Introduction

Mathematics is a science that has developed and evolved over time, helping humans in countless discoveries and achievements. It is the tool that helps us understand the world around us, from the way that planets orbit the sun to the way we manage our money. To this end, we use different sets of numbers, each with its characteristics and applications. In the 7th grade, we learn about one of these sets: the integers, which include positive numbers, zero, and negative numbers.

Negative numbers are a bit peculiar and may seem odd at first. But they are extremely useful and are found in our daily lives in many different ways. For example, when we check the temperature and it is below 0, we are referring to negative numbers. Or when our soccer team loses a goal, it gets a negative point on the scoreboard. Therefore, understanding the concept of negative numbers is crucial to comprehending many physical and economic phenomena.

Negative numbers first appear in the history of mathematics in China around the 2nd century B.C. They represented debts, and this concept was especially useful for mathematicians and merchants at the time. The Chinese numeric system was a decimal positional system, similar to the one we use today, and they used a red stick to represent positive numbers and a black stick to represent negative numbers.

Introduction

In this project, we will thoroughly explore the concept of negative numbers, their history, properties, and real-world applications. We will work in groups and learn to collaborate with each other, sharing tasks and responsibilities. We will also make connections with other subjects, like History and Physics, and develop essential skills like time management, communication, and problem-solving.

As a starting point, we recommend reading the following resources:

1. Khan Academy website: Negative Numbers
2. Book "Mathematics: Single Volume," by Gelson Iezzi and Osvaldo Dolce. Chapter on integers.
3. Mundo Educação website: History of Negative Numbers

These resources provide an in-depth look at the topic and will be useful in developing the project.

Practical Activity

Activity Title: "Navigating the Negative Numbers"

Project Objective

The goal of this project is to deepen students’ understanding of negative numbers by creating a historical timeline and an educational game. The project is designed to introduce concepts of negative numbers, explore the historical development of negative numbers, and apply them in a practical context.

Detailed Project Description

The project will be carried out in groups of three to five students and will be divided into two main parts: researching and creating a historical timeline of negative numbers and developing a board game involving negative numbers.

Part 1: Historical Timeline Students will investigate the history of negative numbers, highlighting their development, uses, and acceptance in different cultures and periods in history. When creating the timeline, students should include important events and the civilizations or individuals responsible for the contributions. The timeline should be visually appealing and include brief descriptions for each event.

Part 2: Board Game Students will create a board game using negative numbers. The game should be designed in a way that players practice addition, subtraction, multiplication, and division using negative numbers. The game should also incorporate elements of decision-making and strategy. Creativity in the game design is highly encouraged.

Required Materials

To complete the project, groups will need the following materials:

• Card stock or poster board for the timeline and game board
• Colored pens, markers, and/or crayons
• Internet access for research
• Various materials for creating game pieces, such as popsicle sticks, buttons, bottle caps, etc.

Activity Steps in Detail

Part 1: Historical Timeline

1. Research the origin and evolution of negative numbers in the history of mathematics using books and reliable websites.
2. Based on the information researched, create a timeline, highlighting important events and people. Ensure the timeline is visually engaging and informative.

Part 2: Board Game

1. Start by conceptualizing the game idea. What will be the goal of the game? How will negative numbers be used in it?
2. Design the board. It can be of any shape (circle, square, rectangle, etc.). Consider creating areas or regions on the board that result in gaining or losing points (positive or negative numbers).
3. Create clear rules for the game. The rules must involve operations with negative numbers.

At the end of the project, each group must produce a report in a written document format that contains the following sections:

• Introduction: Provide the context of the importance of negative numbers and the project's objectives.
• Development: Describe the theory of negative numbers and how the historical timeline and board game were developed. Explain the methodology used and present the obtained results (include pictures of the timeline and game in this section).
• Conclusion: Summarize the main points and discuss what was learned throughout the project.
• Bibliography: List the references used in the project.

This report should complement the developed practical work, consolidating the concepts learned and providing a record of the creative and collaborative process experienced by the group.