Objectives (5 - 7 minutes)

1. Understand what regular polygons are: Students should be able to identify and define regular polygons, understanding their main characteristics, such as the congruence of sides and angles. The teacher can use visual and interactive examples to facilitate understanding.

2. Differentiate regular polygons from irregular ones: Students should be able to distinguish between regular and irregular polygons, identifying the properties that define each type. The teacher can use examples of each type of polygon and ask students to describe the differences.

3. Calculate the measure of an internal angle of a regular polygon: Students should be able to use the formula (n - 2) * 180 / n to calculate the measure of an internal angle of a regular polygon, where n is the number of sides. The teacher should provide students with calculation examples and step-by-step guidance.

Secondary Objectives:

• Stimulate critical thinking and problem-solving: The teacher should encourage students to think critically about the concepts presented and apply them to solve problems. This can be done through guiding questions and practical activities.

• Promote active participation in the classroom: The teacher should create an interactive learning environment, encouraging students to actively participate in discussions and activities. This can be done through group activities, oral presentations, and class discussions.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by reviewing the concepts of angles and polygons that were previously studied. This can be done through a quick five-minute review using interactive questions and drawings on the board to engage students in the review.

2. Problem situation 1: Next, the teacher can propose the following problem situation: "Imagine that you have been hired to design an amusement park. The client wants you to create an area with toys in the shape of polygons. He asked that all polygons be regular, but you realize that you don't exactly know what that means. How would you explain to the client what regular polygons are and how to differentiate them from irregular polygons?"

3. Contextualization: The teacher can then contextualize the importance of the subject, explaining that regular polygons are very common in our daily lives, often used in architecture, design, engineering, and even in games and toys. Therefore, understanding and being able to differentiate regular polygons from irregular ones is a valuable and useful skill.

4. Problem situation 2: To spark students' interest, the teacher can propose another problem situation: "Let's suppose you are playing a strategy game where you need to calculate the area of a battlefield, which is a regular hexagon. You know that each side of the hexagon measures 3 meters. How can you use your knowledge about regular polygons to calculate the area of the battlefield?"

5. Curiosity: Finally, the teacher can share the curiosity that regular polygons are one of the most common shapes in nature, appearing in structures such as beehives, honeycombs, and crystals. This curiosity can help spark students' interest and motivate them to learn more about the topic.

Development (20 - 25 minutes)

1. Activity "Building Regular Polygons" (10 - 12 minutes):

   • The teacher should divide the class into groups of five students and provide each group with a ruler, compass, and paper.
   • The activity consists of each group building, using the provided materials, three different regular polygons (triangle, square, and pentagon) and three irregular polygons (triangle, square, and pentagon).
   • During the activity, the teacher should circulate around the room, assisting groups that encounter difficulties and asking questions to promote reflection and understanding of the concept. For example, "Why do you think this polygon is irregular?" or "How could you transform this irregular polygon into a regular one?"
   • After the construction, each group should present their polygons to the class, explaining why they consider them to be regular or irregular. The teacher should correct and complement the explanations if necessary.

2. Activity "Calculating Internal Angles" (10 - 12 minutes):

   • Still in groups, students should receive cards with different regular polygons drawn, but without the measure of the internal angles.
   • The challenge is to calculate the measure of each internal angle of the polygon, using the formula (n - 2) * 180 / n, where n is the number of sides of the polygon. Students should record their answers on the back of the card.
   • After the calculation, groups should exchange cards with other groups, who will verify if the calculation was done correctly. The teacher should supervise this activity and clarify doubts.
   • At the end of the activity, the teacher should correct the calculations with the class, reinforcing the application of the formula.

3. Activity "Polygons in Nature and Culture" (5 - 7 minutes):

   • To conclude the Development stage, the teacher should propose a class discussion about the presence and importance of regular polygons in nature and culture.
   • The teacher can start the discussion by asking students if they can remember or identify any examples of regular polygons in nature (such as beehives, for example) or in culture (such as in games or artworks).
   • Students should be encouraged to share their observations and make connections between the theory learned and the world around them.

These activities aim to promote the understanding of the concept of regular polygons, the application of the formula for calculating internal angles, and the ability to differentiate regular polygons from irregular ones. In addition, group activities promote collaboration and communication among students, contributing to the development of socio-emotional skills.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should gather all students and start a group discussion. Each group will have a maximum of 3 minutes to share their solutions, conclusions, or observations from the activities carried out. During the presentations, the teacher should encourage other students to ask questions and make comments, promoting a collaborative learning environment. The teacher should ensure that all groups have the opportunity to speak and that all voices are heard.

2. Connection with Theory (2 - 3 minutes): After the presentations, the teacher should make the connection between the activities carried out and the theory presented at the beginning of the lesson. The teacher can highlight how the practical activities helped reinforce the theoretical concepts and the application of the formula for calculating internal angles. Additionally, the teacher should clarify any misunderstandings or misconceptions that may have arisen during the activities.

3. Individual Reflection (2 - 3 minutes): To conclude the lesson, the teacher should propose that students reflect individually on what they have learned. The teacher can ask questions such as:

   • What was the most important concept you learned today?
   • What questions have not been answered yet?
   • How can you apply what you learned today in everyday situations or in other subjects?
   • What would you like to learn more about on this topic?

4. Feedback and Closure (1 minute): The teacher should ask students to share their reflections, doubts, or suggestions. The teacher should thank the students for their participation and effort, and conclude the lesson by reinforcing the importance of the subject and motivating students to continue studying and practicing at home. The teacher can suggest complementary study materials, such as videos, interactive games, or math problems involving regular polygons.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes): The teacher should start the Conclusion of the lesson by briefly summarizing the main points covered. They should recap the definition of regular polygons, the formula for calculating the measure of an internal angle, and the characteristics that distinguish regular polygons from irregular ones. The teacher can use the board or slides to write down these points and facilitate students' visualization.

2. Connection between Theory and Practice (1 minute): The teacher should emphasize how the lesson connected theory with practice. They can highlight how the activities of building polygons and calculating internal angles allowed students to apply theoretical concepts in a practical and concrete way. The teacher can also recall how the discussion about polygons in nature and culture helped contextualize the importance of the subject in students' daily lives.

3. Complementary Materials (1 - 2 minutes): The teacher should suggest complementary study materials for students who wish to deepen their knowledge on the subject. These materials may include textbooks, educational websites, explanatory videos, interactive games, and math problems. The teacher can share these suggestions through the school's virtual learning environment or via email, so that students can easily access them.

4. Application in Daily Life (1 minute): Finally, the teacher should emphasize the importance of the subject for students' daily lives. They can reinforce that the ability to identify and differentiate regular polygons from irregular ones is useful in various areas, such as architecture, engineering, design, games, and even in everyday situations, such as organizing spaces or solving puzzles. The teacher can also encourage students to observe the environment around them for examples of regular polygons, reinforcing the connection between mathematics and the real world.