Contextualization

The concept of functions in mathematics is fundamental and pervasive. They are like the building blocks for many other mathematical concepts and have widespread applications in various fields, including physics, engineering, economics, computer science, and more.

In this project, we will be focusing on a specific kind of function, the absolute value function. This function, denoted as |x|, returns the absolute value of a number x, which is its value without regard to its sign. In simpler terms, it gives you the distance of the number from zero on a number line.

The absolute value function is unique as it always returns a positive value, irrespective of the sign of the input number. For example, the absolute value of 5 and -5 is the same, which is 5. This property is key to understanding and working with absolute value functions.

Understanding absolute value functions is not only important from a theoretical standpoint but also has many practical applications. For instance, in physics, the magnitude of a physical quantity is often represented using the absolute value function. In economics, absolute value functions can model situations where only the size of a change is important, not the direction.

To help you gain a deeper understanding of absolute value functions, I have curated a list of resources that you can refer to.

1. Khan Academy: Absolute value & number lines
2. Math is Fun: Absolute Value
3. Purple Math: The Absolute Value Function
4. Book: Algebra and Trigonometry by Michael Sullivan (Chapter 1: Equations and Inequalities)

These resources will provide you with the necessary theoretical foundations and practical applications of absolute value functions. Happy learning!

Practical Activity

Activity Title: "The Absolute Value Adventure"

Objective of the Project

The main objective of this project is to deepen your understanding of absolute value functions through real-world applications. You will also develop your problem-solving, teamwork, and creative thinking skills.

Detailed Description of the Project

In this project, you will work in groups of 3-5 students to create a "Math Adventure Book" that tells a story about the journey of absolute value functions. This book should involve anecdotes, examples, and exercises that demonstrate the concepts and properties of absolute value functions. Your adventure book should be a blend of fun and learning, engaging the reader (your classmates, teachers, and even parents) with colorful illustrations, interesting characters, and intriguing plotlines.

Necessary Materials

• Large sheets of paper or a poster board
• Markers, colored pencils, and other art materials
• Rulers and protractors
• Access to a library or Internet for research

Detailed Step-By-Step for Carrying Out the Activity

1. Form a Group and Allocate Roles Form a group of 3-5 students. Each student should have a specific role in the project, such as a writer, illustrator, researcher, or editor.

2. Brainstorm Ideas As a group, brainstorm ideas for your "Math Adventure Book". Think about a story that involves absolute value functions as a key element. It could be a journey, a mystery, a rescue mission, or anything else you can imagine.

3. Plan Your Story Once you have a concept, plan your story. Divide it into chapters or sections, and decide what you want to teach the reader in each section.

4. Research and Understand Absolute Value Functions Before you start writing, make sure everyone in your group has a solid understanding of absolute value functions. Use the provided resources, textbooks, and other reliable sources to research and clarify any doubts.

5. Write the Story Start writing your story. Remember to incorporate absolute value functions in a way that is both educational and entertaining. Use examples, exercises, and illustrations to make the concepts clear.

6. Create Illustrations While one group member is writing, other members should be creating illustrations for the book. These could be diagrams explaining the concepts, illustrations of the characters or scenes from the story, or anything else you think will enhance your book.

7. Edit and Review Once you have finished writing and illustrating, review your work as a group. Make sure the story flows well, the illustrations match the text, and the concepts are clear. Make any necessary edits.

8. Compile and Present Compile all your chapters or sections into one "Math Adventure Book". Make sure it is neat, organized, and presentable. Prepare a brief presentation to explain your book to the class.

Project Deliverables

At the end of the project, your group should submit the following:

1. A "Math Adventure Book" that tells a story involving absolute value functions. The book should be neat, well-organized, and visually appealing, with clear explanations and examples of absolute value functions.

2. A brief presentation (5-10 minutes) where your group explains the story, how you incorporated absolute value functions, and what you learned from the project.

3. A written report in the format of an essay, with the following sections:

   • Introduction: Here, you should provide context about your story, explain why you chose the particular theme, and state the objective of the project.

   • Development: In this section, you should detail the theory behind absolute value functions, explain the activity in detail, indicate the methodology used, and finally present and discuss the obtained results. The discussion should focus on the learning outcomes, the challenges faced, and how you overcame them.

   • Conclusion: Revisit the main points of your project, explicitly state what you learned, and draw conclusions about the project.

   • Used Bibliography: List all the resources you used throughout the project, such as textbooks, web pages, videos, and so on.

Remember, your book and report should demonstrate not only your understanding of absolute value functions but also your creative thinking, problem-solving, and teamwork skills. Good luck, and have fun on your "Absolute Value Adventure"!