Contextualization
Theoretical Introduction
Polygons are geometric figures formed by line segments that consecutively connect to each other. The points where these segments meet are called vertices, and the segments themselves are known as sides. A fundamental property of polygons, and the focus of our study, is the sum of their internal angles.
The concept of a polygon and the sum of its internal angles is an important topic in geometry. Depending on the number of sides of a polygon, the value of the sum of all internal angles changes. For a triangle, with three sides, the sum is 180 degrees. For a square or rectangle (quadrilaterals), this sum increases to 360 degrees. For polygons with more sides, there is a general formula that allows us to calculate the total sum of the internal angles: [(n-2) * 180], where n is the number of sides.
Contextualization and Importance
Studying the sum of the internal angles of polygons has broad applicability in various real situations. Architects and engineers, for example, employ these concepts when designing and constructing buildings. Furthermore, these principles are fundamental in creating 3D objects in computer games, digital animation, and many other areas of technology.
Moreover, understanding this topic allows us to better understand the world around us. Paying attention to polygons and angles in our environment can help develop observation skills and understand how things are built.
Practical Activity
Title: "Creating Polygon Models and Studying their Angles"
Project Objective
The objective of this project is for students to engage in teamwork to enhance their understanding of polygons and the sum of internal angles. Students will be involved in both the creative process of building polygon models and the practical application of the theoretical concept - sum of internal angles.
Detailed Project Description
Groups will be invited to create manual models of various polygons using toothpicks and modeling clay for the vertices. They will then measure the internal angles of each created polygon using a protractor and sum all internal angles. They will compare this sum with the theory learned ([(n-2) * 180], where n is the number of sides) to validate the sum of internal angles.
Required Materials
- Toothpicks
- Modeling clay
- Protractors
- Calculators
- Pens and paper for notes
- Cameras to document the process
Detailed Step-by-Step for Activity Execution
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Group Formation: Form groups of 3 to 5 students. Each group will be responsible for creating a specific polygon: triangle, quadrilateral, pentagon, etc. The division of the polygons to be modeled can be done through drawing lots.
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Polygon Construction: Each group should use toothpicks and modeling clay to create their polygon. Use the clay to join the toothpicks and form the vertices.
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Angle Measurement: With the help of the protractor, measure each internal angle of the polygon.
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Calculation of Angle Sum: Add up all measured angles and compare with the theoretical sum of internal angles of the polygon according to the formula [(n-2) * 180].
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Process Documentation: The entire process should be photographed and documented to create a final project report. Make sure to include photos, angle measurements, and comparison with the theoretical sum in the report.
About the Report
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Introduction: Explain the importance of polygons and the sum of internal angles, and describe the project's objective.
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Development: Describe in detail the process that was done to build the polygon, measure the angles, and calculate the sum. Discuss the results by comparing the obtained sum with the theoretical sum of internal angles, indicating if they were consistent and why.
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Conclusions: Explain what was learned from the project, the relevance of this learning, and suggest possible improvements or ideas for future projects.
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Bibliography: Cite all sources used for research, including books, websites, videos, among others.
The report should be submitted in PDF format and each group member should participate in some part of the writing. The deadline for submission is one week.
