Contextualization

The resolution of systems of linear equations is one of the most important foundations in mathematics, being an essential tool in various fields of knowledge. Among the existing methods for solving these systems, we highlight the 'scheduling method', which will be the focus of our project.

In mathematics, scheduling is a procedure that consists of performing basic operations on rows of a matrix, with the aim of simplifying it and transforming it into a scheduled matrix. This matrix facilitates the resolution of systems of linear equations, allowing the values of the variables to be obtained more directly and quickly.

Understanding how this method works and knowing how to apply it correctly is essential for us to advance in more complex studies of mathematics, as well as to understand how mathematics is applied in solving practical problems in areas such as engineering, economics, physics, among others.

But why are systems of linear equations so important? In various fields of science and technology, there is a common need to find solutions to problems involving several interdependent variables. In many situations, these relationships between variables can be expressed through linear equations, thus forming a system of equations.

Therefore, knowing how to solve these types of systems is a very valuable skill. In engineering, for example, systems of linear equations are used to calculate stresses in structures, optimize production processes, among others. In economics, they are used to model markets, calculate equilibriums, among others. In physics, they are used to solve kinematics, dynamics, electromagnetism problems, among others.

Practical Activity

Activity Title: Scheduling Game - Solving Systems in Team

Project Objective

The project's objective is to provide a meaningful and playful learning of the scheduling method for solving systems of equations. Students will apply theoretical knowledge in a practical activity by playing in teams, exploring technical and socio-emotional skills.

Detailed Project Description

The activity consists of creating a 'Scheduling Game'. Each group will be responsible for creating a game that involves the scheduling method of systems of equations, where each station of the game corresponds to a step of the scheduling. Players must follow the instructions to solve each step, progressively advancing to the final solution. The game should be designed in a way that understanding the scheduling method is necessary to progress.

Required Materials

• Graph paper;
• Colored cardboards;
• Colored pens;
• Scissors;
• Ruler;
• Notebook and internet access for research.

Detailed Step-by-Step for Activity Execution

1. Form groups of 3 to 5 students. Each group will be responsible for developing a 'Scheduling Game'.

2. Research about the scheduling method. Use the materials indicated in the contextualization and look for other sources such as books, websites, and videos. Preserve the bibliography to cite in the final report.

3. As you research, start drawing a sketch of the game. Look for ways to make it interesting and educational at the same time. The game should be complex enough to involve solving a system of equations by the scheduling method.

4. After deciding on the game structure, start producing the board with the available materials. Make each station of the game represent a step of the scheduling method.

5. Develop the game rules, making sure they are clear and coherent. The game should be designed in a way that only those who understand and apply the scheduling method correctly can win.

6. Test the game several times within the group to ensure that everything is working as expected.

7. Prepare a presentation for the class explaining the game, the rules, and how it relates to the scheduling method.

8. Write a report detailing the game development process, the application of scheduling, and the game rules (see project submission below).

Project Submission

At the end of this process, each group will make an oral presentation to the class, demonstrating their game, explaining the rules, and showing how solving the system of equations by the scheduling method is necessary to win the game. In addition, each group must submit a written report with the following topics:

1. Introduction: Provide context to the problem, its relevance and real-world application, as well as the objective of this project.

2. Development: Explain the theory involved in the game creation, detail the activity, the methodology used, present and discuss the results obtained.

3. Conclusion: Summarize your main points, explain the learnings obtained, and draw conclusions about the project.

4. Bibliography: Indicate the sources you relied on to work on the project such as books, web pages, videos, etc.

The report should be between 3 to 5 pages. Teachers will evaluate the report based on the clarity of the presentation, the correct application of the scheduling method, the creativity in creating the game, and teamwork.