Objectives (5 - 7 minutes)

1. Understand the concept of average scalar speed: The teacher must ensure that students have a clear understanding of what average scalar speed is, how it is calculated, and what it represents in a physical context.

2. Apply the formula for average scalar speed in practical problems: The goal is for students to be able to apply the formula for average scalar speed in different situations of physical problems involving uniform motion.

3. Solve problems of average scalar speed: Students should be able to solve problems involving average scalar speed. This includes understanding the problem, identifying relevant information, applying the formula correctly, and arriving at the final answer.

Secondary Objectives

1. Develop critical thinking skills: By solving problems of average scalar speed, students will be challenged to think critically, analyze information, and make logical decisions.

2. Promote collaboration in the classroom: The teacher should encourage collaboration among students, encouraging them to work together to solve problems. This will help promote an environment of active and engaged learning.

Introduction (10 - 12 minutes)

1. Review of necessary concepts: The teacher will start the lesson by briefly reviewing the concepts of speed and uniform motion. This is crucial to ensure that all students have a solid foundation before moving on to average scalar speed. The teacher can do this through a quick classroom discussion, asking students to recall what they know about these concepts.

2. Problem situations: The teacher will present two problem situations to arouse students' interest. The first one could be: 'Imagine you are traveling by car from one city to another. It takes you 4 hours to complete the trip, and the distance between the cities is 200 km. What is your average scalar speed?' The second situation could be: 'An athlete runs a race track in 60 seconds. The track is 400 meters long. What is the athlete's average scalar speed?'

3. Contextualization of the subject's importance: The teacher should explain that calculating average scalar speed is an essential tool in many fields, including physics, engineering, navigation, sports, among others. This can be illustrated with practical examples, such as the use of GPS in cars, weather forecasting, and performance analysis of athletes in sports.

4. Introduction to the topic with curiosities or applications: To further arouse students' interest, the teacher can share some interesting curiosities or applications related to the topic. For example, they can mention that the average scalar speed of sound is approximately 340 meters per second, or that the average scalar speed of a commercial airplane is about 900 km/h. The teacher can also mention that average scalar speed is used to calculate the expected travel time in GPS apps.

Finally, the teacher should formally introduce the topic of the lesson - average scalar speed - and explain that the goal of the lesson is for students to understand the concept, know how to calculate it, and be able to apply it in practical problems.

Development (20 - 25 minutes)

1. Theory (10 - 12 minutes):

   • Definition of Average Scalar Speed: The teacher should start by explaining that average scalar speed is the ratio between the variation in distance traveled and the corresponding time interval. Therefore, average scalar speed is calculated by dividing the total distance traveled by the total time spent to cover that distance.
   • Formula for Average Scalar Speed: The teacher should present the mathematical formula to calculate average scalar speed: Vm = ΔS/Δt, where Vm is the average scalar speed, ΔS is the variation in distance, and Δt is the variation in time.
   • Units of Measurement: The teacher should explain that speed is a quantity that has a numerical value and a unit of measurement. In the International System of Units (SI), the unit of measurement for speed is meters per second (m/s).
   • Examples and Applications: The teacher should provide examples of how to calculate average scalar speed in different situations. This may include examples of cars on a race track, athletes in a marathon, airplanes on a trip, among others.

2. Practice (10 - 13 minutes):

   • Problem Solving: The teacher should propose some problems involving average scalar speed and ask students to solve them. The problems should vary in difficulty to meet the needs of all students.
   • Discussion of Problems: The teacher should discuss the solutions with the class, clarifying any doubts and explaining the resolution steps.

3. Application (5 - 7 minutes):

   • Practical Activity: The teacher should propose a practical activity in which students apply what they have learned about average scalar speed. This may include solving real-world problems, such as calculating the average speed of a cyclist on a road, the average speed of a boat at sea, among others. The teacher should guide the students during the activity and provide constructive feedback.
   • Discussion and Conclusion: After students finish the activity, the teacher should promote a classroom discussion. Students should be encouraged to share their solutions and discuss any difficulties encountered. The teacher should conclude the activity by reinforcing the main points learned and clarifying any remaining doubts.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should promote a group discussion for students to share their experiences during the practical activity. Each group will have a maximum of 2 minutes to present their conclusions. During the presentations, the teacher should ensure that all students are involved and listening attentively.

2. Connection with theory (2 - 3 minutes): The teacher should then make the connection between the practical activities and the theory discussed in the lesson. They should highlight how the formula for average scalar speed was applied to solve the problems and how the theory helped understand the solutions. For example, the teacher can ask students how they used the formula for average scalar speed to calculate the athlete's speed in the practical activity.

3. Individual Reflection (1 - 2 minutes): The teacher should propose that students reflect individually on what they learned in the lesson. They can do this by asking questions like: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'. Students should have a minute to reflect and formulate their answers.

4. Sharing Reflections (2 - 3 minutes): Next, the teacher should ask some students to share their reflections with the class. This will provide an opportunity for students to learn from each other and for the teacher to assess students' understanding of the lesson's topic. The teacher should encourage students to be honest and to express any difficulties or doubts they may still have.

5. Closure (1 minute): Finally, the teacher should end the lesson by summarizing the main points discussed and reinforcing the importance of average scalar speed in physics and in various real-world applications. The teacher should also inform students about the next topic to be discussed and any tasks or readings required for the next lesson.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should recap the main points covered during the lesson. This includes the concept of average scalar speed, the formula for calculating this quantity, and the importance of context in applying the formula. The teacher can use a diagram or scheme to visualize these concepts, helping students remember and understand better.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should reinforce how the lesson connected theory and practice. They should remind students that the theory of average scalar speed was applied in solving practical problems, and how this concept has real-world applications, such as in calculating travel time, athlete performance, among others.

3. Additional Materials (1 minute): The teacher should suggest extra materials for students who wish to deepen their knowledge on the topic. This may include physics books, educational websites, explanatory videos, among others. For example, the teacher can suggest that students watch a YouTube video that explains the concept of average scalar speed visually and intuitively.

4. Relevance of the Subject (1 - 2 minutes): Finally, the teacher should highlight the importance of the topic for daily life and other disciplines. They should remind students that physics is an applied science, and that many of the things we use and see in everyday life are possible thanks to physical principles. For example, the teacher can mention that speed calculation is fundamental in many fields, such as engineering, architecture, transportation, among others.

5. Closure (1 minute): The teacher should end the lesson by thanking students for their participation, encouraging them to continue studying and preparing for the next lesson. They can also reinforce that they are available to answer questions and support students in their studies.