Objectives (5 - 10 minutes)

1. Understanding the Concept of Instantaneous Velocity: Students should be able to understand and define the concept of instantaneous velocity, which is the measure of velocity at a specific point on a trajectory. This includes understanding that instantaneous velocity can vary over time.

2. Calculating Instantaneous Velocity: Students should learn how to calculate the instantaneous velocity of a moving object. This involves applying the formula for average velocity and understanding how the variation of time can affect instantaneous velocity.

3. Connection between Average Velocity and Instantaneous Velocity: Students should be able to establish the relationship between average velocity and instantaneous velocity. This includes understanding that in uniform motion, average velocity is equal to instantaneous velocity.

Secondary Objectives

• Application of Instantaneous Velocity Concept in Practical Situations: Students should be able to apply the concept of instantaneous velocity in practical everyday situations, such as calculating the velocity of a vehicle at a specific moment.
• Development of Problem-Solving Skills: Through solving practical exercises, students should develop the ability to apply the concept of instantaneous velocity to solve complex problems.

Introduction (10 - 15 minutes)

1. Review of Basic Concepts: The teacher should start the lesson by reviewing the concepts of average velocity and uniform motion, which were covered in previous classes. This is essential for students to understand the difference between average velocity and instantaneous velocity, which will be the focus of the lesson.

2. Problem Situations: The teacher can propose two problem situations to arouse students' interest and contextualize the theme. The first may involve a car in accelerated motion and the need to calculate its velocity at a specific point. The second could be an example of an object that changes its velocity over time, such as an elevator that starts to rise slowly and then accelerates.

3. Contextualization of the Subject's Importance: The teacher should explain how instantaneous velocity is a fundamental concept for physics and engineering. Examples of how instantaneous velocity is used in everyday situations, such as calculating speed in sports, designing cars and airplanes, among others, can be mentioned.

4. Introduction of the Topic: The teacher should introduce the topic of the lesson, explaining that instantaneous velocity is the velocity of an object at a specific point on its trajectory and that it can vary over time. The teacher can use visual examples, such as a video of a moving car, to illustrate the concept.

5. Related Curiosities and Stories: To make the lesson more interesting, the teacher can share some curiosities about instantaneous velocity. For example, it can be mentioned that instantaneous velocity is the concept that allows traffic radars to calculate the speed of vehicles. Another curiosity is that instantaneous velocity is what allows Formula 1 drivers to control their cars in high-speed curves.

Development (20 - 25 minutes)

1. Activity with Interactive Video (10 - 15 minutes): The teacher should introduce an activity using an interactive video that simulates a moving car. The video should show the car's speedometer, which varies the speed over time. Students, in groups of up to 5 people, should watch the video and note the car's speed at regular time intervals.

   • Activity Steps:
     1. The teacher should divide the class into groups and distribute the necessary materials for the activity (sheets of paper, pencils, stopwatches, etc.).
     2. The teacher should project the interactive video on the board or a screen and explain the activity's objective.
     3. Groups should watch the video and note the car's speed at regular time intervals.
     4. After the video ends, groups should discuss the notes and calculate the car's instantaneous velocity at each time interval.
     5. Finally, each group should present their calculations to the class, promoting a discussion about the differences between average velocity and instantaneous velocity.

2. Board Game (10 - 15 minutes): The teacher should propose a thematic board game where students, still in groups, will move their pawns according to the game's rules, but with the condition that each pawn's velocity must be calculated at each move.

   • Game Steps:
     1. The teacher should divide the class into groups and distribute the materials needed for the game (board, pawns, dice, movement cards, etc.).
     2. The teacher should explain the game's rules, which include moving the pawns according to the movement cards and calculating the instantaneous velocity of each pawn at each move.
     3. Groups should play, moving their pawns and calculating the instantaneous velocity of each pawn at each move.
     4. The teacher should walk around the room, assisting groups and answering questions.
     5. The game ends when one of the groups reaches the end of the board. The winning group will be the first to arrive, but it will also be necessary to consider the accuracy of the instantaneous velocity calculations made during the game.

Both activities aim to promote understanding and calculation of instantaneous velocity in a playful and contextualized way, encouraging cooperation and discussion among students.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should promote a group discussion with all students, where each group will have up to 3 minutes to share the solutions or conclusions they reached during the activities. During this discussion, the teacher should encourage students to explain the reasoning used to calculate instantaneous velocity and relate it to the theoretical concept presented at the beginning of the lesson.

   • Discussion Steps:
     1. The teacher should call a representative from each group to share their conclusions with the class.
     2. The group's representative should briefly explain how they reached the solution or conclusion, highlighting the reasoning used and the difficulties encountered.
     3. The teacher should ask questions to clarify the group's reasoning and to stimulate reflection on the concept of instantaneous velocity.
     4. Other students can also ask questions and make comments, thus promoting a collective and in-depth discussion.

2. Connection with Theory (2 - 3 minutes): After the discussion, the teacher should provide a brief summary of the main conclusions, relating them to the theory presented at the beginning of the lesson. The teacher should highlight how the practical activities helped consolidate the concept of instantaneous velocity and the application of the average velocity formula.

3. Individual Reflection (3 - 5 minutes): The teacher should suggest that students reflect individually on what they learned in the lesson. To do this, the teacher should ask the following questions:

   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?

   Students should write down their answers on a piece of paper. The teacher may ask some students to share their reflections with the class, but this should be done voluntarily and respecting the students' privacy.

4. Feedback (1 - 2 minutes): Finally, the teacher should ask for feedback from the students about the lesson, asking what they liked the most and what could be improved. This information is valuable for the teacher to adjust their future lessons and ensure student engagement and learning.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should recap the main points covered during the lesson. This includes the definition of instantaneous velocity, the difference between average velocity and instantaneous velocity, the formula for calculating instantaneous velocity, and the relationship between average velocity and instantaneous velocity. The teacher can use a whiteboard or a slide presentation to reinforce these concepts.

2. Connection between Theory and Practice (1 - 2 minutes): The teacher should highlight how the lesson connected theory, practice, and application. This can be done by recalling the practical activities carried out, such as analyzing the video of the moving car and the board game, and how they helped illustrate and apply the concept of instantaneous velocity. The teacher can also emphasize the importance of calculating instantaneous velocity in everyday situations and in various areas, such as physics, engineering, and sports.

3. Extra Materials (1 - 2 minutes): The teacher should suggest extra materials for students who wish to deepen their knowledge on the subject. This may include books, articles, videos, websites, and apps that present the concept of instantaneous velocity and its applications in a didactic and interactive way. For example, the teacher may suggest that students watch an explanatory video on YouTube, read a chapter from a textbook, or explore a physics app that allows simulating and calculating the velocity of moving objects.

4. Importance of the Topic (1 - 2 minutes): Finally, the teacher should emphasize the importance of the topic addressed for students' daily lives. For example, the teacher may mention that instantaneous velocity is what allows traffic radars to calculate vehicle speeds, or that it is a fundamental concept for understanding the movement of objects in the physical and digital worlds. Additionally, the teacher can emphasize that developing the skill of calculating instantaneous velocity contributes to the development of critical thinking, problem-solving, and the ability to apply mathematical concepts in practical situations.