Contextualization

Introduction

Linear equations are one of the main topics studied in algebra. They are, basically, first-degree polynomial equations and can be expressed in the form ax + by = c, where a, b, and c are real numbers. The study of linear equations is fundamental for understanding more advanced mathematical concepts, and their applications are numerous, ranging from simple daily calculations to the basis for linear programming in computer science.

One of the important concepts related to linear equations is the system of linear equations. A system of linear equations consists of two or more equations that are solved simultaneously. A solution to a system of linear equations is a set of values for the variables that satisfy all the equations simultaneously.

Another extremely relevant topic that will be addressed during this project is the Cartesian plane. It is a graphical representation that helps in the visualization and resolution of mathematical problems, especially those involving equations and systems of linear equations. On the Cartesian plane, we can graphically represent a linear equation and, from that, obtain its solutions visually.

Importance of Linear Equations and Their Contextualization

Mathematics, as a whole, is an essential tool for understanding and describing the world around us. Linear equations, specifically, are present in numerous practical situations. For example, they can be used to calculate the total production cost in an industry (where the equation can be the multiplication of the unit cost by the number of units produced), to determine the time required for a certain job to be completed (based on the work rate), among other everyday applications.

Moreover, linear equations are fundamental in various fields of knowledge, such as physics, chemistry, economics, computer science, etc. In physics, for example, they are used to calculate speed and acceleration in rectilinear motions. In economics, they are applied to optimize production and maximize profits. In computer science, linear equations form the basis of linear programming, which is used, among other things, for resource planning and solving optimization problems.

Practical Activity

Activity Title: Project "Linear Equations in Action!"

Project Objective

This project aims to provide students with the opportunity to explore and apply the theoretical concepts of linear equations and systems of linear equations in a practical and contextualized manner. The central idea is to unite mathematics with the disciplines of Arts and Literature, creating an engaging story where the resolution of conflicts is achieved through solving linear equations and systems.

Detailed Project Description

Students will be divided into groups of 3 to 5 people, and each group will be responsible for creating a comic book or a play that involves problems that can be solved using linear equations or systems of linear equations.

The setting of the story is free, it can be a medieval adventure, a modern drama, a space episode, among others. The characters must face problems that will be solved using linear equations. For example, they may find hidden mysterious treasures and need to solve systems of equations to find the correct location, they may have to equitably divide food using equations, among other situations.

It will be necessary to elaborate at least 5 problems involving linear equations and/or systems of linear equations that are integral parts of the story's plot.

The project will be carried out in two stages: the first stage will be the planning and writing of the story, and the second stage will be the presentation of the story in the form of a comic book or play.

Necessary Materials

• Paper and pencil (for initial drafts and calculations);
• Drawing materials (if opting for comics);
• Computer with internet access (for research);
• Access to text editing software (Word, Google Docs) and drawing software (if opting for comics);
• Materials for costumes and scenery (if opting for the play).

Detailed Step-by-Step for the Activity

1. Group formation should be done considering the diversity of students' skills, so that everyone contributes to the development of the project.

2. Define the story's plot and characters. Remember that the plot should be interesting and involve solving problems using linear equations.

3. Develop at least 5 problems involving linear equations and/or systems of linear equations that are part of the story's plot. Remember that you must present the detailing of these equations, as well as their step-by-step solutions.

4. Create the script for the comic book or play, insert the problems at appropriate moments in the plot. Ensure that the problem-solving is well explained and contextualized in the plot.

5. If opting for the comic book, create the drawings by dividing each page into panels and narrating the story sequentially. If opting for the play, rehearse the presentation, build the sets, and prepare the costumes.

6. Conduct a final review and refine the details of the story, making it attractive and educational.

Project Submission

The final result of the project should be the comic book or the play presentation, accompanied by a written report, containing:

1. Introduction: Contextualize the project, presenting the chosen plot and its relevance. Briefly explain how linear equations and systems of linear equations are applied in the context of the story.

2. Development: Present the details of the project's development, explaining how the problems were created, the resolution of the equations, and how they were inserted into the plot. Also present the methodology for creating the comic book or play.

3. Conclusions: Describe what was learned during the project, how the experience of combining mathematics with other disciplines and working in a team was. Comment on how the understanding of linear equations and systems of linear equations was deepened with the project.

4. Bibliography: List all the sources that were consulted during the project, such as books, websites, videos, etc.

Finally, students should be prepared to present and explain the project to the class, showing the created story and explaining the equations used and solved.