Contextualization

Mathematics is a science that is all around us, and one of its most interesting aspects is Geometry. In this project, you will be challenged to dive into the universe of Regular Polygons - flat geometric figures formed by closed line segments that have all sides and angles congruent.

Have you noticed that they are everywhere? Just look at nature, architecture, design, and even certain foods to see how present they are in our daily lives. The base of a pizza, for example, is a perfect circle, which can be divided into several isosceles triangles - which are a type of polygon!

Introduction

To understand the geometry of regular polygons, we need to talk about some basic concepts. Polygons are geometric figures formed by three or more line segments (sides), where each one meets two others forming vertices. Regular polygons are those in which all sides and angles are equal.

All regular polygons have something in common: they can be inscribed in a circle, meaning it is possible to draw a circle that passes through all their vertices. Additionally, the sum of the internal angles of a polygon is also a key concept and can be calculated using the formula (n-2)*180, where "n" is the number of sides of the polygon.

Regular polygons are also classified by specific names according to the number of sides: triangle (3), square (4), pentagon (5), hexagon (6), heptagon (7), octagon (8), nonagon (9), decagon (10), and so on.

Practical Activity: "Discovering Polygons"

Project Objective

Based on the concepts of regular polygons learned, students will conduct an investigation to identify, analyze, and construct these figures in different aspects of everyday life. The objective of this project is to expand students' perception of the presence of regular polygons around them, as well as to strengthen their understanding of the theory of these geometric shapes. Additionally, by carrying out this project, students will integrate mathematical concepts with art to stimulate manual skills and creativity.

This work will be carried out in groups of 3 to 5 students and should take more than 12 hours per student to complete. The involvement with the project will be intensive and will require teamwork, time management, problem-solving, and creative thinking.

Detailed Project Description

1. Investigation of Regular Polygons in Everyday Life: Students should collect examples of regular polygons in different aspects of their daily lives, whether in architecture, nature, everyday objects, design, and even food. They should photograph at least 10 different examples and classify each one according to the number of sides.

2. Construction of a Regular Polygon Mosaic: Students should create a mosaic formed by regular polygons. They are free to draw any image of their choice, as long as it uses only polygonal shapes. Each group must use at least four different types of regular polygons.

3. Project Presentation: Students should prepare a presentation for the class, explaining the theoretical concepts of regular polygons, presenting the examples they found, and explaining the mosaic they created.

4. Preparation of a Report: At the end of the project, each group should write a report detailing all the stages of the project and the conclusions obtained. The report should be organized into the following sections:

• Introduction: Explain what a regular polygon is, its importance, and present the objective of the project.
• Development: Detail the theory of regular polygons, explain the activities carried out, the methodology used, and discuss the results obtained.
• Conclusion: Summarize the main points of the work, talk about what they learned, and what conclusions were possible to draw from the project.
• Bibliography: Indicate all sources from which they obtained information to work on the project.

Necessary Materials

• Camera or cell phone to take photos
• Drawing materials (colored pencils, crayons, markers)
• Office paper or cardboard

Detailed Step-by-Step for the Activity

1. Formation of Groups: Organize into groups of 3 to 5 people. Each group should select a leader to coordinate the team and ensure that everyone is participating and collaborating.

2. Study of Regular Polygons: Each group should study regular polygons, reviewing the lessons and consulting the recommended references.

3. Investigation of Regular Polygons: Next, they will conduct an investigation to identify regular polygons in different aspects of daily life. Each example found should be photographed and classified according to the number of sides.

4. Construction of the Mosaic: With the acquired knowledge, each group should design and draw a mosaic using at least four different types of regular polygons. The aesthetics of the drawing and the correct representation of the polygons should be taken into account.

5. Preparation of the Presentation: Each team should prepare a presentation for the class, explaining the process they went through and showing the examples of polygons they found and the design decisions made in creating their mosaic.

6. Writing the Report: Finally, each group should write a report detailing the entire project, from the daily investigation, the creation of the mosaic, the class presentation, and the conclusions they were able to draw from the project.

Remember: this project requires teamwork and dedication. Enjoy learning while having fun!