Lesson plan of Regular Polygons: Introduction

Objectives (5-10 minutes)

1. Familiarize students with the concept of regular polygons, explaining that they are polygons whose sides and internal angles are all congruent.

2. Develop students' ability to identify regular polygons, with a focus on triangles, squares, and regular pentagons.

3. Introduce the concept of the interior angle formula for a regular polygon, which is given by (n-2) * 180°, where n is the number of sides of the polygon.

Secondary objectives:

• Encourage active student participation by having them ask questions and contribute ideas during the class discussion.

• Promote critical thinking and problem-solving through hands-on activities and challenges that involve the use of regular polygon concepts.

Introduction (10-15 minutes)

1. Review of previous content (3-5 minutes): The teacher should begin the lesson by reviewing the concepts of polygons and angles, which were previously studied. It is important for students to recall what a polygon is and how to calculate the sum of the interior angles of a polygon. This review can be done through a brief class discussion or a quick exercise.

2. Problem situations (5-7 minutes): Next, the teacher should present two problem situations that involve the concept of regular polygons. For example, show a picture of a kindergarten with various geometric shapes and ask students which of them are considered regular polygons. Another possibility is to show a photo of a building with a clock on the facade and ask students how they could calculate the value of each angle of the clock, considering that it is a regular polygon.

3. Contextualization (2-3 minutes): The teacher should then contextualize the importance of regular polygons, explaining that they are present in various aspects of our daily lives, such as architecture, nature, and even games and toys. For example, it can be mentioned that many buildings are designed based on regular polygons and that the symmetry and regularity of these shapes contribute to the beauty and stability of these structures.

4. Introduction to the topic (2-3 minutes): Finally, the teacher should introduce the topic of the day - regular polygons - explaining that they are special figures that have unique properties. One way to do this is to present some curiosities or interesting facts about regular polygons. For example, it can be mentioned that there are only three regular polygons that can be constructed with a ruler and compass, or that regular polygons are the basis for the construction of many other geometric figures and solids.

Development (20-25 minutes)

1. Activity to construct regular polygons (10-12 minutes): The teacher should divide the class into groups of no more than 4 students. Each group will receive a construction kit consisting of a ruler and compass. The objective of this activity is for students to construct regular polygons of different sizes. The teacher should guide students to start with the triangle, then the square, and finally the pentagon. During the activity, the teacher should circulate around the room, assisting groups that encounter difficulties. In the end, each group should present their polygons to the class and explain how they arrived at the result.

   a. Materials needed: Ruler, compass, paper, and pencil.

   b. Step-by-step activity: - Step 1: Each group receives a construction kit. - Step 2: Guide students to construct a triangle, a square, and a regular pentagon. - Step 3: The groups should write down the length of the sides and the value of the angles of each polygon. - Step 4: Presentation of the constructed polygons to the class. - Step 5: Class discussion about the similarities and differences between the constructed polygons.

2. Activity to calculate internal angles (5-7 minutes): After constructing the polygons, the teacher should propose that students calculate the value of the internal angles of each one. The teacher should guide students to use the interior angle formula for a regular polygon: (n-2) * 180°, where n is the number of sides of the polygon.

   a. Materials needed: Ruler, compass, paper, pencil, and calculator (if necessary).

   b. Step-by-step activity: - Step 1: Each group is given the task of calculating the value of the internal angles of each of the polygons they constructed. - Step 2: Students should write down the calculation and the result for each polygon. - Step 3: Presentation of the results to the class. - Step 4: Class discussion about the results obtained and the importance of the interior angle formula for a regular polygon.

3. Activity to identify regular polygons (5-6 minutes): To conclude the Development part of the lesson, the teacher should present students with a series of images of geometric figures and challenge the groups to identify which of them are considered regular polygons. This activity aims to reinforce students' ability to recognize regular polygons.

   a. Materials needed: Images of geometric figures (triangles, squares, pentagons, and other non-regular figures).

   b. Step-by-step activity: - Step 1: Present the images to the groups. - Step 2: Each group must identify which of the figures are considered regular polygons and justify their answer. - Step 3: Presentation of the answers to the class. - Step 4: Class discussion about the answers given by the groups and the importance of the regularity of the sides and angles to identify a polygon as regular.

Review (10-15 minutes)

1. Group discussion (5-7 minutes): The teacher should organize a sharing time, where each group will have up to 3 minutes to present their conclusions and solutions to the activities carried out. During the presentations, the teacher should encourage interaction between the groups, allowing them to ask questions and exchange ideas. The objective is for students to notice different approaches to the same problem.

   a. Step-by-step activity: - Step 1: Organize the order of the group presentations. - Step 2: Each group will have up to 3 minutes to share their conclusions and solutions. - Step 3: After each presentation, allow the other groups to ask questions or make comments for 1 minute.

2. Connection with the theory (3-5 minutes): After the presentations, the teacher should revisit the theoretical concepts discussed at the beginning of the lesson and make the connection with the practical activities carried out. The teacher should emphasize the importance of the regularity of the sides and angles for classifying a polygon as regular and how the interior angle formula for a regular polygon can be used to calculate the value of each interior angle.

   a. Step-by-step activity: - Step 1: Make a brief summary of the group presentations. - Step 2: Connect the conclusions of the groups with the theoretical concepts. - Step 3: Highlight the importance of the regularity of the sides and angles for classifying a polygon as regular. - Step 4: Recall the interior angle formula for a regular polygon and how it was used to calculate the value of the interior angles.

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?" and "What questions have not yet been answered?" The objective of this activity is for students to internalize the concepts learned and identify possible doubts or difficulties that need to be clarified.

   a. Step-by-step activity: - Step 1: Propose that students reflect individually for 1 minute. - Step 2: Ask the reflection questions and have students write down their answers for 1 more minute. - Step 3: End the lesson, but encourage students to bring their doubts or reflections to the next lessons.

Conclusion (5-7 minutes)

1. Content summary (2-3 minutes): The teacher should summarize the main points covered during the lesson. This includes the definition of regular polygons, the identification of regular polygons (triangles, squares, and pentagons), the construction of regular polygons, the calculation of internal angles, and the interior angle formula for a regular polygon.

2. Connection of theory, practice, and applications (1-2 minutes): The teacher should highlight how the lesson was able to connect the theory, practice, and applications of regular polygons. This can be done by recalling the practical activities carried out, such as the construction of regular polygons and the calculation of internal angles, and explaining how these activities reinforced the theoretical concepts presented. The teacher can also mention the applications of regular polygons in everyday life, such as architecture and nature, and how understanding these geometric shapes can be useful in different contexts.

3. Extra materials (1-2 minutes): The teacher should suggest extra materials for students who wish to deepen their knowledge of regular polygons. This can include math books, educational websites, YouTube videos, among others. The teacher can, for example, suggest that students watch a video explaining the construction of regular polygons with a ruler and compass or read a chapter of a book about the history of regular polygons and their mathematical properties.

4. Relevance of the subject (1 minute): Finally, the teacher should emphasize the importance of regular polygons for the study of mathematics and for understanding the world around us. The teacher can explain that, although regular polygons may seem like simple figures, they are of great importance and have practical applications in various areas, from architecture to physics. The teacher should end the lesson by encouraging students to continue exploring and questioning mathematics and reinforcing that, with practice and dedication, they will be able to master the concepts of regular polygons and many other mathematics topics.