Contextualization

Theoretical Introduction

Opposite numbers, also known as symmetric numbers, are fundamental to our understanding of basic mathematical concepts, particularly for the comprehension of the system of integers. It is a simple but essential impression that each integer has an opposite, which is the same number but with the opposite sign. It is interesting to note that when we add a number and its opposite, the result is always zero.

The need for opposite numbers arises in both everyday situations and complex areas of study. For example, when we think about temperatures below zero, we are dealing with opposite numbers, that is, negatives. In physics, concepts such as reaction force, which is equal and opposite to the action force, depend on a complete understanding of the idea of opposite numbers. In economics, opposite numbers are necessary to record debts and credits.

Contextualization

Opposite numbers are essential for navigating daily life and understanding various situations we encounter. When we look at a thermometer, we easily understand the idea of temperatures below zero — a concept that directly connects with the idea of opposite numbers. When analyzing our finances, we deal with debts and credits, another example of situations where opposite numbers are relevant.

Moreover, it is in the 7th grade that students begin to delve more deeply into mathematics, and the understanding of concepts like opposite numbers is a crucial step in this journey. A solid understanding of integers and their opposites provides an important foundation for more advanced topics, such as algebra, and paves the way for a deeper study of mathematics.

Practical Activity

Activity Title: "Time Travel with Opposite Numbers!"

Project Objective

This interdisciplinary project aims to develop students' understanding of the concept of opposite numbers and how they are used in different contexts, linking with History to explore numerical systems of ancient civilizations.

Detailed Project Description

Students, divided into groups of 3 to 5, will conduct a historical investigation on how different ancient civilizations dealt with the concept of negative and opposite numbers. They should include at least four civilizations in their research, such as the Egyptians, Babylonians, Mayans, and Romans. Alongside this research, they will explore mathematical problems that could have been solved using opposite numbers by the chosen civilizations. Finally, the groups will develop a math workshop designed to teach the concept of opposite numbers to peers, using the knowledge acquired in the research.

Required Materials

1. Textbooks or online resources for research.
2. Computer and internet access.
3. Paper and colored pens for creating workshop materials.

Step-by-Step Guide for Carrying Out the Practical Activity

Step 1: Conduct an in-depth historical research on four ancient civilizations of your choice and how they dealt with the concept of negative and opposite numbers.

Step 2: Create a short presentation, in slides, narrating the evolution of the concept of opposite numbers for each researched civilization.

Step 3: Solve and/or create mathematical problems that could have been solved using opposite numbers in the time of each studied civilization.

Step 4: Prepare a 30-minute workshop, based on the research results, with the aim of teaching the concept of opposite numbers to peers.

Step 5: Conduct the workshop with other students from the school (preferably 7th graders) and document the activity with photos and/or videos.

Project Delivery

The final project delivery is a comprehensive report covering the following aspects:

1. Introduction: Contextualize the theme, its relevance and real-world application, the objective of this project, and the methodology used.

2. Development: Explain the theory behind the central theme of the project, describe the activity in detail, indicate the methodology used, and present and discuss the results obtained.

3. Conclusion: Conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.

4. Bibliography: Indicate the sources on which you relied to work on the project such as books, web pages, videos, etc.

The photos and/or videos of the conducted workshop should be attached at the end of the report.

This project should have a total duration of 15 hours per student, spread over four weeks.