Contextualization

Mathematics, more than just a school subject, is a universal language that allows describing, analyzing, and solving real-world problems. In this context, the concepts of Absolute Value and Modulus play a fundamental role.

Theoretical Introduction

The Absolute Value of a number is its magnitude, meaning its value without considering its sign. For example, the absolute value of -5 is 5. The Absolute Value is represented by two vertical bars around the number, like |5| or |-5|.

On the other hand, the Modulus is a concept that applies to vectors, complex numbers, or any element that can have direction and magnitude. Like the Absolute Value, the Modulus represents the magnitude of an element, regardless of its direction. In the case of complex numbers, for instance, the modulus is the distance from the number to the origin in the complex plane.

The Relevance of Absolute Value and Modulus

In the real world, Absolute Value and Modulus have numerous applications. In Physics, for example, the Modulus is used to represent the magnitude of vectors, which in turn are used to represent quantities like force, velocity, and acceleration.

In Economics, Absolute Value is often used to ignore the direction of a change and focus only on its magnitude. For instance, if the price of a stock drops from 100 to 90, the absolute value of the change is 10, regardless of the fact that the change was a decrease and not an increase.

Understanding these concepts is therefore essential to apply Mathematics in solving real-world problems, whether in Physics, Economics, Engineering, or any other field of knowledge.

Practical Activity: Exploring Absolute Value and Modulus

Project Objective

The objective of this project is to provide a practical and engaging learning experience about the concept of Absolute Value and Modulus, allowing students to apply them in real-world situations and practical experiments.

To carry out this project, groups should consist of 3 to 5 students, and the total duration of the project should be approximately 12 to 15 hours.

Project Description

In this activity, students will work in groups to create a series of physical experiments to illustrate the concept of Vectors, Absolute Value, and Modulus. Additionally, they will perform economic analyses using the concept of Absolute Value.

Part 1: Exploration of Vectors

Students will conduct a series of physical experiments to illustrate vectors. For this, they will use materials conducive to the proposed experiments, such as marbles, an inclined board, a stopwatch, and a ruler.

1.1 Experiment 1: They will release a marble on an inclined board, record the time it takes to reach the base of the board, and measure the distance traveled. These data will be used to calculate the average velocity of the marble, which is a vector. They should represent this velocity as a vector, drawing its magnitude and direction.

1.2 Experiment 2: They will repeat the experiment, but this time releasing the marble from a higher or lower height, thus modifying the velocity. They should represent this new velocity as a vector and compare it with the vector from the previous experiment.

Part 2: Economic Analysis with Absolute Value

In this part, students will research the stock prices of companies listed on the stock exchange for a period of 5 days. They should record the daily variations in the prices of these stocks and calculate the absolute value of each variation. In the end, they should write a report describing the variations in the stock market and how the use of absolute value can help understand the magnitude of these variations, regardless of the direction.

Project Deliverables

At the end of the project, each group must present:

1. Written Report: The report should contain four main sections: Introduction, Development, Conclusions, and Bibliography. The Introduction should introduce the topic of Absolute Value and Modulus, its relevance and application in the real world, and the project's objective. The Development should describe in detail the experiments carried out and the stock market analysis, explain the theory behind these concepts, and discuss the results obtained. The Conclusion should summarize the main points of the project, the learnings acquired, and the conclusions drawn from the project. The Bibliography should cite all sources of information used, such as books, web pages, videos, etc.

2. Oral Presentation: Each group must prepare a 15-minute oral presentation of the project for the rest of the class. The presentation should follow the same structure as the written report and include demonstrations of the experiments conducted, if possible.

3. Supporting Material: Any material produced during the project, such as graphs, tables, images, should be presented along with the written report and oral presentation.

Remember, the objective of this project is not only to acquire mathematical skills but also to develop socio-emotional skills such as time management, communication, problem-solving, creative thinking, proactivity, among others.