Contextualization

Quadrilaterals are geometric figures that stand out for their ubiquitous presence in our daily lives. In the shapes of our electronic devices, in the formats of the paper sheets used for writing, in the architecture of our homes and cities, quadrilaterals are protagonists of our environment.

This general presence in our daily lives is not by chance. When we observe their characteristics and properties, we realize that quadrilaterals are remarkable for their geometric versatility. With simple concepts, we can deal with a multitude of shapes and structures, be they squares, rectangles, rhombuses, trapezoids, or parallelograms.

Introduction to the Project

Starting our project, it is important to emphasize that the goal is to develop a deep understanding of what quadrilaterals are, their main characteristics, properties, and classifications. In addition, we aim to explore the practical application of these theoretical concepts, understanding how they manifest and are used in the reality that surrounds us.

In general terms, a quadrilateral is any polygon that has four sides. However, the study of quadrilaterals is not limited to just counting sides. Each quadrilateral has its peculiarities, its specific properties that distinguish them from each other. And it is these particularities that we want to explore in depth.

Therefore, we will discuss the concept of internal angles, their properties, and how they allow us to differentiate between types of quadrilaterals. We will also address the relationship between diagonals and sides, how they are determinants for the classification of quadrilaterals.

Practical Activity: Construction and Investigation of Quadrilaterals

Project Objective

The proposed activity aims to provide students with the opportunity to practically explore the theoretical concepts about quadrilaterals, investigate their properties and classifications, and apply their knowledge in a real and concrete context.

Students will build different types of quadrilaterals, observe their characteristics, and from that, discuss and understand the properties of these geometric figures. The project will also promote the development of socio-emotional skills, such as teamwork, time management, problem-solving, and creative thinking.

Detailed Project Description

Students will be divided into groups of 3 to 5 people. Each group will have the task of building and investigating the main types of quadrilaterals: square, rectangle, rhombus, parallelogram, and trapezoid.

The groups will build these quadrilaterals using simple and accessible materials, such as popsicle sticks, yarn, adhesive tape, and ruler. With the quadrilaterals built, students will then investigate their properties, focusing on internal angles, the relationship between diagonals and sides, and other relevant aspects that differentiate one quadrilateral from another.

Required Materials

• Popsicle sticks (for building the sides of the quadrilaterals)
• Ruler (for precise measurements of sides and angles)
• Adhesive tapes (for joining the sticks)
• Yarn (for building the diagonals)
• Colored pens (for identifying and recording information)
• Paper (for recording observations and results)

Detailed Step-by-Step for Carrying Out the Activity

1. Divide the class into groups of 3 to 5 students.

2. Each group will receive a set of materials for building the quadrilaterals.

3. The groups will first build the quadrilaterals, taking care to correctly follow the characteristics and properties of each one. Use adhesive tapes to join the sticks.

4. With all the quadrilaterals built, students will start investigating their properties. They should measure the internal angles with the ruler, observe the relationship between diagonals and sides, etc.

5. With each new observation, the groups should record on a sheet of paper what was perceived. They can use colored pens to organize and highlight the information.

6. After the constructions and investigations, the groups will gather to discuss and analyze their findings. They should also think of real examples of each quadrilateral in the environment around them.

7. Finally, each group should write a written document report on the project, detailing their experiences, discoveries, and reflections.

Project Deliverables and Writing of the Written Document

At the end of the project, each group must deliver:

1. Built quadrilaterals: The built quadrilaterals will be the practical proof of the work done by the students.

2. Written document reporting the project: This document should be divided into the following sections:

   • Introduction: In this section, the group must contextualize the project and indicate its objective, as well as highlight the relevance of quadrilaterals in the real world.

   • Development: Here, the groups must discuss the theory behind quadrilaterals, explain the activities carried out, present the methodology used, and the results obtained. It is important that the group explains the properties of the different observed quadrilaterals and how these were identified.

   • Conclusions: Students should emphasize the main learnings obtained, the difficulties encountered and how they were overcome, as well as comment on the relevance of this knowledge for practical life.

   • Bibliography: Finally, it is important to cite the sources consulted for the development of the work. This shows the seriousness of the research carried out and gives credit to the authors consulted.

This project should take about 5 to 10 hours to complete and will have a one-month deadline. We hope that this activity will provide a richer and more applied understanding of the theory of quadrilaterals!