Context

Theoretical Introduction

Mathematics is a world full of concepts that help us better understand the universe around us. One of these concepts is that of absolute numbers. The absolute value of a number is its distance to zero in the number system. This means that the absolute value is always positive or zero, never negative. So, for example, the absolute value of -6 is 6, and the absolute value of 6 is also 6. As you can see, this is a way to visualize numbers differently from what we are used to.

Another concept we will explore in this project is the order of numbers. Numbers can be ordered in many different ways, but the most common are in ascending or descending order. When we put numbers in ascending order, we start from the smallest value to the largest, and in descending order, we do the opposite. Ordering numbers helps us better understand data sets and make decisions based on them.

Furthermore, we will study rational numbers. Rational numbers can be expressed as the ratio of two integers, where the denominator is not zero.

Connection to the Real World

The concept of absolute value is very important in many everyday situations. For example, when we talk about temperature, the difference between two temperatures is the absolute value of the difference between them. If we had a temperature of -3 degrees and another of 2 degrees, the difference between them would be 5 degrees, since what matters here is the absolute difference, the actual amount of difference, regardless of the sign.

Ordering numbers is also an essential skill in everyday life. For example, when we are comparing prices in a store, we want to put the prices in order to understand which is the best deal. Similarly, if we are analyzing the results of a competition, we need to order the times or scores to know who won.

Practical Activity

Activity Title: "The Number Staircase"

Project Objective

To develop a deep understanding of the concept of absolute value, the ability to order rational numbers, and the recognition of negative numbers. Additionally, the project will also aim to acquire important socio-emotional skills such as time management, teamwork, critical thinking, and effective communication.

Detailed Project Description

Students will be divided into groups of three to five and will be assigned the task of designing and creating a board game titled "The Number Staircase." This game should incorporate mathematical concepts such as absolute value, order of numbers, and rational numbers, as well as have rules that promote collaboration and effective communication within the group.

Required Materials

1. Cardboard or paperboard for the base of the game board.
2. Colored markers or paints for decorating and marking the board.
3. Magnets or small objects to be used as game pieces.
4. Paper and pencil to create questions and challenges for the game.

Detailed Step-by-Step for Activity Completion

1. First, students should research and study the concepts of absolute value, order of numbers, and rational numbers using the provided resources and any additional ones they may find.

2. Next, the group needs to outline a plan for their board game. They can draw inspiration from popular board games, but the design and rules should be original.

3. The group then needs to develop the game rules that should involve the studied mathematical concepts. For example, they can create challenges where players have to put a sequence of numbers in order, calculate the absolute value of a number, or answer questions about rational numbers.

4. Students should work together to build the game board using the provided materials. They should also create the questions and challenges that will be used in the game.

5. After building the game, group members should test the game to ensure it works correctly and that the rules are clear and fair.

6. Each group will present their game to the class, explaining the rules and how the mathematical concepts are incorporated. They should also document the entire process in a written report.

Project Delivery and Written Document

Each group must deliver the board game they created and a written report.

The report should contain the following elements:

• Introduction: Description of the importance of absolute value, order of numbers, and rational numbers in mathematics and everyday life. It should also include the project's objective.

• Development: An explanation of how the board game was created, what rules were established, and how the mathematical concepts were incorporated into the game. This section should also detail the methodology used and discuss the results obtained during the game testing phase.

• Conclusion: Here, students should summarize the main points and share what they learned during the project and what conclusions they drew from it. They can also talk about the socio-emotional skills they developed during the project.

• Bibliography: Students should list all resources (books, websites, videos, etc.) they used to support their project.

This project should be carried out over a period of approximately three weeks, with each student spending at least twelve hours in total on it. It is important for students to record and manage their time properly to ensure that all aspects of the project are completed on time.