Context

Simple permutation is one of the basic operations in the discipline of Discrete Mathematics and is defined as the number of different ways a set of elements can be arranged. Calculating permutations is essential for the development of combinations, which are responsible for solving various mathematical problems in a wide range of areas.

The initial step in learning about permutations is understanding the concepts of factorial and the possibilities of arranging a set of distinct objects. From there, it is possible to expand understanding to more complex situations, such as circular permutations and permutations with repetition. Therefore, investing in the study of permutations strengthens both students' mathematical foundation and opens doors to more advanced applications in the future.

Relevance

The application of permutations extends across various areas, increasing its relevance in the real world. In the field of computer science, for example, it is used for creating passwords and security codes, where the number of possible options makes a difference. Probability, a fundamental area of mathematics, uses permutations for calculating probabilities in different sets. In planning activities and tasks, permutations help optimize the use of resources, from organizing a personal schedule to programming machines in an industry.

Therefore, understanding the concept of permutation is not only an essential mathematical skill but also a highly useful tool for solving everyday problems and in various professions.

Practical Activity: 'Permutating the World'

Objective

The purpose of this project is to promote understanding of permutation through the development of practical activities involving the direct application of the concept.

Project Description

Students will be divided into groups of 3 to 5 and will be challenged to create a real-life situation involving permutation. This situation can be a hypothetical scenario, a game, or even a real problem that can be solved using permutation.

Required Materials

• Pencils and paper for notes and calculations
• Computer with internet access for research
• Mathematics books for reference
• Presentation software (PowerPoint, Google Slides)

Step by Step

1. Formation of groups according to the teacher's instructions.
2. Group discussion to define the situation they will address where permutation will be necessary.
3. Research and theoretical deepening on the topic of permutation.
4. Development of the scenario, problematization, and resolution of the proposed challenge using permutation.
5. Creation of a presentation explaining the created scenario, permutation as a solution, and how they carried out the resolution.
6. Writing the report containing the four main topics: Introduction, Development, Conclusions, and Bibliography used.

Project Deliverables

• Presentation: The group must create a slide presentation explaining the created situation, how permutation is used for its resolution, and the results obtained. The presentation should be clear and engaging, showing how permutation can be applied in the real world.

• Final Report: The written document should be organized into four main topics:

  • Introduction: Students must contextualize the created situation, explain how permutation applies to it, and why they chose this scenario.

  • Development: Students must explain the theory of permutation, how they applied it to solve the situation, and discuss the results obtained. In this part, students must demonstrate the calculations performed and the analysis of the results.

  • Conclusion: Students must revisit their project, highlighting the main points, what they learned about permutation, and its applicability.

  • Bibliography: Students must list all sources consulted during the research, such as books, websites, videos, etc.