Context

Introduction

The first-degree function is one of the most fundamental concepts in Mathematics, as it is a simple and extremely useful concept that transcends the boundaries of basic education and is present in various areas of knowledge such as Economics, Physics, and Engineering. From a mathematical point of view, the first-degree function corresponds to a dependency relationship between two variables in which the value of one is determined by multiplying the other by a constant and adding or subtracting a fixed value.

This can be expressed in the form of an equation y = ax + b, where y is the dependent variable, x is the independent variable, a is the coefficient that determines the slope of the function, and b is the independent term that defines the point at which the function intercepts the y-axis. The graph of the function is a line that can have a positive slope (when a > 0), negative slope (when a < 0), or zero slope (when a = 0).

The first-degree function is presented early in high school precisely because it is a concept that opens doors to the understanding of other more complex functions that are studied later on. Therefore, it is essential for students to have a good understanding of this subject.

Context

In everyday life, the first-degree function can be found in many contexts. For example, if we consider the price of a product as a function of the quantity sold, we may have a situation where the price decreases as the quantity increases, which can be represented by a first-degree function with a negative slope.

Similarly, if we consider the amount of gasoline consumed by a car as a function of the distance traveled, we would probably have a first-degree function with a positive slope, as the greater the distance, the higher the consumption. And even in Economics, when analyzing the relationship between production and production cost, we can use the first-degree function to represent this relationship.

Understanding the first-degree function is, therefore, understanding a bit of the world around us and being able to make predictions and decisions based on mathematical analysis.

In this project, you will explore the first-degree function in a practical and playful way, creating models and solving problems involving this function.

Practical Activity

Activity Title: "Game of First Degree Functions"

Project Objective

The project's objective is to allow students to become familiar with the first-degree function, applying the concepts learned to solve a set of challenges in a game. Students will have to apply their knowledge in order to progress in the game, which will encourage active learning and promote teamwork.

Detailed Project Description

The "Game of First Degree Functions" is a board game where students must solve problems related to first-degree functions to advance. The game will be played in groups of 3 to 5 students, and each match should last approximately one class.

Required Materials

To carry out this activity, the following materials will be necessary:

• Game board (which can be downloaded and printed or hand-drawn);
• Challenge cards with first-degree function problems;
• Pieces to represent each team on the board.

Project Step by Step

1. Form groups with 3 to 5 students.

2. Present the board and game rules to the students.

3. Distribute a booklet with the challenges to be solved during the game. Each problem will be related to the first-degree function and will require students to apply their knowledge to solve it.

4. Students take turns playing, with each team solving one problem at a time. If the team answers correctly, they advance on the board. If they answer incorrectly, they stay in the same place or move back, depending on the established rules.

5. The game continues until a team reaches the end of the board.

6. Once the game is completed, students must prepare a report detailing the experiences and learnings acquired during the activity.

Project Deliverables and Connection to the Activity

Project Report

After completing the practical activity, each team must prepare a detailed report covering the following topics:

Introduction

• Brief description of the project and its objective.
• Importance of the topic "First Degree Function" and its real-world application.

Development

• Detailing the problems faced during the game, the proposed solutions, and the mathematical reasoning used to reach each solution.
• Discussion on the effectiveness of the chosen strategy and the challenges encountered.
• The methodology used in the project and the results obtained.

Conclusions

• Lessons learned about the first-degree function during the game.
• Comments on the experience of working in a team and the socio-emotional skills developed.
• Reflection and final comments on the project.

Bibliography

• Indication of the sources used for theoretical foundation and problem-solving.

The report must be submitted within one week after the game is completed, allowing students adequate time for preparation. Remember, the report is a key piece of this project and should reflect teamwork, learning, and understanding of the topic involved.