Contextualization

Mathematics is a science that is present in all areas of life, whether it's paying a bill, dividing a pizza, calculating distances, among many other situations. In particular, the concept of unequal sharing is widely used in various situations in our daily lives, from splitting a restaurant bill among friends to distributing profits in a company.

In this project, we will focus on the concept of unequal sharing and its applications. In real life, we do not always divide things equally, and mathematics allows us to understand and manage these differences in a fair and equitable manner. The ability to solve problems involving unequal sharing is essential to make informed and fair decisions in various situations.

To understand unequal sharing, we first need to understand the concept of ratio. Ratio is the relationship between two quantities and in mathematics, it is used to compare quantities. Ratios can be expressed in different ways, such as fractions, decimals, or percentages. For example, a ratio of 1 to 3 (written as 1:3) means that the first quantity is one-third of the second.

Unequal sharing, on the other hand, involves dividing a whole into parts of different sizes, according to a specified ratio. For example, if we want to divide a prize of R$100.00 in a ratio of 2:3, the amount will be divided into unequal parts of R$40.00 and R$60.00.

Introduction

By understanding unequal sharing, students will be able to solve various real-life problems. This concept is crucial in many areas, including economics, commerce, sciences, and engineering. Understanding it not only improves students' mathematical understanding but also enhances their problem-solving skills and decision-making.

In this project, we will explore unequal sharing through a practical project involving family economics and money management, making an interdisciplinary connection with Financial Education. Throughout our project, students will learn fundamental concepts such as ratios, proportions, percentages, unequal sharing, and the application of these concepts in the real scenario of money management.

This project is designed to be challenging and will require over twelve hours of work for each student. But don't worry! You won't be alone on this journey. You will work in groups, which will help you improve your teamwork, communication, and time management skills.

Below, we suggest some reliable resources to assist you in your research:

1. Unequal sharing: This link from the Dia a Dia Educação Portal presents unequal sharing in a playful way.
2. Unequal sharing: This YouTube video clearly explains the concept of unequal sharing.
3. Ratio and Proportion: On this website, you will find theory and exercises on ratio and proportion.

Practical Activity

Activity Title: "Unequal Family Budget"

Project Objective

The objective of this project is to apply the learned concepts of unequal sharing and ratio in a real and practical scenario, which is managing money in a family budget. The activity will allow students to understand how money is distributed for different family needs, promoting the understanding of the concept and practical experience in solving problems involving unequal sharing.

Detailed Project Description

Students will be divided into groups of three to five members. Each group will receive a fictional family budget, with different detailed needs and priorities. The group's task will be to divide this budget unequally, based on the specified needs, taking into account different proportions for each spending item.

For example, if the budget is R$5000.00 and the family's needs are distributed in categories such as Food, Housing, Education, Transportation, and Other needs, students must divide the budget using ratios. They will have to decide the proportion of the budget that each category will receive.

Students must think critically about the choices they make, discuss the reasons behind their decisions, and write a detailed report about it.

Required Materials

• Paper and pencil for notes and calculations.
• Calculator for more complex calculations.
• Computer with internet access for research and report writing.

Detailed Step-by-Step for Activity Execution

1. Formation of groups of three to five students. Definition of a name for the group and distribution of roles for each member. For example, there will be a writer for the report, a researcher to obtain relevant information, and a manager to ensure that everyone is contributing appropriately.

2. Delivery of the fictional family budget scenario to each group. Students will need to understand the listed needs and think about how to allocate the budget among them.

3. The group must discuss and decide the proportion of money to be allocated to each item. Each decision must be justified and recorded for inclusion in the final report.

4. Students will calculate the budget allocation using the concepts of ratio and unequal sharing.

5. Report writing. The report should include an introduction to the family budget scenario, a detailed description of the decision-making process and budget distribution, an explanation of the calculations performed, and the conclusions reached.

6. Project conclusion. Students must review their work and ensure that all parts of the report are complete and well-written.

This project is expected to take more than twelve hours for each student, including time for group discussions, research, calculations, and report writing.

Project Deliverables

At the end of the project, groups must deliver:

• The complete report, containing: Introduction (context, relevance, and project objective), Development (theory, activity, methodology, and results), Conclusion (summary of key points, learnings, and conclusions about the project), and Bibliography.
• Detailed calculation of the unequal sharing performed and its justifications.
• Oral presentation of the work results to the entire class.

It is important to remember that, even though it is a group work, each student must contribute to the project and report preparation. In the report, students should detail the contribution of each group member. Therefore, both technical skills (mastery of mathematical concepts) and socio-emotional skills (teamwork, time management, communication, etc.) will be evaluated.