Contextualization

Introduction

Modular inequalities are a fundamental concept in mathematics. They are inequalities that involve the absolute value of an expression, and solving these inequalities is one of the basic skills required in solving more complex problems. The term 'module' is used to express the distance between a number and zero in the real number; therefore, the module always has a non-negative value. Understanding the concept of module helps students to deeply understand the relationships and structure of real numbers.

In mathematics, solving modular inequalities is an important topic that connects to algebra, geometry, calculus, and number theory. These inequalities may seem complex at first glance, but by unraveling the concept of module, students understand that it is a direct extension of the linear and quadratic inequalities they have already studied.

In addition to being a powerful tool for problem-solving, modular inequalities also contribute to the development of logical and abstract reasoning skills.

Contextualization

Modular inequalities have numerous applications in the real world. They are used in economics to model costs and profits, in physics to describe phenomena, and in engineering to design and optimize systems.

For example, they can be used to calculate the shortest distance between points on a map, or to determine the range of acceptable values in industry quality control. They are also behind the functioning of GPS and location systems.

Understanding this topic is therefore fundamental not only for mathematics but for many other disciplines and professional areas. Through it, students realize how mathematical theory can be applied to solve real-life problems.

Practical Activity

Activity Title: 'Deciphering Modular Inequalities Through the Board Game'

Project Objective:

Students will be challenged to create an educational board game whose objective is to help players learn how to solve modular inequalities. The project will address various topics of modular inequalities and stimulate the student to think about the applicability of this topic in everyday situations. Each question in the game should be a practical problem that can be solved with modular inequalities.

In addition, students must write a detailed document about the project developed, following the proposed structure: introduction, development, conclusions, and bibliography.

Detailed Project Description:

The project will be divided into two main parts: the creation of the board game and the writing of the document.

For the board game, students must develop an educational game based on modular inequalities. The goal of the game is for players to learn how to solve modular inequalities while having fun playing. The game should include questions of different difficulty levels, addressing various key concepts of modular inequalities.

For the document, students must write in a clear and concise manner a detailed description of the board game, explaining the rules, the logic behind the questions, and how modular inequalities are applied. In addition, students should explain the skills acquired during the project, highlighting the collaborative and interdisciplinary aspects of teamwork in creating the game.

Required Materials:

• Office supplies (pencils, pens, erasers, ruler, A3 paper)
• Computer with internet access for research
• Materials for creating the board (cardboard, scissors, glue, markers)
• Game pieces (can be created by students or reused from other games)

Detailed Step-by-Step for Carrying Out the Activity:

1. Divide the class into groups of 3 to 5 students.

2. Each group should research modular inequalities, including concepts, examples, and real-world applications. This research should be used to create the questions and answers for the board game.

3. The groups should then create the layout of the board game, including the path that players will follow, the spaces where players will land, and the questions that will be asked.

4. After creating the board, the groups should develop the rules of the game. The rules should ensure that players practice solving modular inequalities.

5. Finally, each group should write the document explaining the board game and how it teaches modular inequalities.

Project Delivery:

Students must present the created board game and deliver the written document about the project. The document should follow the proposed structure, contextualizing the theme in the introduction, describing the project's development, presenting the results and conclusions, and indicating the bibliography used for the study and creation of the game.

The presentation of the game is extremely important, as it will allow students to demonstrate the game and explain how it contributes to the understanding of modular inequalities.

The document should complement the game presentation, offering students an opportunity to explain in more detail the process of creating the game, the mathematical concepts involved, and the skills that were developed during the project.