Contextualization

Mathematics is an essential discipline that permeates many areas of our daily lives and knowledge. In the universe of this science, a prominent topic is the study of matrices and, especially, the notion of determinants. It may seem like an abstract and complex concept at first glance, but I assure you that understanding determinants is fundamental for the development of many processes in exact sciences and engineering.

The determinant of a 1x1 matrix, which is the theme of this project, is one of the first steps to understand the concept of matrix determinants. The 1x1 matrix consists of a single row and a single column, in other words, a single element. And the determinant of a 1x1 matrix is precisely this single element.

Introduction

Before we dive into the practical activity of this project, it is necessary to understand some theories involving matrices and determinants. Matrices are arrangements of numbers arranged in rows and columns. They are widely used in various branches of mathematics, physics, and engineering.

Determinants, on the other hand, are numerical values calculated from a matrix. They are extremely useful in various areas, such as solving systems of linear equations, calculating areas and volumes, and even in quantum physics.

For 1x1 matrices, the determinant calculation is simple because it corresponds to the element of the matrix itself. For example, if we have the matrix [2], its determinant will be 2.

Check out the following resources to delve deeper into the subject:

• Book "Linear Algebra with Applications", by Anton Howard. This book is a reference in the study of Linear Algebra, containing various topics on matrices and determinants. Available in some libraries and specialized stores.
• OBMEP Mathematics Portal, Matrices and Determinants section. This portal has several lessons and exercises for you to practice. Link to access.
• Video "Determinants - What are they and what are they for", from the channel "Matemática Rio with Prof. Rafael Procopio", available on YouTube. This video teaches in a fun and relaxed way what determinants are and how to calculate them. Link to access.

Practical Activity

Activity Title: "The World of 1x1 Determinants"

Project Objective

This project aims to address the concept of the determinant of a 1x1 matrix in a playful, interactive, and collaborative way. Students will practice calculating determinants and, in addition, develop skills in teamwork, communication, time management, content creation, and technical reports.

Detailed Project Description

Each group of 3 to 5 students will be responsible for creating a "Board Game" where players will have to calculate 1x1 determinants as part of the game actions. From this, they should elaborate a game instruction manual and a report presenting the entire project development.

Required Materials

• Cardboard or card paper for the base of the board.
• Colored paper for board decoration.
• Colored pens, colored pencils, or paints for decoration.
• Dice or numbered cards (can be made by the students themselves).
• Computer with Text Editor for the final report.

Detailed Step-by-Step for Activity Execution

1. The groups should initially research 1x1 matrix determinants, reviewing the theoretical concept and studying practical examples.

2. The students should then create a board game, whose theme can be freely chosen by them, but must somehow integrate the calculation of 1x1 determinants into the gameplay.

3. The students must develop and define the game rules, ensuring that the calculation of determinants is one of the main actions of the game.

4. After developing the game, the students should test it and, if necessary, make adjustments to the rules to make it fair and fun to play.

5. In parallel with the game creation, the students should work on the elaboration of an instruction manual that presents the game, the rules, and how the calculation of 1x1 determinants was integrated into the gameplay of the game.

6. Finally, the students should prepare a final report on the project, presenting an introduction to the topic, the development (including difficulties, solutions found, actions taken), conclusions and learnings, and the bibliographic references used during the project.

Project Deliverables

1. Physical Board Game: Must be delivered to the teacher.

2. Instruction Manual: Must be delivered digitally (in a .pdf file), where students must explain the game, the rules, and how the calculation of 1x1 determinants was integrated into the game.

3. Final Report: Should follow the following structure -

   • Introduction: Describing what a 1x1 matrix and determinant are, their importance, the game proposal, and how it relates to the theme.
   • Development: Describing the game creation, the rules, the gameplay, the teamwork process, the difficulties encountered, and how they were solved. It should also explain the work methodology, how tasks were divided, how time was managed, among others.
   • Conclusions: Descriptive of the group's learnings, the project highlights, the skills developed, and how the objective of studying 1x1 matrix determinants was achieved.
   • Bibliography: References used for the work, covering books, websites, videos, among others.

Remember that this work must be done by groups of 3 to 5 students, and each student must spend 5 to 10 hours on the work as a whole.