Introduction and Contextualization

Introduction

Algebra and geometry are fundamental areas of mathematics that help us understand and describe the world around us. When we study areas, especially those of geometric figures, we are applying concepts from these two fields. In this project, we will specifically focus on a figure called a trapezoid.

A trapezoid is a quadrilateral (a figure with four sides) that has exactly two parallel sides. The parallel sides are called bases, and the distance between them is the height of the trapezoid. A notable characteristic of trapezoids is that the area can be calculated by the average of the bases multiplied by the height.

To calculate the area of a trapezoid, we need the formula:

A = (B+b) / 2 * h

where:

A is the area,
B is the larger base,
b is the smaller base,
h is the height of the trapezoid.

Contextualization

But why study trapezoids? It turns out they appear unexpectedly in our daily lives and in many professions. For example, architects and engineers use the area of trapezoids to design and build efficient structures. In the world of science, trapezoid calculation is a method for approximating the definite integral of a function. In art and design, trapezoid rules can be used to create interesting shapes and patterns.

Furthermore, working with trapezoids also helps develop important skills such as logical thinking, spatial reasoning, and problem-solving. Learning to calculate the area of a trapezoid also prepares students for more advanced topics in mathematics, such as trigonometry and calculus.

Practical Activity

Activity Title: MISSION TRAPEZOID

Project Objective

The 'Mission Trapezoid' aims to engage students in understanding the theoretical and practical concepts of trapezoid area, applying them in a playful and collaborative way. Additionally, it aims to develop cross-cutting skills such as teamwork, problem-solving, time management, and critical thinking.

Detailed Project Description

Students will be divided into groups of 3 to 5 participants. Each group will receive a 'mission' where they must use their mathematical knowledge and practical skills to calculate the area of the trapezoid in various contexts.

The 'mission' is a fictional scenario that involves building a water park. In this scenario, a water park is being designed, and the group, acting as an engineering team, needs to calculate the area of the trapezoids in the park layout to estimate the volume of water needed for each pool. Each pool has a trapezoid shape.

Required Materials

• Graph paper
• Ruler
• Pencils, erasers, and colored pens
• Calculator

Detailed Step-by-Step for Activity Execution

1. Students will receive the water park layout, which will contain several trapezoid-shaped pools. Each group will receive a different layout.

2. Using the graph paper and ruler, they must measure the bases and height of each trapezoid and record the values.

3. Applying the trapezoid area formula, students must calculate the area of each pool and add up all the areas to obtain the total area of the pools.

4. Each group must then prepare a presentation, explaining how they performed the calculations and how mathematical concepts were applied in the project.

5. Finally, students must prepare a detailed written report, where they will explain the entire process and present their conclusions.

Project Deliverables

The deliverables of this project are:

1. The project presentation, in which students will explain the process they followed to calculate the area of the trapezoids, justifying their measurements and calculations.

2. The written report detailing the entire process carried out by the group. The report should contain an introduction where students explain the importance of studying trapezoid areas in daily life and in various professions. The development should explain the theory behind the trapezoid area, explain the activity in detail, indicate the methodology used, and present and discuss the results obtained. In the conclusion, it should summarize the main points of the work, explain the learnings obtained, and conclude on the project. Finally, they should indicate in the bibliography the sources they relied on to work on the project.

3. The layout with the measurements and calculations recorded, which will be attached to the report, serving as evidence of the practical work carried out.

4. A reflection from each student on what they learned from the activity and how it helped in the development of their technical and socio-emotional skills.

Students must organize their time management so that the project can be completed within a minimum of 12 hours per student.