Objectives (5 - 10 minutes)

1. Understanding Regular Polygons: The teacher must ensure that students understand what polygons are, and in particular, what regular polygons are. Students should be able to identify the main characteristics of a regular polygon, such as equal sides and angles.

2. Identification of Regular Polygons: Students should be able to identify various examples of regular polygons in their environment, such as a circle, a square, a hexagon, etc. The teacher can encourage students to look for examples in their classroom, school, or even in their homes.

3. Calculation of Measures in Regular Polygons: Once students understand what regular polygons are and how to identify them, the teacher should teach them how to calculate the measures of the sides and angles in a regular polygon. This can be done through specific formulas and practical examples.

   Secondary Objectives:

   • Development of Critical Thinking Skills: When working with regular polygons, students will have the opportunity to develop their critical thinking skills, as they will need to solve problems and make decisions based on their knowledge of regular polygons. The teacher should encourage students to think critically and discuss their ideas and solutions with the class.

   • Encouragement of Autonomous Study: The teacher should promote students' autonomy, encouraging them to study the lesson content outside the school environment. To do this, they can suggest additional readings, educational online videos, and practical exercises to be done at home.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the lesson by reviewing the concepts of polygons and angles that were studied in previous classes. This is essential for students to understand the new content that will be presented. Questions can be asked to verify the retention of these concepts.

2. Problem Situations: The teacher should propose two problem situations involving regular polygons. For example:

   • "Have you noticed that clocks have hands that move in a circle? And that often, they stop in positions that form right angles with the number 12? Why does this happen?"

   • "When you look at a soccer ball, what do you see? What geometric shapes can you identify in it? And how can we know if these shapes are regular polygons?"

3. Contextualization: The teacher should explain the importance of regular polygons in everyday life, citing examples such as clocks, soccer balls, traffic signs (which are usually hexagons), among others. This helps students understand the relevance of the content they are learning.

4. Introduction to the Topic: The teacher should introduce the topic of regular polygons in an interesting and engaging way. For example:

   • Curiosity 1: "Did you know that nature also creates regular polygons? Insect hives, for example, are composed of hexagons, which are regular polygons."

   • Curiosity 2: "And what if I told you that the ancient Greeks used regular polygons to build many of the famous buildings we know today? After all, the word 'polygon' comes from Greek and means 'many sides'."

5. Lesson Objectives: Finally, the teacher should present the lesson objectives, which include understanding what regular polygons are, identifying examples in everyday life, and calculating measures in regular polygons.

Development (20 - 25 minutes)

1. Theory (10 - 15 minutes): The teacher should present the theory about regular polygons, explaining clearly and in detail the following points:

   • Definition of Regular Polygons: The teacher should start by explaining that a polygon is a closed flat figure, formed by line segments. And that a regular polygon is a polygon that has all sides and angles congruent (equal).

   • Characteristics of Regular Polygons: The teacher should explain that in a regular polygon, all internal angles have the same measure (using the formula 180°(n-2)/n, where n is the number of sides of the polygon) and that all sides have the same measure.

   • Examples of Regular Polygons: The teacher should present several examples of regular polygons, both in the form of drawings and in real figures, such as a circle, a square, a hexagon, etc.

   • Identification of Regular Polygons: The teacher should teach students how to identify regular polygons in their environment, encouraging them to look for examples in their classroom, school, or even in their homes.

   • Formulas for Calculating Measures in Regular Polygons: The teacher should teach students the formulas for calculating the measure of internal angles and the measure of sides in a regular polygon. For example, the formula 180°(n-2)/n for calculating the measure of internal angles, and the formula perimeter = n * side for calculating the measure of sides.

2. Practice (10 - 15 minutes): After the theory presentation, the teacher should propose practical activities for students to apply what they have learned. The activities may include:

   • Analysis of Figures: The teacher can show students various geometric figures and ask them to identify which are regular polygons and which are not, justifying their answers.

   • Calculation of Measures: The teacher can propose that students calculate the measures of internal angles and sides of various regular polygons, using the formulas they have learned. The teacher should walk around the classroom, assisting students who have difficulties.

   • Creation of Regular Polygons: The teacher can propose that students build their own regular polygons using a ruler and compass. This will help students visualize the characteristics of regular polygons better.

   • Online Activities: The teacher can suggest that students do online activities, such as games and quizzes, to reinforce the content they have learned. For example, they can suggest the game "Building Polygons" from the website "Fun Mathematics", which allows students to virtually build their own regular polygons.

The teacher should encourage active student participation by asking questions, promoting discussions, and correcting possible misconceptions. Additionally, the teacher should provide constant feedback to students, praising their achievements and pointing out areas that need improvement.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should organize a group discussion so that students can share their solutions and conclusions from the practical activities. Each group will have a limited time to present their answers. During the presentations, the teacher should ask questions to verify students' understanding and promote discussion. This stage aims to consolidate the concepts learned and promote interaction among students.

2. Connection with Theory (3 - 5 minutes): After the presentations, the teacher should review the theoretical concepts, connecting them with the practical activities carried out. For example, the teacher can ask: "How did the formulas we learned help you calculate the measures of the sides and angles of the polygons you built?", "What characteristics of regular polygons were you able to identify in the figures you analyzed?" This stage helps students realize the applicability of theory in solving practical problems.

3. Individual Reflection (2 - 3 minutes): Next, 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?" and "What questions have not been answered yet?" Students will have a minute to think about their answers. This stage aims to stimulate metacognition, that is, reflection on the learning process.

4. Sharing Reflections (2 - 3 minutes): Finally, the teacher should invite some students to share their reflections with the class. This stage is important for the teacher to assess the level of students' understanding and identify possible gaps in learning. The teacher should encourage students to express their opinions and ask questions, promoting an open and welcoming learning environment.

Throughout the Return, the teacher should maintain a posture of attentive listening and respect for different opinions and forms of expression from students. The teacher should value students' efforts and encourage them to continue studying and delving into the subject. Additionally, the teacher should make it clear that they are available to clarify doubts and provide additional support if needed.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes): The teacher should give a brief summary of the main points covered during the lesson. This helps reinforce the content in students' memory and ensure they have understood the fundamental concepts. The summary may include:

   • Definition of Regular Polygons: Remind that a regular polygon is one that has all sides and angles congruent.
   • Characteristics of Regular Polygons: Review the main characteristics of regular polygons, such as the measure of internal angles and sides.
   • Identification and Examples of Regular Polygons: Reinforce the importance of being able to identify regular polygons in everyday life, presenting again the examples mentioned during the lesson.
   • Calculation of Measures in Regular Polygons: Recall the formulas used to calculate the measures of internal angles and sides of a regular polygon.

2. Connection with Practice (1 - 2 minutes): The teacher should explain how the presented theory connects with practice. This can be done by recalling the practical activities carried out during the lesson and highlighting how the theoretical concepts were applied to solve the proposed problems.

3. Additional Materials (1 minute): The teacher should suggest additional study materials for students who wish to deepen their knowledge on the subject. This may include math books, educational websites, online videos, among others. The teacher should encourage students to explore these materials on their own as a way to stimulate autonomous study.

4. Relevance of the Subject (1 minute): Finally, the teacher should emphasize the importance of studying regular polygons for everyday life. This can be done by mentioning again the examples of regular polygons found in everyday life and explaining how knowledge about these geometric figures can be useful in various situations, such as solving practical problems, understanding natural phenomena, and appreciating art and architecture.

The Conclusion is a crucial stage of the lesson plan, as it allows the teacher to consolidate students' learning, reinforce the importance of the presented content, and motivate students to continue studying and exploring the topic.