Contextualization

Geometry is an area of mathematics that is dedicated to the study of shapes, sizes, and properties of figures and spaces. Within it, the calculation of areas occupies a prominent place, especially that of the area of rectangles and squares, which are widely applied in everyday life, both in personal situations and in industrial and scientific contexts.

A key concept in understanding the calculation of the area of a rectangle is the definition of the rectangle itself. A rectangle is a four-sided polygon (quadrilateral) in which all the interior angles are right angles (90 degrees). Another fundamental concept is that of area, which is the amount of space within the boundaries of a two-dimensional figure.

The formula for calculating the area of a rectangle is given by the product of the base measurement and the height measurement. This formula is easy to understand and apply, and it is one of the first steps in learning more complex concepts in geometry.

In the real world, calculating the area of a rectangle is applied in countless situations. In civil construction, for example, architects and engineers calculate the area of walls, floors, and ceilings to determine the amount of material needed. In agriculture, calculating the area of land helps to plan the distribution of crops or the construction of facilities.

Even in areas seemingly disconnected from mathematics, such as design and art, calculating areas is also fundamental. For example, a graphic designer may need to calculate the area of a banner or a package, while an artist may need to calculate the area of a canvas or a wall to be painted.

Practical Activity: "Calculating and Applying the Area of a Rectangle"

Objective of the project

The objective of this activity is to provide students with a practical and fun experience in applying the concept of the area of a rectangle and to stimulate teamwork, creativity, and problem-solving skills.

Detailed description of the project

Students, divided into groups of 3-5 people, will develop a plan for creating a small rectangular garden, simulating a space in the schoolyard, which will be the land for application. The project should include the choice of plants to be cultivated, the distribution in space, and the calculation of the amount of material to be used (such as soil and fertilizer), based on the calculation of the area of the land.

Materials required

1. Graph paper
2. Pencil and eraser
3. Ruler
4. Calculator
5. Internet access to research information about plants and garden materials

Detailed step-by-step instructions for carrying out the activity

1. Groups should begin the project by defining the dimensions of the rectangular plot, which will be the garden. They can choose any measurements they wish, as long as they are consistent with reality.

2. With the dimensions defined, students should calculate the area of the land. This calculation should be explained in detail and justified in the project report.

3. Students should research different types of plants that can be grown in the garden and choose some for their project. They should create a sketch of the garden on graph paper, defining where each plant will be placed.

4. Students should calculate the amount of material (such as soil and fertilizer) that will be needed for the garden, considering the area of the land. They should explain their reasoning and show the calculations in the report.

5. In the report, groups should explain the choice of plants, their distribution in the garden, and the amount of material needed. They should also reflect on the teamwork process, including challenges faced and how they were overcome.

Project deliverables

The final deliverable of the project should be a written report with the following sections:

1. Introduction: In this section, students should provide context for the project, explaining the importance and application of calculating the area of a rectangle in the real world. They should also present the objective of the project.

2. Development: Students should explain the theory behind calculating the area of a rectangle and provide details about the practical activity carried out. They should indicate the methodology used and present and discuss the results obtained.

3. Conclusions: In this section, students should revisit the main points of the project, reflect on the learning acquired, and draw conclusions about the project.

4. Bibliography: Students should indicate the sources they used to work on the project, such as books, web pages, videos, etc.

The report should demonstrate understanding of the mathematical concepts involved and the students' ability to apply them in a practical context. In addition, it should be clear that the students collaborated and worked as a team to carry out the project.