Contextualization

The concept of Absolute Value and Modulus is one of the fundamental tools of mathematics and you already use it in everyday life, even without realizing it. When you measure distances, for example, you don't usually care if the measurement is to the right or to the left, up or down. What really matters is the amount, the magnitude of the distance, and that is the Absolute Value.

In mathematics, the Absolute Value and the Modulus are used to indicate the distance of a number to the origin on the real number line, regardless of the direction. That is, the absolute value of a real number is always a non-negative number. For example, the absolute value of -7 is 7 because the distance between -7 and 0 on the real number line is 7.

Introduction

The Absolute Value or the Modulus of a real number can be defined as its value without its sign. Therefore, the Absolute Value of a number can be defined as its distance from the origin on the real number line. This definition seems simple and straightforward, but it has significant implications for solving many mathematical problems, some of which you will explore in this project.

The concept of Absolute Value and Modulus has several practical and theoretical applications in mathematics and in various areas, including physics, engineering, economics, statistics, among others. It is used to describe magnitudes that are independent of direction. For example, when we refer to the velocity of an object, we are talking about an absolute value.

To delve deeper into the subject, I suggest you consult the following sources:

1. The book "Fundamentals of Elementary Mathematics - Volume 1: Sets and Functions" by Gelson Iezzi. This book has an excellent approach to the topic.
2. The YouTube channel "Matemática Rio com Prof. Rafael Procopio". The videos are very didactic and help to understand the subject in a fun way.
3. The website "Só Matemática" (https://www.somatematica.com.br) has a section dedicated to absolute value and modulus that can be very useful for consultation.

Practical Activity

Title of the activity: Mathematical Rescue

Objective of the project

At the end of the project, you and your colleagues will be able to:

• Understand the concept of absolute value and modulus.
• Apply the concept of absolute value and modulus in solving practical problems.
• Write a detailed report of the project and its execution.

Detailed description of the project

Imagine that you and your group are a rescue team in charge of finding lost treasures. Each treasure is hidden in a mysterious location. To find them, you do not receive a map, but a series of mathematical clues involving the absolute value and the modulus of real numbers. Your goal is to decipher the clues, find the treasure and document the whole process!

Materials needed

• Pencils, pens, eraser and paper.
• Calculators.
• Internet and computer (for research and documentation).

Detailed step-by-step instructions for the activity

Part 1: Understanding the concept

1. All group members should first study and understand absolute value and modulus concepts using the suggested sources and any other credible sources.

2. Discuss as a group what each one has learned and make sure that all members understand the concepts.

Part 2: Deciphering the clues

3. The teacher will provide a series of mathematical puzzles involving absolute value and modulus calculations. Each puzzle leads to a clue for the location of the treasure.

4. Solve each puzzle as a group, documenting each step of the process.

Part 3: Finding the treasure and documentation

5. Complete all the necessary clues to determine the location of the treasure. Once the treasure has been 'found', start the project documentation phase.

6. Write a document in report format containing Introduction (contextualization of the project and relevance of the concepts of absolute value and modulus), Development (theory, practical activity carried out, methodology used and results obtained), Conclusions (learnings and conclusions) and Bibliography (sources consulted).

7. The conclusion should focus on the group's experiences during the project, observing how the concepts of absolute value and modulus were applied in solving the problems, as well as the socio-emotional skills developed.

8. Submit the document for evaluation.

Project deliverables

• List with the answers to the mathematical puzzles.
• Written document formatted as a report, detailing the entire project process.
• This report should clearly show how the concepts of absolute value and modulus were applied throughout the project, and should be limited to four main topics: Introduction, Development, Conclusions, and Bibliography.