Lesson plan of Polygons: Classification

Objectives (5 - 7 minutes)

1. Grasp the definition of polygons: Students should be able to define polygons, recognizing the characteristics that differentiate them from other geometric shapes.

2. Identify and classify polygons by sides and angles: Students should acquire the ability to count and identify the sides and angles of a polygon, as well as classify polygons according to these characteristics.

3. Apply knowledge to solve practical problems: Students will be challenged to apply the knowledge acquired to solve practical problems that involve identifying and classifying polygons.

Secondary objectives:

• Develop logical and analytical thinking skills: Through the study of polygons, students will develop logical and analytical thinking skills, which are fundamental for solving mathematical problems.

• Promote interaction and group work: During the practical activities, students will be encouraged to work in groups, promoting interaction and the exchange of ideas.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher begins the class by quickly reviewing the concepts of plane geometry, geometric figures, and their elements (sides, vertices, angles). This review is essential for students to understand and follow the content of the class. (3 - 5 minutes)

2. Problem situation 1 - "The polygon challenge": The teacher presents a situation in which students are challenged to identify and classify polygons. Images of different geometric figures will be shown, and students will have to say whether or not they are polygons and, if they are, classify them. (3 - 5 minutes)

3. Contextualization: The teacher explains the importance of polygons in our daily lives, citing examples of where they can be found, such as in the architecture of buildings, in road signs, in the manufacture of objects, etc. In addition, it highlights the relevance of the study of geometry for the development of logical and analytical skills. (1 - 2 minutes)

4. Introduction to the topic - "Polygon curiosities": The teacher shares two curiosities about polygons to arouse students' interest:

   • Curiosity 1 - The largest polygon in the universe: The teacher comments that the largest known polygon in the universe is the Great Wall of China, which is over 21,000 miles long and is made up of countless polygons.

   • Curiosity 2 - The smallest polygon in the universe: The teacher mentions that the smallest known polygon in the universe is the hexagon, which is the shape that bees use to build their hives, due to the efficiency of this geometric shape.

These curiosities serve to arouse students' curiosity and show the practical application and relevance of polygons. (3 - 5 minutes)

Development (20 - 25 minutes)

1. Activity 1 - "Polygons in everyday life": The teacher suggests that students, in groups of up to 5 members, search the school environment or in images from magazines and newspapers for examples of polygons present in our daily lives. Each group should photograph or draw the polygons found and write down the number of sides and angles of each one. At the end of the activity, the groups present their findings to the class, which should try to guess the polygon. This activity aims to make students realize the presence of polygons in our daily lives, as well as reinforce the concept of classification. (8 - 10 minutes)

   • Step by step activity:

     1. The teacher organizes the students into groups and distributes the necessary materials (cameras, paper, pencils, etc.).
     2. Students set out to find the polygons, drawing or photographing them.
     3. Back in the classroom, the students count the sides and angles of each polygon and prepare the presentation.
     4. Each group presents its polygons to the class, which tries to guess which polygon it is.

2. Activity 2 - "Building polygons": The teacher provides each group of students with a ruler, a compass, and a protractor. The teacher then suggests that the students build regular polygons (triangle, square, pentagon, hexagon, etc.), using the materials provided. This activity aims to allow students to manipulate the polygons, which makes it easier to understand the characteristics that differentiate them. (10 - 12 minutes)

   • Step by step activity:

     1. The teacher distributes the material to each group.
     2. The students, in groups, choose a polygon to build.
     3. Using the ruler and compass, the students build the chosen polygon.
     4. Then, they use the protractor to measure the angles of the polygon.
     5. Finally, the students present the constructed polygon to the class.

At the end of the activities, the teacher promotes a classroom discussion, going back over the concepts of polygon classification and relating them to the experiences gained in the activities. In addition, the teacher clarifies any doubts that may have arisen during the activities. (2 - 3 minutes)

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher gathers all the students and promotes a group discussion about the solutions or conclusions obtained by the different groups in the previous activities. The aim is for students to share their experiences and learning, allowing everyone to enrich their knowledge of polygon classification. During the discussion, the teacher can intervene, if necessary, to clarify doubts, reinforce concepts, or correct possible errors.

   • Discussion step by step:

     1. The teacher calls everyone's attention and asks the students to share their solutions or conclusions.
     2. The students, one at a time, briefly present what they discovered or learned during the activities.
     3. The teacher asks questions to encourage everyone's participation and promote reflection on the concepts studied.

2. Connection with Theory (2 - 3 minutes): Based on the group discussions, the teacher makes the connection between the practical activities carried out and the theory studied. The aim is for students to perceive the practical application of theoretical concepts, strengthening their understanding and appreciation for mathematics. The teacher could, for example, ask: "How did the polygon construction activity help you to better understand polygon classification?" or "What were the difficulties encountered in the polygon identification activity and how did you manage to overcome them?".

   • Connection step by step:

     1. The teacher recalls the theoretical concepts studied and asks questions so that the students can perceive the connection with the practical activities.
     2. The students, based on their experiences, answer the teacher's questions.

3. Final Reflection (2 - 3 minutes): The teacher suggests that the students reflect for a minute on the following questions: "What was the most important concept learned today?" and "What questions have not yet been answered?". After the reflection, the students are encouraged to share their answers with the class. The aim of this stage is for the students to internalize what they have learned and identify possible gaps in their understanding, which can be addressed in future classes.

   • Reflection step by step:

     1. The teacher proposes the reflection questions and gives the students a minute to think about their answers.
     2. The students, one at a time, share their answers with the class.
     3. The teacher thanks everyone for their participation and ends the class, reminding the students of the content that will be studied in the next class.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes): The teacher begins the conclusion of the class with a brief summary of the main content covered. He reinforces the definition of polygons, the importance of sides and angles in the classification of polygons, and the characteristics of regular and irregular polygons. The teacher can use diagrams or drawings to illustrate the concepts, making the explanation more visual and understandable for the students.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher then highlights how the class connected theory, practice, and applications. He reinforces that, through the practical activities, the students were able to manipulate the polygons, which made it easier to understand the characteristics that differentiate them. In addition, the teacher emphasizes the importance of understanding polygon classification, as this skill is used in various areas of knowledge and everyday life, such as architecture, engineering, art, and even road signs.

3. Supplementary Materials (1 - 2 minutes): The teacher suggests supplementary materials for students who wish to further their study of polygons. He can suggest geometry books, educational websites, explanatory videos, and virtual games that approach the topic in a fun and interactive way. In addition, the teacher can suggest that students practice identifying and classifying polygons in everyday situations, such as observing road signs or analyzing the structure of a building.

4. Importance of the Subject (1 minute): Finally, the teacher reinforces the importance of the subject presented for the students' lives. He stresses that geometry, and in particular the study of polygons, is not restricted to the classroom but is present in various everyday situations. In addition, the teacher emphasizes that the study of geometry contributes to the development of logical, analytical, and visual skills, which are essential in various areas of knowledge and work.