Contextualization

Let's embark on a journey into one of the most fundamental areas of mathematics: linear functions. Functions play a central role in mathematics as they allow us to analyze and understand the relationships between quantities. In this project, we will specifically focus on linear functions, also known as first-degree functions.

First-degree functions represent one of the foundations of algebra and are deeply rooted in many aspects of mathematical study. They are defined by a first-degree equation and have a very special characteristic: each value of x corresponds to only one value of y. This uniqueness property makes first-degree functions an extremely useful tool for representing many real-world phenomena.

These functions can be easily visualized on the Cartesian plane as a straight line. This is not a coincidence: first-degree functions describe linear relationships between two quantities. This representation allows for a graphical visualization of the relationships that the function describes, making it possible to have a more intuitive interpretation of mathematical relationships.

By learning about first-degree functions, you will be taking a significant step in your mathematical journey. Linear functions are essential for more advanced studies in mathematics and are found in a wide range of applications, from finance to physics.

In this modern world, understanding how functions work allows us to better comprehend the phenomena around us. An example of this is the applications of functions in economics. Economists use functions to model everything from the relationships between interest rates and investment to the relationships between supply and demand for a product in the market.

To start researching and delving deeper into the subject, we recommend the Khan Academy website, which has a collection of videos and interactive exercises on first-degree functions that are an excellent way to complement what will be learned in this project. Additionally, the book 'Fundamentals of Elementary Mathematics' by Gelson Iezzi, Carlos Murakami, and others is also a great reference for the study of first-degree functions.

Let's have fun and learn together on this mathematical discovery journey!

Practical Activity: 'Unveiling the World of Linear Functions'

Project Objective:

The objective of this project is for students to become familiar with first-degree functions by carrying out practical activities that involve the development and resolution of real problems, represented through the use of these functions.

Detailed Project Description:

Students will be divided into groups of 3 to 5, and each group will receive a problem situation that involves the use of first-degree functions. The situation will be something related to the students' reality, such as the evolution of a video game over time, the relationship between distances traveled and the time taken to travel them, among others.

Students should analyze the problem situation, create a first-degree equation that represents the situation, solve this equation, and finally, graphically represent the solution on the Cartesian plane.

Required Materials:

1. Paper and pen for notes and calculations
2. Computer with internet access for research and preparation of presentation material
3. Presentation software (such as PowerPoint or Google Slides)
4. Charting software (such as GeoGebra or Desmos)

Detailed Step-by-Step:

1. Form groups of 3 to 5 students.
2. Assign a different problem situation to each group.
3. Instruct students to analyze the situation, identify the variables, and define the relationship between them. They should write this relationship in the form of a first-degree equation.
4. After defining the equation, students should solve it and discuss the solution found.
5. Once done, students should graphically represent the solution on a Cartesian plane.
6. Each group should prepare a presentation, explaining the problem situation, the equation they defined, the solution found, and the graphical representation.
7. Finally, groups should present their work to the class, sharing their discoveries and learnings.

Written Document:

After completing the practical activity, each group should prepare a report that explores the activity carried out. The report should be divided into four parts:

1. Introduction: In this section, students should contextualize the proposed problem situation, explain why they decided to represent the situation through a first-degree function, and mention the objective of this project.

2. Development: Here, students should explain in detail the first-degree function that was used, indicate the methodology for solving the equation, and present the results obtained, both numerical and graphical.

3. Conclusion: Students should summarize the most important points of the project, demonstrate the learnings obtained, and draw conclusions about the importance of first-degree functions in representing real situations.

4. Bibliography: Finally, students should indicate the research sources used for the work, such as books, websites, videos, among others.

Correction Criteria:

Projects will be evaluated considering the following criteria:

• The quality of the analysis of the problem situation.
• The suitability of the chosen first-degree function to represent the situation.
• The effectiveness of the solution found.
• The clarity of the graphical representation of the solution.
• The quality of the in-class presentation.
• The quality of the written report, including the clarity of the project description, the demonstrated understanding of the concepts involved, and the accuracy of the conclusions drawn.

Be creative, have fun, and learn a lot on this mathematical adventure!