Contextualization

Theoretical Introduction

A trapezoid is a flat geometric figure with four sides, where at least two are parallel to each other, called bases. The other two sides are called lateral sides. The angles formed by the bases and the lateral sides are called base angles. We can have isosceles trapezoids, where the measures of the lateral sides are equal and the base angles are also equal, and rectangular trapezoids with one or two right angles.

Trapezoids have several important properties, including the property that the median of a trapezoid, which is the segmented line connecting the midpoints of the lateral sides, is equal to the average of the measures of the bases. Furthermore, if the lateral sides are equal in length, then the trapezoid is isosceles and the base angles are equal.

Moreover, trapezoids are useful in many areas of mathematics, especially in geometry and calculus, where they are often used to approximate the area under a curve.

Theme Contextualization

Trapezoids have a multitude of practical applications in the real world. They are used in architecture and design, given that many buildings and structures have trapezoidal shapes to provide stability and pleasing aesthetics. Additionally, trapezoids are used in engineering and construction for the design of beams, bridges, and roof structures. In mathematics, they are used in calculus to estimate the area under a curve, which is an essential skill in fields such as physics and engineering.

Therefore, the study of trapezoids not only enriches our knowledge of geometry but also equips us with practical skills that are very useful in various areas of life.

Activity

Activity Title: The Construction of the Trapezoid

Project Objective:

Apply the theoretical concepts of the trapezoid in the construction of a trapezoidal bridge model, emphasizing the calculation of measurements, problem-solving involving trapezoids, and teamwork.

Detailed Project Description:

For this project, groups of 3 to 5 students must build a trapezoidal bridge model using recyclable materials and precise measurements. The bridge must have sides and angles that represent an isosceles trapezoid. The activity will be divided into four parts: Planning, Calculations, Construction, and Preparation of a project report.

Required Materials:

1. Wooden sticks or plastic rods.
2. Glue.
3. Ruler.
4. Protractor.
5. Cardboard or cardstock.

Detailed Step-by-Step for Activity Execution:

1. Planning: The first step of the project is planning. Group members should gather and discuss the bridge design, ensuring that it represents an isosceles trapezoid. The planning should also include a list of required materials and task division among group members.

2. Calculations: With the bridge design in mind, students should calculate the measurements of the sides, bases, and angles of the trapezoid. Students should consider the available materials and how they influence the dimensions of the bridge. All calculations should be noted and verified by all group members.

3. Construction: Based on the calculations, students should build the bridge model. This step requires collaboration, attention to detail, and precision. The bridge must be stable and appropriately represent an isosceles trapezoid.

4. Project Report Preparation: Students should write a detailed report on the project. The report should be divided into sections of Introduction, Development, Conclusions, and Bibliography used.

The project should be completed in one month, and each student should invest between 5 to 10 hours.

Project Deliverables

1. Bridge Model: Students must deliver the built isosceles trapezoidal bridge model.

2. Project Report: Students must deliver a written report containing:

   1.1. Introduction: A description of the project, its relevance, and real-world application.

   1.2. Development: Detailed description of the project steps, including planning, calculations performed, and the model construction process. Explain the theory behind the isosceles trapezoid and how it was applied in the bridge construction.

   1.3. Conclusions: An evaluation of what was learned during the project and an analysis of the accuracy of the model in relation to the calculations performed.

   1.4. Bibliography: References to the resources used for the project execution.

Through this project, students will gain a deep understanding of the trapezoid concept and its practical applications, as well as important skills such as time management, communication, problem-solving, and creative thinking.