Contextualization

Mathematics is one of the most widely used disciplines in our lives. It is not limited to just calculations and formulas in the classroom, but is present in almost all of our daily activities. One of the most notable aspects of mathematics is the manipulation and interpretation of data, especially graphs.

In our daily lives, we interpret graphs in various ways, from tracking price trends of products, checking population growth, analyzing the evolution of a disease to measuring progress in a project. Proportions and their graphical representation on a Cartesian plane, therefore, play a fundamental role in the interpretation and understanding of this data.

Graphs are powerful tools that aid in visualizing sets of data; moreover, they are often used to represent two quantities that are in a proportional relationship. Knowing how to plot a graph and understand the graphical representation of proportions on the Cartesian plane is, therefore, a fundamental skill that everyone should have.

To deepen your knowledge and understanding of these topics, I recommend some reliable sources such as study platforms. The book 'Fundamentals of Elementary Mathematics: Analytical Geometry, Plane and Space' by Gelson Iezzi and Carlos Murakami, published by Editora Atual, offers a solid theoretical understanding of the subject. In addition, the website 'Só Matemática' (www.somatematica.com.br) contains an entire section dedicated to the subject, covering theory and providing practical examples. Another interesting source is the YouTube channel 'Matemática Rio with Prof. Rafael Procópio' (www.youtube.com/user/matematicario), where he explains mathematical concepts in a simple and interesting way.

Now that we understand the importance of the graphical representation of proportions on the Cartesian plane in our lives and in the broader context, let's dive into a group project to explore this concept more deeply.

Practical Activity: 'Exploring the Universe of Proportions'

Project Objective

This project aims to provide students with the opportunity to understand and apply the concept of proportions and their graphical representation on the Cartesian plane through a practical team project, encouraging collaboration, problem-solving, and creative thinking.

Project Description

Students will be divided into groups of 3 to 5 members, where each group will receive a special mission: to be a 'research team' that must study and present a historical technological or scientific advancement that involves the use of proportions in its foundation. This can range from the invention of the wheel, the creation of a calendar, to more recent advances such as the creation of a machine learning algorithm.

In this adventure, the team must clearly identify where proportions were used in this advancement and develop a detailed presentation and report explaining the concept of proportions and their graphical representation on the Cartesian plane, how this advancement used them, and what impact this has on the evolution of science and technology.

Required Materials

1. Research materials (books, internet access, among others);
2. Paper and pencil for sketches and notes;
3. Graphic presentation software (e.g., PowerPoint or Google Slides);
4. Text editing software (e.g., Word or Google Docs).

Project Steps

1. Topic Selection: Each group must choose and approve with the teacher a technological or scientific advancement that involves the use of proportions in its foundation.

2. Research and Learning: During this stage, students should research in detail the selected technology, its proportions, and its graphical representation. They must understand the basic principles, the history behind the advancement, and its importance in science and technology.

3. Report Elaboration: Each group must prepare a detailed project report, addressing the four main topics: Introduction, Development, Conclusion, and Bibliography.

4. Presentation Preparation: Each group must prepare a slide presentation that synthesizes the information from the report, highlighting visual representations, graphs, and diagrams that demonstrate the proportions and their graphical representation on the Cartesian plane.

5. Project Presentation: Each group must present their project to the class, explaining their findings, showing the created graphs, and discussing the importance of proportions in the chosen scientific advancement.

Project Deliverables

Each group must deliver:

1. Project Report: Detailed document covering all the aforementioned topics (introduction, development, conclusion, and bibliography). The report must follow the established guidelines above and must contain at least 1500 words.

2. Slide Presentation: Presentation that synthesizes the information from the report and visually presents the relationship between proportions and the technology under study.

By carrying out this project, students will not only deepen their knowledge of proportions and their graphical representation on the Cartesian plane but also learn to work in a team, manage their time, and enhance their research and presentation skills.