Contextualization

Rational Numbers are numbers that can be expressed in the form of a fraction, where the numerator and denominator are integers and the denominator is different from zero. Thus, rational numbers include: integers, fractions, and finite or periodic decimal numbers. They represent a fundamental concept in mathematics, encompassing a wide variety of everyday situations, such as dividing items or measuring quantities.

In the real world, rational numbers are used in various applications. For example, they are used to represent divisions of resources such as money or food, or to express a fraction of a whole, such as half of a pizza or a third of a glass of water. They are also essential for expressing chances or probabilities, representing data in graphs, or making precise measurements.

The ability to understand and use rational numbers is crucial for students, as they will form the basis for learning other mathematical topics, such as irrational and real numbers, proportions, percentages, and measurements. Thus, the introduction to the study of rational numbers is an important step in the learning journey in mathematics.

Introduction

The concept of rational numbers is generally introduced in elementary school as an extension to integers. Students learn that fractions and decimal numbers are different representations of rational numbers and begin to understand that such numbers can be used to represent quantities that are not whole.

The notion of rational numbers is a significant advancement over the concept of natural numbers. It allows the representation of quantities that are not whole, and gives students tools to understand and solve everyday problems involving such quantities. For example, if you have a pizza and want to divide it equally among three people, you need to use rational numbers to represent the amount of pizza each person will receive.

Furthermore, rational numbers are important for developing the ability to solve mathematical problems and understand real-world situations involving proportions, rates, measurements, probabilities, and many other concepts. Thus, the study of rational numbers prepares students for future topics in mathematics and helps them develop logical reasoning and problem-solving skills.

Practical Activity

Activity Title: "Rational Numbers in Game"

Project Objective

This project aims to practically apply the concept of rational numbers through the development of a dynamic and engaging game that stimulates teamwork, strategic thinking, and the practical application of the concepts learned.

Detailed Project Description

Students, organized in groups of 3 to 5, should create a board game involving the use of rational numbers. The game should be dynamic and fun, engaging participants and promoting the learning and understanding of rational numbers, fractions, and decimal numbers.

Required Materials

• Cardboard
• Colored pens
• Graph paper
• Scissors
• Ruler
• Die or spinner

Detailed Step-by-Step

1. Research and Planning (2 hours): Students should start the project with research on board games and their structure, as well as the application of rational numbers in these games.

2. Board Design (3 hours): After the research, students should draw the game board using cardboard and colored pens. The board should have spaces that can be filled with challenges related to rational numbers.

3. Creation of Questions and Challenges (3 hours): Students should create questions and challenges that will be on the board spaces. These challenges should involve problems that need to be solved using rational numbers, fractions, or decimal numbers.

4. Game Testing (2 hours): With the game ready, students should play among themselves to test if the game is fun and if it really helps to understand the concept of rational numbers.

Project Deliverables

Students should deliver, in addition to the created game:

• Project Report: The report should contain sections of Introduction, Development, Conclusion, and Bibliography.

  • Introduction: Students should contextualize the project, explaining the concept of rational numbers and its practical application in the created game.
  • Development: In this section, students should describe in detail the creation of the game, explaining the chosen theme, the game mechanics, and how the concept of rational numbers was applied in the different phases of the project. Including photos of the game and students working can enrich this part.
  • Conclusion: Students should reflect on the experience of creating the game, listing what they learned about rational numbers and what they learned about teamwork and time management. They should conclude the report by describing if the game achieved its objectives and suggesting possible improvements for next time.
  • Bibliography: Students should list the sources used to study the concept of rational numbers and to learn about creating board games.

• Game Presentation: Each group should make a 10-minute presentation of their game to the class. This presentation should explain the game rules and how rational numbers were applied. It is recommended that students demonstrate how to play to facilitate understanding.