Contextualization

Polygons… What do they actually mean and why are they important to us? Polygons are geometric shapes defined by a sequence of points on a plane, called vertices, connected in sequence by line segments, called sides. Thus, polygons can have several sides, and can be called: triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and even a decagon (10 sides). These are just a few examples of regular polygons, where all sides have the same length. Just imagine! There are polygons with 100, 1000, or even 1,000,000 sides!

They are the basis of plane geometry and represent a way of describing and understanding the world around us. From the shape of a simple rectangular sheet of paper to the complex architecture of modern metropolises, polygons are present in diverse forms and on different scales. Understanding their properties and applications allows us to build more comprehensive and integrated knowledge of the natural and human world.

Polygons play a fundamental role in our modern society. Imagine the engineers who design our houses, schools, and buildings. They need to understand the properties of polygons in order to design safe and efficient buildings. Or think about video game designers or film animators. They use polygons to create the realistic virtual worlds we admire on the screens.

And that's not all! Polygons are fundamental in other areas of mathematics, such as trigonometry, algebra, and calculus. They are used to calculate areas, perimeters, angles, and distances.

Resources to help you delve deeper into the subject:

• Khan Academy: Polygons
• OBMEP Math Portal: Polygons
• Só Matemática: Polygons

Practical Activity

Activity Title: The Magical World of Polygons

Project Objective:

To understand the properties and characteristics of polygons through a fun and engaging activity that integrates visual arts and mathematics, fostering the development of technical and socioemotional skills.

Detailed Project Description:

Students, divided into groups of 3 to 5, will research different types of polygons and their properties. After the research phase, they will create a "model" where each polygon studied will be represented in some way. This model will be planned and executed by the group, using recycled materials, paper, glue, scissors, and the knowledge acquired in the research. In addition to assembling the model, each group must produce a detailed report on the process and lessons learned.

Materials Required:

• Cardboard or paperboard;
• Colored pencils;
• Ruler and protractor;
• Scissors;
• Glue;
• Recyclable materials.

Detailed Step-by-Step Instructions for Completing the Activity:

Part 1 - Research

1. Each group will research polygons, focusing on the following aspects: definition, characteristics, properties, classification, and practical applications.
2. This research should include, at minimum, the following polygons: triangle, square, pentagon, hexagon, and octagon.
3. The groups should write down the important points of their research, as they will be useful in Part 2 and in the final report.

Part 2 - Model Planning

4. Based on the research, each group will plan the model, deciding how each polygon will be represented and what materials they will use.
5. The groups should create an outline of their project, listing the steps needed to execute it.

Part 3 - Model Construction

6. After planning, the groups will build the model, following the outline created in the planning phase.
7. During construction, they must ensure that all polygon properties are being represented.

Part 4 - Final Report

8. Each group must write a detailed report on the project, following the format specified below:
   • Introduction: The student should contextualize the topic, its relevance and application in the real world, and the objective of this project.
   • Development: In this section, students should detail the theory behind polygons, explain the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.
   • Conclusion: Students should conclude the work by reiterating their main points, making explicit the lessons learned and the conclusions drawn about the project.
   • Bibliography: Indication of the sources that served as the basis for the project.

The practical activity "The Magical World of Polygons" is a comprehensive project that allows students to explore, understand, and apply theoretical concepts about polygons in a fun and engaging way. Upon completing the project, students will have demonstrated not only their understanding of polygons, but also their teamwork, planning, problem-solving, critical thinking, and creativity skills.