Objectives (5 - 10 minutes)

1. Understand the concept of Trajectory in Kinematics: The teacher should guide the students to understand the trajectory as the path traveled by a body. This includes differentiating between rectilinear and curvilinear trajectories, as well as trajectories in different dimensions (two-dimensional and three-dimensional).

2. Identify and Describe Different Types of Trajectories: The teacher should help students identify and describe the different types of possible trajectories, such as rectilinear, circular, and elliptical. In addition, students should be able to describe the motion of a body in each type of trajectory.

3. Apply the Theory of Trajectory in Problem Solving: Finally, students should be able to apply the theoretical concepts learned in solving practical problems. This involves interpreting questions involving the trajectory of a body and applying the corresponding formulas and principles to reach a solution.

Secondary Objectives:

• Stimulate Active Student Participation: The teacher should encourage active student participation throughout the class, promoting discussions and group activities that allow the exchange of ideas and clarification of doubts.

• Develop Critical Thinking and Problem Solving Skills: By solving practical questions involving the trajectory of a body, students will have the opportunity to develop important skills, such as critical thinking and problem solving.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher starts the class by briefly reviewing fundamental concepts that will be necessary for understanding the topic of the lesson. He may review the definition of kinematics, motion, and frame of reference, as these concepts are the basis for understanding the trajectory of a body. For example, the teacher can ask students questions to activate prior knowledge and ensure that everyone is on the same page.

2. Problem Situation 1: The teacher proposes the following situation: "Imagine you are watching a soccer game from the stands. Player A passes the ball to Player B, who kicks it towards the goal. How can we describe the trajectory of the ball? Is it rectilinear, curvilinear, circular, elliptical? Why?" The teacher encourages students to share their ideas and hypotheses, but does not provide the answer immediately.

3. Problem Situation 2: Next, the teacher proposes another situation: "Now, imagine you are on a roller coaster. You notice that when going up a hill, the sensation is that you are being 'pulled' downwards. Does this indicate that the roller coaster's trajectory is rectilinear?" The teacher again encourages students to think and discuss the situation.

4. Contextualization: The teacher explains that trajectory is a fundamental concept in physics and is used to describe the motion of bodies in different everyday situations. He may cite examples such as the movement of a car on the road, the movement of a satellite in orbit around the Earth, or even the movement of planets in our solar system.

5. Introduction to the Topic: The teacher introduces the topic of the lesson - "Body Trajectory" - and arouses students' interest with curiosities or related facts. For example, he may mention that the trajectory of a body can be influenced by various factors, such as gravity, air resistance, or even the presence of other bodies. Another curiosity could be that, in quantum physics, the trajectory of a subatomic particle can be described not as a line, but as a cloud of probabilities!

Development (20 - 25 minutes)

1. Practical Activity 1 - "Trajectories in Everyday Life" (10 - 15 minutes):

   • Preparation: The teacher prepares in advance a series of photos or videos showing different everyday situations where the movement of a body can be observed. For example, a car on a road, a ball being kicked, a person walking in a square, etc.
   • Execution: Students, divided into groups, receive a photo or video and must analyze and discuss what is the type of trajectory of the body in question. They must justify their answers based on the concepts discussed in class.
   • Group Discussion: Each group presents their analysis to the class, promoting a discussion about the different interpretations and justifications. The teacher provides the necessary clarifications and corrections, if necessary.

2. Practical Activity 2 - "Solving the Problem" (10 - 15 minutes):

   • Preparation: The teacher prepares in advance a series of problems involving the trajectory of a body. The problems should vary in difficulty and complexity to meet the different skills and levels of understanding of the students.
   • Execution: Students, again divided into groups, receive a problem to solve. They must read the problem carefully, identify what is being asked, and how they can reach the solution. They must apply the concepts and formulas learned in class to solve the problem.
   • Group Discussion: Each group presents their solution to the class. The teacher guides the discussion, asking questions to ensure that students understand the reasoning behind the solution. If necessary, the teacher can provide tips or guidance to help groups that are struggling.

3. Synthesis Activity - "Creating an Experiment" (5 - 10 minutes):

   • Preparation: The teacher proposes a challenge to the students: they must create a simple experiment that illustrates the concept of the trajectory of a body.
   • Execution: Students, again divided into groups, must discuss and plan the experiment. They must consider what materials will be needed, how they will conduct the experiment, and how they will record the results.
   • Presentation: Each group presents their experiment plan to the class. The teacher evaluates the plans and, if feasible, the experiments can be conducted in future classes.

Return (10 - 15 minutes)

1. Group Discussion (3 - 5 minutes): The teacher gathers all students for a general discussion. Each group has up to 3 minutes to share the solutions or conclusions they found during the practical activities. The goal is for students to learn from each other and see different approaches to problem solving. The teacher should intervene, if necessary, to correct any conceptual errors or reinforce important points.

2. Connection with Theory (3 - 5 minutes): After the group discussion, the teacher should make the connection between the practical activities and the theory seen in class. For example, he can ask students how they applied the theory to solve the problems or how they identified the type of trajectory in each situation. The goal is for students to understand that theory is not something isolated, but something that can be applied and tested in practice.

3. Individual Reflection (3 - 5 minutes): The teacher suggests that students make an individual reflection on what they learned in class. He can ask questions like:

   1. What was the most important concept you learned today?
   2. What questions have not been answered yet?
   3. How can you apply what you learned today in everyday situations or in other disciplines? Students have a minute to think about their answers. Then, the teacher asks some students to share their reflections with the class. The goal is for students to consolidate their learning and identify possible gaps in their understanding.

4. Feedback and Closure (1 - 2 minutes): Finally, the teacher requests feedback from students about the class. He can ask what they liked the most, what they found most challenging, and what they would like to learn more about. The teacher thanks everyone for their participation, gives the appropriate compliments, and encourages students to continue studying the subject on their own. He can also provide guidance on what will be covered in the next class.

Conclusion (5 - 10 minutes)

1. Summary and Recapitulation (2 - 3 minutes): The teacher starts the Conclusion by recalling the key points covered in the class. He recaps the concept of trajectory in kinematics, the differentiation between rectilinear and curvilinear trajectories, and trajectories in different dimensions. The teacher also revisits the different types of trajectories, such as rectilinear, circular, and elliptical, and how to describe the motion of a body in each of them. He emphasizes the most important concepts and answers any remaining questions.

2. Connection between Theory, Practice, and Applications (2 - 3 minutes): The teacher highlights how the class connected theory, practice, and applications. He emphasizes how the practical activities allowed students to apply theoretical concepts in problem solving and interpreting everyday situations. Additionally, the teacher emphasizes that understanding the trajectory of a body is fundamental in various areas, such as engineering, architecture, astronomy, among others.

3. Extra Materials (1 - 2 minutes): The teacher suggests extra materials for students who wish to deepen their knowledge on the topic. He may recommend books, websites, videos, or simulation apps that address the trajectory of a body in a detailed and interactive way. The teacher can also provide additional problems for students to practice at home.

4. Importance of the Subject (1 - 2 minutes): Finally, the teacher concludes the class by emphasizing the importance of the subject in everyday life. He can cite examples of how understanding the trajectory of a body is relevant in daily situations, such as predicting the trajectory of a ball in a soccer game, understanding the movement of a car on the road, or even calculating the trajectory of a rocket in space. The teacher reinforces that physics is not just a theoretical discipline, but a science that allows us to understand and describe the world around us.