Introduction and Contextualization

Contextualization

Mathematics is a universal language, essential in our daily lives, from the time we buy on the market to the construction of a building. A subarea of Mathematics that is also very applied in everyday life is geometry, specifically polygons. They are everywhere, in traffic signs, in the structure of a table, in the facade of a house and even in the organization of gardens. Therefore, the classification of geometric shapes is a very necessary knowledge, not only for solving mathematical problems but also for better understanding the world around us.

In this project, we will delve into polygons, which are closed plane figures with three or more sides. They are classified according to the number of sides and the nature of their angles. We will learn to recognize them, name them, compare them and draw them. In addition, we will explore how to classify them according to their sides and angles.

Theoretical Introduction

This work is based on three essential concepts of plane geometry: polygons, sides, and angles. Polygons are closed plane figures with three or more sides. Sides are straight lines that form the boundary of a polygon. Angles are the intersections of two sides, forming corners or vertices of the polygon.

The classification is made mainly by the number of sides. For example, a three-sided polygon is called a triangle, a four-sided one is a quadrilateral, a five-sided one is a pentagon, and so on. Another important feature is the nature of the angles of the polygons. A polygon can be classified as regular if all its sides and angles are equal and irregular if they are not.

In addition, there are the concepts of equilateral and equiangular polygons. An equilateral polygon has all sides equal, while an equiangular polygon has all angles equal. A polygon can be both equilateral and equiangular at the same time, which is the case for regular polygons.

Practical Activity - Construction and Classification of Polygons

Title of the Activity:

PolygonWorld: Exploring the World of Shapes

Project Objective:

To apply the theoretical concepts of the classification of geometric shapes, specifically polygons, in the construction of models, to promote practical understanding about polygons, their classifications, and applications in real life. The work will be carried out in groups of 3 to 5 students, with a recommended duration of at least 12 hours of dedication per student.

Detailed Project Description:

Each group will be responsible for building a model representing a "city," where each element must be a representation of a different type of polygon. For example, a building could be a hexagon, the central square an octagon, the roof of a house a triangle, and so on.

The composition of the city is free, but each group must use at least 5 different shapes of polygons, and each polygon must be correctly classified according to its sides and angles. The model must be accompanied by a map, where each geometric shape will be identified with its respective name (triangle, square, pentagon, etc.) and classification (equilateral, equiangular, etc.).

Required materials:

• Cardboard
• Colored paper
• Glue
• Ruler
• Pencil
• Colored markers
• Blunt-tipped scissors

Detailed Step-by-Step:

1. Discussion and Planning: The group will discuss and plan the composition of the city, deciding which structures to include and which polygons will represent each one.
2. Drawing and identification: On a sheet of paper, draw the sketch of your city, identifying each of the shapes that will be used.
3. Construction of the Shapes: Using the ruler and the materials provided, start building the required shapes.
4. City Model Assembly: Assemble the model with the constructed shapes and then color and decorate the model to the taste of the group.
5. Map Creation: Make a map of your city, identifying each shape with its respective name and classification.
6. Model Presentation: All groups will present their models and explain the shapes used and their respective classifications.

Project Deliverables:

• City model: The complete city model with all shapes correctly identified and classified.
• City map: The map must identify each shape and its classification.
• Written report: Including all four main topics indicated.
• In the Introduction, the group should explain the relevance and application of polygons in the real world and the objective of the project.
• In the Development section, you must detail the theory of polygons and how this theory was applied in the construction of the model, planning and execution of the activity, and its results.
• The Conclusion should restate the main points, lessons learned, and conclusions drawn about the project.
• Bibliography: Indicate the sources used to support the theoretical work.