Lesson Plan | Active Learning | Vectors: Addition

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

This stage of the lesson plan aims to establish the learning objectives that will guide the practical activities in the classroom. By clearly defining what is expected of the students, both the teacher and the students can focus on the specific concepts and practices of vectors, ensuring a solid and applicable understanding of the content.

Main Objectives:

1. Enable students to add vectors in the Cartesian plane using the parallelogram rule.

2. Develop skills to perform addition operations between unit vectors and generic vectors.

Side Objectives:

1. Encourage logical reasoning and the spatial visualization ability of the students.

Introduction

Duration: (20 - 25 minutes)

The introduction serves to engage students and bridge what was studied at home with the practical use of vector addition concepts. By presenting problem situations, it stimulates direct application of prior knowledge. The contextualization, in turn, shows the relevance of vectors in real and everyday scenarios, increasing students' interest and understanding of the importance of the topic.

Problem-Based Situations

1. Imagine a boat that sails at 20 km/h eastward. It is affected by a current flowing at 5 km/h southward. How can we calculate the resultant speed of the boat?

2. Consider a plane flying at 800 km/h northeast and is hit by winds blowing at 100 km/h southeast. How to determine the effective speed and direction of the plane?

Contextualization

The ability to add vectors is essential in various fields, from maritime navigation to aerospace engineering. For example, in the development of GPS, it is crucial to accurately calculate the position of a user based on the sum of the vectors representing their speed and direction. Additionally, curiosities like the calculation of forces in sports like tennis, where the wind can alter the direction of the ball, demonstrate the applicability of vector concepts in real life.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to practically and interactively apply the concepts of vector addition they studied at home. The proposed activities aim to consolidate theoretical knowledge in real and contextualized situations, promoting logical reasoning, team collaboration, and the ability to creatively solve problems. This practical approach not only reinforces learning but also makes the content more meaningful and memorable for students.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Vector Race

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of vector addition in a practical and fun context, developing spatial reasoning skills and teamwork.

- Description: In this activity, students will be divided into groups of up to 5 people. Each group will receive a map of the school campus, where strategic points will be marked. Each point represents a 'stop' that the group must reach, and at each stop, they must calculate the route that maximizes the efficiency of their displacement, considering displacement vectors and possible obstacles (represented by vectors of force opposing movement).

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the maps and explain that each point is a 'stop' that must be reached.

• Each group must calculate the best route to reach all points in the least amount of time possible, considering displacement vectors and obstacles.

• After the calculation, each group must draw their route on the map, justifying the vector choices made.

• Conduct a symbolic race where each group shows the calculated and justified route.

Activity 2 - Winds Challenge

> Duration: (60 - 70 minutes)

- Objective: Practice vector addition in a dynamic and technological scenario, improving the understanding of how different vectors can affect movement.

- Description: Students, in groups, will simulate a flight scenario where a plane must reach different cities, each affected by winds of varying directions and intensities. Using a virtual flight simulator, they must calculate the plane's trajectory, adjusting the angle and speed to compensate for the effects of the winds, ensuring that the plane arrives at the final destination.

- Instructions:

• Organize the room into workstations, each with a computer and the flight simulator.

• Divide the students into groups and explain the flight scenario and the effects of the winds in each city.

• Students should use the simulator to calculate and conduct the flight, adjusting the direction and force vectors.

• Each group must note the adjustments made and the results obtained.

• After the simulation, each group presents their strategies and results to the class.

Activity 3 - Rescue Operation

> Duration: (60 - 70 minutes)

- Objective: Develop skills to apply vector concepts in emergency situations and planning, fostering critical thinking and collaboration.

- Description: In this scenario, students will be part of a rescue team in a mountainous area. They will receive a map showing the location of victims, safe areas, and obstacles (such as rivers, ravines, and landslide-prone areas). Using vectors of displacement and rescue, students must calculate the best route to reach all victims, avoiding obstacles and ensuring the safety of the team.

- Instructions:

• Divide the class into groups of up to 5 students.

• Hand each group a rescue area map with locations of victims and obstacles.

• Groups must plan a rescue route, calculating the sum of vectors for each displacement and considering obstacles as opposing force vectors.

• Each group must present their route plan and explain the decisions made.

• Conduct a class discussion on the different approaches and solutions found by the groups.

Feedback

Duration: (15 - 20 minutes)

The purpose of this feedback stage is to allow students to reflect on the practical and theoretical learning of the lesson, consolidating the acquired knowledge. This discussion helps identify gaps in understanding and clarify remaining doubts, as well as reinforce the applicability of vector concepts in real situations. The exchange of experiences among the groups promotes a collaborative learning environment and allows students to see different approaches to the same problems, enriching their understanding of the subject.

Group Discussion

To start the group discussion, the teacher should gather all the students and ask each group to share their experiences and discoveries during the activities. It is recommended that the teacher begin with a brief introduction, highlighting the importance of practical application of vector addition concepts. Then, each group will have the opportunity to present a brief summary of what was done, the challenges faced, and the solutions found. Encourage students to explain how they applied the parallelogram rule and how it affected their choices during the activities.

Key Questions

1. What were the biggest challenges when applying the parallelogram rule during the activities?

2. How did vector addition help to solve the proposed practical problems, such as in the case of the Vector Race or the Winds Challenge?

3. Was there any situation where the theory did not directly apply to the practical problem? How did you deal with that?

Conclusion

Duration: (10 - 15 minutes)

The purpose of the Conclusion stage is to consolidate learning, ensuring that students have a clear and integrated understanding of the principles discussed during the lesson. Recapping the main points helps reinforce memory and the importance of vector concepts, while the discussion about the connection between theory and practice and the relevance of vectors in everyday life increases students' interest and motivation. This stage also serves to lay the groundwork for future lessons and applications of the concepts learned.

Summary

In this final stage, the teacher should summarize the main points addressed during the lesson, recalling the parallelogram rule and the practical applications of vector addition in the Cartesian plane. It is important to recap how vectors were used to solve displacement problems in different scenarios, such as maritime navigation, flight, and rescue situations.

Theory Connection

Today's lesson was carefully structured to connect theory with practice, allowing students to visualize and apply vector concepts in real scenarios. The simulation and route planning activities, which involved vector calculations to optimize movements and overcome obstacles, were designed to illustrate the importance of mathematics and physics in the real world.

Closing

Finally, the teacher should highlight the relevance of studying vectors for everyday life and future studies in physics and mathematics. Understanding vector addition is essential not only for academic success but also for practical application in various fields, from technology to sports and engineering.