Contextualization

Numbers are an integral part of our lives and society. They are used daily for counting, measuring, and performing a variety of everyday tasks, from buying groceries to calculating distances. However, didactically, an aspect of mathematics that is often overlooked is the fact that numbers are not all "equal" - they have different properties and categories. In this project, we will explore two of these categories: prime numbers and composite numbers.

Prime numbers are those that have exactly two distinct divisors, the number one (1) and itself. Therefore, prime numbers are indivisible by any other numbers. Seems simple, right? But this definition has a profound impact on many areas of mathematics. On the other hand, we have composite numbers, which are divisible by more than two distinct numbers. The study of these two categories of numbers is fundamental in understanding the structure of numbers and, ultimately, in understanding mathematics itself.

Prime numbers are especially fascinating. Although they are infinite, they do not appear in a regular or predictable manner in the line of natural numbers, which has puzzled mathematicians for centuries. Furthermore, as simple as they are, prime numbers are at the core of very advanced and sophisticated concepts, such as cryptography. In fact, the internet as we know it would be impossible without the use of prime numbers!

Composite numbers, in turn, also play an important role in mathematics and practical applications. Many math problems can be facilitated when a composite number is broken down into its prime factors. In addition, the decomposition of a number into its prime factors is a process that is often used in areas such as signal processing and operations research.

To help you understand these concepts, we recommend accessing the online platform Khan Academy, which offers excellent free material for learning mathematics. Additionally, the website Só Matemática also has valuable resources, including a section dedicated to prime and composite numbers.

• Khan Academy - Prime and Composite Numbers
• Só Matemática - Prime Numbers

Practical Activity: "Unveiling the World of Prime and Composite Numbers"

Project Objective:

The objective of this project is to provide students with a practical experience in the discovery, understanding, and application of the concepts of prime and composite numbers, through the execution of various tasks involving the identification, factorization, and application of these numbers.

Detailed Project Description:

Students will be divided into groups of 3 to 5 people. Each group will receive a mission: to create an educational presentation on "Prime and Composite Numbers". The format of this presentation may vary (it can be a poster, a PowerPoint presentation, a video, a game, etc.), but it must include:

1. An introduction to the concept of prime and composite numbers and their importance in mathematics.
2. A step-by-step tutorial explaining how to identify whether a number is prime or composite, and how to factor composite numbers into prime factors.
3. A section dedicated to practical applications of prime and composite numbers, where students will explain how these concepts are used in the real world.
4. A game or interactive activity that helps consolidate the understanding of these concepts. This can be a quiz, a board game, a crossword puzzle, a math challenge, etc.

Required Materials:

1. Computers with internet access for research.
2. Drawing materials to create posters or games, or video/presentation editing software if they opt for that format.

Detailed Step-by-Step:

1. The group should start by researching the concepts and applications of prime and composite numbers.
2. Next, they should create a script or plan for their presentation, including all required elements.
3. Once the plan is complete, they can work together to create the final presentation.
4. The group should practice the presentation several times to ensure that all members understand and can explain the concepts involved.
5. Finally, each group will present their project to the class.

Project Deliverables:

At the end of the project, each group must present the practical activity carried out and submit a detailed report, which should include:

1. Introduction: The student must contextualize the theme, its relevance and application in the real world, as well as the objective of this project.
2. Development: The student must explain the theory behind prime and composite numbers, explain the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.
3. Conclusion: The student must conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.
4. Bibliography: The student must indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

This final deliverable will allow students to demonstrate what they have learned about prime and composite numbers and how they relate to the reality around us.