Objectives (5 - 7 minutes)

1. Understand the basic concepts of polygons:

   • Define what a polygon is and identify its main characteristics.
   • Distinguish between regular and irregular polygons, and between convex and non-convex polygons.

2. Learn to classify polygons according to the number of sides:

   • Identify and name polygons with up to 12 sides.

3. Develop problem-solving skills:

   • Apply the acquired knowledge to solve practical problems of polygon classification.

Secondary objectives:

• Stimulate students' critical and logical thinking through the resolution of mathematical problems.
• Encourage active participation of students through practical activities and classroom discussions.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by briefly reviewing the concepts of plane geometric figures, sides, and angles, which are fundamental to understanding polygons. This review can be done through direct questions to the students or through a brief quiz. (3 - 5 minutes)

2. Problem situations: The teacher can present two problem situations to arouse students' interest and introduce the topic of the lesson. For example:

   • "Have you ever seen a building or a house with a curved facade?"
   • "How would you describe the shape of a street sign or a classroom board?" (3 - 5 minutes)

3. Contextualization: The teacher should explain that the study of polygons is essential to understand and describe many of the shapes we encounter in everyday life, from buildings to everyday objects. In addition, the teacher can mention that the classification of polygons is an important tool in various areas, such as architecture, engineering, and physics. (2 - 3 minutes)

4. Introduction to the topic: The teacher should then introduce the topic of the lesson, explaining that polygons are closed flat figures formed by line segments, and that they can be classified according to the number of sides they have. The teacher can also show some images of various polygons to arouse students' curiosity. (2 - 3 minutes)

5. Curiosities: To capture students' attention, the teacher can share some curiosities about polygons. For example:

   • "Did you know that the polygon with the highest number of named sides is the icosahedron, which has 20 faces?"
   • "And that the polygon with the lowest number of sides is the triangle, which has only 3 sides?" (1 - 2 minutes)

Development (20 - 25 minutes)

1. Theory - Definition of polygons and classification (5 - 7 minutes): The teacher should start the theoretical part of the lesson by explaining clearly and concisely what a polygon is, what its characteristics are (closed flat figure formed by line segments), and how it can be classified. The teacher should emphasize the difference between regular and irregular polygons, and between convex and non-convex polygons. They can use drawings and diagrams to illustrate these concepts and should encourage students to ask questions and express their doubts.

   • Activity 1 - Drawing polygons (5 - 7 minutes): After the theoretical explanation, the teacher should distribute sheets of paper and pencils to the students and ask them to draw different polygons (triangles, quadrilaterals, pentagons, etc.). Students should identify and name the polygons they drew, and the teacher should move around the classroom, assisting students and correcting any possible errors.

2. Theory - Classification of polygons by the number of sides (5 - 7 minutes): The teacher should then move on to the second part of the theory, which is the classification of polygons according to the number of sides they have. The teacher should explain that polygons can be classified into three main groups: those with three to nine sides (called regular polygons), those with ten to twelve sides (called star polygons), and polygons with more than twelve sides (called curvilinear polygons). The teacher should show examples of each type of polygon and should encourage students to ask questions and express their doubts.

   • Activity 2 - Identification of polygons (5 - 7 minutes): The teacher should then distribute cards with images of various polygons to the students. Students should identify and name the polygons according to the number of sides they have. The teacher should move around the classroom, assisting students and correcting any possible errors.

3. Practice - Problem solving (5 - 7 minutes): To consolidate the acquired knowledge, the teacher should propose some practical problems of polygon classification for students to solve. The problems can vary in difficulty and should require students to apply the acquired knowledge in a practical way. The teacher should encourage students to work in groups to solve the problems and should move around the classroom, assisting the groups and correcting any possible errors. The teacher should also encourage discussion among the groups so that students can learn from each other and develop critical and logical thinking skills.

   • Activity 3 - Group problem solving (5 - 7 minutes): The teacher should then divide the class into groups of three or four students and propose some polygon classification problems for the groups to solve. The problems can vary in difficulty and should require students to apply the acquired knowledge in a practical way. The teacher should move around the classroom, assisting the groups and correcting any possible errors. The teacher should also encourage discussion among the groups so that students can learn from each other and develop critical and logical thinking skills.

Return (8 - 10 minutes)

1. Review of concepts (3 - 4 minutes): The teacher should start the Return phase by reviewing the main concepts covered in the lesson. This can be done through direct questions to the students or through a brief quiz. The goal is to ensure that students understood and retained the information. For example, the teacher can ask: "What is a polygon?" or "How can polygons be classified?".

2. Connection to practice (2 - 3 minutes): Next, the teacher should make a connection between the presented theory and the practical activities carried out. They can ask students: "How did the polygon drawing activity help understand their classification?" or "How do polygon classification problems relate to the real world?". The goal is to make students realize the relevance of what they have learned and how they can apply this knowledge in everyday situations.

3. Individual reflection (2 - 3 minutes): The teacher should then ask students to reflect individually on what they learned in the lesson. They can propose questions like: "What was the most important concept you learned today?" or "What questions have not been answered yet?". Students should have a minute to think about these questions, and then some volunteers can share their answers with the class. The teacher should listen carefully to the students' answers and, if necessary, clarify any misunderstandings.

4. Feedback and closure (1 minute): Finally, the teacher should thank the students for their participation and effort during the lesson. They should encourage them to continue studying and asking questions, and remind them that learning is a continuous process. The teacher can also ask for feedback from the students about the lesson, so they can make adjustments and improvements in future classes. The teacher should then end the lesson and prepare for the next one.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes): The teacher should start the Conclusion phase by summarizing the main points covered during the lesson. They should reinforce the definition of polygons, the characteristics that distinguish them, and the importance of classifying polygons according to the number of sides. The teacher should also emphasize the difference between regular and irregular polygons, and between convex and non-convex polygons. This summary should be done clearly and concisely to consolidate the knowledge acquired by the students.

2. Connection between Theory, Practice, and Application (1 - 2 minutes): The teacher should then explain how the lesson connected theory, practice, and application. They should recall the practical activities, such as drawing polygons and solving problems, and show how these activities helped apply the learned theoretical concepts. The teacher should also reinforce the relevance of the learned content, showing examples of how polygon classification is used in various areas, such as architecture, engineering, and physics.

3. Additional Materials (1 - 2 minutes): The teacher should suggest some additional materials for students who wish to deepen their knowledge on the subject. These materials may include books, websites, videos, and interactive games that address the topic in a playful and didactic way. For example, the teacher can recommend a YouTube video that explains polygon classification in a fun and easy-to-understand way, or a board game that allows students to practice polygon classification interactively.

4. Everyday Applications (1 minute): Finally, the teacher should highlight some practical applications of the learned content. For example, they can mention that polygon classification is used to describe and understand many of the shapes we encounter in everyday life, from product packaging to everyday objects. The teacher can also mention that the ability to solve polygon classification problems is useful in various situations, from solving puzzles to interpreting maps and building plans.