Lesson Plan | Teachy Methodology | Trigonometric Ratios

Objectives

Duration: 10 - 15 minutes

This stage aims to contextualize students about the specific objectives of the lesson, highlighting what is expected for them to learn and how these skills will be important in the context of practical situations and the modern world. Additionally, it prepares students for the interactive and digital activities that will occur, ensuring that everyone is aligned with the learning purposes.

Main Objectives

1. Recognize the main trigonometric ratios: sine, cosine, and tangent of an angle in a right triangle.

2. Apply the trigonometric ratios of 30º, 45º, and 60º to calculate the length of the sides of a right triangle.

Side Objectives

1. Relate trigonometric ratios to practical situations in daily life.

Introduction

Duration: 10 - 15 minutes

This stage aims to contextualize students about the specific objectives of the lesson, highlighting what is expected for them to learn and how these skills will be important in the context of practical situations and the modern world. Additionally, it prepares students for the interactive and digital activities that will occur, ensuring that everyone is aligned with the learning purposes.

Warming Up

To start the lesson, contextualize students about the importance of trigonometric ratios in practical life, such as in engineering, architecture, and even technology. Then, ask students to use their phones to research an interesting fact about trigonometric ratios. Encourage them to look for curiosities that relate the topic to the modern world, such as the use of trigonometry in video games, GPS, and applications in social networks. After the research, each student should share their interesting fact with the class.

Initial Reflections

1. What are trigonometric ratios and why are they important?

2. In what practical daily life situations can we apply trigonometric ratios?

3. How are trigonometric ratios used in technologies we frequently use, such as GPS and video games?

4. What is the relationship between the trigonometric ratios of 30º, 45º and 60º and the calculation of lengths in right triangles?

Development

Duration: 70 - 80 minutes

The development phase aims to provide students with a practical and immersive experience where they can apply theoretical concepts of trigonometry in real and playful situations, using modern technologies. This allows for a deeper and more engaging understanding of the content, while developing skills such as teamwork, creativity, and the use of digital tools.

Activity Suggestions

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

Activity 1 - Influencer Mission: Trigonometry on Instagram

> Duration: 60 - 70 minutes

- Objective: Develop collaborative and creative teaching skills while reinforcing trigonometric concepts through an immersive experience on social media.

- Description: Students will be challenged to create a series of Instagram posts explaining trigonometric ratios in a fun and visually appealing way.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group must choose an 'influencer' to be the face of the group.

• Groups must create an Instagram account (can be a test account) or use an existing account with the teacher's authorization.

• Each group should create 3 posts that visually explain the trigonometric ratios sine, cosine, and tangent. The posts should be interactive, using polls, quizzes, and short videos.

• Students should use image and video editing apps like Canva and InShot to create high-quality content.

• Encourage students to use popular educational and math hashtags to increase the reach of their posts.

• At the end, each group should present their posts to the class, explaining the creative process and the mathematical content covered.

Activity 2 - The Virtual Trigonometry Game

> Duration: 60 - 70 minutes

- Objective: Encourage collaboration and healthy competition while reinforcing trigonometric concepts through a playful and interactive experience.

- Description: Students will create a trivia game on trigonometric ratios using online gamification platforms like Kahoot! or Quizizz.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group must create an account on a gamification platform (Kahoot! or Quizizz).

• Groups should prepare a quiz covering the trigonometric ratios sine, cosine, and tangent. Be sure to include challenging questions that use practical and theoretical applications.

• Encourage students to include questions involving the angles of 30º, 45º and 60º, as well as the calculation of lengths in right triangles.

• Groups can use visual resources, such as images and graphs, to enrich their questions.

• In the end, each group will play the quiz created by another group, accumulating scores based on their answers.

• The teacher can reward the group that creates the most challenging and educational quiz.

Activity 3 - Augmented Reality Adventures: Exploring Triangles

> Duration: 60 - 70 minutes

- Objective: Incorporate cutting-edge technology into the learning of trigonometric ratios, providing students with a visual and interactive experience that connects theory and practice.

- Description: Students will use augmented reality (AR) apps to explore angles and side lengths in right triangles.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group will need to download an augmented reality app that allows manipulation of geometric shapes, such as GeoGebra 3D or AR MeasureKit.

• Students should use the app to create right triangles and measure the side lengths and angles.

• Each group must choose triangles with angles of 30º, 45º, and 60º and use the learned trigonometric ratios to calculate the lengths of the sides. The app should be used to visualize the triangles in 3D.

• Groups should document their findings and calculations using screenshots and videos from the app.

• At the end, each group will present their triangles and the calculated measures to the class, explaining how they used trigonometry and AR to achieve their results.

Feedback

Group Discussion

Promote a group discussion with all students to share what they learned while completing the activities and their conclusions. A possible script to introduce this discussion may include:

1. Introduction: Briefly explain the purpose of the discussion and how it will help consolidate learning.
2. Group Presentations: Each group should have 3-5 minutes to share their posts or games, highlighting creative aspects and the mathematical content.
3. Open Debate: Encourage students to ask each other questions about their approaches and discoveries, promoting an environment of knowledge and ideas exchange.
4. Conclusion: Summarize the main ideas discussed and how they relate to the objectives of the lesson.

Reflections

1. What were the main challenges of applying trigonometric ratios in digital activities? 2. How did the use of modern technologies, such as social media and augmented reality, help to better understand trigonometric concepts? 3. In what ways do you believe that knowledge of trigonometric ratios can be useful in practical situations in the future?

360° Feedback

Guide students to perform a 360° feedback step, where each student must receive feedback from their group peers. Explain the importance of providing constructive and respectful feedback. Suggest they address points such as:

1. Strengths: What did the peer do well during the activity?
2. Areas to Improve: Is there anything the peer could do better next time?
3. Overall Contribution: How did the peer contribute to the group's success and the collective learning?

Conclusion

Duration: 10 - 15 minutes

🎯 Conclusion Purpose 🎯 This stage aims to reinforce and consolidate the acquired knowledge, connecting theory to practice in an engaging and meaningful way. By reviewing the content in a summarized form and relating the learning to the modern world and its practical applications, students can perceive the relevance of the studied topic, motivating them to continue exploring and applying these concepts in various situations. 📚✨

Summary

🎉 Festive Trigonometric Summary 🎉 Let’s remember the trigonometric ratios in a fun way? Imagine a party where we have three super special guests: Sine, Cosine, and Tangent! Sine is that friend who always looks up (opposite/hypotenuse), Cosine loves to stay side by side (adjacent/hypotenuse), and Tangent, well, he loves to divide things (opposite/adjacent). At the angles of 30º, 45º, and 60º, they form that perfect band, each with their unique mathematical harmony. 🎶🔺

World Connection

🌐 In the Digital World 🌐 Today, we saw how trigonometry is not stuck in textbooks: it is everywhere! From video game design, where angles create realistic graphics, to the algorithms behind GPS that calculate precise routes. Today’s lesson connected our learning to the modern reality, showing that mathematics is a vital tool in the development of the technologies that shape our daily lives. 💻📲

Practical Application

📏 Everyday Applications 📏 Knowing how to calculate trigonometric ratios is like having a magic key to solve various practical problems: from measuring inaccessible heights with the help of angles, to creating perfect structures in architecture and engineering. Moreover, trigonometry helps us to better understand how various technologies we use daily, such as smartphones and navigation systems, work. 🏗️🚀