Contextualization

Mathematics is a science that has been with humanity since the beginning of time, and rational numbers are a fundamental part of it. They arise naturally when we divide one thing by another, such as a pizza into several equal parts. Rational numbers are useful in various everyday situations, such as dividing a bill among friends, calculating the average of a series of numbers, among others.

Rational numbers, present in our daily lives, are all those that can be expressed in the form of a fraction. With them, we can represent non-integer quantities and perform various operations such as addition, subtraction, multiplication, and division. Understanding this topic paves the way for understanding more complex concepts, such as equations and functions, which are fundamental in various fields of knowledge, such as engineering, physics, economics, and countless other areas.

Ordering rational numbers, that is, the possibility of comparing them and organizing them in a sequence from smallest to largest (or vice versa), is essential for analysis and decision-making. It is with this ability that we can, for example, understand the evolution of an economy over the years, determine the best sequence of actions in a project, or even order players in a ranking of any game.

In this project, we will explore the depth of the universe of rational numbers and their ordering, using mathematics, logic, and a little creativity for this. It will be a journey of discovery and improvement of skills such as teamwork, time management, and collaborative problem solving.

To delve deeper into the subject, I recommend the following sources:

1. Book: "Fundamentals of elementary mathematics - Vol. 1" by Gelson Iezzi and Carlos Murakami. This book is an excellent source for a deep understanding of mathematical concepts.

2. OBMEP Mathematics Portal: This website contains several lessons and exercises on rational numbers and their ordering.

3. Khan Academy: This website has a series of videos on the subject, with clear explanations and exercises to practice.

I am eager to see what you will create and learn with this project.

Practical Activity

Activity Title: "The Rational Numbers Staircase"

Project Objective

The objective of this project is to develop students' understanding of the ordering of rational numbers, encouraging the use of problem-solving strategies, logical reasoning, and teamwork.

Detailed Project Description

In this project, students will create a "ladder" representing the number line, on which they will mark the rational numbers, ordering them from smallest to largest. Furthermore, they will be challenged to create everyday situations in which the ordering of rational numbers is used, and to present them in a creative and playful way. Interdisciplinarity will be explored by involving, in addition to Mathematics, disciplines such as Portuguese Language (in the preparation of reports and presentations) and Arts (in making the staircase of rationals and everyday situations).

Required Materials

• Long cardboard (2m x 40cm)
• Ruler
• Colored pens
• Scissors
• Glue
• Colored paper for everyday situation presentations

Detailed Step-by-Step for the Activity

Step 1: Form groups of 3 to 5 students.

Step 2: Each group should draw a vertical number line on the cardboard, marking the position of the integers from -10 to 10.

Step 3: Students should select at least 20 rational numbers (fractions and decimals) with two digits after the decimal point.

Step 4: Then, they should mark these numbers on the ladder, ordered from smallest to largest. It is important that everyone in the group understands why each number was placed in its respective position.

Step 5: Each group must create everyday situations in which the ordering of rational numbers is used and represent them creatively on the back of the cardboard.

Step 6: After making the ladder and everyday situations, each group should prepare a report according to the instructions below.

Project Deliveries and Preparation of the Written Document

Delivery 1 - The Rational Numbers Staircase

The first delivery is the staircase of rationals itself, along with the everyday situations drawn on the back of the cardboard. The staircase must be complete with all the selected rational numbers duly ordered and identified.

Delivery 2 - Written Report

The written report should complement the practical work done. Students should follow the suggested report format, which contains:

• Introduction: Explain what rational numbers are, their importance, and how their ordering is applied in the real world. Also, mention the objective of the project.
• Development: Describe the theory behind rational numbers and their ordering, explaining how the practical activity was carried out, the methodology adopted, the rational numbers chosen, the ordering process, and the creation of everyday situations.
• Conclusions: Review the main points of the work, highlight the lessons learned, and the conclusions about rational numbers and their ordering.
• Bibliography: Cite all sources used during the project development, such as books, websites, videos, and others

The quality and detail of the report will also be evaluated, so it is important that students strive to write good work.