Contextualization

Introduction

Mathematics is a science deeply rooted in our daily lives, and graphs are a powerful visual representation that can make mathematical concepts more understandable. In this context, one of the fundamental skills is being able to represent proportions on the Cartesian plane.

A proportion is a statement that two ratios are equal. Therefore, it is a comparison of two quantities or magnitudes. In the Cartesian plane, a graphical representation is a way to visualize this proportion between two magnitudes.

Knowing how to link proportions with graphs is essential not only for mathematics but also for other disciplines such as physics, economics, biology, among others. This project aims to explore the graphical representation of proportions and make connections with the real world.

Contextualization

The graphical representation of proportions on the Cartesian plane is a study topic of special relevance. Whether in economics studies to understand the relationship between supply and demand, in physics to understand the motion of bodies, in engineering for the design of structures and systems, the ability to read, interpret, and construct graphs associated with proportions is fundamental.

Moreover, in the business world, such as in inventory control, sales performance evaluation, market studies, and many other everyday situations, this skill is essential. Therefore, learning how to represent proportions on the Cartesian plane is a tool that will provide students with a deeper insight into the functioning of various natural and social processes.

Activity

Activity Title: "Creating and Interpreting Proportion Graphs in the Real World"

Project Objective

The objective of this project is to develop skills in the graphical representation of proportions on the Cartesian plane, making concrete connections with real-world situations. Students will work in groups of 3 to 5 people and should apply the concepts of ratio, proportion, functions, and graphical representation in a study focused on real-life situations. This work will require an estimated time of 12 to 15 hours per student.

Detailed Project Description

Each group will be responsible for choosing a real-world scenario where proportions are relevant. Scenarios can include, for example, the relationship between a city's population and the amount of natural resources, the relationship between academic performance and study hours, the relationship between speed and travel time, among others.

Groups will need to have a solid understanding of the chosen theme to represent the proportions graphically. They should be able to identify variables, measure or research their values, and finally map the relationships that these variables establish in graphs on the Cartesian plane.

Required Materials

1. Sheets of paper or graphic design program for creating the graphs.
2. Pens, colored pencils, or digital resources for coloring and marking the graphs.
3. Scientific calculator or calculation program to perform mathematical calculations.
4. Internet access for data research.

Step by Step

1. Team discussion and selection of a real-world scenario involving proportions.
2. Research and data collection or measurements related to the chosen scenario.
3. Identification of variables and definition of a mathematical expression relating these variables.
4. Creation of a value table for the variables.
5. Graphical representation of the proportion on the Cartesian plane based on the table values.
6. Analysis and interpretation of the graph: How do the variables relate? What does the graph demonstrate about the relationship between the variables?
7. Writing the report explaining the process, results, and conclusions reached.

Project Delivery

At the end of the project, each group will deliver a detailed and colorful graph representing the chosen proportion, along with a report describing the process, calculations, and conclusions.

The report should contain the following elements:

1. Introduction: Contextualization of the chosen scenario, relevance and real-world application, and the project's objective.
2. Development: Detailed description of the theoretical concept of proportion and its relation to the chosen scenario, detailed description of the activity carried out, presentation of the methodology used, and discussion of the results obtained.
3. Conclusion: Synthesis of what was learned in the project, lessons learned, and the importance of the subject in real life.
4. Bibliography: Citing all sources on which the students based their work.

Each group should also give an oral presentation of their project to the class, explaining the chosen scenario, showing the final graph, and sharing their conclusions.

This project should help students understand and apply the graphical representation of proportions on the Cartesian plane, while enhancing skills such as teamwork, research, and oral presentation. The use of real-world scenarios will make the content more relevant and meaningful to students.