown, simplify the equation, find the value of the unknown).

3. Apply knowledge to practical problems: Students should be able to apply the concept and skills of solving first-degree equations in practical contexts, such as everyday problems and real-world situations.

Secondary Objectives:

• Develop critical thinking and problem-solving skills: In addition to learning how to solve first-degree equations, students should be encouraged to think critically about the necessary steps and the resolution strategy to be adopted. They should also be able to transfer these skills to solving other types of mathematical problems.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing the basic concepts that will be necessary for understanding the current topic. This includes reviewing what unknowns, coefficients, constant terms, and the concept of equality are. Other concepts that may be relevant to the lesson, such as the distributive property, should also be reviewed. This review can be done through direct questions to the students or small practical exercises.

2. Problem situations: To arouse students' interest and demonstrate the relevance of the topic, the teacher can present some problem situations that involve the use of first-degree equations. For example, 'If a kilo of apples costs R$ 5.00, how many kilos of apples can we buy with R$ 25.00?' or 'If a bicycle costs R$ 200.00 and we want to buy two, how much will we need to pay?' These situations should be presented in a way that highlights that they can be solved using first-degree equations.

3. Contextualization: The teacher should contextualize the importance of first-degree equations, explaining that they are used in everyday situations and in various careers, such as engineering, finance, and computer science. Additionally, it can be mentioned that the ability to solve equations is fundamental for learning more advanced mathematical concepts.

4. Introduction to the topic and gaining attention: To introduce the topic and arouse students' curiosity, the teacher can tell the story of how first-degree equations were developed, highlighting the importance of mathematicians like Euclid, Diophantus, and Al-Khwarizmi. Another curiosity that can be shared is that first-degree equations are considered the simplest and most basic in mathematics, but are still used in a wide variety of complex problems.

5. Explanation of the topic's importance: Finally, the teacher should emphasize that first-degree equations are a powerful tool for solving real-world problems and that mastering this topic can facilitate the understanding and resolution of problems in various areas of life.

This set of steps should help prepare students for the lesson topic, ensuring that they have the necessary prior knowledge and are motivated for learning.

Development (20 - 25 minutes)

1. Mathematical Modeling Activity - The Price of the Snack (10 - 12 minutes):

   • Description: The teacher will propose a contextualized problem to the students. They will be challenged to calculate the price of a snack in a snack bar, which contains a sandwich, a juice, and a fruit, based on the information provided on the menu.
   • Instructions: The teacher should provide students with a fictional menu from a snack bar, where each item has a price. For example, the sandwich costs x reais, the juice costs y reais, and the fruit costs z reais. The challenge is to find the values of x, y, and z, so that the total price of the snack is equal to a specific value, defined by the teacher.
   • Step by step: The teacher should guide the students to identify the unknowns (x, y, z), write the corresponding equation (x + y + z = total price of the snack), and solve the equation to find the values of the unknowns.

2. Practical Activity - Buying Books (10 - 12 minutes):

   • Description: The teacher will propose a practical problem involving the purchase of books. Students will have to solve the equation to find the quantity of books that can be bought with a certain budget.
   • Instructions: The teacher should present students with a catalog of books, where each book has a price. The challenge is to find how many books can be bought with a specific budget, defined by the teacher.
   • Step by step: The teacher should guide the students to identify the unknowns (the quantity of books) and write the corresponding equation (price of the book x quantity of books = total budget). Then, students should solve the equation to find the quantity of books.

3. Discussion and Reflection (5 - 8 minutes):

   • Description: The teacher should promote a classroom discussion where students share their solutions and reflections on the proposed activities.
   • Step by step: The teacher should start the discussion by asking students about the strategies they used to solve the equations. Then, the teacher should ask students to justify their answers and explain the reasoning they used. Additionally, the teacher should take advantage of the discussion to clarify doubts, highlight important points, and reinforce the concepts learned.

These practical and contextualized activities allow students to apply the knowledge acquired about first-degree equations in real situations, develop problem-solving and critical thinking skills, and realize the relevance and applicability of this topic in daily life. Furthermore, the classroom discussion promotes interaction and exchange of ideas among students, enriching the learning process.

Return (8 - 10 minutes)

1. Group Discussion (3 - 5 minutes): The teacher should lead a group discussion with students about the solutions found. Each group should share with the class how they solved the proposed problems, what strategies they used, and what difficulties they encountered. The teacher should encourage the participation of all students, asking questions to stimulate reflection and deepen the understanding of the topic.

2. Connection with Theory (2 - 3 minutes): After the discussion, the teacher should connect the practical activities with the theory presented at the beginning of the lesson. The teacher should highlight how the step-by-step resolution of first-degree equations was applied in the proposed practical situations. This will help students see the relevance of what they learned and understand how to apply this knowledge in different contexts.

3. Analysis and Reflection (2 - 3 minutes): The teacher should propose that students reflect individually on the lesson. They should think about the following questions:

   1. What was the most important concept learned today?
   2. What questions have not been answered yet?
   3. What did I learn today that I can apply in everyday situations? After a minute of reflection, students should share their answers with the class. The teacher should listen carefully to the students' answers, clarify any remaining doubts, and reinforce the most important concepts.

4. Feedback and Conclusion (1 minute): The teacher should end the lesson by giving general feedback on the class's performance. They should praise the students' efforts, highlight strengths, suggest areas for improvement, summarize the main points of the lesson, reinforce the topic's importance, and motivate the students for the next lesson.

This Return stage is crucial for consolidating learning, promoting reflection and metacognition, and ensuring that the lesson's Objectives were achieved. Additionally, it allows the teacher to assess the effectiveness of teaching and make adjustments, if necessary, for future lessons.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should summarize the main points covered in the lesson. This includes the concept of first-degree equations, the identification of their elements (unknown, coefficients, constant terms), and the general form of a first-degree equation (ax + b = 0). The teacher should also recap the steps to solve a first-degree equation (isolate the unknown, simplify the equation, find the value of the unknown). Furthermore, the summary should emphasize the importance of applying the acquired knowledge in practical problems and the relevance of first-degree equations in daily life and in different careers.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should explain how the lesson connected theory (the concepts and steps to solve first-degree equations) with practice (mathematical modeling activities and the book-buying problem) and applications (solving everyday problems and in different careers). This helps students understand the relevance of what they learned and how they can apply this knowledge in different contexts.

3. Additional Materials (1 minute): The teacher should suggest additional study materials for students who wish to deepen their knowledge of first-degree equations. This may include math books, educational websites, explanatory videos, math games, among others. For example, the teacher may suggest that students watch an online video that visually and interactively explains how to solve first-degree equations.

4. Importance of the Topic in Daily Life (1 minute): Finally, the teacher should reinforce the importance of first-degree equations in daily life. They should emphasize that they are used in numerous everyday situations, such as calculating prices, solving financial problems, interpreting graphs and tables, among others. The teacher may also mention that the ability to solve equations is fundamental for learning more advanced mathematical concepts and for developing critical thinking and problem-solving skills.