Contextualization

Theoretical Introduction

Let's embark on a journey aimed at understanding polygons and their classifications. Polygons are flat figures formed by line segments that, in turn, are connected at their ends. This means that polygons are closed and have no curves. It may seem simple, but polygons are of great importance and are everywhere in our daily lives!

Polygons can be classified according to the number of sides (or vertices), ranging from triangles (3 sides) to n-gons (n sides). Furthermore, we can classify them according to their regularity. Regular polygons have all their sides and angles equal, while irregular ones do not have this uniformity.

But it doesn't stop there! We can still categorize polygons according to the equality of their sides (equilateral) or their angles (equiangular). As you can see, the classification of polygons is a rich geometric tapestry that we will explore together!

Contextualization

You might wonder: 'Why study polygons? What is their relevance?'. Well, besides being one of the foundations of geometry, polygons have significant practical applications. For example, in engineering and architecture, knowledge about polygons is vital for the creation of structures and buildings. In computer science, polygons are used to render graphics and model 3D objects.

Polygons are also present in art, design, biology, and even in economics, where they are used to create radar charts! In summary, polygons are not just abstract shapes in a textbook, but an essential mathematical tool in various fields.

Activity

Activity Title: The Faces of the Polygon

Project Objective

The objective of this project is to familiarize students with the different classifications of polygons and their presence in our daily lives. For this, groups will be challenged to explore the environment in which they live, identify and create polygons, classify them, and present their relevance in the real world.

Detailed Project Description

1. Identification and Classification of Polygons: In this stage, groups should identify different polygons in objects or constructions around them. They can be found in places like their homes, schools, or even in public spaces. Students must record the polygons found through photos and classify them according to the number of sides, regularity, and whether they are equilateral or equiangular.

2. Applications of Polygons: After identifying the polygons, teams should research and present their practical applications in the contexts where they were found. They should try to connect the characteristics of the polygons to the function they perform in the object or construction.

3. Creation of Polygons: Finally, each group must create a regular polygon using materials of their choice (papers, cardboards, newspapers, tapes, ruler, etc.). They must ensure that all measurements are uniform and the angles are equal.

Required Materials

• Digital camera (can be a cellphone camera);
• Papers, cardboards, recyclable materials;
• Ruler;
• Scissors;
• Glue;
• Pencil and eraser.

Detailed Step-by-Step

1. Form groups of 3 to 5 students.
2. Explore the environment in search of polygons present in objects or constructions, recording them in photographs.
3. Classify the polygons found according to the number of sides, regularity, and whether they are equilateral or equiangular.
4. Research the applications of the identified polygons in the context where they were found and connect their characteristics to the function they perform.
5. Create a regular polygon, ensuring that all measurements are uniform and the angles are equal.
6. Document the entire process, from the identification to the creation of the polygons, organizing the information in a report.

Project Submission

Groups must submit a written report, which should include:

1. Introduction: In this section, students should contextualize the project, indicating the importance of polygons and their practical applications.
2. Development: Here, groups should include photos of the identified polygons, classify them, and explain their characteristics. They should also present the practical application of the polygons found, connecting their characteristics to the functions they perform. The creation of the regular polygon should also be documented in this section, including photos and measurements.
3. Conclusion: Students should summarize the main points of the work, reflect on what they have learned, and how this learning can be important for daily life.
4. Bibliography: Students should list all sources of information consulted to carry out the project.

The report must be presented in one week, and each student must contribute approximately two to four hours of work.

In addition to the report, the regular polygon created must also be submitted, being an integral part of the project evaluations.