Lesson Plan | Teachy Methodology | Inscribed Polygons

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to clarify the main and secondary objectives of the lesson on inscribed polygons, providing a clear understanding of what is expected to be achieved. By defining the objectives, students will be able to direct their learning efforts more effectively, while the teacher can structure activities and mediate them in alignment with these objectives.

Main Objectives

1. Understand the concept of inscribed polygons and their importance in geometry.

2. Relate the length of the side of an inscribed polygon to the radius of the circumscribed circle.

3. Apply knowledge about inscribed polygons to solve practical problems.

Side Objectives

1. Develop critical thinking and problem-solving skills.
2. Encourage collaboration and effective communication among students.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to introduce the topic in an engaging and relevant way, connecting it to the students' reality. By using mobile devices to research interesting facts, students begin to establish a personal connection with the topic. The key questions facilitate an initial debate, helping to align students' prior understanding and prepare the ground for practical activities, where they will apply the concepts already studied.

Warming Up

Inscribed polygons are geometric figures drawn within a circle, where all vertices touch the circumference. This creates an interesting mathematical relationship between the sides of the polygon and the radius of the circle. To engage students from the start, ask them to use their cell phones to find an interesting fact about inscribed polygons. It can be a historical curiosity, a practical application, or even something related to their appearance in different cultures or technologies.

Initial Reflections

1. What are inscribed polygons and where can we find them in the real world?

2. How does the geometry of inscribed polygons relate to the circle that encompasses them?

3. What are some examples of inscribed polygons that you already knew before studying this topic?

4. Why is it important to understand the relationship between the side of the inscribed polygon and the radius of the circle?

5. How could inscribed polygons be useful in fields like engineering, architecture, and art?

Development

Duration: 65 - 75 minutes

The purpose of this stage is to deepen students' knowledge about inscribed polygons through interactive and practical activities that utilize modern technology. By working in groups, students develop skills in collaboration, communication, and critical thinking while applying mathematical concepts in relevant and engaging contexts.

Activity Suggestions

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

Activity 1 - TikTok Polygon Challenge 📱🎬

> Duration: 60 - 70 minutes

- Objective: Engage students in learning through the creation of digital content, encouraging the use of new technologies and effective communication of mathematical concepts.

- Description: Students must create a TikTok video creatively explaining the concept of inscribed polygons and showing step by step how to calculate the relationship between the side of the polygon and the radius of the circumscribed circle. In the video, they can use animations, hand-drawn graphics, or even enact a small story that contextualizes the application of inscribed polygons in real life.

- Instructions:

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

• Each group must create a specific TikTok account for the video (or use a personal account, if preferred).

• Research examples of educational TikTok videos for inspiration.

• Draft a script that explains the concept of inscribed polygons and the relationship between the side of the polygon and the radius of the circumscribed circle.

• Record the video using resources like animations, illustrations, or enactments.

• Edit the video to ensure it is clear and engaging.

• Publish the video on TikTok with a specific hashtag created for the activity, such as #PolygonChallenge.

• Share the video link with the class and the teacher for assessment.

Activity 2 - Mathematical Treasure Hunt 🔍📏

> Duration: 60 - 70 minutes

- Objective: Stimulate collaboration, critical thinking, and practical application of mathematical concepts through a gamified activity.

- Description: Students will participate in a 'treasure hunt' where each clue requires solving a problem involving inscribed polygons. The activity will take place in an online environment (such as Google Classroom or Microsoft Teams) where clues will be provided sequentially. Each group must solve the clues to advance and find the final 'treasure', which can be a digital certificate of 'Polygon Master'.

- Instructions:

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

• Use an online platform to distribute the clues (Google Classroom, Microsoft Teams, etc.).

• Provide the first clue to all groups simultaneously.

• Each clue must involve a practical problem related to inscribed polygons, such as calculating the side of an n-sided polygon inscribed in a circle of radius r.

• Groups must submit the correct answer for each clue to advance to the next clue.

• The team that solves all the clues first wins the 'treasure' and receives a digital certificate.

Activity 3 - Mathematical Digital Influencer 🧑‍🏫💡

> Duration: 60 - 70 minutes

- Objective: Promote effective communication and the use of social media as an educational tool, transforming students into facilitators of mathematical knowledge.

- Description: Students must create a post on Instagram or a series of stories explaining the concept of inscribed polygons and applying them in everyday situations. In addition to the post, they must interact with peers and answer questions or comments, acting as true digital influencers in the field of mathematics.

- Instructions:

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

• Each group must create an Instagram account specifically for the activity (or use a personal account).

• Research how digital influencers communicate complex information in simple and engaging ways.

• Create a post or a series of stories explaining the concept of inscribed polygons.

• Use images, graphics, and examples from everyday life to make the content more accessible.

• Publish the content on Instagram with a specific hashtag, such as #InscribedPolygonOnInsta.

• Interact with comments and questions raised by peers or other followers, reinforcing collaborative learning.

Feedback

Duration: 25 - 30 minutes

The purpose of this stage is to provide a moment for reflection and sharing of experiences, allowing students to consolidate their learning collectively. Through group discussion and 360° feedback, students can recognize their strengths and areas for improvement while developing communication and collaboration skills essential for learning and professional life.

Group Discussion

Conduct a group discussion with all students, where each group shares what they learned while carrying out the proposed activities and their conclusions about the topic of inscribed polygons. Use the following script to introduce the discussion:

1. Introduction: Thank the students for their effort in the activities and explain the importance of sharing what they learned.
2. Group Presentations: Request that each group presents their work in up to 5 minutes, highlighting the main points of their activity.
3. Open Discussion: After each presentation, open the floor to questions and comments from other students about the presented work.
4. Connection to the Real World: Ask students to discuss how the concepts learned about inscribed polygons can be applied in everyday situations in various fields such as engineering, architecture, and art.
5. Conclusion: Summarize the main learnings from the discussion and thank everyone for their active participation.

Reflections

1. What were the biggest difficulties encountered while conducting the activities and how did you overcome them? 2. How did the activities help you better understand the relationship between the side of the inscribed polygon and the radius of the circle? 3. How do you think knowledge about inscribed polygons can be applied in your lives or future careers?

360° Feedback

Conduct a 360° feedback phase where each student must receive feedback from the other group members. Guide the class to ensure that the feedback is constructive and respectful, highlighting strengths and areas for improvement. Use the following steps to guide the feedback:

1. Positive Feedback: Each student highlights something positive about the contributions of their classmates.
2. Areas for Improvement: Each student suggests one or two areas where their classmates can improve.
3. Appreciation: Encourage students to thank each other for the feedback received and for collaborating during the activity.

Conclusion

Duration: 10 - 15 minutes

📝 Purpose: The purpose of this stage is to consolidate learning, ensuring that students leave the lesson with a clear and applicable understanding of the discussed concepts. Through a fun and relevant recap, this section aims to connect the material learned with the real world and its numerous possibilities for application, reinforcing the practical importance of inscribed polygons. 🎯✅

Summary

📚 Fun Summary: Imagine being in a mathematical theme park! Today, we talked about inscribed polygons, which are geometric figures drawn inside a circle, with all vertices touching the circumference. We learned to make the connection between the length of the side of the polygon and the radius of the circle. This is like uncovering hidden secrets behind the magical doors of mathematics! 🧙‍♂️🔮

World Connection

🌐 Connection to the Current World: In the frantic digital universe we live in, the concepts studied today apply directly to fields like engineering, architecture, and even digital animations. The techniques used here are similar to those that allow futuristic buildings to be designed or that create stunning graphics in video games and our favorite social media! 🎮🏙️

Practical Application

🔧 Importance for Everyday Life: Understanding inscribed polygons is not just an academic exercise; it is a practical skill that can be used to solve real problems. From designing everyday objects to creating complex architectural structures, knowledge of inscribed polygons allows us to navigate and shape our world more effectively. 🏗️🔍