Contextualization

Unequal sharing is a mathematical concept that appears in several situations of our daily lives. In essence, it consists of dividing a quantity into unequal parts. For example, suppose that you and a friend won 30 candies. However, instead of dividing equally, with each one getting 15, you decide that one person should receive double the amount of the other. In this case, one person would get 20 candies, while the other would get 10, i.e., an unequal distribution was made.

The concept helps us better understand how to handle situations in which equal division is not possible or desired. Unequal sharing is especially important when we consider social justice, since equality is not always the fairest approach. For instance, social welfare programs are structured so that the poorest families receive more resources. This is also unequal sharing but seeks better equity.

Unequal sharing is part of everyone’s lives, even if we often do not realize it. When we pay taxes, for example, we are participating in unequal sharing. People who earn more money pay more taxes, and this money is partially used to finance public services that benefit everyone, especially the poorest. This happens because, in a fair society, it is believed that those who have more resources should contribute more to the common good.

Resources Suggestion

To further explore the theme, students may resort to different materials, such as educational videos, interactive games, and textbooks. Additionally, the Internet is an invaluable resource for research. However, it is important to remember that not all information found online is reliable, which is why it is essential to seek reliable sources.

1. Video: "Unequal Sharing" available on Nova Escola's YouTube channel
2. Book: "Mathematics - Understanding and Teaching" - Ruy Berger
3. Website: Khan Academy (www.khanacademy.org), a free online resource offering interactive math classes.

Keep in mind that it is essential for students to understand that unequal sharing is a very important concept to deal with everyday situations, and even more so, to develop a critical awareness of important social issues.

Practical Activity

Activity Title: "The Great Unequal Sharing Picnic"

Project Objective:

This project aims to familiarize students with the concept of unequal sharing, its implications, and practical applications, while also developing teamwork, critical thinking, and problem-solving skills.

Project Description:

In this project, groups of students (3 to 5 students per group) will be responsible for planning a picnic for their team. They will receive a fixed number of tokens (e.g., 100 tokens) that represent the food that will be taken to the picnic. However, the tokens should be distributed unequally among the group members, on the condition that one member receives twice the number of tokens another member receives.

Students should prepare a plan establishing who gets how many tokens and why. They should consider criteria such as need, preferences and contributions to the group, among others, to make their decisions. The idea is that, at the end, they have made an unequal distribution.

Necessary Materials:

1. Colored paper tokens (100 for each group)
2. Paper sheets
3. Pencils and erasers
4. Ruler
5. Compass or protractor (optional)

Step by Step:

1. Group Organization and Material Distribution: Each group of 3 to 5 students receives 100 tokens and the necessary materials.

2. Definition of the Distribution Rules: Groups should discuss and define the rules for dividing the tokens. Remember, the division should be unequal, and one member must receive double the number of tokens another member receives.

3. Development of the Distribution Plan: With the rules set, each group should then distribute the tokens, documenting in detail the process and the reasons for their decisions.

4. Implementation of the Distribution: The tokens are then physically distributed according to the plan. If necessary, plans can be adjusted to ensure successful implementation of the distribution.

5. Project Report Development: Upon completion of the distribution, each group should prepare a detailed project report.

Project Deliverables:

Students should submit a project report featuring four main parts: Introduction, Development, Conclusions, and References.

Introduction: The report should start with a contextualization of the theme of unequal sharing, its relevance and real-world applications, and the objective of the project.

Development: In this section, students should explain the theory behind unequal sharing, describe in detail the activities carried out, including how the tokens were distributed, the methodology used, and the results obtained.

Conclusions: The students should conclude the work by reviewing their main points, discussing what they learned, and what conclusions were drawn from the project.

References: The students should indicate the sources of information used to work on the project, such as books, websites, videos, etc.

This report is very important because it will show the group's entire work process, from the understanding of the concept to the implementation of the practice. What is more, writing the report is an exercise of argumentation and justification, essential skills in all areas of knowledge.