Contextualization

Mathematics is a universal language and an essential discipline, used in many aspects of daily life and necessary for understanding many areas of knowledge. One of the topics studied in mathematics is Unequal Sharing, that is, dividing a quantity into two parts of different sizes.

This topic is the main concept behind many situations we encounter in our daily lives. For example, when we divide a package of cookies between two people and one person receives more cookies than the other, or when we divide a package of snacks among ourselves and our friends and want to ensure that each person receives a fair share, we need to understand Unequal Sharing. In this project, we will explore this concept in detail and learn how to apply it in real situations.

Introduction

In Unequal Sharing, we divide a quantity into two unequal parts. There are two key theoretical concepts that are important to understand Unequal Sharing: additive relationships and multiplicative relationships.

Additive relationships are based on the addition operation. For example, if we have a package of 20 cookies and want to divide it between two people, but one person receives 15 cookies and the other receives 5, we have an additive relationship because the sum of the parts (15 + 5) is equal to the whole (20).

Multiplicative relationships are based on the multiplication operation. For example, if one person receives twice as many cookies as the other, we have a multiplicative relationship. For example, if one person receives 4 cookies and the other receives 8, the person who receives 8 cookies received twice as much as the first.

Additionally, the ratio between the parts and between one of the parts and the whole is another important concept to be understood in Unequal Sharing. The ratio is a way to compare quantities or measurements of two different things.

Practical Activity

Activity Title: "The Cookie Game"

Project Objective

The objective of this project is to apply the concepts of Unequal Sharing, additive relationships, multiplicative relationships, and ratio in a playful and collaborative game environment.

Detailed Project Description

Students will be divided into groups of 3 to 5 people. Each group will receive a specific number of cookies (for example, 100 cookies). The task of each group will be to divide the cookies among the group members unequally, according to specific rules provided by the teacher, which will involve the application of additive relationships, multiplicative relationships, and ratios.

Required Materials

1. Cookies: each group needs a package of cookies.
2. Paper and pen: for notes and calculations.

Detailed Step-by-Step for Activity Execution

1. First, students divide into groups of 3 to 5 people.
2. Each group receives a package of cookies.
3. The teacher provides the division rule for each round of the game. For example, in the first round, the rule may be that one person should receive exactly twice as many cookies as another.
4. The groups divide the cookies according to the rule, making the necessary calculations and noting their decisions and results on paper.
5. After completing several rounds, each group should have a list of how the cookies were divided in each round, along with the calculations made.
6. Finally, each group should prepare a report to present their results.

Project Delivery and Writing of the Written Document

After completing the practical part of the project, students should work together to write a report on the activity. The report should be structured as follows:

1. Introduction: Contextualize the problem of unequal sharing, explaining why it is relevant and how it applies to real-world situations. Present the project's objective and briefly describe the rules of The Cookie Game.

2. Development: Explain in detail the methodology and rules of the game, as well as the strategies your group used. Describe how you applied additive and multiplicative relationships and ratio in dividing the cookies. Provide concrete examples of your calculations and results. Discuss the difficulties encountered and how they were overcome.

3. Conclusions: Review the main concepts of unequal sharing addressed in the project. Talk about what your group learned by applying these concepts practically during the game. Discuss what you realized about the importance of teamwork, especially in solving problems that involve dividing resources unequally.

4. Bibliography: Indicate sources of information, such as books, websites, and videos, that you used to learn about unequal sharing and to develop your strategies for the game.

Students should submit the printed report and notes with the calculations made during the game, which will serve as proof of their teamwork and their learning about unequal sharing.