Objectives (5 - 7 minutes)

1. Understanding the concept of second degree equation and its importance: Students should be able to differentiate a second degree equation from other types of equations, understand what 'second degree' means, and realize the relevance of this type of equation in solving mathematical problems.

2. Development of second degree equation solving skills: Students should learn to solve second degree equations using the Bhaskara formula. This includes the ability to identify the coefficients (a, b, and c) in the equation, calculate the discriminant, and apply the Bhaskara formula correctly.

3. Practical application of the Bhaskara formula: In addition to solving the equations, students should be able to apply the acquired knowledge to solve practical problems that involve the Bhaskara formula. This may include determining real and imaginary roots, identifying the number of solutions, and interpreting the meaning of these solutions in a real context.

Secondary Objectives:

• Development of logical and analytical thinking: Solving second degree equations requires sharp logical and analytical thinking. Therefore, a secondary objective is the development of these skills.

• Promotion of autonomy and self-confidence: Through solving complex equations, students will be encouraged to seek solutions on their own, thus promoting autonomy and self-confidence.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by reviewing the concepts of first degree equations, as they are fundamental to understanding the lesson topic. Additionally, it is important to review factoring and notable products, as these concepts will be useful during the resolution of second degree equations.

2. Problem situations: After reviewing the previous content, the teacher can propose two problem situations that involve solving second degree equations. For example:

   • 'A farmer wants to build a rectangular fence around a pasture area. He has 100 meters of fencing available. How can he maximize the area of the fence?'

   • 'An object is thrown upwards with an initial velocity of 20m/s. What will be the maximum height the object reaches and how long will it take to fall back to the ground?'

   These situations will spark students' interest in the subject, showing that mathematics can be applied in real-life situations.

3. Contextualization: The teacher should explain that solving second degree equations is a valuable tool in various areas such as physics, engineering, economics, and social sciences. For example, in physics, the equation of motion of an object under the action of gravity is a second degree equation. In economics, the equation of a supply or demand curve is also a second degree equation. Therefore, understanding and being able to solve these equations is fundamental for success in these areas.

4. Introduction to the topic: To capture students' attention, the teacher can share some curiosities about the second degree equation. For example:

   • 'Did you know that the Bhaskara formula, which we are going to learn today, was discovered in India over 2000 years ago?'

   • 'And, interestingly, the Bhaskara formula is actually a universal formula that can be used to solve any second degree equation, no matter how complex it is?'

   These curiosities can arouse students' curiosity and make the topic more interesting. Additionally, the teacher should explain that although the Bhaskara formula is a powerful tool, it is not the only way to solve second degree equations. In some cases, factoring or completing the square may be more efficient. However, the Bhaskara formula is the most general and therefore the most important to learn.

Development (20 - 25 minutes)

1. Group Activity - Resolution of contextualized problems (10 - 12 minutes): The teacher should divide the class into groups of 3 to 4 students and provide each group with a series of problems that involve solving second degree equations. The problems should be contextualized, meaning they should refer to real or concrete situations, so that students can visualize the practical application of what they are learning.

   • Example of problem 1: 'An object is thrown upwards with an initial velocity of 20m/s. What will be the maximum height the object reaches and how long will it take to fall back to the ground?'

   • Example of problem 2: 'A farmer wants to build a rectangular fence around a pasture area. He has 100 meters of fencing available. How can he maximize the area of the fence?'

   Each group should discuss and solve the problems together, applying the Bhaskara formula to solve the second degree equations. The teacher should circulate around the room, assisting the groups when necessary and encouraging discussion and participation from all students.

2. Practical Activity - Application of the Bhaskara formula (5 - 7 minutes): After discussing and solving the problems in groups, each group should choose one of the problems to present to the class. They should explain the situation, present the equation that models the problem, and then solve the equation step by step, showing how they applied the Bhaskara formula.

   During the presentations, other students should pay attention, ask questions and make comments, and compare the solutions presented by different groups. This will promote interaction among students, critical thinking, and understanding of the topic.

3. Class Discussion - Reflection on the Application of the Bhaskara Formula (5 - 6 minutes): After all presentations, the teacher should lead a class discussion where students will have the opportunity to reflect on the application of the Bhaskara formula in the proposed problems.

   The teacher should ask questions like: 'How did the Bhaskara formula help us solve these problems?', 'Can you think of other situations where the Bhaskara formula could be useful?' and 'What were the difficulties you encountered when solving these problems and how did you overcome them?'.

   This discussion will allow students to consolidate what they have learned, identify areas where they still have doubts, and reflect on how they can apply what they have learned in other situations.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should gather the whole class and promote a group discussion about the solutions presented by each group. At this stage, the teacher should encourage students to share their insights and ideas, allowing them to learn from each other. The teacher should reinforce the importance of all students feeling comfortable to participate and ask questions.

2. Connection with Theory (2 - 3 minutes): After the group discussion, the teacher should provide a brief recap of the main theoretical concepts covered during the lesson. For example, the teacher can review the Bhaskara formula, the importance of identifying the coefficients in the equation, and calculating the discriminant, among others. The goal is to ensure that students understand the theory behind solving second degree equations and feel more confident to apply this knowledge in future problems.

3. Learning Verification (1 - 2 minutes): After connecting with the theory, the teacher should verify if the lesson Objectives were achieved. To do this, the teacher can ask questions like 'Can you identify and calculate the coefficients in a second degree equation?', 'Do you feel comfortable with the application of the Bhaskara formula?' and 'Can you solve practical problems involving the Bhaskara formula?'. The students' answers to these questions will indicate if they have achieved the lesson Objectives and any areas where they may still have doubts.

4. Final Reflection (2 - 3 minutes): To conclude the lesson, the teacher should propose that students reflect on what they have learned. The teacher can ask questions like 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'. This final reflection will allow students to consolidate their learning and identify any areas where they may need further review or additional study.

5. Teacher Feedback (1 minute): Finally, the teacher should provide overall feedback on the lesson, highlighting strengths and areas that need improvement. The teacher should encourage students to continue studying the subject and ask questions if they have doubts. Additionally, the teacher can provide some guidance on what students can expect in the next lesson and what they should review at home.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion of the lesson by summarizing the main points covered. This includes the definition of second degree equations, the Bhaskara formula, how to identify and calculate the coefficients (a, b, and c), and how to calculate the discriminant. The teacher should reinforce the importance of each of these elements in solving second degree equations and applying the Bhaskara formula.

2. Connection between Theory, Practice, and Application (1 minute): Next, the teacher should explain how the lesson connected theory, practice, and application. The teacher should emphasize that the theory was presented through clear explanations and examples, practice was carried out through group problem-solving, and application was demonstrated through contextualized problems. The teacher should stress that understanding the theory is important to be able to apply it correctly in practice and in solving real problems.

3. Additional Materials (1 - 2 minutes): The teacher should suggest some materials for additional study. This may include textbooks, math websites, explanatory videos, online exercises, among others. The teacher should emphasize that individual study is essential to deepen understanding of the subject and prepare for future lessons and assessments.

4. Importance of the Topic (1 minute): Finally, the teacher should explain the importance of the lesson topic in daily life and in other disciplines. The teacher can cite examples of how solving second degree equations is used in different areas such as physics, engineering, economics, among others. The teacher should emphasize that the ability to solve second degree equations is a valuable tool, not only for mathematics, but also for problem-solving in general.

5. Closure (1 minute): The teacher should end the lesson by thanking the students for their participation and encouraging them to continue studying and asking questions. The teacher should remind students about the importance of reviewing the lesson contents and preparing for the next lesson. Additionally, the teacher should inform students about the topic of the next lesson and any materials or preparation needed.