Contextualization

Mathematics is a universal language and periodic decimals are an example of how it can be shown in a curious and interesting way. A periodic decimal is a decimal number that has digits that repeat infinitely. Examples include the number 0.3333... which is a simple periodic decimal and the number 0.123123123... which is a compound periodic decimal.

In this universe of repetitions, we can find a connection with fractions! That's right, every periodic decimal can be converted into a fraction and vice versa. For example, the decimal 0.333... is the same as the fraction 1/3 and the decimal 0.123123... is the same as the fraction 41/333. This process of converting a periodic decimal into a fraction is known as 'determination of the generating fraction of a periodic decimal'.

Mastering this knowledge is crucial for dealing with everyday problems, such as understanding your grades in school, comprehending statistics presented in news, or even for doing calculations in the kitchen. It is also essential for the study of more advanced disciplines, such as Physics and Economics.

Introduction to the Project

In this project, we will explore in a didactic and playful way the periodic decimals and how to convert them into fractions. The goal is to deepen our knowledge, putting into practice collaboratively and funnily the theoretical concepts learned in the classroom. Additionally, we will also develop important skills, such as teamwork, problem-solving, and time management.

Here are some resources you can use to delve deeper into the topic and prepare for the project:

• How to find the generating fraction of a periodic decimal - Mundo Educação
• Periodic Decimal - Só Matemática
• The Generating Fraction - Brasil Escola

Are you ready? Let's get started!

Practical Activity: 'Creation and Game of the Periodic Decimal'

Project Objective

Understand the concept of periodic decimals and their relationship with fractions. Identify a periodic decimal and find its corresponding generating fraction.

Detailed Project Description

The groups will consist of 3 to 5 members. Each group will be responsible for creating a board game with the theme 'Periodic Decimal'. The game should include questions about periodic decimals and their corresponding generating fractions. Additionally, the group must produce a rule guide that explains how to play and the correct answers for each question.

Required Materials

• Cardboard, cardboard, or other material for the board.
• Colored paper for questions and answers.
• Colored pens or markers.
• Scissors.
• Small objects to serve as game pieces.

Step by Step

1. Research and Planning: Based on the suggested resources and other sources, research about periodic decimals and how to find the corresponding generating fraction. Plan the format and rules of the game according to what you have learned.

2. Board Construction: Construct the game board, which can be a path type with numbered squares, for example.

3. Questions and Answers: Create question and answer cards. The questions should propose challenges related to the transformation of periodic decimals into generating fractions and vice versa. For example: 'What is the generating fraction for the decimal 0.6666...?' or 'What is the corresponding periodic decimal to the fraction 3/7?'.

4. Game Rules: Write a small manual with the game rules. Include details such as how many players can participate, how they should move on the board, how questions should be asked and answered, and what happens if a question is answered correctly or incorrectly.

5. Test the Game: Play the game in your group to verify that everything is working as expected and the rules are clear.

6. Final Report: After completing the game, each group should prepare a detailed report containing:

• Introduction: Explain what periodic decimals are and why they are important. Present the project's objective and how it relates to what was learned in class.
• Development: Describe the process of creating the game, the concept behind each question elaborated, and how they found the answers. Describe the game rules.
• Conclusions: Discuss what was learned during the project execution and how this experience can help in understanding periodic decimals. What worked in the game? What could be improved?
• Bibliography: Cite all sources consulted during the project execution.

This project lasts for one week. Then, there will be a presentation session where each group will explain their game and present their report.