Contextualization

Throughout our lives, we are faced with an enormous variety of shapes and figures. In mathematics, plane figures are studied in the discipline called Plane Geometry, and among them, an important class is that of polygons.

Polygons are plane geometric figures, delimited by line segments, the sides, which meet at their ends, the vertices. Polygons can be classified as regular or irregular. A regular polygon, by definition, has all its sides and angles congruent.

Polygons are present in a very broad way in our daily lives: in the streets and avenues of city maps (predominantly irregular polygons), in dining tables (usually regular polygons, such as rectangles or circumferences), in bathroom tiles (squares, hexagons), in computer screens (rectangles), among many other examples.

Mathematics, and in this case, Geometry, are sciences with a great capacity for abstraction, but which need moments that connect their more theoretical concepts with practical applications, inserting the students in reality and allowing a deeper and more significant understanding of the content.

For the understanding of polygons and the understanding of their implications, I recommend the use of two main sources. The first is the book "Fundamentals of Elementary Mathematics: Plane Geometry", by Gelson Iezzi. This book, easy to understand, gives a comprehensive overview of polygons and other topics of Plane Geometry. Another source of study is the Só Matemática website, which has a section dedicated to polygons, with explanations, problems, and solutions that will help in understanding the subject.

Practical Activity

Activity title: Construction and Application of Regular Polygons

Project objective:

Conduct a practical study on regular polygons, involving their construction, classification, and application in a real context.

Detailed project description:

The project is divided into three stages. In the first stage, students should build different regular polygons using a drawing tool of their choice and identify them. In the second stage, students should design and build a model of a city using the studied polygons. Finally, in the third stage, the students should write a report on the project.

Required materials:

• A3 cardstock.
• Pencil.
• Compass.
• Ruler.
• Building materials for the model (cardboard, glue, scissors, paint, etc.).

Detailed step-by-step to carry out the activity:

Stage 1: Construction of Polygons

• Using a drawing tool (pencil, ruler, and compass), students should draw and identify at least five different types of regular polygons (e.g.: equilateral triangle, square, regular pentagon, regular hexagon, etc.). The polygons must be drawn accurately, with all sides and angles equal.

Stage 2: Construction of the Model

• Based on the polygons constructed in the previous stage, the students should design and build a model of a city. The model should use the polygons drawn in the previous stage as the basis for the structure of the buildings. For example, houses can be represented by squares, streets by triangles, buildings by hexagons, etc.

Stage 3: Preparation of the Report

• Students should write a detailed report on the project, including the following topics: Introduction (contextualization of the theme, project objective), Development (theory on the polygons used, detailed description of the activity, methodology used, presentation, and discussion of results), Conclusion (reiteration of the main points, lessons learned, conclusions about the project) and Bibliography.

The project deliverables are the drawings of the polygons, the model, and the report. All of this must be done in groups of 3 to 5 students, with a delivery time of one month. Each student should spend between five to ten hours in total on the project.

The drawings and the model will work as practical tools for the understanding of polygons and their applications, while the report will make the connection between practice and theory feasible, helping to internalize the concepts worked on during the project.