Practical Activity: 'Cramer in Everyday Life'

Project Objective

The objective of this project is to use Cramer's Rule to solve real-life issues from everyday life, integrating mathematics with other areas of study such as Economics and Biology.

Detailed Project Description

Divided into groups of 3 to 5 students, you will identify everyday situations in the community or school environment that can be modeled by a system of linear equations and, from there, seek solutions by applying Cramer's Rule.

Required Materials

• Notebook to record ideas and findings;
• Internet access for research and to use digital calculation tools, such as spreadsheets or math software;
• Office supplies for preparing the poster and final report.

Step-by-Step Guide for the Activity

1. Brainstorming: With the group gathered, brainstorm situations that can be modeled by a system of linear equations. It can be something from everyday life, the community, or even the school environment.

2. Research: After choosing the scenario, delve deeper into the situation. What are the variables involved? How do they relate? What kind of data would you need to set up a system of equations?

3. System Construction: With the data in hand, build the system of linear equations that models the chosen situation.

4. Resolution: Solve the system using Cramer's Rule. For this, you can use digital calculation tools, such as spreadsheets or math software.

5. Solution Analysis: What does the solution of the system of equations say about the real situation you modeled? Was there any surprise?

6. Results Communication: Prepare a poster and a presentation to show your work to the rest of the class. Explain the situation you chose, show the system of equations, the solution, and discuss the interpretation of the results.

Deliverables

As part of the evaluation of this project, each group must deliver:

1. A written report including:

• Introduction: Description of the chosen situation, reason for the choice, and explanation of the relevance and application of modeling by systems of linear equations.
• Development: Description of the constructed system of linear equations, the calculation methods used, and a detailed discussion of the results.
• Conclusion: Summarizing your main points, explaining the learnings obtained, and the conclusions drawn about the project.
• Bibliography: Citation of all information sources used during the project.

2. An illustrative poster illustrating the chosen situation, the construction of the system of equations, the resolution by Cramer's Rule, and the interpretation of the results.

3. Presentation to the class about the project, explaining the chosen situation, the construction and resolution of the system of equations, and the conclusions drawn.

When writing the document, students should elaborate on the key topics of the report, always seeking to make connections with the practical activity carried out and their experiences in the project development.