Contextualization

Mathematics is everywhere, even in the simplest things. In objects of our daily lives, in art, in architecture, in every detail of nature, and of course, in geometry. Geometry is part of one of the branches of mathematics that studies shapes and their attributes. Here, we will focus on one of these basic shapes, but no less important - the rectangle.

A rectangle is a geometric shape with four sides and four right angles (measuring 90 degrees). This simple yet fundamental shape has special attributes that are essential for a deeper understanding of geometry. Rectangles have opposite sides of equal measures and, because they have right angles, they are classified as parallelograms, which are polygons with opposite sides parallel.

To venture into geometry, it is extremely important to understand well what a rectangle is, its properties, and how to calculate various measures associated with it, such as perimeter and area. But besides knowing these theoretical aspects, it is crucial to understand the presence and application of rectangles in our daily lives.

Rectangles are present in many things we use or see every day. Have you ever noticed that your computer, your smartphone, your notebook, and even your TV screen are in the shape of a rectangle? Architects and engineers use rectangles in their construction projects, artists in their works, and mathematicians in calculations and equations. They are not just static geometric shapes, they are functional pieces in the design of our everyday world.

Therefore, delving into the study of rectangles is not just about learning geometry, it is also about understanding a little more about how the world around us is built and functions. A conversation about rectangles is, therefore, a conversation about mathematics itself and its applications.

And to help you dive into the geometry of rectangles, we suggest some sources:

1. NEM, Ruy Affonso. Princípios de Geometria - Vol. 1. 1st ed. São Paulo: Edgar Blucher, 2002.
2. Khan Academy - Area and Perimeter: Rectangle and Square
3. Mundo Educação - Rectangle

Practical Activity

Activity Title: Rectangle in Real Life

Project Objective

This project aims to solidify the concept of a rectangle, its properties, and associated calculations, while working on creativity, collaboration, and the ability to see mathematics in the real world.

Detailed Project Description

Each group of 3 to 5 students must identify and document, both textually and photographically, 10 examples of rectangles in the real world, detailing the measurements of each rectangle found and calculating their areas and perimeters.

With this data, the groups must prepare a detailed report, including photos, measurements, and calculations of the rectangles. Then, the report should present a discussion on how rectangles contribute to the functionality or aesthetics of the object or location where they were found.

Each group member must actively participate in the identification, measurement, calculation, and report writing. The project must be completed within one week.

Required Materials

1. Ruler or tape measure
2. Camera or smartphone (for taking photos)
3. Paper and pen (for notes)
4. Calculator (for calculations)
5. Computer (for report writing)

Detailed Step-by-Step

1. Form groups of 3 to 5 students.
2. Review the concept of a rectangle and how to calculate the area and perimeter of the rectangle.
3. Ask students to identify 10 examples of rectangles in real life. They can be from anywhere: school, home, park, etc.
4. Students should take photos of each identified rectangle.
5. Students should measure the sides of each rectangle using a ruler or tape measure and write down the measurements.
6. Using the obtained measurements, students should calculate the area and perimeter of each rectangle.
7. Students should prepare a detailed report, including:
   • Introduction: Summary of the activity and the importance of the rectangle in the world around us.
   • Development: Include photos of each rectangle, with annotated measurements and calculations, and a discussion on how the rectangle contributes to the functionality or aesthetics of the object or location.
   • Conclusion: Comments on what was learned throughout the project, including any difficulties encountered and how they were resolved.
   • Bibliography: References used for the project.
8. All group members must participate in each stage of the report preparation.
9. Reports should be submitted in digital format at the end of the week.

The report will be a key piece in assessing students' understanding of the concepts of a rectangle, area, and perimeter, as well as their observation, measurement, calculation, and written expression skills. It will also indicate how well students can work as a team and apply mathematical concepts in real-world situations.