Contextualization

Theoretical Introduction

Mathematics goes beyond numbers and formulas. It is a language that helps us understand and describe the world around us. One of these concepts is the 'Univocal Dependency Relationship' between two variables, usually represented on a Cartesian Plane. In this plane, a line or curve is drawn, where each point represents the relationship between the values of x and y.

Cartesian Plane is a graphical tool that allows us to visualize these relationships. In it, each point is represented by a pair of coordinates (x, y), allowing the representation of different mathematical functions and concepts such as proportions.

Proportion is a concept that describes how two or more quantities relate to each other. For example, if we have two glasses of water for every three people, we have a ratio of 2:3.

Contextualization and Importance

The use of mathematics is broad, and the Cartesian Plane is frequently used in various areas such as physics, economics, biology, engineering, among others. It allows us to visually see how one variable depends on another, facilitating the understanding of various everyday situations.

The graphical representation of proportions can be useful, for example, to understand the relationship between the amount of hours studied and performance on a test, the relationship between a person's income and the amount of money they save, among many other practical examples.

Understanding these concepts is the first step to a better understanding of the phenomena around us, which is why we will explore the 'Graphical Representation of Proportions on the Cartesian Plane' in this project.

Below, I provide some reliable resources for you to delve deeper into the topic:

1. Brazil School: Function Graph
2. World Education: Proportion
3. Khan Academy: Cartesian Plane

Practical Activity

Activity Title: 'Unraveling Proportions through the Cartesian Plane'

Project Objective

The objective of this project is to explore and understand the relationships of proportionality and how they can be graphically represented on the Cartesian plane. Students will also learn valuable skills such as teamwork, effective communication, and time management.

Detailed Project Description

The groups, consisting of 3 to 5 students, will create a fictional situation that requires understanding the proportion relationship between two different quantities. They will create a story and graphically represent it on a Cartesian plane. The story should be related to real situations, and the graph should show the proportion relationship between the chosen quantities in the story.

Required Materials

• Notebook or paper for notes and sketches
• Pencil, Pen
• Ruler
• Computer with Internet access (for research and project development)
• Presentation software (e.g., PowerPoint, Google Slides)

Detailed Step-by-Step for Activity Completion

1. Group Formation: Each group should consist of 3 to 5 students.

2. Creation of the fictional situation: Each group should create a fictional situation involving the proportion between two different quantities. The story needs to be coherent and have a connection to real situations.

3. Graph development: Once the fictional situation is ready, students should develop a graph on the Cartesian plane that represents the proportion relationship between the chosen quantities.

4. Report elaboration: The report should include the fictional situation, the description of the quantities used, the construction of the graph on the Cartesian plane, and the analysis of results.

5. Presentation preparation: The group should prepare a slide presentation that synthesizes the created situation, the graph developed, and the main achievements of the project. The presentation will be made to the class.

The project will last one week, and each student should dedicate 2 to 4 hours to complete the project.

Project Deliverables

The two main project deliverables will be:

1. Detailed report: A written report including:

   • Introduction: Contextualization of the created fictional situation and the quantities used.
   • Development: Theory on proportion and Cartesian plane used, detailed description of the graph, and results analysis.
   • Conclusion: Recap of the main points, lessons learned, and conclusions drawn.
   • Bibliography: Sources consulted for the project.

2. Slide presentation: The presentation should synthesize the fictional situation, the graph on the Cartesian plane, and the main project achievements. The presentation should be clear and concise, as it will be presented to the class.

The report and the presentation should complement each other. While the report is a detailed and technical document, the presentation allows the information to be conveyed in a more visual and interactive way, promoting better understanding for all students in the class.