Context

Mathematics is the language of the universe, being essential for the understanding of natural phenomena and, of course, for our daily activities. In this project, we will focus on the First Degree Equation, a simple but extremely powerful and versatile mathematical tool.

The first degree equation is a fundamental concept in Algebra, a branch of mathematics that uses letters to represent numbers in mathematical equations. In its simplest form, the first degree equation has this format: ax + b = 0, where a and b are real numbers and a ≠ 0.

In our daily lives, we can find examples of situations that can be solved through first degree equations. For example, if you want to divide a number of cookies equally among a number of friends, or if you want to calculate how many hours you need to work to reach a certain amount of money, or even if you want to find out at what speed a car was moving in a given interval of time. All these situations can be expressed and solved from a first degree equation.

The First Degree Equation is also a prerequisite for understanding more advanced topics in mathematics. It is a starting point for studying functions, graphs, geometry, and even calculus. Therefore, a solid understanding of this topic is crucial for any subsequent study in mathematics.

To delve deeper into the subject, we recommend using the following resources: The book "Fundamentos de Matemática Elementar: Volume 3 - Álgebra" by Gelson Iezzi and Carlos Murakami, the video lessons from the YouTube channel "Matemática Rio with Prof. Rafael Procopio" that detail the theory and solve exercises step by step, and the Khan Academy platform that presents a learning path in algebra with interactive exercises.

Practical Activity: "The First Degree Equation Solver"

Project Objective

This project aims to understand and apply the first degree equation in solving everyday problems through a board game created by the group.

Detailed Project Description

Groups will create a board game whose objective is to solve everyday problems involving first degree equations. Each space on the board will correspond to a problem situation that players will need to solve to progress in the game. Creativity is essential for the execution of this project, both in the elaboration of the problems and in the design of the board and its rules.

Required Materials

• Cardboard or card for the board
• Paper and pencil for the elaboration of the questions
• Dice (to determine the progression of the players)
• Pieces (which can be made of cardboard, clay, or any other available material)

Detailed Step-by-Step for Carrying Out the Activity

1. Form groups of 3 to 5 students.
2. Research and discuss various everyday contexts where the first degree equation can be applied.
3. Together, develop a minimum of 20 problems involving first degree equations. Remember to vary the level of complexity of the problems.
4. Draw and build the game board on cardboard or card. The board can contain alternative paths, advance or retreat spaces, pause spaces, among others.
5. Create the game rules. For example: each player rolls the dice and advances the number of spaces indicated, then must solve the first degree equation in the problem of the space they landed on. If they get it right, they continue to the next round; if they get it wrong, they must go back to the beginning.
6. Test the game, adjusting the rules if necessary.
7. After finishing the game, each group must produce a report detailing the entire creation process and the learnings.

Project Deliverables

In addition to the board game, groups must deliver a written report that should include:

1. Introduction: Provide context for the project, explaining why first degree equations are important and how they appear in our daily lives. Describe the project's objective and what was expected to be learned from it.
2. Development: Describe in detail the process of creating the game. Include how the problems were elaborated, how the board was built, and the rules were defined. Discuss the theory of first degree equations behind the game activities and explain the methodology used to create and test the game. Show some examples of problems used in the game and how they were solved.
3. Conclusion: Revisit the project's objectives and discuss if they were achieved. Comment on the main challenges and how they were overcome. Share the insights and knowledge gained throughout the project development, and how it deepened your understanding of first degree equations.
4. Bibliography: List all sources of information used to create the game and prepare the report. This includes books, websites, videos, etc.