Context

Theoretical Introduction

Linear equations, also known as first-degree equations, are part of one of the fundamental contents of mathematics. They are present in almost all areas of study, from physics to economics, and are an essential tool for solving everyday problems.

A linear equation has one or more variables that are raised to the first degree, meaning their variables are not raised to higher powers nor multiplied together. The simplest form of a linear equation is ax + b = 0, where 'a' and 'b' are known numbers and 'x' is the variable to be found.

In our project, we will focus on systems of linear equations – which are a set of two or more linear equations that contain the same set of variables. A common example is a system of two equations with two variables (x and y). Solving a system means finding the values of the variables that satisfy all equations simultaneously.

Context

In our daily lives, situations involving linear equations are more common than we realize. For example, they are useful in solving financial problems, such as calculating the price of discounted products or understanding how simple interest works. In engineering, they are fundamental in the analysis of structures and in the design of electrical circuits. In physics, linear equations are used to describe motion in a straight line.

Furthermore, learning to solve linear equations develops our logical reasoning skills and helps us understand and model situations we encounter in other disciplines and in the world around us.

Practical Activity

Activity Title: "Unraveling the Mysterious World of Linear Equations"

Project Objective:

The objective is to strengthen students' understanding of linear equations and systems of equations, develop the ability to work in teams, stimulate creative thinking, and reinforce time management skills.

Detailed Project Description:

In this project, students will be challenged to create and execute an "Escape Room" game based on linear equations.

"Escape Room" games are interactive adventure games where players are locked in an environment and must use elements of that environment to solve a series of puzzles, find clues, and escape from the environment within a set time frame.

Students will need to develop a set of mathematical problems based on linear equations and systems of linear equations that, when solved sequentially, lead to a final "key" representing the "exit" of the "Escape Room".

Each group will have to develop their own game, and at the end, the groups will exchange the games they created so that they can be played and solved by the other groups.

Required Materials:

• Paper, pencil, and eraser
• Computer with internet access for research
• Presentation software (e.g., PowerPoint, Google Slides)
• Video conferencing software (e.g., Zoom, Google Meet) for teams opting to conduct the game virtually

Detailed Step-by-Step for Activity Execution:

1. Group Formation: Students should be divided into groups of 3 to 5 members.

2. Study of Linear Equations: In the initial hours, each group should study linear equations, focusing on systems of first-degree equations with two unknowns.

3. Creation of the Escape Room Game: After studying, the groups should start planning and building the "Escape Room" game. Each game must contain at least 5 problems that require the use of linear equations or systems of linear equations to be solved. The resolution of these problems should be sequential, with the answer to one problem providing hints or directing to the next problem.

4. Execution of the Escape Room Game: After creating the game, each group will play the game created by another group. The games can be conducted in person or virtually.

5. Report Elaboration: After playing the game, each group must prepare a detailed report describing the game creation process and the experience of playing another group's game.

Project Deliverables and How They Connect to the Suggested Activities:

At the end of the project, each group must deliver a report that should include, but not be limited to, four main topics:

1. Introduction: Provide context on the theme of linear equations and their relevance, project objectives, the approach used for learning, and a description of the "Escape Room" created.
2. Development: Describe the theory behind linear equations, explain in detail the game creation, the problems used, the logic behind the construction and sequence of these problems, and the methodology used to solve the problems. It should also present and discuss the experience of playing the game created by another group and the results obtained.
3. Conclusion: Conclude the work by summarizing its main points, the learnings acquired, and the conclusions drawn about the project and the connection between the theory of linear equations and their practical applications.
4. Bibliography: Indicate the sources used to study and work on the project, such as books, web pages, videos, etc.