Introduction

Mathematics, especially rational numbers, is at the core of many natural and artificial phenomena. Rational numbers are all numbers that can be expressed as a fraction, where the numerator and denominator are integers and the denominator is not zero. This includes integers, negatives, finite decimals, and repeating infinite decimals.

Operations with rational numbers, i.e., addition, subtraction, multiplication, and division, are fundamental and utilitarian. Mastering these operations and understanding their principles is a crucial skill, as it allows for solving a wide range of mathematical problems and real-life situations.

Mathematics itself is a language, and mastering the concept of rational numbers, as well as their operations, is equivalent to learning vocabulary and grammar in this language. This is crucial not only for your future academic activities but also for the development of problem-solving skills and critical thinking.

Contextualization

Operations with rational numbers are widely used in various disciplines and everyday situations. When we calculate averages, split restaurant bills, use scales on maps, read recipes, or take measurements, we are applying rational numbers.

In the context of engineering or physics, rational numbers are used to calculate densities, rates, proportions, and much more. In the financial sector, interest, discounts, taxes, and profitability calculations depend on the same concepts. Therefore, understanding rational numbers is not just a mathematical skill but a basic life skill.

To learn more about this topic, you can consult the following sources:

• OBMep Mathematics Portal: Rational Numbers
• Khan Academy: Fraction Operations
• Brasil Escola: Rational Numbers
• Só Matemática: Mathematical Operations with Rational Numbers

Practical Activity

Activity Title: The Rational Numbers Marathon

Project Objective

The objective of this project is to develop a deeper understanding of operations with rational numbers through the practice of problems solving. Additionally, students will learn to work effectively in teams, creating problem-solving strategies and presenting their findings in an organized and logical manner.

Detailed Project Description

Groups will be responsible for developing and solving a set of problems involving operations with rational numbers. Each team must formulate and solve 10 different problems. The problems should involve everyday situations such as shopping, temperature, time, distance, speed, among others. Additionally, students will create a report describing the theory behind rational number operations, explaining their problems in detail, and discussing the results.

Required Materials

• Textbooks/support materials to research operations with rational numbers
• Pencils, erasers, and paper for problem elaboration
• Computer with internet access (optional) for researching examples of problems and writing the project

Activity Steps

1. Divide the class into groups of 3 to 5 students. Each group will be a team responsible for creating and solving a set of problems involving operations with rational numbers.

2. Initially, each group should research operations with rational numbers to understand the theory behind the concepts that will be used to create the problems.

3. After the research, students should create 10 problems involving operations with rational numbers, with situations related to everyday life, thus demonstrating the applicability of the studied concepts. These problems should be solved, and the solutions will be compiled into a document.

4. The groups should then discuss the solution method for each problem and write a detailed explanation for each solution.

5. Next, each group should prepare a report that includes the following topics:

   • Introduction: the relevance and application of operations with rational numbers in the real world and the objective of this project.
   • Development: the theory behind operations with rational numbers, detailing the activity performed, explaining each problem created, the methodology used, and presenting the solution and discussion for each problem.
   • Conclusions: a summary of the main points of the work, the lessons learned, and the conclusions drawn about the understanding of operations with rational numbers.
   • Bibliography: the sources used for research and project development.

6. Each group should present their report and problems to the class.

Project Deliverables:

Students must submit a written report containing the theory of rational numbers and operations, the description of the problems, and the solution for each of them. The report should follow the structure: Introduction, Development, Conclusion, and Bibliography.

Additionally, students must orally present their work to the class, discussing the problems they developed and the solutions they found.

The writing of the report and the oral presentation are directly connected to the proposed practical activity, as they allow for the consolidation of theoretical and practical learning of the students, and the verification of the application of rational number concepts in problems related to everyday life.