Contextualization
Polygons are a fascinating area of study in math, especially when we start exploring concepts such as diagonals. In geometry, a polygon is a closed plane figure formed by line segments, called sides, that intersect two by two at their endpoints called vertices. Diagonals are line segments that join two non-consecutive vertices of a polygon.
Understanding diagonals is a critical element toward exploring more complex properties of polygons. The number of diagonals a polygon can have follows specific patterns based on the number of sides (or vertices) the polygon has.
Polygons are essential tools not only in theoretical contexts but also in practical applications. They are used in diverse areas such as graphic design, architecture, engineering, cartography, among others. For example, in civil engineering, polygons are used to calculate areas and volumes in construction projects, while in digital art and video games, they are used for modeling shapes and characters.
To help in understanding the subject, students can access the following resources for research:
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"Matemática e suas Tecnologias" (Mathematics and its Technologies) by CECIERJ, available at https://www.cecierj.edu.br/wp-content/uploads/2019/03/Matem%C3%A1tica-e-suas-tecnologias.pdf
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"Mundo Educação" website, which features excellent articles on polygons and their properties, available at https://mundoeducacao.uol.com.br/matematica/poligonos.htm
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"Matemática Rio" channel on YouTube, which features explanatory videos on the subject, available at https://www.youtube.com/user/matematicario
Practical Activity
Activity Title: "Unveiling the Diagonals of Polygons"
Project Goal
This activity aims to provide a fun and practical approach to understanding the pattern of diagonals in polygons. The end goal is to deliver a well-structured report that exemplifies the concepts learned through the hands-on activity.
Detailed Project Description
Groups will use popsicle sticks and modeling clay to create the vertices and edges of different polygons, and then use colored strings to represent the diagonals of those polygons. Upon completing the hands-on activity, each group will come forward and describe their findings in the form of a report.
Materials Needed
- Popsicle sticks
- Modeling clay
- Colored strings
- Paper and pens
Detailed Step-by-Step Instructions
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Students will divide themselves into groups of 3 to 5 members, and each group will receive the materials needed to build the models.
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Each group will start by creating a 3-sided polygon (triangle) using popsicle sticks and modeling clay.
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The diagonals of the polygon will be represented using colored strings.
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Groups will make the necessary notes on their observations (for example, a triangle has no diagonals).
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Each group will repeat steps 2 to 4 for polygons with 4, 5, 6, and so on, up to 8 sides.
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Students will then observe a pattern in the diagonals as the number of sides of the polygon increases.
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With their observations, each group should be able to create a formula that establishes a pattern to calculate the number of diagonals based on the number of sides of a polygon.
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Finally, each group will present their findings in a report.
Project Deliverables
The primary deliverable for this project will be a well-structured report. The format should follow a standard structure divided into four parts: Introduction, Development, Conclusions, and References.
In the introduction, students should provide context for the topic by explaining what polygons and diagonals are, how they apply in the real world, and the importance of understanding their patterns and relationships. The introduction should also include a statement of the goal of this project.
In the development section, students will explain the theoretical concept of diagonals in polygons, detail the hands-on activity conducted, describe the methodology used, and present the results obtained. It is important to demonstrate the observations made, the formula created, and justify its validity.
In the conclusions, students should restate their main points, explain their key takeaways from the project, and the conclusions drawn from the project. It is also important for students to reflect on teamwork, time management, and the problem-solving process.
In the references section, students will provide a list of sources they used to complete the project, such as books, websites, videos, etc. It is important to cite the sources properly, according to ABNT or APA standards.
In summary, the written document is an essential part of the project, as it allows students to present everything they learned during the hands-on activity in an organized, clear, and precise manner. Therefore, it should complement the practical activities conducted, showcase the discoveries and learning, especially the observations on the diagonals of polygons and how to calculate their number.
