Contextualization

Mathematics is a fascinating science that aims to study patterns, structures, numbers, and figures. And within this science, there are themes that are fundamental to our understanding of the world around us, and one of the most interesting is Algorithms and Problems.

An algorithm is a set of instructions that describes a procedure to be followed, to solve a problem or perform a task. They are present in our daily lives, even without us realizing it. For example, a cake recipe is a type of algorithm: it provides us with clear steps to follow to achieve the desired result.

But algorithms are not only used in the kitchen. They are also fundamental in various areas of science, such as computing, physics, biology, and of course, mathematics. In mathematics, algorithms are used to solve everything from the simplest to the most complex problems.

The Importance of Algorithms

Algorithms are crucially important because they provide a clear and defined method for solving a problem. Without algorithms, we would have to solve each problem from scratch, without any guidance. They allow us to solve complex problems efficiently and quickly.

Algorithms are also fundamental to computing. In fact, every action a computer performs is the result of an algorithm. From sending an email to running a video game, all are executed through algorithms. Therefore, understanding algorithms and how they work is crucial for anyone who wants to work in the field of technology or SCIENCES.

Algorithms have a wide range of practical applications. They are used in industries such as engineering, medicine, finance, sports, and much more. Thus, learning about algorithms will not only increase your understanding of mathematics but also open many doors for future careers.

Practical Activity: Algorithms Challenge

Project Objective

The objective of this project is for groups to develop a serious problem-solving skill through the use of algorithms. During the activity, they will also exercise teamwork, communication, critical thinking, and time management skills.

Project Description

For this challenging project, each group of 3 to 5 students must solve four different problems that will be presented by the teacher. Each of these problems must be solved through a different algorithm, which will be developed and executed by the group.

As part of the project, students must also prepare a presentation of the algorithm developed to solve each problem. The presentation should explain how the algorithm works and present the results obtained in the execution.

The resolutions of these problems will involve mathematical concepts, but will also require research and the use of skills from the Portuguese discipline, as students will be effectively communicating and writing a report.

Necessary Materials

1. Computer or Notebook with Internet access
2. Software for creating flowcharts (e.g., Microsoft PowerPoint, Draw.io, LucidChart)
3. Paper and pencil for drafts

Step by Step

1. Organize into groups of 3 to 5 students.
2. The teacher will present the four problems to be solved.
3. For each problem, the group must discuss and decide on the best approach to solve it. The group must consider which mathematical concepts apply to the problem.
4. After deciding on the best approach, students must write an algorithm to solve the problem. They should note down all the steps that will be necessary.
5. Once the algorithm is complete, the group must test it to ensure that it actually solves the problem.
6. After testing, students must create a flowchart representing the algorithm. The flowchart should be clear and easy to understand.
7. Repeat steps 3 to 6 for each of the four problems.
8. Prepare a presentation detailing the algorithms and how they were used to solve each problem.
9. Finally, the group must prepare a final report presenting the solutions obtained, the algorithms used, the corresponding flowcharts, the methodology used, and the discussion of the results.

Project Deliverables

1. Algorithms: Each group must deliver the four written algorithms and their respective corresponding flowcharts.
2. Presentation: Each group must prepare a detailed presentation explaining each of the algorithms and the results obtained.
3. Report: Each group must prepare a final report. This report should follow the report format indicated at the beginning, including the Introduction, Development, Conclusions, and Bibliography topics. In the Introduction, it is important to contextualize the theme, its relevance, and the objective of this project. In the Development, students must explain the theory behind the theme, explain the activity in detail, indicate the methodology used, and present and discuss the results. In the Conclusion, they must explain the learnings, the conclusions drawn about the project, and recap their main points. Finally, in the Bibliography, students must indicate the sources used to carry out the project.