Context

Mathematics is a discipline of great importance in an individual's education, as it is present in everyday life and has a universal language. Therefore, understanding some mathematical concepts is essential for a complete education. One of these concepts is algorithms. An algorithm is a finite sequence of well-defined and unambiguous instructions, each of which must be executed mechanically in a finite period of time and with a finite amount of effort. In other words, an algorithm is a logical and step-by-step procedure that solves a specific problem.

Algorithms are widely used in solving mathematical problems. They define the steps we must follow to perform mathematical calculations, whether they are simple like adding two numbers, or more complex like solving equations. Therefore, learning about algorithms is a significant step in understanding mathematics and its practical application.

The role of algorithms goes beyond mathematics. They are fundamental in various areas, especially in computer science, where they are used to program computers and give instructions for them to perform a specific task as efficiently as possible. So, besides being an important tool for the study of mathematics, learning about algorithms can also open doors to the study of other areas, such as computer science.

Now, the relevance of algorithms stands out in the real world. Just think about how many times a day you use an application on your smartphone. Each of these applications is run by a set of algorithms that have been programmed to perform specific tasks. Furthermore, algorithms are essential in solving everyday problems, from determining the fastest route to a location, to choosing a movie on a streaming application.

The study of algorithms, therefore, is not only theoretical but also practical, and essential for understanding the technological world we live in. Understanding algorithms allows us to better understand how things around us work and gives us the tools to solve problems effectively.

To delve deeper into the topic of algorithms, we recommend the following resources:

• Book: "Algorithms: logic for computer programming development", by José Augusto Manzano.
• Khan Academy website, with free and interactive lessons on the subject: Khan Academy Link
• YouTube videos like "What is an algorithm?" from Peixe Babel Channel. Video Link

Practical Activity

Activity Title: Solving Everyday Problems with Algorithms

Project Objectives:

1. Understand the concept of algorithms and how they are used in problem-solving.
2. Develop problem-solving, communication, and collaboration skills while working in a team.
3. Practice technical and scientific writing, describing in a clear and objective manner the steps to solve a problem.

Project Description:

In this practical activity, students will work in groups of 3 to 5 people. Each group should select a simple everyday problem, such as organizing a birthday party, preparing a recipe, deciding the best route to go to school, etc. The goal will be to create an algorithm that solves this problem.

Students will describe the chosen problem, identify the necessary actions to solve it, and then organize these actions into a logical and clear sequence – their algorithm. The final representation of the algorithm can be done in both natural language and through a flowchart.

Next, each group should test their algorithm by performing the described actions and verifying if the problem was solved. Otherwise, they should review and correct their algorithm.

Required Materials:

• Paper and pen to draw the flowchart and write the algorithm instructions.
• Internet access for research and study on algorithms.
• Reproduction of the video "What is an algorithm?" from Peixe Babel Channel for a better understanding of algorithms.
• Specific materials for executing the algorithm (depending on the problem chosen by the group).

Step by Step:

1. Formation of groups of 3 to 5 students.
2. Selection of an everyday problem to be solved.
3. Study on the concept and application of algorithms for problem-solving.
4. Development of the algorithm to solve the chosen problem.
5. Representation of the algorithm in natural language and/or flowchart.
6. Testing the algorithm – execution of the described actions.
7. Review and correction of the algorithm, if necessary.
8. Writing the final report, describing the problem, the created algorithm, and the results obtained.

Deliverables:

At the end of the project, in addition to the practical experience with algorithms, each group must submit a written report describing the project. The report should contain the following sections:

1. Introduction: Description of the chosen problem and its relevance. It should also indicate the objective of creating an algorithm to solve it.
2. Development: Detailed description of the developed algorithm, including the explanation in natural language and/or flowchart. It should also describe the methodology used to test the algorithm and the results obtained.
3. Conclusions: Reflection on the results, mentioning what worked, what did not work, and what could be improved. It should also highlight what was learned throughout the project.
4. Bibliography: References to all materials consulted during the project development, including books, websites, videos, etc.

The report should follow a scientific format, with clear and objective language. The report submission will take place one week after the start of the project, allowing enough time to research, execute, test the algorithm, and write the report.