Context

Mathematics, often seen as a discipline of static formulas and equations, is actually full of curiosities and concepts that apply to our daily lives. Among these concepts is the Modular Function, which is the focus of our project.

The Modular Function is a mathematical function that returns the 'distance' that a number has from zero on a number line. In practical terms, it is represented by |x|, where the value of x is always positive, regardless of whether the original value is positive or negative. This is because the modulus of -3 is 3, just as the modulus of 3 is 3.

The modulus of a number is widely used in various disciplines and contexts, such as physics, engineering, economics, statistics, and much more. Imagine, for example, that you are using a GPS to navigate and the device says your destination is 3km away. It doesn't matter if these 3km are to the North, South, East, or West, what really matters is the distance between you and your destination, which is always a positive number.

Understanding modular functions can open new windows for a broader understanding of mathematics and other disciplines that use it as a tool. This project will explore the core concepts of the Modular Function, its real-world applications, and practices involving inputs and outputs of these functions, providing interactive and collaborative learning.

To develop this project, you will need to understand the concepts of the Modular Function, its applications, and practices well. We recommend the following study sources:

• Book: 'Fundamentals of Elementary Mathematics - Volume 1' by Osvaldo Teixeira Do Nascimento and Gilberto Leventhal (SME-TME Publisher)
• Website: Brazil School Portal
• Video: Modular Function - Rio Mathematics by the Mathematics teacher and communicator Rafael Procópio.

Practical Activity - 'Follow the Map: Exploring Modular Functions'

Project Objective

The main objective of the project is to familiarize students with the Modular Function, its properties, how to calculate the values of inputs (x) and outputs (y), and its application in the real world through an interactive and collaborative activity.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will receive a fictional map of a city with various points of interest (schools, parks, supermarkets, etc.) and distances in kilometers. The task of the groups is to plan a route that passes through all points of interest in the shortest possible way using the concept of the Modular Function.

The project will be divided into two parts:

1. Study Phase: During this phase, students must study the concept of the Modular Function, how to calculate the values of inputs (x) and outputs (y), and how to apply it in real-world situations. Students should use the provided reference sources, as well as other learning sources they find convenient.

2. Application Phase: In this phase, students must apply what they have learned to solve the proposed problem. They will determine the shortest routes using the Modular Function.

Necessary Materials

• Map of the fictional city
• Ruler
• Calculator
• Pens of different colors to trace routes
• Blank sheets for calculations and notes

Step by Step

1. Students gather in groups, which will receive the map.
2. They study the concept of the Modular Function, how to calculate the values of inputs (x) and outputs (y), and how to apply it in real-world situations.
3. They note down questions to be researched and solved, and distribute tasks within the group.
4. They hold a group meeting to combine learning and apply the concepts learned to the map.
5. They trace the route on the map based on the concept of the Modular Function.
6. Each group must record the entire process, including how they distributed tasks, how they applied the Modular Function, and the shortest routes found.

Project Delivery

After completing the practical activity, each group must submit a report consisting of:

• Introduction: Provide context on the Modular Function, its relevance and application in the real world, as well as the project's objective.
• Development: Explain the methodology used, detail how the activity was carried out, and present the results obtained. Here, students should also talk about task division, the application of modular functions in practice, and the difficulties encountered.
• Conclusion: Review the most important points, what they learned, and conclude about the project experience.
• Bibliography: Indicate the study sources used in the project.

This report goes beyond being purely an academic activity, as it is also a way for students to learn to communicate clearly and organized. By the end of the project, in addition to mathematical learning, students will have developed important socio-emotional skills such as time management, communication, problem-solving, creative thinking, proactivity, among others.