Contextualization

Mathematics is a vast area of human knowledge involving numerous concepts and applications. One of these concepts is the classification of shapes, which is essential for understanding many mathematical and physical ideas.

Geometric shapes are elements that surround us in all aspects of life, from the architecture of the buildings to the positioning of objects around us. To learn about the classification of shapes is to learn to recognize and interpret the world around us more precisely and completely.

Theoretical Introduction

In mathematics, we consider shapes in two dimensions, known as plane figures, and in three dimensions, known as spatial figures. Plane figures are formed by lines and points, and include concepts such as sides, vertices, and angles. They can be polygons - which are figures closed by straight lines - or non-polygons - figures that do not fit the definition of polygons.

Polygons are classified according to the number of sides they have: triangles have three sides, quadrilaterals have four, pentagons have five, and so on. In addition to the number of sides, polygons can also be classified according to the equality of their sides and angles, being called equilateral, equiangular, or regular.

Importance of Shape Classification

The classification of shapes has great relevance in several areas of daily and professional life. In architecture and design, for example, the use of shapes and their classification is essential for the creation of projects and constructions. In the sciences, these concepts are used for understanding physical and natural phenomena, such as the shape of crystals or the way light refracts.

In addition to practical uses, shape classification is also important for developing critical thinking and logical reasoning skills. By learning to classify shapes, we are learning to identify patterns, make comparisons, and organize information, skills that are valuable in many aspects of life.

Practical Activity: "Polygon Collage"

Project Goal

In order to practice the knowledge acquired about the classification of shapes, especially polygons, and to stimulate collaboration and communication among students, we suggest the project "Polygon Collage". In this activity, the groups shall create a collective work of art using different types of polygons.

Detailed Description of the Project

Each group shall be responsible for creating a work of art using paper polygons that have been cut out. The theme of the art is free, but all drawings must be made only with polygons. Therefore, the groups must plan, draw, cut, and glue all the polygons necessary to compose their work of art. They must also classify all the polygons used (as to the number of sides and angles) and present this classification in the final report.

Necessary Materials

• Colored paper
• Scissors
• Glue
• Pencil and eraser
• Ruler

Detailed Step by Step

1. Divide the class into groups of 3 to 5 students.
2. Each group must discuss and decide on the theme of the work of art that they will create.
3. Using a pencil, ruler, and paper, students must draw the polygons that will be used in the work of art.
4. Cut out the polygons with scissors.
5. Organize and glue the polygons on the paper to compose the work of art.
6. Classify each polygon used according to its number of sides and angles.
7. Write a final report explaining the process of creating the work, the classification of the polygons used, and a reflection on the activity.

The duration of this project should be between 5 to 10 hours per participating student, over the course of a month.

Project Deliverables

For the conclusion of the project, each group must deliver the work of art and a written report with the following topics:

1. Introduction: Contextualization of the project (relevance and application in the real world), objective of the work, and its motivations.
2. Development: Description of each step of the work production process, from conception of the theme to gluing the polygons. One should explain the theory behind the classification of polygons, present the methodology used, and the results obtained. In addition, it is necessary to list all the polygons used in the work of art, classifying them according to the number of sides and angles.
3. Conclusion: Students must revisit the main points of the work, explain what they learned, and the conclusions drawn about the project. In addition, students must reflect on the teamwork, collaboration, and the importance of managing time for the delivery of the project.
4. Bibliography: Indication of the sources consulted for the project, such as books, websites, videos, etc.

The project deliverables must be submitted to the teacher by the end of the month.