Context

Introduction

The world we live in today is largely governed by computer science. From our cell phones to the most sophisticated supercomputers, everything operates based on programming languages, and the foundation of these languages are algorithms, which are nothing more than a logical and finite sequence of actions to be executed.

Algorithms are like recipes that the computer uses to perform operations and solve problems. They are not only used in technology, but are also an important part of mathematics, and studying them can help develop essential problem-solving skills.

The notion of an algorithm is extremely ancient, predating even the invention of computers, and frequently arises in everyday life when we learn or teach how to perform a task step by step. In mathematics, they are used, for example, to perform addition, subtraction, multiplication, and division operations.

Context

Every time you follow a recipe, drive home, or put together a puzzle, you are using algorithms. Understanding them and knowing how to build them is an essential skill not only for programmers, but also for anyone who wants to work in the modern world.

Understanding algorithms can help you make better-informed decisions and develop more efficient strategies to solve problems in your personal and professional life. Moreover, many of the greatest problems we face as a society, such as climate change or the management of limited resources, also require algorithms to be solved.

Practical Activity

Activity Title: "Creating and Solving Mazes with Algorithms"

Project Objective:

This project aims to apply algorithm concepts to solve practical problems. In this case, students will have the mission of creating and solving a maze.

Detailed Project Description:

Students, divided into groups of 3 to 5 members, must draw their own maze on a grid paper. The maze should be constructed considering that each square on the paper represents a "cell" of the maze. The idea is to use search algorithms to find the path from the start to the end of the maze.

The search algorithms used can be "Breadth First Search" (BFS) and "Depth-First Search" (DFS). Studying these two algorithms is a crucial part of the project, and students must understand how these work to apply them to the maze.

This document must be delivered within one month after the project start date. Each student should invest five to ten hours in project execution.

Required Materials:

• Grid paper for drawing the maze.
• Colored pens or pencils.
• Educational resources for study, such as books, websites, and videos.

Detailed Step-by-Step:

1. Division of students into groups of 3 to 5 students.
2. Study of algorithm concepts and search algorithms (BFS and DFS), using the suggested educational resources.
3. Drawing the maze on grid paper according to the established rules.
4. Applying the search algorithms to find the path from the start to the end of the maze.
5. Recording the sequence of steps for solving the maze using a flowchart.
6. Each group must produce a report containing Introduction, Development (studied theory, activity details, methodology, and results), Conclusions, and Bibliography.
7. Final Report Submission.

Project Deliverables:

At the end of the project, students must deliver:

1. The original maze drawn.
2. The flowchart representing the sequence of steps of the search algorithms.
3. The final report.

In the final report, they must explain the entire project process, including understanding of the algorithms, maze construction, and application of algorithms to solve the maze. Students should highlight the challenges encountered and the solutions used to overcome them. The document should clearly demonstrate the time management, communication, and problem-solving skills acquired during project execution.