Contextualization

Hello, class! Let's talk about one of the most important concepts in Mathematics: Functions. In this project, we will explore linear functions, also known as linear functions, and to understand this, you will need to remember what linear equations are.

Functions are a mathematical tool that allows us to describe relationships between two or more quantities. In particular, a first-degree function relates two quantities in such a way that each value of one corresponds to exactly one value of the other. First-degree functions are extremely important because they model many real-world phenomena that involve a constant rate of change, such as the constant speed of a moving car, for example.

One of the first topics we study in algebra is the concept of a first-degree linear equation with two unknowns. These equations, when graphically represented, result in a straight line, which explains the term 'linear'. More importantly, a first-degree linear equation with two unknowns also presents itself as a function. Therefore, associating a first-degree linear equation with two unknowns with a line on the Cartesian plane is a skill that will be greatly explored in this project.

Mathematically, functions are of utmost importance. However, beyond that, they have a great application in the real world. Functions are everywhere! We use functions to describe and understand many of the things that surround us. For example, the growth rate of a plant, the speed of a moving car, a company's profits in relation to the number of sales - all of these are examples of phenomena that can be modeled using functions.

Therefore, understanding functions and knowing how to work with them is a skill that will benefit you in various areas, from exact and natural sciences to economics and business. So, we are excited to see what you will learn and create in this project!

As supporting material, we suggest the following references:

1. Khan Academy: Functions using real-world applications - An excellent learning platform that offers free educational materials. This link directs to a module that uses real-world applications to address functions.

2. Professor Ferretto: First-Degree Functions - A well-made series of YouTube lesson videos that explains the topic in a simple and objective way.

3. Só Matemática: First-Degree Function - Educational website with clear text and examples on the subject.

Practical Activity: 'The World in Lines'

Project Objective

In this project, you will explore the real world through first-degree functions and, while doing so, develop important technical and socio-emotional skills. You will have to work together, manage your time effectively, think creatively, and solve problems proactively.

Detailed Project Description

Each group will choose a real-world phenomenon that can be described by a first-degree function. You must collect data, create mathematical models, conduct analyses, and finally, present your findings in a detailed report and an oral presentation.

Necessary Materials

1. Notebook or paper for notes
2. Pencils, erasers, and colored pens
3. Computer or tablet with internet access
4. Spreadsheet software (Google Sheets, Excel, etc.)
5. Presentation software (Google Slides, PowerPoint, etc.)

Activity Step by Step

1. Group Formation: Form groups of 3 to 5 students.

2. Phenomenon Selection: Each group must choose a real-world phenomenon that can be modeled using a first-degree function. For example, the distance traveled by a car over time at a constant speed, or the growth of a plant over time.

3. Data Collection: Conduct research to collect data on the chosen phenomenon. This data can be obtained through experiments, observations, or online research.

4. Creation of the Mathematical Model: Use the collected data to form the equation of the linear function that represents your phenomenon. This is where you will associate the first-degree linear equation with two unknowns with a line on the Cartesian plane.

5. Analysis: Analyze the created function. What does it represent? How does it behave? What are its main characteristics?

6. Report Development: Write a detailed report of your findings. The report should include:

   • Introduction: Provide context for the theme, its relevance, and real-world applications.
   • Development: Explain the theory behind the central theme, detail the activity, indicate the methodology used, and present and discuss the results.
   • Conclusion: Summarize the main points of the work, explaining the learnings obtained and the conclusions drawn.
   • Bibliography: List the sources used in the project.

7. Presentation: Prepare an oral presentation to share your findings with the class. The presentation should be informative, engaging, and clear.

The expectation is that this project will be completed in about a month, with a workload of 5 to 10 hours per student. It is important to manage your time well in order to adequately complete all parts of the project.

The project should be delivered in two parts: the written report and the oral presentation. The report should be submitted on the day of the presentation, which will be scheduled after the month-long project is completed.