Contextualization

The fundamental concept of absolute value is a cornerstone in the realm of mathematics. It is defined as the distance of a number from zero on the number line, regardless of its direction or sign. In simpler terms, the absolute value of a number is its value without any consideration of its positive or negative sign. For example, both -3 and 3 have an absolute value of 3. At first glance, absolute value might seem like a simple concept, but it enables us to tackle complex mathematical problems in a variety of fields such as engineering, physics, computer science, and more. It's a building block for understanding more advanced mathematical topics and it's also crucial in developing deeper logical thinking skills.

The topic of absolute value stretches beyond mathematics and is profoundly applicable in a myriad of real-world contexts and scenarios. Whether we are measuring distances, comparing temperatures, or calculating changes in stock market values, the absolute value plays a crucial role. It allows us to make objective comparisons without the influence of direction or sign. It helps us to answer questions like "how much", rather than "more or less".

In this project, we will explore the concept of absolute value, its functions, its theoretical underpinnings, and its diverse applications in real-world contexts. From the exploration of absolute value properties to the role it plays in equation solving and function graphing, we will unpack the world of absolute values and its implications.

Students can utilize the following resources to delve deeper into the concept and applications of Absolute Value:

• Khan Academy: Offers comprehensive videos and practice problems on absolute values, their properties, and functions.
• Math is Fun: Provides a simple explanation of absolute values, along with interactive examples to showcase its practical applications.
• Wolfram MathWorld: An excellent resource for a deeper dive into the theoretical and complex aspects of absolute values. Ideal for advanced learning and extended research.

Let's embark on this mathematical journey and delve into the fascinating world of absolute value!

Practical Activity

Activity Title: Absolute Value in the Real World

Objective of the Project: The objective of this project is to create an interactive and engaging scenario in which the concept of absolute value is applied. Students will research, design, execute, and report on a project illustrating the use of absolute value in a real-world context.

Group Size: This project is designed for groups of 3 to 5 students.

Duration: This project will require more than twelve hours per student to complete, spanning over two weeks.

Necessary Materials:

• Notebook for brainstorming and preliminary sketching
• Computer with internet access for research and written report
• Mathematical software or online graphing tools (e.g., Desmos, Geogebra)
• Presentation software (e.g., PowerPoint, Prezi)
• Rule, pencil, and eraser for manual graphing
• Optional: Camera or smartphone for capturing practical applications

Detailed Steps:

Step 1: Brainstorming and Research

In this stage, students will brainstorm possible real-world scenarios where the concept of absolute value is relevant. Students should then conduct a thorough research on their chosen scenario, considering questions like: How is absolute value used in this context? What is the significance of absolute value in this scenario?

Step 2: Project Design

Based on their research, students will design a project illustrating the use of absolute value in their chosen scenario. This may include drawing graphs, writing equations, and creating models or simulations.

Step 3: Project Execution

Students will execute their project design. This may involve creating graph plots, simulating scenarios, running calculations, performing experiments, etc.

Step 4: Driven Analysis

Based on the project execution, students will analyze their results and make interpretations. This may involve comparing expected results with actual results, reflecting on discrepancies, and discussing the implications and significance of their findings.

Step 5: Written Document

The final step involves writing a project report to summarize their journey. The report should be divided into four main sections:

• Introduction: The students should contextualize the absolute value theme, its relevance, and real-world application. The objective of the project and the chosen scenario should also be explained.

• Development: The students should detail the theory behind absolute value, explain the designed activity in detail, indicate the methodology used, and present the obtained results.

• Conclusion: The students should conclude the work by revisiting its main points, stating what they have learned, and drawing conclusions about the project.

• Bibliography: The students should indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.

Step 6: Presentation

Students will present their project to the class, showing their process and results. The presentations should be engaging, educational, and illustrative of the real-world scenario they chose.

In this project, students are expected to collaborate effectively, exercise creativity, manage time, communicate effectively, and solve problems. By the end of this project, students should have a deep understanding of the role and application of absolute value in the real world.

Finally, this project should serve as a tool to encourage further exploration of mathematical concepts and their applications. Good luck, and remember to have fun with it! Learning is a journey, not a destination.