Contextualization
Introduction
Mathematics is a vast and fascinating field of study that goes beyond what we normally learn in school. One of its most intriguing elements is the algorithm, a series of steps we follow to solve a problem. In the world of mathematics, an algorithm can be as simple as the operations we perform to solve an equation or the steps we follow to find the LCM of two numbers.
However, the real beauty of algorithms comes to light when they are used to solve more complex problems. Algorithms are behind the computer codes that power the digital world, enabling everything from internet searches to space flights. Understanding the logic of algorithms and their relationship to problem-solving is a fundamental step in understanding the modern world.
In this project, we will address the topic of algorithms broadly. We will learn how they work, how they are built, and how they can be applied in practice to solve real-world problems.
Contextualization
Algorithms are present in our daily lives, often without us realizing it. When you follow a recipe to prepare a dish, you are using an algorithm. When you set your alarm clock to wake up at the right time, you are also using an algorithm. In a broader sense, algorithms are used in all areas of life, from agriculture and medicine to engineering and computer science.
In the information age, mastering algorithms is particularly important. As more and more professions require digital skills, understanding how algorithms work can open up a universe of opportunities. Furthermore, algorithms are the foundation of computer programming, a skill that is increasingly valuable in our society.
Practical Activity - Building Algorithms to Solve Real-World Problems
Title: "Unraveling Algorithms: From Theory to Practice"
Project Objective
In this project, students will learn to apply mathematical concepts in problem-solving through the construction of algorithms. The goal is not only to enhance theoretical knowledge but also to develop practical skills, such as logical thinking, teamwork, and the ability to communicate ideas clearly and effectively.
Project Description
Students will work in groups of 3 to 5 people. The project consists of identifying a real-world problem (such as organizing a study routine, planning a trip, etc.) and developing an algorithm to solve this problem, going through the processes of defining the problem, formulating hypotheses, developing a flowchart, and finally, executing the algorithm through a simple prototype.
The project is estimated to take more than 12 hours per participating student.
Required Materials
- Notebook or sheets of paper for notes and drawings
- Pencils and erasers
- Colored markers
- Ruler or square
- Internet access for research
Detailed Step-by-Step
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Problem Definition: Each group must choose a specific real-world problem they want to solve. They should describe the problem in detail, discussing its implications and why it is worth solving.
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Formulation of Hypotheses: Students should then develop a series of hypotheses about possible solutions to the chosen problem. They should research, discuss, and write down all ideas, even if they seem absurd at first.
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Solution Development: Once the hypotheses have been established, students should choose the most promising one to further develop. They should build an algorithm that solves the problem, in natural language, step by step.
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Flowchart Elaboration: With the solution in hand, students should represent their algorithm in the form of a flowchart. The flowchart should be clear, concise, and easy to follow, indicating all the steps for problem resolution.
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Prototype Construction: Finally, students should create a simple prototype that executes their algorithm. The prototype can be a paper simulation, a miniature model, or even a real-time demonstration.
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Presentation and Evaluation: Each group must present their work to the class, explaining the problem they chose, the algorithm they developed, and the prototype they built. They should be prepared to answer questions and receive feedback from their peers and teacher.
Project Deliverables
At the end of the project, each group must deliver:
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Final Report: The report should include a detailed description of the chosen problem, a summary of the research conducted, the description of the algorithm developed (in natural language and in the form of a flowchart), and a discussion of the results obtained with the prototype. The report should have a clear structure, with introduction, development, conclusions, and bibliography.
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Prototype: The prototype created to execute the algorithm will also be evaluated. Even if it is a simple model, it must clearly demonstrate how the algorithm works in practice.
The report writing should be done collaboratively, with each group member contributing to different parts of the document. The report should be a reflection of the teamwork, highlighting not only the theoretical knowledge acquired but also the socio-emotional skills developed during the project.
