Contextualization

Theoretical Introduction

Mathematics is an area of knowledge whose application is evidenced in our daily lives in various ways. Within this science, a fundamental concept is that of absolute numbers and order. When we talk about an absolute number, we are referring to the "value" that a number represents, regardless of its "direction" or "sense". In the numeric system, numbers have direction, going to the right being positive and to the left being negative. The absolute value of a number is always positive or zero and is represented by "| |". For example, the absolute value of -3 and +3 is 3.

Regarding the concept of order, it basically involves organizing numbers following a logic, which can be from smallest to largest (ascending order) or from largest to smallest (descending order). Order also applies to negative numbers, where, for example, -3 is greater than -5.

Contextualization

Absolute numbers are applied in many areas of life, from checking the temperature to measuring distance. If, for example, we are 5 meters below sea level, the depth is -5 meters, but the distance is the absolute value, that is, 5 meters. Absolute numbers are also used in statistics and exact sciences.

As for ordering, it is a concept we use daily, whether to organize tasks in a list of what needs to be done first, or to organize data in a graph for easy reading. The concept of "greater" and "smaller" is widely applied in our routine, from checking prices at the market to measuring performance in a competition.

Practical Activity

Activity Title: "Unraveling Absolutes and Ordering Numbers"

Project Objective

The objective of this project is to apply the concepts of absolute value and order of numbers in a playful and interactive way, using practical activities and group discussions.

Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will receive a list of mixed numbers (positive, negative, and zeros). Their task will be, first, to calculate the absolute value for each number on the list and, subsequently, to organize the numbers (along with their absolute values) in ascending and descending order.

The project will be carried out in two main parts. The first part involves calculating the absolute values. The second part involves organizing the numbers and their absolute values. Group discussion and cooperation will be essential for completing the task.

Required Materials

• List of mixed numbers (can be generated by the teacher)
• Paper and pencil for calculations and notes
• Computer with internet access for research and complementary studies.

Detailed Step-by-Step

1. The teacher divides the students into groups and hands out the list of mixed numbers to each group. Each group should:
2. Define among the members who will be responsible for each task (calculating the absolute value, organizing in ascending order, organizing in descending order, and reviewing).
3. Calculate the absolute value of each number on the list. This calculation should be done by hand, using paper and pencil.
4. Organize the list of numbers and their respective absolute values in ascending order and then start the same process for descending order.
5. After completing the tasks, the member responsible for the review should check all the work and correct any errors found.
6. The entire process should be documented in detail, including the description of each member's functions, the difficulties encountered and how they were overcome, the results obtained, and the conclusions reached.

Project Delivery

• With the project completed, each group must prepare a detailed report, including:
  1. Introduction: Contextualization of the theme and project objective.
  2. Development: Explanation of the theory behind the concept of absolute value and order of numbers, detailing the activity carried out, methodology used, presentation and discussion of the results obtained.
  3. Conclusion: Recap of the main points, explanation of the learnings obtained by the team, and conclusions about the project.
  4. Bibliography: Indication of the sources used to work on the project, such as books, web pages, videos, etc.
• The delivery will be one week after the start of the project. Each group member will have an active role both in the project and in the preparation of the report.

This project will not only help students understand the concepts of absolute value and order, but will also develop their teamwork skills, time management, effective communication, and problem-solving abilities.