Contextualization

The Rectangle Area is a fundamental concept in plane geometry, being one of the first that students learn when venturing into this branch of Mathematics. The subject is one of the pillars on which more complex and advanced branches of mathematics such as spatial geometry, trigonometry, and differential and integral calculus are based. To understand the importance of this theme, it is necessary to first understand what area is.

Area is a measure of surface, that is, it is a numerical value that we can associate with a two-dimensional object. In other words, when we measure the area of an object, we want to know how much of that object we have. For example, when painting a wall, the painter needs to know the area of that wall in order to calculate the amount of paint to be used.

The area of a rectangle is calculated using the formula: base times height. Here, the base and height are the perpendicular sides of the rectangle. But what does this mean in everyday life? How do we apply this formula and what is it for?

Understanding and applying the concept of the rectangle area is of fundamental importance for various areas of knowledge, directly influencing everyday situations such as in the planning and execution of civil architecture and engineering, textile industry, agriculture, among others. For example, an engineer when designing a house, besides considering the ceiling height, the height between the floor and the ceiling, needs to take into account the area of the rooms so that he can make an adequate planning for the use and comfort of the future residents.

For this study, you can refer to the following reference materials:

1. Brazil School - How to Calculate the Rectangle Area
2. World Education - Rectangle Area
3. Youtube/Mathematics: How to Calculate the Rectangle Area

In addition to these materials, refer to High School Mathematics textbooks to reinforce understanding of the subject.

Practical Activity

Activity Title: "Measuring Life: A Practical Approach to the Rectangle Area"

Project Objective:

To understand the concept of the rectangle area, apply it in a practical and collaborative way, developing competencies such as teamwork, problem-solving, communication, and creative thinking.

Detailed Project Description:

Students will be divided into groups of 3 to 5, and each group will have the mission of calculating the area of a rectangular object or space in the school environment, such as the blackboard, a door, a table, the floor of a room, or the top of a workbench, for example. Each group will choose a different object or space.

Then, they will apply the theory learned in practice, by measuring the dimensions of their respective objects or spaces and calculating their areas. Next, they should think of a practical situation where measuring the area of the chosen object or space would be necessary or useful and explain this situation.

Necessary Materials:

1. Tape measure or large ruler
2. Notebook and pen for notes
3. Camera (from the cell phone, for example) to document the process

Detailed Step-by-Step for Carrying Out the Activity:

1. Form your groups of 3 to 5 members.
2. Choose a rectangular object or space in the school environment to measure. Make sure each group has chosen a different object or space.
3. Using the ruler or tape measure, measure the dimensions (base and height) of the chosen object or space.
4. Record the measurements obtained.
5. Calculate the area of the object or space using the rectangle area formula.
6. Think of a practical situation where measuring the area of the chosen object or space would be important. For example, if the chosen object was a door, a situation would be the need to paint it.
7. Document the entire process through photos and/or videos.
8. Prepare a final report containing the following sections: Introduction, Development, Conclusions, and Bibliography used.

The report should be written according to the following guidelines:

• Introduction: In this section, contextualize the theme, its relevance and application in the real world, the chosen object or space, and the project's objective.

• Development: Here, explain the theory behind the rectangle area, detail the activity, indicate the methodology used (how the measurements were taken, who did what in the group), present the measurements and results obtained, and discuss the practical situation proposed.

• Conclusion: Summarize the main points of the work, explain the learnings obtained from the project, and draw conclusions.

• Bibliography: Indicate the sources on which you based your work on the project such as books, web pages, videos, etc.

The project should be executed within a week, and the final report should be delivered at the end of this period.