Lesson Plan | Active Learning | Polygon 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)

This stage of the lesson plan is crucial for establishing the knowledge base that will be applied and deepened throughout the lesson. The outlined objectives aim to ensure that students can not only theoretically understand but also practically apply the formulas and concepts related to the angles of polygons, essential for the construction of mathematical and geometric reasoning.

Main Objectives:

1. Enable students to calculate the measures of the internal angles of regular polygons.

2. Develop the ability to establish and apply the relationships between internal and external angles in polygons.

Side Objectives:

1. Encourage collaboration and debate among students during practical activities to promote a deeper understanding of the concepts.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the content they studied previously, using problem-based situations that stimulate practical application of the concepts of angles in polygons. Additionally, the contextualization seeks to show the relevance of the subject, connecting it with real situations and inspiring students to see mathematics as an essential and interesting tool. This approach aims to increase students' motivation and understanding of the importance of the topic.

Problem-Based Situations

1. Imagine you are an architect and need to design a conference room in the shape of a regular octagon. How would you calculate the internal angles to ensure all walls fit perfectly?

2. A gardener is planning a new bed in their garden, and they want the bed to have the shape of a regular pentagon. What are the internal angles of this pentagon and how could they use these measures to divide the space symmetrically?

Contextualization

The angles of polygons are not just mathematical abstractions; they play a fundamental role in various everyday applications, from architecture to gardening. For example, in architecture, using regular polygons can create aesthetically pleasing forms and stable structures. Additionally, understanding the relationships between internal and external angles of polygons can assist in engineering and design projects, where symmetry and precision are essential.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to apply and deepen their knowledge about angles in polygons through practical and engaging activities. These activities are meant to be carried out in groups, fostering collaboration, debate, and team problem-solving. Choosing only one of the proposed activities aims to deepen the understanding of mathematical concepts in a more playful and applied context.

Activity Suggestions

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

Activity 1 - Designing the Polygon City

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge about angles in regular polygons to solve a practical drawing and architecture problem.

- Description: In this activity, students will design a city on graph paper, where each building must be represented by a regular polygon. They must calculate and draw the internal angles to ensure that each structure fits correctly in the city plan.

- Instructions:

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

• Distribute graph paper, rulers, and compasses to each group.

• Ask each group to draw on paper a 'blueprint' of a city, where each building must be represented by a different regular polygon.

• Students must calculate the internal angles of each polygon and record their measures next to the drawing.

• After completion, each group presents their city, explaining how they calculated the angles and the relationships they found.

Activity 2 - The Great Polygon Tournament

> Duration: (60 - 70 minutes)

- Objective: Develop problem-solving skills and practical application of mathematical concepts in a competitive and collaborative context.

- Description: Students will compete in a math tournament where they must solve problems related to the internal and external angles of polygons. Each round of the tournament will present challenges of increasing difficulty.

- Instructions:

• Organize the room into challenge stations, each with a different mathematical problem related to angles in polygons.

• Each group of students starts at a station and has a limited time to solve the problem before moving to the next station.

• Each station should have a clear solution attached, so students can verify their answers.

• At the end, score the groups based on the number of problems solved correctly and the accuracy of the solutions.

• Reward the group with the highest score.

Activity 3 - Polygon Explorers

> Duration: (60 - 70 minutes)

- Objective: Apply geometry knowledge in a real context, promoting interaction and active learning.

- Description: In this activity, students will explore the school space in search of polygonal shapes. They must measure and calculate the internal and external angles of each polygon found and create a report of their discoveries.

- Instructions:

• Give each group a list of polygons to find in the school (courtyard, classrooms, hallways).

• Provide each group with a measurement kit (ruler, protractor) and a sheet to record measures and calculations.

• Students should explore the school, measuring and recording the angles of each polygon found.

• Back in the classroom, each group presents their report, highlighting the most interesting measures and the relationships between angles.

• Promote a discussion on how mathematical concepts are present in the school and everyday environment.

Feedback

Duration: (15 - 20 minutes)

This feedback stage is essential to consolidate students' learning, allowing them to reflect on the activities carried out and articulate what they learned. Through group discussion, students have the opportunity to verbalize and share their understanding, which can help clarify doubts and reinforce concepts. Additionally, hearing peers' perspectives can enrich learning, allowing them to see different approaches to the same problems and fostering a deeper and broader understanding of the covered topics.

Group Discussion

At the end of the activities, gather all students for a group discussion. Start the discussion by reminding students of the lesson objectives and encouraging them to share their experiences and discoveries. Use questions such as 'What did you find most challenging about the activities?' and 'How would you apply what you learned outside the classroom?' to guide the conversation and ensure all students have the opportunity to participate and express their ideas.

Key Questions

1. What strategies did you use to calculate the internal angles of the polygons during the activities?

2. How did the relationships between internal and external angles help in solving the proposed problems?

3. Was there any moment when you had to adjust the calculation of the angles? How did you solve it?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is vital to ensure that students have understood and internalized the concepts discussed during the lesson. By summarizing and recapping the content, the teacher reinforces learning, ensuring that students can recall and apply the knowledge acquired. Moreover, emphasizing the practical relevance of the topic helps to motivate students and view mathematics as an essential and interesting tool.

Summary

To conclude, the teacher should summarize the main concepts covered, reiterating the formulas and methods to calculate internal and external angles of regular polygons. It should emphasize the importance of symmetry and precision in architecture and design, fundamental concepts to solve the practical problems proposed during the lesson.

Theory Connection

During the lesson, the connection between the studied theory and practical applications was clearly established. Activities such as 'Designing the Polygon City' and 'The Great Polygon Tournament' allowed students to see the real use of geometric concepts in everyday situations and real projects, solidifying theoretical understanding through practice.

Closing

Finally, it is crucial to highlight that knowledge about angles in polygons is not limited to the school environment but applies to various practical situations in everyday and professional life, such as in design, engineering, architecture, and even art. Therefore, understanding these concepts is essential for developing important mathematical and spatial skills.