Contextualization

Algorithms are a sequence of well-defined and organized instructions to solve a problem or perform a task. They are the basis of everything involving computation, but they are also present in our daily lives, even when we don't realize it. For example, a cake recipe can be considered an algorithm: it gives us a step-by-step guide on how to make a cake, and if we follow all the steps correctly, we will have a ready cake in the end.

In the field of mathematics, algorithms are used to solve complex problems and calculations. In fact, mathematics is the basic language of algorithms. For these reasons, understanding algorithms and knowing how to apply them is an essential skill in our digital and technological world.

Understanding that there are several ways to solve the same problem is an extremely valuable skill. And that's exactly what we will learn from our study on 'Algorithms and Problems 2'. We are about to embark on an adventure that will teach us not only technical skills but also socio-emotional skills such as time management, communication, problem-solving, and creative thinking.

Introduction

In this unit, we will explore different ways to solve the same problem. How so? Imagine you need to go from your home to school. There are several routes you can take! Some are faster, others more beautiful, others safer... so, what is the best route? This is a complicated question, and the answer depends on several things. Similarly, there are many ways to solve a mathematical problem. And each way has its pros and cons.

We will learn to recognize that the solutions to a group of problems that have the same structure can be obtained using the same procedures, learning to represent through a flowchart the steps used to solve a problem.

Finally, we will write a document reporting in the format of a report containing four main topics: Introduction, Development, Conclusions, and Bibliography used. This document will allow us to remember what we have learned and share our knowledge with others.

Practical Activity

Activity Title:

Unveiling Paths: Exploring Algorithms through Mazes

Project Objective:

The objective of this activity is to use the concept of algorithms to solve the same problem in different ways: finding the exit of a maze. In groups of 3 to 5 students, you will develop two different algorithms to solve the same maze and will present the step-by-step of each algorithm through a flowchart. The project also aims to improve skills such as time management, communication, and teamwork.

Detailed Project Description:

1. Each group will receive a maze that must be solved. The maze can be virtual or physical, depending on the available resources.

2. The groups must develop two different algorithms to find the exit of the maze. The algorithms must be clear and well-defined so that anyone who follows the instructions can solve the maze.

3. The algorithms will be represented through flowcharts. Each flowchart must detail each step of the respective maze-solving algorithm.

4. Students will have one week to complete the project. Each group must divide responsibilities among the members to meet the deadline.

Necessary Materials:

1. Mazes (physical or virtual).
2. Paper and pen to draft the algorithms.
3. Access to digital tools to create the flowchart (can be PowerPoint, Google Slides, among others).

Detailed Step-by-Step for Activity Execution:

1. The teacher will distribute the mazes.

2. The groups will analyze the maze and develop the first algorithm for the solution. They can decide on trial and error, or use any strategy they deem appropriate.

3. The same step will be repeated for the creation of the second algorithm.

4. After creating the algorithms, the groups must represent each of them through a flowchart.

5. With the flowcharts ready, the groups must test if the algorithms really work, trying to solve the maze using the created instructions.

6. After verifying that the flowcharts are correct, it is time to start preparing the final report. The report must have the following elements: Introduction, Development, Conclusions, and Bibliography used.

In the Introduction, the group must explain the importance of algorithms in mathematics and daily life, and what the project objectives were. In the Development, the group must detail the created algorithms, present the flowcharts, and discuss the results obtained. In the Conclusions, the group must talk about the skills that were developed in the project and the main learnings. In the Bibliography, the group must list the sources consulted during the work.

The team must work so that each student contributes significantly to all parts of the project: from solving the mazes, to creating the algorithms, elaborating the flowcharts, and writing the report. This way, learning will be broad and well distributed.