Lesson Plan | Teachy Methodology | Trigonometric Lines of 75º, 15º, 22.5º

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to clearly establish the learning objectives and guide students on the focus of the lesson. By outlining the main objectives, students will better understand what is expected of them and how the knowledge will be applied practically, ensuring targeted and effective learning.

Main Objectives

1. Calculate the trigonometric lines of 75º, 15º, and 22.5º using specific formulas.

2. Apply the knowledge of trigonometric lines in solving practical and contextual problems.

Side Objectives

1. Encourage collaboration and teamwork during problem-solving.
2. Enhance students' logical and analytical reasoning skills.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to engage students and connect them with the topic in a practical and relevant way. By using mobile devices and exploring real applications of trigonometric lines, students can see the relevance of the content in the modern world. The key questions encourage interaction, collaboration, and discussion, setting the stage for the practical activities that will follow.

Warming Up

Introduce the topic by briefly discussing the importance of trigonometric lines of angles such as 75º, 15º, and 22.5º in various fields, such as engineering, physics, and even in the creation of computational graphics and animations. After this brief explanation, ask students to use their phones to find an interesting or curious fact about any of these angles and how they are applied in real life or modern technologies. This will help connect the content to students' daily lives and spark their interest in the topic.

Initial Reflections

1. Why is calculating the trigonometric lines of specific angles important in practical applications?

2. Did anyone find an interesting example of using the trigonometric lines of 75º, 15º, or 22.5º?

3. How are trigonometric calculations used in other subjects you have studied, such as Physics or Geometry?

4. What difficulties have you encountered when studying this topic at home?

5. How can digital tools and apps facilitate the learning and application of trigonometry?

Development

Duration: 70 - 80 minutes

The purpose of this stage of the lesson plan is to provide an interactive and practical learning experience where students can apply their knowledge of trigonometric lines in an engaging and contextualized manner. The proposed activities encourage teamwork, creativity, and the use of digital technologies, making learning more dynamic and relevant to students' realities.

Activity Suggestions

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

Activity 1 - Trigonometric Detectives on the Web

> Duration: 60 - 70 minutes

- Objective: Connect theoretical knowledge of trigonometric lines with practical and technological applications, developing research and presentation skills.

- Description: Students will be divided into groups and become 'Trigonometric Detectives'. Using their phones and computers, they must discover real and technological applications of the angles 75º, 15º, and 22.5º on the internet. Each group will create a multimedia presentation (slides, videos, etc.) to share their findings with the class.

- Instructions:

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

• Explain that each group should search for practical and technological applications of the angles 75º, 15º, and 22.5º on the internet.

• Groups should collect information, images, videos, and practical examples related to these angles.

• Each group will create a multimedia presentation using tools like Google Slides, Prezi or Canva.

• Groups must prepare a brief presentation (5-7 minutes) to share their findings with the rest of the class.

Activity 2 - Digital Influencers of Trigonometry

> Duration: 60 - 70 minutes

- Objective: Develop creativity, communication skills, and the use of social media to disseminate mathematical knowledge in an engaging and accessible manner.

- Description: Students will create a social media campaign as if they were digital influencers, explaining the trigonometric lines of the angles 75º, 15º, and 22.5º. They should create engaging content, such as short videos, posts, infographics, and hashtags to disseminate knowledge creatively and accessibly.

- Instructions:

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

• Explain that each group will be a team of digital influencers in trigonometry.

• Groups should choose a social media platform (Instagram, TikTok, Twitter, etc.) to create their campaign.

• Each group will create multimedia content, including short videos, posts, infographics, and hashtags, explaining the trigonometric lines of the angles 75º, 15º, and 22.5º.

• Groups must plan the best way to engage their 'followers' with curiosities and practical applications of the angles.

• Groups will present their campaigns to the class, highlighting the strategy and content created.

Activity 3 - Gamification: The Angle Challenge

> Duration: 60 - 70 minutes

- Objective: Stimulate active and collaborative learning through gamification, promoting logical reasoning and the practical application of trigonometric knowledge.

- Description: Students will participate in a digital game where they must solve trigonometry problems related to the angles 75º, 15º, and 22.5º. Using a gamification app or platform, groups will compete to see who solves the most problems correctly in time, accumulating points and climbing the class ranking.

- Instructions:

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

• Choose and set up an appropriate gamification platform, such as Kahoot!, Quizizz, or a similar tool.

• Explain the rules of the game: groups must solve trigonometry problems related to the angles 75º, 15º, and 22.5º to accumulate points.

• Start the game and monitor the progress of the groups in real-time.

• During the game, encourage students to explain their strategies and calculation methods.

• At the end of the game, reveal the winning group and conduct a brief debriefing, discussing the most challenging problems and the strategies used.

Feedback

Duration: 15 - 20 minutes

The purpose of this stage of the lesson plan is to consolidate learning through the exchange of experiences and reflection. By sharing their discoveries and receiving feedback from their peers, students can gain new perspectives, reinforce understanding, and identify areas for personal and academic growth.

Group Discussion

Promote a group discussion with all students where each group shares their discoveries and learnings from the activities. Use the following outline to guide the discussion:

1. Introduction: Ask the groups what surprised them the most when researching the angles 75º, 15º, and 22.5º.
2. Practical Applications: Ask each group to explain a practical or technological application they discovered during their research.
3. Challenges Faced: Ask what the biggest challenges were during the activities and how they overcame them.
4. Collaboration and Digital Tools: Discuss how the use of digital tools helped in learning and executing the activities.

Reflections

1. How did the research and practical activities change your understanding of trigonometric lines? 2. What skills and knowledge do you think you developed the most throughout this lesson? 3. How can you apply what you learned today in other contexts, whether in other subjects or in everyday life?

360° Feedback

Instruct students to conduct a 360° feedback stage within their groups. Each student should receive feedback from their peers on their participation and contribution during the activities. Guide them to provide feedback in a constructive and respectful manner, following these guidelines:

1. Be Specific: Mention specific behaviors and actions that helped in completing the tasks.
2. Be Kind: Use a positive but sincere tone to point out areas for improvement.
3. Be Constructive: Offer practical suggestions on how the peer can improve in future activities.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to consolidate learning in a light and fun way, reinforcing the relevance of the content taught. By summarizing the key points, connecting the lesson to the current world, and highlighting its practical applications, students can see the importance of the topic, recognizing the role of trigonometry in their lives and the digital environment they live in.

Summary

📐 Summarizing the Trigonometric Adventure! 📐

Today, we dived headfirst into the fascinating world of trigonometric lines of the angles 75º, 15º, and 22.5º! We saw how to use formulas and solve complex mathematical problems involving these angles. Furthermore, we connected theory to practice by discovering applications and technological contexts where these calculations are essential!

🎮 Together, we explored innovative learning methods, from online research to the use of social media and gamification. After all, who would have thought that trigonometry could be so fun and engaging?

World Connection

🌍 Trigonometry and the Modern World! 🌍

Today's lesson showed how trigonometry is present in almost everything around us! From engineering and physics to the animations we watch and the games we play, the angles 75º, 15º, and 22.5º play crucial roles. By using mobile devices, social media, and gamification platforms, students realize the relevance and application of trigonometry in the digital and technological everyday, bringing mathematics closer to modern reality.

Practical Application

🔧 Importance of Trigonometric Knowledge! 🔧

Understanding and calculating the trigonometric lines of angles like 75º, 15º, and 22.5º is fundamental not only in mathematics but also in many other subjects and professions. This knowledge is applied to everyday problems and solving technological challenges, making it a valuable skill for any student, professional, and curious person in the modern world!