Project: Real Numbers Mission: Saving the Continuum with Math and Physics

Contextualization

Real numbers are a numeric set that includes rational and irrational numbers and are essential for organizing the numeric system as we know it. Their existence allows us to express measurements, calculate quantities, solve equations, and understand various phenomena through mathematical language.

Working with real numbers requires understanding mathematical and operational concepts, as it involves calculations using addition, subtraction, multiplication, division, exponentiation, and root extraction. Each of these operations has its specificities and applications, and together they allow us to solve various everyday problems.

But the universe of real numbers is not limited to Mathematics! They are fundamental in several other disciplines, such as Physics and Chemistry, where they are constantly used in calculations of speed, acceleration, energy, mass, volume, pressure, and many others. They are also important in Geography and History, as they can represent distances, historical periods, populations, etc.

Introduction

In this project, we will delve into the study of real numbers and understand how to operate them. We will begin by understanding the concept of real numbers, their classification, and representation on the number line. Then, we will study the properties of operations with real numbers, namely: addition, subtraction, multiplication, division, exponentiation, and root extraction. We will explore each of these operations, understanding how and when to use them.

During the project, we will also take an interdisciplinary approach, understanding how operations with real numbers are applied in other disciplines, such as Physics, when calculating the average speed of an object, or in Chemistry, when calculating the molar mass of a substance.

To deepen your knowledge, we suggest the following resources:

• Textbook: "Mathematics - Science and Applications" by Gelson Iezzi. The book presents the concepts clearly and with several examples and exercises for reinforcement.
• Website: Khan Academy (www.khanacademy.org). On the website, you will find a whole section dedicated to real numbers, with explanatory videos, exercises, and quizzes.
• Videos: The "Matemática Rio" channel on YouTube has several lessons on real numbers and their operations.

Remember: Mathematics is like a puzzle. Each concept fits with the others, forming a complete and comprehensive view of the world around us. Shall we begin?

Practical Activity

Activity title: "Space-Time Operation: An Adventure with Real Numbers"

Project objective: Apply skills in operations with real numbers and integrate knowledge of Mathematics and Physics to solve a challenge based on the theme of time and space.

Detailed project description: Groups of 3 to 5 students will assume the role of scientists on a mission to decipher a hidden code that will reveal the location and time of a critical event. The code was left by a time traveler who used real numbers to create a complex sequence. The numbers were organized according to specific mathematical and physical relationships, combining operations with real numbers and physical concepts, such as speed and acceleration. The group's mission is to decipher the code, solve the mystery, and save the space-time continuum.

Required materials: Basic school supplies (notebook, pencil, eraser), internet access for research, calculator, graph paper, ruler, and compass.

Detailed step-by-step instructions for the activity:

1. The teacher will provide a series of mathematical and physical challenges that the group will have to solve. The challenges will have an order that must be followed, as each answer is a piece of the final code.

2. Students must organize an action plan that efficiently distributes tasks among group members, considering each one's skills.

3. The group must research and study the theoretical concepts necessary to solve each challenge. The concepts will involve operations with real numbers, measurements of time and space, speed, and acceleration.

4. After the theoretical study, the group must apply the concepts learned to solve each challenge. The challenges will be of increasing complexity, and each correct solution will take the group one step closer to unraveling the code.

5. At the end of solving the challenges, the group must compile all the answers to decipher the final code. This code will indicate the location and time period of the event they are trying to prevent.

6. Finally, students must produce a detailed final presentation, including the theory learned, the methodology applied, the answers to the challenges, and the final solution to the code.

7. In addition to the presentation, students must produce a written report, including the following items: Introduction (contextualizing the project and its relevance), Development (explaining the theory, methodology, challenges, and their solutions), Conclusions (including the lessons learned and the final solution to the code), and Bibliography used.

Project deliverables: The project will be delivered in two parts. The first part will be the oral presentation, in which the group will present their journey, from understanding the theory to deciphering the code. The second part will be the delivery of the written report, which should be well-written and contain all the information about the project, including the theory studied, the challenges solved, and the deciphering of the code, as well as students' reflections on the project and their learning.

For the report, the group must follow the DIDÁCTICO project guidelines. Each section of the report must be connected to the practical activity carried out, i.e., the Introduction must introduce and contextualize the project; the Development must explain in detail the theory and methodology, as well as the challenges and their solutions; the Conclusions must present the final considerations and lessons learned; and the Bibliography must list the sources consulted.