Project: Building and Exploring the World of Trapezoids

Contextualization and Introduction

Mathematics is present in everything that surrounds us. Although we often don't realize it, it appears in our lives in the most varied and diverse ways. In nature, in art, in economics, in engineering, in practically all spheres of human knowledge. One of these forms is through geometric shapes, more specifically, the trapezoid.

The trapezoid is a quadrilateral - that is, a figure with four sides - which has the peculiarity of having only two parallel sides. This attribute gives it unique characteristics, which can be explored in various ways. In mathematics, it is through the study of the properties of these figures that we can develop our spatial reasoning ability, an important skill for dealing with problems ranging from simple spatial organization to more complex issues, such as those found in fields like architecture and engineering.

Now, you must be wondering: "But where can we see trapezoids in practice?" After all, what does this have to do with the real world? Well, the answer is: in many places! If you look at the buildings around you, for example, you will see that many of them have a trapezoidal shape. This is because this format makes it possible to make better use of space, while providing a safer structure for construction. In addition, in arts and design, trapezoids are also widely used because they provide a different and pleasing aesthetic.

Practical Activity

Activity Title: "Building and Exploring the World of Trapezoids"

Project Objective:

The objective of this project is to enable students to learn more about trapezoids by building and exploring their properties and applications in real-world situations. In addition, the project aims to enhance teamwork skills, time management, and the application of mathematical concepts in practice.

Detailed Project Description:

The project will be divided into two main parts. The first consists of building trapezoid models using basic materials and then exploring their properties. The second involves applying this knowledge in a real-life context, where students will have to identify and solve a problem that involves the use of trapezoids.

Students will be divided into groups of 3 to 5 members and will have one week to complete the project. We recommend a dedication time of 2 to 4 hours per student.

Necessary Materials:

1. Cardboard or cardstock
2. Ruler
3. Markers
4. Scissors
5. Glue

Step-by-Step Activity:

Part 1 - Building Trapezoids

1. With the ruler, draw several trapezoids on the cardstock, varying the sizes and shapes.
2. Cut out the trapezoids and write the measurements of the sides and angles on each of them with the marker pen.
3. Use these models to explore the properties of trapezoids, such as the sum of the interior angles, the proportionality of the parallel sides, among others. Record your findings for later discussion.

Part 2 - Applying Trapezoids to Real Life 4. Think of an everyday problem that can be solved using trapezoids. These can be problems of architecture, design, space organization, etc. Describe the problem to be solved well. 5. Think of solutions to the identified problem and how the trapezoid could be applied. Draw and build a model of your solution using the cardboard trapezoids. 6. Document the entire process, with photos, videos, or drawings, demonstrating the development of ideas, the construction of the models, and the solution of the proposed problem.

Part 3 - Final Document 7. Based on the notes and records made during the project, students must produce a detailed report. This report must contain at least:

• Introduction: contextualization of the trapezoid and its importance, in addition to presenting the objective of the project.
• Development: theory on trapezoids, details of the activities carried out, methodology used, and presentation of the results obtained.
• Conclusions: resuming the main points of the work, lessons learned, and conclusions drawn about the project.
• Bibliography: indication of the reference sources used in the project.

We hope that this project will not only bring knowledge about trapezoids, but also awareness of the presence of mathematics in our daily lives and the importance of teamwork for problem-solving.