Lesson Plan | Active Learning | Inscribed Angles

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The objective-setting stage is crucial for establishing the direction of learning and ensuring that students are aligned with learning goals. By focusing on calculating and solving problems with inscribed angles, this lesson aims to consolidate students' theoretical and practical understanding of the topic, preparing them to apply these concepts in more complex contexts. Furthermore, the skills developed are essential for understanding geometry at more advanced levels and for applications in various fields of knowledge.

Main Objectives:

1. Empower students to calculate inscribed angles in a circle, using the relationship between the inscribed angle and the central angle, understanding that the central angle is double the inscribed angle.

2. Develop the ability to solve practical problems involving inscribed angles, reinforcing theory through concrete applications.

Side Objectives:

1. Encourage students' curiosity and logical reasoning through challenges involving inscribed angles in unconventional situations.
2. Promote teamwork and effective communication during practical activities, reinforcing the importance of dialogue and collaboration in the learning process.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and activate prior knowledge, using problem situations that stimulate curiosity and the practical application of inscribed angles. Furthermore, contextualization seeks to connect the content with the real world, showing the relevance of inscribed angles in various everyday and professional situations, thereby increasing students' interest in the topic.

Problem-Based Situations

1. Consider a clock whose hands are perfectly aligned at 12:00. If the minute hand moves 30 degrees, what angle is formed by the hour hand relative to noon?

2. Imagine a circular park with a large clock in the center. A person is sitting 40 meters from the center, looking at the clock. They see that the angle between the positions of the hands is 90 degrees. What is the minimum distance this person needs to travel to be 20 meters from one of the hands?

Contextualization

Inscribed angles are not just a mathematical curiosity, but have practical applications in everyday life. For example, in engineering and navigation, where the notion of directions and distances is crucial, or in graphic design, where precision in the arrangement of elements is essential. Additionally, the history of measuring angles and their use in different civilizations can be explored to understand how these concepts have evolved and become fundamental to various fields of knowledge.

Development

Duration: (65 - 75 minutes)

The development stage is designed to allow students to practically and interactively apply the concepts of inscribed angles they studied previously. The proposed activities aim to reinforce learning through challenging and contextualized situations, encouraging collaboration, critical thinking, and problem-solving. This approach not only solidifies theoretical knowledge but also develops teamwork skills and creative mathematical thinking.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Angle Race

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of inscribed angles in a dynamic and collaborative way, developing calculation and quick reasoning skills.

- Description: In this playful activity, students will be divided into groups of up to 5 people and participate in a relay race, where each station contains a mathematical challenge involving inscribed angles. Each station will have a circle marked on the ground, representing a clock, and students will need to calculate the angle formed by the hands at different times.

- Instructions:

• Split the class into groups of no more than 5 students.

• Each group starts at the first station, where they will find a clock drawn on the ground and a specific time (e.g., 3:00).

• Students must calculate the angle formed by the clock hands and write down the answer.

• After calculating, the group runs to the next station, where they will find another time, and so on.

• The first group to correctly complete all the stations and cross the finish line wins.

Activity 2 - The Treasure of the Geometric Pirates

> Duration: (60 - 70 minutes)

- Objective: Develop spatial orientation skills and practical application of inscribed angle concepts in a game context, reinforcing teamwork.

- Description: Students, organized in groups, take on the role of pirates searching for a hidden treasure on an island. To find the treasure, they must decipher a map that contains clues based on calculations of inscribed angles at strategic points on the island.

- Instructions:

• Each group receives a map of the island that contains points marked with coordinates.

• Students must use the coordinates to locate themselves on the map and calculate the necessary inscribed angles to advance to the next clue.

• The clues lead to different points on the island, and the final challenge is to find the X that marks the treasure's location, using the calculations of inscribed angles to guide the way.

• The group that finds the treasure first, showing the correct calculations of the angles, wins the activity.

Activity 3 - Builders of Mathematical Bridges

> Duration: (60 - 70 minutes)

- Objective: Apply the concepts of inscribed angles in practice, promoting critical thinking and the resolution of simple engineering problems.

- Description: In this activity, groups of students are challenged to build a bridge out of popsicle sticks that must support a small cart. To do this, they need to correctly calculate and apply the inscribed angles to ensure the stability of the structure.

- Instructions:

• Provide each group with popsicle sticks, glue, a small cart, and a sheet with specifications for the necessary angle for each joint of the sticks.

• Students must calculate the necessary inscribed angles and build the bridge according to the project's specifications.

• After construction, each group tests their bridge by placing the cart on it. The bridge that supports the most weight and is the most stable wins.

• At the end, each group presents their bridge, explaining the calculations made and the solutions found.

Feedback

Duration: (15 - 20 minutes)

This stage of the lesson plan aims to consolidate students' practical learning, allowing them to reflect on the application of the concepts of inscribed angles in different contexts. The group discussion helps reinforce collective understanding and promotes valuable idea exchange, where students can learn from each other and develop communication and argumentation skills. Additionally, this stage is essential for the teacher to assess students' understanding and clarify any remaining doubts, ensuring the effectiveness of teaching.

Group Discussion

Start the group discussion by inviting all students to gather in a circle and share their experiences during the activities. Suggest that each group comment on the challenges faced, the strategies used to overcome them, and what they learned about inscribed angles. Encourage students to express how the practical activities helped consolidate theoretical knowledge and the applicability of the topic in real situations.

Key Questions

1. What were the main challenges your group faced when applying the concepts of inscribed angles in the activities, and how did you overcome them?

2. How did the relationship between the inscribed angle and the central angle help in solving the proposed problems?

3. What lessons can you take from these activities to apply in other mathematical or everyday situations?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage is crucial for reinforcing learning and ensuring that students have a clear and consolidated understanding of the concepts discussed during the lesson. By summarizing the topics addressed and highlighting the connection between theory and practice, this section helps to fix the content in students' memories. Moreover, by discussing the relevance of inscribed angles in the real world, students can visualize the importance of mathematical concepts and their applicability, motivating them to explore the subject more deeply.

Summary

In conclusion, it is essential to summarize the concepts of inscribed angles covered in today's lesson. Students learned to calculate and solve problems involving inscribed angles in a circle, understanding the relationship between the inscribed angle and the central angle, which is double the former. Through practical activities such as 'The Angle Race' and 'The Treasure of the Geometric Pirates', they were able to apply these concepts in a dynamic and collaborative manner.

Theory Connection

Today's lesson was structured to effectively connect theory and practice. We started with an introduction that encompassed problem situations and practical contextualizations, setting the stage for the interactive activities. During the execution of the tasks, students could see how the theoretical concepts of inscribed angles apply in real situations, strengthening their understanding and memory of the content.

Closing

Understanding inscribed angles is crucial not only for mathematics but also for practical applications in various fields, such as engineering, design, and even in daily activities. The ability to calculate and analyze inscribed angles allows students to better visualize geometric relationships and apply this knowledge in various contexts, making mathematics more tangible and relevant to their lives.