Objectives (5 - 7 minutes)

1. Identify and differentiate polygons: Students should be able to identify and differentiate polygons from other types of geometric figures, such as circles or curves. This includes understanding the definition of polygons as closed flat figures, formed by line segments, and distinguishing between regular and irregular polygons.

2. Classify polygons by number of sides and angles: Students should be able to classify polygons based on the number of sides and angles they have. This involves memorizing and understanding common classifications (triangles, quadrilaterals, pentagons, hexagons, etc.) and applying these classifications in practical examples.

3. Describe polygon characteristics: Students should be able to describe the characteristics of polygons, such as the type of angles they have (acute, obtuse, or right) and the measure of internal and external angles. This involves applying the formulas for the sum of internal and external angles of a polygon.

   Secondary Objectives:

   • Stimulate critical thinking and problem-solving: By working with the classification and description of polygons, students will be encouraged to think critically and solve problems, developing essential skills for mathematics and beyond.

   • Promote autonomous and collaborative learning: Through the inverted classroom method, students will be encouraged to take responsibility for their own learning, working autonomously and collaboratively to achieve the lesson's objectives.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher starts the lesson by briefly reviewing the concepts of plane geometry that were covered in previous classes and are essential for understanding the current content. This includes the definition of geometric figure, the difference between flat and spatial figures, and the types of lines (line, ray, and line segment). (2 - 3 minutes)

2. Problem situations: The teacher presents two problem situations to arouse students' interest in the topic:

   • "Have you ever stopped to think why most traffic signs are polygons? Why aren't they circles, for example?"
   • "When watching a soccer game, have you noticed that the field is a rectangle and that the ball, when rolling, follows trajectories that resemble geometric figures? How can we describe these figures?"

   These problematic situations aim to contextualize the content and perceive its applicability in everyday life. (3 - 5 minutes)

3. Contextualization: The teacher contextualizes the importance of polygons, highlighting that they are present in various everyday situations, from the geometry of constructions to the creation of drawings and arts. Furthermore, they are fundamental in areas such as architecture, design, engineering, computer science, and board games. (2 - 3 minutes)

4. Attention gain: To capture students' attention, the teacher can share some curiosities about polygons:

   • "Did you know that the largest polygon ever discovered in the universe is the Great Wall of the Galaxy? It is composed of about 400 billion stars, all forming a gigantic irregular polygon."
   • "And how about the curiosity that the smallest possible polygon is the triangle with sides of only 1 nanometer? That is so small that it can only be seen with the help of very powerful electron microscopes!"

   These curiosities serve to arouse curiosity and interest in the students on the subject. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 'Forming Polygons' (10 - 12 minutes)

   • Description: The teacher divides the class into groups of up to 5 students. Each group receives a sheet of paper, a compass, a ruler, and a protractor. The objective of the activity is for students to construct as many different polygons as possible, using the sheet of paper as a base. They should draw the polygons, measure and record the number of sides, the measure of each internal angle, and the sum of the internal angles.

   • Step by step: The teacher explains the rules of the activity and guides the students to start. Then, they circulate around the room, assisting groups that encounter difficulties and asking questions that lead them to reflect on the characteristics of the polygons they are constructing. At the end of the activity, each group must present one or two polygons to the class, explaining the observed characteristics.

   • Objective: The activity aims to provide students with a practical experience of constructing and observing polygons, contributing to the development of the notion of shape and space, and to the understanding of polygon properties.

2. Activity 'Polygons in Everyday Life' (10 - 12 minutes)

   • Description: After the previous activity, the groups receive a list of everyday situations involving polygons, such as identifying polygons on traffic signs, buildings, packaging, board games, among others. The challenge is to identify and describe the polygons present in each situation, classify them according to the number of sides and angles, and describe their characteristics.

   • Step by step: The teacher guides the groups to analyze the proposed situations, identify the polygons, and describe their characteristics. During the activity, the teacher circulates around the room, answering questions, asking questions, and promoting discussion among the students. At the end, each group presents their answers to the class.

   • Objective: The activity aims to stimulate students' perception of the presence of polygons in their daily lives, promote the application of studied concepts, and develop geometric thinking.

3. Activity 'Polygon Game' (5 - 7 minutes)

   • Description: The teacher presents a board game created by them, called 'Polygon Game.' Each group receives a board, cards with images of polygons, and cards with polygon descriptions. The goal is for students, in their groups, to correctly match the image and description cards, moving their pieces on the board.

   • Step by step: The teacher explains the rules of the game and guides the groups to play. During the game, the teacher circulates around the room, assisting groups that encounter difficulties and promoting discussion about the characteristics of polygons. At the end of the game, the group that has moved their piece on the board in the shortest time is the winner.

   • Objective: The activity aims to promote the review of studied concepts, the application of acquired knowledge, and the development of logical and strategic thinking. Additionally, the game contributes to strengthening teamwork and promoting interaction and engagement among students.

Return (10 - 12 minutes)

1. Group Discussion (4 - 5 minutes)

   • Description: The teacher proposes that each group shares their solutions and conclusions about the activities carried out. Each group will have up to 3 minutes to make their presentation. During the presentations, other students are encouraged to ask questions and make comments.

   • Step by step: The teacher organizes the order of the presentations and, one by one, calls the groups to share their conclusions. During the presentations, the teacher makes specific interventions, clarifies doubts, and stimulates discussion.

   • Objective: Group discussion allows students to share their perceptions, clarify doubts, learn from each other, and develop communication and argumentation skills.

2. Connection with Theory (2 - 3 minutes)

   • Description: The teacher makes the connection between the activities carried out and the theory presented in the Introduction of the lesson. They highlight how the observed characteristics of polygons in the activities (number of sides, measure of internal angles, classification, etc.) correspond to theoretical concepts.

   • Step by step: The teacher reviews the main theoretical points of the lesson, relating them to the observations made by students during the activities. For example, they may ask: "How did the 'Forming Polygons' activity help us understand the definition of polygons? And the 'Polygons in Everyday Life' activity, how did it help us perceive the presence of polygons in our daily lives?"

   • Objective: The connection with theory reinforces the understanding of concepts and the importance of practice for learning.

3. Individual Reflection (2 - 3 minutes)

   • Description: The teacher suggests that students take a moment to reflect individually on what they learned in the lesson. They propose the following questions to guide the reflection:

     1. "What was the most important concept you learned today?"
     2. "What questions have not been answered yet?"

   • Step by step: The teacher asks students to close their eyes, take a deep breath, and silently think about the proposed questions. After a few moments, they ask students to open their eyes and share their reflections.

   • Objective: Individual reflection allows students to internalize what they learned, identify possible gaps in their understanding, and express their doubts or difficulties.

4. Feedback and Closure (1 minute)

   • Description: The teacher thanks everyone for their participation, praises the effort and dedication shown by the students, and reinforces the importance of continuous study for the consolidation of learning.

   • Objective: Feedback and closure serve to reinforce students' motivation and to value the work done. Additionally, the teacher can take this opportunity to make adjustments and improvements in future lessons based on student feedback.

Conclusion (5 - 7 minutes)

1. Summary of Contents (1 - 2 minutes)

   • Description: The teacher gives a brief summary of the main points covered during the lesson, reinforcing the concepts of polygons, their characteristics, classification, and their importance in everyday life.

   • Objective: The summary aims to consolidate what was learned, reinforce key concepts, and help students make connections between different aspects of the topic.

2. Theory-Practice Connection (1 - 2 minutes)

   • Description: The teacher emphasizes how the lesson connected theory (definition and categorization of polygons, characteristics, etc.) with practice (polygon construction, analysis of everyday situations, polygon game).

   • Objective: The connection between theory and practice helps students understand the relevance of what they learned and the applicability of mathematical concepts in different situations.

3. Supplementary Materials (1 - 2 minutes)

   • Description: The teacher suggests supplementary materials for students to deepen their studies on polygons. This may include books, websites, videos, online games, among other resources. For example, the teacher may suggest the use of drawing apps for polygon construction or reading articles discussing the presence of polygons in nature.

   • Objective: Supplementary materials aim to enrich learning, allowing students to explore the topic from different perspectives and at their own pace.

4. Subject Relevance (1 minute)

   • Description: Finally, the teacher highlights the importance of studying polygons, not only as a mathematical content but also for the development of practical and cognitive skills. They can emphasize how understanding polygons is fundamental for various areas of knowledge, such as architecture, design, engineering, computer science, among others.

   • Objective: By highlighting the relevance of the subject, the teacher helps motivate students, showing that what they are learning has practical and significant applications in their lives.