Contextualization

Mathematics is a fundamental tool in our daily lives, and one of the most important concepts is sharing. When we talk about sharing, we are referring to the division of something into equal or unequal parts. In some situations, we need to divide something in an unequal way, with one part being larger than the other. For example, imagine you are with friends and have a candy to share, but you have to give two parts to one friend and one to another. That's unequal sharing!

The concept of 'unequal sharing' has various uses in mathematics and in many real-life situations we face every day. It is used, for example, when we want to divide a pizza among friends, divide tasks in a school project, calculate taxes, share profits from a business, and so on. That's why it's so important to understand how unequal sharing works and how we can use it correctly.

Theoretical Introduction

Unequal sharing is an aspect of division in mathematics that deals with dividing a whole into parts that are not equal. This means that some parts will be larger than others. In our daily lives, we often need to perform unequal sharing. For example, when we divide tasks among team members, sometimes some members receive more tasks than others, based on their skills, availability of time, among other factors.

Unequal sharing is related to a mathematical concept called ratio. Ratio is a way to express the relationship between two quantities. For example, the ratio between 3 and 2 is 3:2, which means the first quantity is 1.5 times larger than the second. Understanding ratio is essential to comprehend unequal sharing.

Mastering the concept of unequal sharing is essential not only for solving mathematical problems, but also for the development of logical and critical thinking, as well as for practical application in various everyday situations. It is a key concept in mathematics that has a wide range of practical applications.

Practical Activity: 'Unequal Sharing'

Project Objective

The main objective of this project is to allow you, students, to understand in a practical and clear way how unequal sharing works. You will learn to deal with situations that require a non-equal division of a whole and understand how this skill can be useful in daily life.

Detailed Project Description

In groups of 3 to 5 students, you will perform a simulation of unequal sharing of a fictitious product. An initial quantity of units of this product (for example, 100 units) should be divided among team members unequally, following the following proportions:

• The group leader will receive 40% of the total.
• The other group members will receive a dividend equal to the remainder.

After that, group members will have to exchange a quantity of the product among themselves so that, in the end, everyone has quantities compatible with the following rule: the quantity each member has is twice the sum of the quantities of the members that precede them.

Necessary Materials

• Paper and pen for notes.
• Calculator

Detailed Step-by-Step for Activity Execution

1. Define a group leader.
2. The group leader must calculate 40% of the total quantity of the product (using simple three-rule) and write down this quantity.
3. The other group members will equally divide the remaining product among themselves, and each will write down the quantity they received.
4. Then the 'exchange' of the product will begin, following the rule that the quantity each member has is twice the sum of the quantities of the members that precede them. For this, students can exchange among themselves until reaching the amount determined by this rule.
5. Write down all steps taken (calculations, divisions, exchanges) to later report in the final report.

Project Deliverables

Groups must submit a final report, handwritten or typed, which should include:

1. Introduction: Description of the project, its relevance, and practical application.

2. Development: Details of project execution. Clear and detailed explanation of the problem presented, the calculations performed, and the unequal sharing carried out. Students must demonstrate that they understood the concept of unequal sharing and ratio through a detailed explanation of the methodology used to solve the activity and the discussion of the results obtained.

3. Conclusion: Students must summarize the main points of the project, explaining the lessons learned, the difficulties encountered, and the conclusions drawn from the project. For example, it should be explained how the sharing was resolved, what strategies were used to reach the final proportions, and what was learned from the experience.

4. Bibliography: Indication of sources that assisted in the project execution, such as books, web pages, videos, etc. These must comply with ABNT standards.

At the end of the project, in addition to the report, students must present the detailed sharing results, with the quantities each group member ended up with, and explain how they arrived at these results.