Contextualization

Mathematics is often seen as a complex discipline disconnected from everyday reality. However, it is closer to our daily lives than we imagine. An example of this phenomenon is Set Theory, which, despite its pompous name, addresses a relatively simple and widely used concept: the idea of grouping. This theory is, in essence, the study of groups - or sets - of objects, things, or numbers.

In Set Theory, we work with the idea of membership (an element belongs to a set), inclusion (one set is contained in another), and various operations such as union, intersection, and set difference. Additionally, in this theory, it is also possible to analyze the relationships between sets and subsets, as well as the notion of the power set.

In practice, Set Theory is present in organizing information in databases, grouping characteristics in market studies, analyzing trends on social networks, recommendation algorithms, among many other examples. Understanding this theory is essential for the comprehension and resolution of various real-world problems.

The purpose of this project is to help students understand the fundamental concepts of Set Theory through practical and playful activities, also working on socio-emotional skills such as time management, teamwork, communication, and problem-solving. You will be divided into groups of 3 to 5 students, and each group will be responsible for choosing a real-life situation where Set Theory is applied, developing a set of practical activities related to this situation, and presenting the results obtained.

As reference sources for the study of Set Theory, we recommend consulting the following reliable resources:

1. Book: "Mathematics: A New Approach" - Sets, Functions, and Real Numbers, by Elon Lages Lima.
2. Website: Just Mathematics.
3. Website: World Education.
4. Video: Mathematics Course - Set Theory - YouTube Channel Matemática Rio with Prof. Rafael Procopio.

Practical Activity

Activity Title: "Sets in the Real World - A Case Study"

Project Objectives:

1. Understand and apply the concepts of Set Theory in real-life situations.
2. Develop research, planning, and group project presentation skills.
3. Apply Set Theory to solve real-world problems and situations.

Detailed Project Description:

Each group will choose a real-life situation where Set Theory is applied. It can be in data organization, social network analysis, business strategies, among others. Based on this decision, the group will develop a series of practical activities related to this situation, applying the concepts of membership, inclusion, union, intersection, set difference, relationships between sets and subsets, and the notion of the power set.

Required Materials:

1. Books, websites, videos, and other materials for studying Set Theory.
2. Computer with internet access for research purposes.
3. Materials for presenting the results (can be a slide, a poster, a video, or any other form chosen by the group).

Detailed Activity Steps:

1. Group Formation and Choice of Real-Life Situation to be Studied: Form your group of 3 to 5 students and discuss real-life situations where Set Theory can be applied. Choose a situation to be the focus of your project.
2. Study of Set Theory Concepts: Research and study the concepts of Set Theory using the suggested resources and others you consider relevant.
3. Planning of Practical Activities: Based on the chosen situation and the studied concepts, plan a series of practical activities that help understand the application of Set Theory in the chosen situation. Remember to think about activities that involve the application of various theory concepts.
4. Execution of Practical Activities: Carry out the planned practical activities, documenting each step and the results obtained.
5. Preparation of Results Presentation: Organize a presentation to explain the application of Set Theory in the chosen situation and show the results of the practical activities. The presentation can be in slides, poster, video, etc.
6. Writing the Final Report: Each group must write a report detailing the project's implementation process and its results. The report should include an Introduction (with the contextualization of the theme, its relevance and real-world application, as well as the objective of this project), Development (explaining the theory, the activities in detail, the methodology, and the results), Conclusion (summarizing the main points, explaining the learnings obtained, and drawing conclusions about the project), and Bibliography used.

Project Deliverables:

1. Results Presentation: Each group must present the results of their project to the class, explaining the chosen real-life situation, the practical activities carried out, and the Set Theory concepts applied. The presentation can be in slide format, video, poster, or any other format chosen by the group.
2. Final Report: In addition to the presentation, each group must submit a written report, detailing the entire project implementation process, from the situation choice, planning and execution of activities, to the analysis of results. The report should follow the structure of scientific reports, including sections of Introduction, Development, Conclusion, and Bibliography. This report should demonstrate the students' understanding of the topic and the practical application of Set Theory concepts.