Contextualization

Quadrilaterals are geometric figures that have four sides, four internal angles, and four vertices. They are classified as: square, rectangle, parallelogram, rhombus, trapezoid, and trapezium. Each of these types of quadrilaterals has distinct characteristics and properties, which provide a series of practical and theoretical applications in multiple fields of knowledge.

Plane geometry, of which quadrilaterals are an integral part, is one of the oldest areas of mathematics. It has its roots in the solutions that ancient civilizations found for practical problems. Understanding the properties of quadrilaterals and their detailed study allows for a better understanding of geometry as a whole.

Introduction

In this project, we will have the opportunity to explore in depth the different aspects of quadrilaterals. Firstly, we will investigate the fundamental properties of each type of quadrilateral and how we can define each type based on these properties. Next, we will pay special attention to the relationship between the internal angles of quadrilaterals, as well as the relationship of these angles with their sum and differences. Finally, we will explore how we can calculate the area of each type of quadrilateral based on the known information about their sides and angles.

Understanding these concepts will not only deepen our mathematical knowledge but also provide us with tools to understand and solve concrete problems. For example, by learning about quadrilaterals, we will be able to solve complex trigonometric problems and perform calculations in contexts ranging from engineering to graphic design.

Students can use the following resources as starting points and references for their projects:

1. Brazil School - Quadrilaterals
2. Just Mathematics - Quadrilaterals
3. Khan Academy - Quadrilaterals
4. World Education - Quadrilaterals

Practical Activity

"Activity Title: Quadrilaterals - Concepts, Properties, and Applications"

Project Objective

The general objective of this project is to provide a deep and comprehensive understanding of quadrilaterals, covering their definitions, properties, and practical applications. Specifically, the project aims to enable students to:

1. Investigate and understand the main types of quadrilaterals and their properties.
2. Compute the sum of the internal angles of different types of quadrilaterals.
3. Discuss and explore the practical applications of quadrilaterals in the real world.
4. Develop teamwork, time management, and other socio-emotional skills.

Detailed Project Description

Groups should investigate five types of quadrilaterals: square, rectangle, parallelogram, rhombus, and trapezoid. For each quadrilateral, the groups must:

1. Define the quadrilateral and its properties:

   • Sum of the internal angles
   • Relationship between the sides and angles
   • Specific properties (for example, all sides of the square are equal)

2. Develop a three-dimensional model for each quadrilateral using materials of their choice (paper, sticks, modeling clay, etc.).

3. Investigate and present a practical application of each quadrilateral (for example, a soccer field is a rectangle, etc.).

Required Materials

• Books and internet resources for research
• Materials for building three-dimensional models (cardboard, scissors, glue, popsicle sticks, modeling clay, etc.)
• Paper and pen for notes and calculations

Step by Step

1. Form groups of 3 to 5 students.
2. Each group chooses and researches about five types of quadrilaterals: square, rectangle, parallelogram, rhombus, and trapezoid.
3. The groups define each quadrilateral, investigate their properties, and calculate the sum of the internal angles.
4. The groups build a three-dimensional model for each quadrilateral.
5. The groups research and present a practical application of each quadrilateral.
6. The groups prepare and present a final report.

Project Deliverables

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

1. Five three-dimensional models, one for each type of quadrilateral.
2. A written report containing:
   • Introduction: The importance and relevance of quadrilaterals, and the project's objective.
   • Development: Definition of each quadrilateral, discussion of their properties, calculation of the sum of the internal angles, details of the construction of the models, and explanation of the practical applications.
   • Conclusion: Recap of the main points, learnings, and conclusions about the project.
   • Bibliography: References used in the project.
3. Oral presentation of the project to the class.

Students should dedicate at least 12 hours to the project, involving research, model construction, report elaboration, and presentation preparation. Remember, teamwork is essential for the project's success!