Lesson Plan | Teachy Methodology | Trigonometric Function: Inputs and Outputs

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to provide a clear understanding of what will be covered in the lesson, establishing expectations and specific objectives that will guide the practical activities and the deepening of students' prior knowledge about trigonometric functions.

Main Objectives

1. Understand the relationship between the inputs (angles) and outputs (values) of the trigonometric functions sine, cosine, and tangent.

2. Apply knowledge about trigonometric functions to solve practical and contextual problems using digital tools.

Side Objectives

1. Develop critical thinking and problem-solving skills using digital technologies.
2. Encourage collaboration and teamwork through interactive activities.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to provide a clear understanding of what will be covered in the lesson, establishing expectations and specific objectives that will guide the practical activities and the deepening of students' prior knowledge about trigonometric functions.

Warming Up

 Introduce the topic of trigonometric functions by explaining that they are used to relate angles and sides in triangles and have vast applications in different fields, from engineering to music. Ask students to use their cell phones to search for an interesting fact or a real application of trigonometric functions in everyday life and share it with the class. This will help contextualize the topic in a practical and updated way.

Initial Reflections

1.  What are the basic trigonometric functions, and how do they relate to each other?

2. 類 How can sine, cosine, and tangent functions be used to solve everyday problems?

3.  What is the importance of understanding the inputs and outputs of these functions?

4.  In which fields of knowledge and professions are trigonometric functions most used?

Development

Duration: 70 - 80 minutes

The purpose of this stage is to allow students to apply the knowledge acquired about trigonometric functions in practical and contemporary situations, using digital tools to solve complex problems. This approach not only reinforces the understanding of mathematical concepts but also makes learning more interesting and relevant by contextualizing problems in the modern world.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 -  Trigoland: Build Your Interactive Game!

> Duration: 60 - 70 minutes

- Objective: Use digital tools to create a game that illustrates the practical application of trigonometric functions, promoting students' understanding and interest through gamification.

- Description: Students will create an interactive game using an online game creation platform (such as Scratch). The game must involve characters that use trigonometric functions to solve challenges and advance to the next level. Each group will have creative freedom to develop the game's narrative but must include at least three different levels that require the use of sine, cosine, and tangent to be solved.

- Instructions:

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

• Ask students to register on Scratch or another online game creation platform.

• Guide the groups to create a basic outline of the game, defining characters, setting, and challenges.

• Each level of the game must contain a challenge that requires the use of one of the trigonometric functions to be solved.

• Students can use available online tutorials on the platform to understand how to program the challenges.

• Once completed, each group should test their game and make adjustments if necessary.

• Each group must present their game to the class, explaining how trigonometric functions were used in the challenges.

Activity 2 -  InstaTrig: The Life of a Trigonometric Influencer

> Duration: 60 - 70 minutes

- Objective: Develop the ability to communicate mathematical concepts clearly and accessibly, using social networks as an educational tool.

- Description: Students will create a series of posts on a fictional social media platform where they explain everyday situations involving trigonometric functions. Each post must contain an image, a brief description of the problem, how the trigonometric functions are applied, and a detailed solution.

- Instructions:

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

• Each group must choose a practical situation from everyday life where trigonometric functions are applied (for example, architecture, engineering, music).

• Students must take photos or create digital images illustrating the chosen situation.

• Using image editing applications on their cell phones or computers, students should create posts that explain the application of trigonometric functions in the illustrated situation.

• Each post must contain the image, a brief description of the problem, and the solution using trigonometric functions.

• Students must post the series on a fictional social media platform created for the activity and share the link with the class.

• Each group must present their posts to the class, explaining the context of the photos and the application of the trigonometric functions.

Activity 3 -  Mission Trigonometry: Exploring Mars

> Duration: 60 - 70 minutes

- Objective: Apply trigonometric functions in a scientific simulation context, stimulating critical thinking and the resolution of complex problems.

- Description: Students will simulate a space mission to explore Mars, where they will need to use trigonometric functions to solve navigation, landing, and exploration problems. Using an online simulator, students must calculate trajectories, entry angles, and other necessary parameters for the mission.

- Instructions:

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

• Guide students to register for an online simulator.

• Each group must plan a complete mission to Mars, including launch, interplanetary navigation, entry into the Martian atmosphere, and landing.

• Students must use trigonometric functions to calculate launch angles, trajectories, and entry angles.

• The groups must document each stage of the mission in a digital report, explaining the calculations made and the results obtained.

• Students must carry out the simulation in the program, adjusting parameters as necessary.

• Each group must present the results of the mission to the class, highlighting how trigonometric functions were essential for the success of the mission.

Feedback

Duration: (10 - 15 minutes)

 Purpose: The purpose of this stage is to consolidate learning, allowing students to reflect on their experiences, share acquired knowledge, and receive constructive feedback from peers. The group discussion and feedback exchange promote a collaborative and mutually beneficial environment, as well as reinforce the importance of trigonometric functions and their practical applications.

Group Discussion

 Group Discussion: Promote a group discussion with all students to share what they learned while conducting the experiences and their conclusions. Use the following script to introduce the discussion:

1. Start by thanking everyone for their effort and cooperation during the activities.
2. Invite each group to briefly present the results of their activities, highlighting the main learnings and challenges faced.
3. Encourage students to ask questions to the presenting groups and share their own observations and insights.
4. Lead the discussion to reflect on the importance of trigonometric functions in various fields and how the digital methodology helped in understanding the content.

Reflections

1. 樂 Reflection Questions:

1. How did the use of digital tools help in understanding trigonometric functions? 2. What challenges were faced when applying trigonometric functions in practical activities, and how were they overcome? 3. How do you see the application of trigonometric functions in your daily life or in your future professional career?

360° Feedback

 360° Feedback: Conduct a 360° feedback stage where each student should receive feedback from other students in their group during the activity. Guide the class to ensure that the feedback is constructive and respectful. Use the following script to guide this stage:

1. Explain the importance of constructive feedback for personal and academic growth.
2. Instruct students to mention positive aspects of their peers' work and also areas where there is room for improvement.
3. Ensure that all students have the opportunity to give and receive feedback, promoting an environment of respect and cooperation.

Conclusion

Duration: (10 - 15 minutes)

 Purpose: To consolidate learning and connect abstract trigonometric concepts with practical and current situations. This final stage serves to reinforce the importance of what has been learned, showing its multiple applications and relevance in the modern world, in addition to making it clear that mathematics can be engaging and useful in daily life.

Summary

易 Creative Summary: Imagine a superhero called Trigonomaster! He uses his powers of sine, cosine, and tangent to solve problems and save the day! Today, all of you became little Trigomasters, discovering how these magical functions help us calculate angles and distances. Remember the games, posts, and space missions? That’s how we learned to tame these functions and apply them in practice!

World Connection

 In Today's World: Trigonometric functions are everywhere! From navigation apps we use to find our way, to the engineering that builds bridges and buildings, through entertainment like games and movies. All of this is part of our digital and modern reality, where understanding trigonometry is a superpower in the real world.

Practical Application

 Applications: In everyday life, trigonometric functions are essential in areas such as architecture, engineering, information technology, and even music. They help us design structures, create sound graphs, and develop innovative technologies. Knowing these functions makes mathematics a practical and indispensable tool for solving real problems.