Lesson Plan | Teachy Methodology | Inscribed Angles

Objectives

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to ensure that students understand the main objectives of the class and know what is expected of them. This stage serves as a clear guideline on the knowledge and skills that students need to acquire throughout the lesson, preparing them for the practical activities that will follow.

Main Objectives

1. Understand the relationship between inscribed angles and central angles in a circle.

2. Calculate inscribed angles using the relationship with central angles.

Side Objectives

1. Apply concepts of inscribed angles in practical problems.
2. Develop skills in solving mathematical problems through collaborative activities.

Introduction

Duration: 15 to 20 minutes

The purpose of this stage of the lesson plan is to engage students from the beginning, establishing a connection between the content that will be explored and its practical applications in the real world. Additionally, this moment creates an interactive and collaborative environment, preparing students for the practical activities that will follow.

Warming Up

Explain to students that today’s lesson will focus on inscribed angles and how they relate to central angles in a circle. Ask students to use their phones to research an interesting fact about inscribed angles and share it with the class. For example, they can look for information about the applications of inscribed angles in architecture, engineering, or even in art. Encourage them to be quick and creative in their search, highlighting the importance of connecting what is studied in class with the world around them.

Initial Reflections

1. What is an inscribed angle?

2. How does a central angle relate to an inscribed angle?

3. In what practical everyday situations do you think knowing inscribed angles could be useful?

4. Did anyone find an interesting fact about inscribed angles during the research that they would like to share?

Development

Duration: 70 to 80 minutes

The purpose of this stage of the lesson plan is to provide students with the opportunity to apply the studied concepts about inscribed angles practically and creatively, using digital tools. The activities are designed to stimulate collaboration, problem-solving, and the connection of mathematical knowledge with the modern world.

Activity Suggestions

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

Activity 1 - Inscribed Angles in Video

> Duration: 60 to 70 minutes

- Objective: Allow students to explore and explain the relationship between inscribed angles and central angles in a creative and practical way, using modern digital tools.

- Description: Students will be divided into groups and create a 'YouTuber' style video explaining the relationship between inscribed angles and central angles. They should use practical examples, such as drawing circles and solving problems, while recording their videos.

- Instructions:

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

• Each group will use their phones to record an explanatory video about the relationship between inscribed angles and central angles.

• Encourage students to be creative and use visual elements, such as drawings, animations or everyday objects to illustrate the concepts.

• The videos must include practical examples and problem-solving.

• Each group will have 40 minutes to plan, record, and edit the video.

• In the final 20 minutes, each group will present their video to the class.

Activity 2 - Online Geometric Treasure Hunt

> Duration: 60 to 70 minutes

- Objective: Stimulate problem-solving and practical application of the concepts of inscribed and central angles through a fun and engaging activity using digital tools.

- Description: Students will participate in an online treasure hunt game, where they will need to solve riddles and problems involving inscribed and central angles. Each riddle solved will lead to the next, until reaching the final 'treasure'.

- Instructions:

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

• Provide each group with a link to access the online treasure hunt platform.

• Each challenge or riddle presented on the platform will include problems about inscribed and central angles.

• Students must solve each riddle to advance to the next.

• Encourage the use of digital tools, such as geometry apps, online calculators and tutorial videos.

• The first group to find the final 'treasure' wins the activity.

Activity 3 - Mathematical Influencers on Instagram

> Duration: 60 to 70 minutes

- Objective: Develop students' ability to explain mathematical concepts clearly and engagingly using popular digital platforms and visual resources.

- Description: Students will create educational posts for a fictional Instagram profile, explaining concepts and curiosities about inscribed angles and their relationship with central angles. They should use images, graphics, and short texts to make the content interesting and easy to understand.

- Instructions:

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

• Each group will create a series of educational posts for a fictional Instagram profile.

• The posts must explain concepts about inscribed and central angles, using images, graphics and short texts.

• Encourage students to think like digital influencers, creating content that grabs attention and is shareable.

• Each group will have 40 minutes to create their posts using design apps or online image editors.

• In the final 20 minutes, each group will present their creations to the class.

Feedback

Duration: 15 to 20 minutes

The purpose of this stage of the lesson plan is to provide a moment for reflection and exchange of experiences, strengthening collaborative learning. Through group discussion, students have the opportunity to consolidate the acquired knowledge, share difficulties and solutions, and receive feedback from peers, promoting a constructive and inclusive learning environment.

Group Discussion

Promote a group discussion with all students. Start by asking each group to share their experiences creating their videos, participating in the treasure hunt, and developing posts for Instagram. Encourage each group to explain the main challenges they encountered and how they overcame them. Use the following script to introduce the discussion:

1. Introduction: 'Now that we have concluded our activities, let's share our experiences. Each group will have a few minutes to talk about what they learned and the challenges they faced.'
2. Sharing Experiences: 'We will start with the group that made the YouTuber style video. What did you find most interesting about the activity? Did you encounter any difficulties? How did you solve them?'
3. Discussion on Applicability: 'How do you think you can apply the concepts of inscribed and central angles outside the classroom?'
4. Final Reflection: 'What do you think you could have done differently? Is there anything you learned today that changed the way you see mathematics?'

Reflections

1. What was the biggest challenge you encountered during the activities, and how did you manage to overcome it? 2. How did the use of digital tools help in understanding the concepts of inscribed and central angles? 3. In what ways do you think you can apply the knowledge of inscribed angles in everyday situations?

360° Feedback

For the 360° Feedback stage, explain to students that each of them will give and receive feedback from their group peers constructively and respectfully. Instruct students to follow this scheme for providing feedback:

1. Positive Aspects: Each student should mention something positive about each peer's contribution to the group. Examples: 'I liked the way you explained the concepts in the video' or 'Your idea for the Instagram post was very creative.'
2. Areas for Improvement: Respectfully, each student should mention something that the peer could improve. Examples: 'I think we could have used more visual examples' or 'Maybe we could have planned our recording time better.'
3. Final Suggestions: Each student should give a suggestion on how the peer can continue improving. Examples: 'You could practice explaining out loud more before recording' or 'It would be interesting if you explored more design tools for the posts.'

Conclusion

Duration: 10 to 15 minutes

 Purpose of the Conclusion 

The purpose of this last stage is to consolidate the knowledge acquired throughout the lesson and show students the relevance of the concepts learned in the context of the modern world. It is a moment to reflect on how learning can be applied outside the classroom, encouraging students to see mathematics in a practical and engaging way.

Summary

 Class Summary: Inscribed Angles 

Imagine that the inscribed angle is like the spectator in a circular stadium, and the central angles are the spotlights illuminating the stage in the middle. Basically, the central angle is twice the inscribed angle!  During the lesson, you became mathematical influencers, solved riddles in a geometric treasure hunt, and produced YouTuber style videos. You really dug into the relationship between inscribed and central angles! 

World Connection

 In the Modern World 

The concepts we learned today appear in many places, from clock designs and building architectures to video games that use complex graphics. Understanding these angles helps us better understand how the world around us is structured and how we can interact with it in more meaningful and innovative ways.

Practical Application

 Applications 

Knowing how to calculate and solve problems involving inscribed angles is not just useful for passing the test! These skills are fundamental in areas such as engineering, architecture, graphic design, and even in emerging professions like game development and augmented reality. In daily life, this can be applied in tasks such as space planning and solving practical issues involving geometry.