Objectives (5 - 7 minutes)

1. Understand the concept of Regular Polygon: Students should be able to define what a regular polygon is, recognizing its main characteristics, such as equal sides and angles. They should also understand the importance of this type of geometric figure in mathematics and practical applications.

2. Construct Regular Polygons: Through a practical method, students should learn how to construct regular polygons. They should be able to use tools such as a ruler, compass, and protractor efficiently to achieve this goal.

3. Identify and Name Regular Polygons: In addition to knowing how to construct regular polygons, students should be able to identify and name these geometric figures. They should understand the correct nomenclature for regular polygons, such as equilateral triangle, square, pentagon, etc.

Secondary Objectives:

• Promote Problem Solving: Through the construction of regular polygons, students will be challenged to solve practical problems, such as determining the center of the polygon, the radius measurement, and the correct positioning of the compass.

• Stimulate Critical Thinking: During the learning process, students will be encouraged to question and reflect on the concepts presented, thus promoting the development of critical thinking.

Introduction (10 - 15 minutes)

1. Reviewing Basic Concepts: The teacher starts the lesson by reviewing basic geometry concepts, such as lines, segments, rays, and angles. It is important that students are familiar with these concepts before moving on to the construction of regular polygons.

2. Problem Situation 1: The teacher presents the first problem situation: 'Imagine that you need to build a perfect soccer field, with a regular hexagon shape. How would you ensure that all sides and angles are equal?'

3. Problem Situation 2: Next, the teacher presents the second problem situation: 'Suppose you are designing a bridge and need a section with a regular pentagon shape. How could you build this geometric figure with precision?'

4. Contextualization of the Subject's Importance: The teacher contextualizes the importance of the subject, explaining that the ability to construct and identify regular polygons is essential in various areas, such as architecture, engineering, design, and even art.

5. Topic Introduction with Curiosities: To spark students' interest, the teacher shares some curiosities about regular polygons. For example, such as the fact that the number of regular polygons is limited and that, besides the triangle, square, and pentagon, there are no more regular polygons with fewer than 360 sides. Another curiosity is that, contrary to what many think, most honeycombs are not perfect hexagons, but rather irregular shapes.

6. Topic Presentation: Finally, the teacher introduces the topic of the lesson: 'Today, we will learn about regular polygons and how to construct them. By the end of the lesson, you will be able to construct, identify, and name regular polygons accurately and efficiently.'

Development (20 - 25 minutes)

1. Regular Polygon Construction Activity (10 - 12 minutes): The teacher divides the class into groups of up to five students. Each group receives a sheet of paper, a compass, a ruler, and a protractor. The teacher then challenges the groups to construct regular polygons of different sizes, starting with the triangle and square and progressing to polygons with more sides, such as pentagons, hexagons, etc. During the activity, the teacher circulates around the room, observing and guiding the students as needed.

   • Step 1: Each group should start by drawing a circle on the paper using the compass. The circle will serve as the base for the construction of the regular polygon.

   • Step 2: Next, the students should use the ruler to draw a diameter of the circle. The diameter is the line that passes through the center of the circle and divides it into two equal parts.

   • Step 3: From the point where the diameter meets the circle's circumference, the students should use the compass to mark points along the circumference, equally spaced. The number of points to be marked will depend on the polygon the group is trying to construct. For example, for a triangle, three points will be needed; for a square, four points; and so on.

   • Step 4: Finally, the students should use the ruler to connect each marked point on the circumference with the neighboring point until all points are connected, and the regular polygon is complete.

2. Regular Polygon Identification and Naming Activity (5 - 7 minutes): After constructing the regular polygons, the teacher proposes a new challenge: students must identify and name the polygons they built. The teacher provides a list of names of regular polygons (triangle, square, pentagon, hexagon, etc.), and the students must associate the correct name with each figure they constructed. This activity allows students to consolidate the concept of regular polygons and practice the correct nomenclature.

3. Problem-Solving Activity (5 - 6 minutes): Finally, the teacher presents students with some practical application problems involving regular polygons. For example, 'If the side length of a regular polygon is 5 cm, what is the radius of the circle that circumscribes it?' or 'If the radius of the circle circumscribing a regular pentagon is 10 cm, what is the length of the pentagon's side?' Students, in their groups, should try to solve the problems, applying the knowledge acquired during the lesson. The teacher circulates around the room, assisting groups that encounter difficulties and correcting answers when necessary. This activity allows students to see the practical application of regular polygons and develop problem-solving skills.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher calls on each group to share their solutions and conclusions with the class. Each group has a maximum of 3 minutes to present. During the presentations, the teacher should encourage the participation of all students, asking questions to ensure everyone understands the concepts discussed. This helps to consolidate learning and promote the exchange of ideas among students.

2. Connection with Theory (1 - 2 minutes): After all presentations, the teacher summarizes the main points discussed, connecting them with the theory presented at the beginning of the lesson. He reinforces the importance of understanding the concepts of regular polygons and their practical applications. Additionally, the teacher can highlight the skills students developed during the lesson, such as the ability to solve problems, work in teams, and think critically.

3. Learning Verification (2 - 3 minutes): The teacher then verifies students' learning with targeted questions. He may ask, for example, 'What is a regular polygon?' or 'What tools did you use to construct the regular polygons?' The teacher should ensure that all students participate in the discussion, allowing everyone the opportunity to express what they have learned.

4. Final Reflection (1 minute): To conclude the lesson, the teacher proposes that students reflect for a minute on what they have learned. He may ask questions like 'What was the most important concept you learned today?' or 'What questions have not been answered yet?' The goal of this reflection is to encourage students to become aware of their own learning and identify any gaps in their understanding that may need further clarification.

5. Teacher Feedback (1 minute): Finally, the teacher thanks the students for their participation and provides brief feedback on the class's performance. He may praise students' efforts, point out strengths, and suggest areas for improvement. Teacher feedback is essential for students' continuous development and to motivate them to keep learning.

Conclusion (5 - 7 minutes)

1. Summary of Contents (1 - 2 minutes): The teacher summarizes the main points covered in the lesson. He reiterates the definition of regular polygons, highlighting their main characteristics, such as equal sides and angles. He then recalls the process of constructing regular polygons, emphasizing the importance of correctly using tools like compasses and rulers. Finally, he reviews the correct nomenclature for regular polygons, reinforcing the identification and naming of these geometric figures.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher emphasizes how the lesson connected the theory, practice, and applications of regular polygons. He reminds students how the theoretical understanding of concepts like equal sides and angles was applied in practice during the construction of regular polygons. Additionally, the teacher highlights how the ability to construct and identify regular polygons has practical applications in various areas, such as architecture, engineering, and design.

3. Extra Materials (1 - 2 minutes): The teacher suggests some extra materials for students who wish to deepen their knowledge of regular polygons. He may recommend math books, educational websites, YouTube videos, and geometry apps. Additionally, the teacher may provide additional exercises for students to practice at home, reinforcing what was learned in the classroom.

4. Subject Relevance (1 minute): Finally, the teacher emphasizes the importance of the subject for students' daily lives. He explains that the ability to construct and identify regular polygons is useful not only in practical applications but also in developing problem-solving skills, critical thinking, and teamwork. The teacher encourages students to apply what they have learned not only in their future careers but also in their everyday lives.