Introduction

Hello dear students! Our project will explore the fascinating world of rectangles. But first, let's start with a question: What is a rectangle? A rectangle is a flat quadrilateral, that is, a four-sided figure that has no curves in Euclidean geometry. And what distinguishes it? Let's look at its characteristics. A rectangle has four right angles, all equal to 90 degrees. The opposite sides of a rectangle are always of equal length, while its adjacent sides can have different lengths.

Mathematics is a world of discoveries and knowledge, so it is essential to understand how the concepts we learn relate to each other. The rectangle, for example, is a special case of a parallelogram. It is a close relative of the square, which is a rectangle with all sides equal. In this project, we will explore the concepts of area and perimeter within the universe of the rectangle.

An interesting fact is that the concept of a rectangle can be extended to larger dimensions. In the world of 3D geometry, for example, we have the rectangular parallelepiped, which is nothing more than a rectangle in three dimensions.

Contextualization

"But, teacher, why do we need to learn about rectangles?" A common but important question. The rectangle is present in our daily lives and we don't always realize it. When we look at a book, a door, a window, a painting, a bank card, we are seeing rectangles.

Moreover, the rectangle is very important in various areas of knowledge. Civil engineers use the geometry of the rectangle to design and build houses and buildings. In art, the rectangle is used in compositions to draw attention to certain areas of the image. In graphic design, rectangles are used abundantly to create clean and effective layouts.

The study of rectangles is also crucial in computing. After all, the screens of our computers and phones are rectangles. Therefore, learning about rectangles is learning about the world around us.

To deepen your knowledge, I suggest using the following resources:

• The book "Plana Euclidean Geometry" by Olga de Sá.
• The website "Mundo Educação" which has a section dedicated to plane geometry.
• The videos from Khan Academy in Portuguese.

Practical Activity

Activity Title: "The Art of Rectangles"

Project Objective:

The objective of this project is to provide students with a practical and engaging experience of the concept of rectangles. Through this project, students will learn to calculate the areas and perimeters of rectangles, and also understand the application of rectangles in everyday life, specifically in the fields of art and graphic design.

Detailed Project Description:

This project will involve the creation of an artistic composition in which the rectangle will be the main element. Students will work in groups of 3 to 5 people and the estimated time for project completion is 5 to 10 hours per student. The total duration of the project will be one month.

Required Materials:

1. Graph paper
2. Colored pencils
3. Ruler
4. Compass
5. Calculator

Steps for Activity Completion:

1. Students will research different works of art and graphic design that make use of rectangles.
2. Students will choose an inspiring work of art or graphic design.
3. Using graph paper, students will redraw the chosen work.
4. The drawing must be done using only rectangles.
5. Each group member will be responsible for calculating the area and perimeter of at least one of the rectangles used in the composition.
6. Next, students will use their communication and collaboration skills to discuss the challenges encountered, the decisions made, and how they overcame the challenges together.
7. Finally, students will color the drawing with colored pencils.

Project Delivery:

At the end of the project, each group must deliver the following documentation:

1. The final artistic composition.
2. A written report that should include: introduction, development, conclusions, and bibliography used.

In the Introduction, students should contextualize the theme, its relevance and application in the real world as well as the objective of this project.

In the Development of the report, students should explain the theory of rectangles, the activity in detail, the methodology used, and finally present and discuss the calculations and results obtained. It is also important that this section addresses the challenges encountered and how they were overcome.

In the Conclusions, the group should summarize their main points, highlight the learnings obtained, and draw conclusions about the project. Students are expected to demonstrate their understanding of the concept of rectangles, as well as the socio-emotional skills developed during the project execution, such as time management, communication, problem-solving, creative thinking, proactivity, etc.

In the Bibliography section, students should indicate the sources they relied on to work on the project such as books, web pages, videos, etc.