Introduction

The Modular Function is one of the main concepts in mathematics and plays a significant role in many fields of study such as economics, engineering, physics, and computer science. In a simplified way, a modular function describes the distance of a number to zero on the real number line.

In the Modular Function, the sign of a number will always be positive, even if the number is negative. This is because we are interested in the distance of this number from zero, not in its direction. In other words, the modular function will always give us the absolute value of a number.

The topic of Modular Function - Inputs and Outputs is crucial to understand how the variation of input values (x) affects the output values (y) in a modular function. In this project, we will explore the peculiarities of the modular function and how it behaves with different inputs.

Contextualization

The study of the Modular Function goes beyond the limits of mathematics and finds application in many real-world situations. In economics, for example, it is used to calculate the absolute difference between two prices, or in physics, to determine the distance between two points in space.

There is also a very relevant practical application in the field of computing, where absolute values are used to calculate differences in pixels, useful in image and graphics manipulation. The inputs and outputs in a modular function allow us to perform complex mathematical operations that are fundamental in these processes.

Practical Activity

Activity Title: The Modular Maze

Project Objective:

This project aims to understand the modular function and how input values (x) influence output values (y), through the creation of a board game called "The Modular Maze". This game will allow students to explore, in a playful and practical way, the influence of input and output values in a modular function.

Detailed Project Description:

Students, divided into groups of 3 to 5, will create the "Modular Maze" where each path on the board is guided by modular function equations. With each move, players must calculate the output value of the modular function and move their pieces accordingly. The game ends when a player reaches the exit of the maze.

Required Materials:

• Cardboards or cardboard for the base of the board
• Pieces to represent the players (can be made of paper, clay, etc.)
• Cards with modular function equations
• Calculators
• Paper and pen for notes

Detailed Step-by-Step for Activity Execution:

1. Board Creation: The group must create a simple maze board on cardboard or cardboard. It is important to have various paths and intersections.

2. Creation of Modular Function Equations: Each group must create different modular function equations, representing different game situations. For example: a path may be blocked by a function that only allows passage if the output value is greater than 5.

3. Game: Each player starts at the entrance of the maze with a representative piece. On each turn, the player must choose the path to follow based on the calculation of a modular function present on the chosen path.

4. Documentation: While the game is set up and played, the group must document the process in a report, including the reasoning behind the choice of functions, the impact of inputs and outputs on game progress, and how the modular function was applied in the game context.

Project Deliverables:

• Board Game "The Modular Maze": This is the final product of the practical activity. Each group must explain the specific rules of their game and how the modular function is used.

• Report: Students must write a report detailing the game creation process, the application of the modular function, the relevance of input and output in modular functions, and the application of this concept in solving the game. The report should be divided into: Introduction (context and relevance of the theme, project objective), Development (explanation of the modular function concept, detailed game description, methodology used), Conclusions (review of the main points, learning and conclusions drawn from the project), and Bibliography.

This project will develop students' technical skills in calculating the input (x) and output (y) values of modular functions, and will also underpin socio-emotional skills such as time management, communication, problem-solving, creative thinking, and proactivity.