Contextualization

The Cartesian coordinate system is one of the most important tools in mathematics and various sciences, including physics and engineering. This system helps us represent points on a straight line (one axis) or on a plane (two axes) or in space (three axes).

The system was developed by the French mathematician René Descartes in the 17th century, which is why it is called 'Cartesian' in his honor. In the Cartesian coordinate system, each point is represented by a pair (or a trio) of numbers, called coordinates. The coordinates of a point are the distances from the point to the axes.

For our study, we will focus on a plane of Cartesian coordinates, which is formed by two perpendicular lines, called axes. The horizontal axis is called the X-axis, while the vertical axis is the Y-axis. The point where they intersect is called the origin and is the point with coordinates (0,0).

The Importance of Cartesian Coordinates

Cartesian coordinates are extremely useful in a variety of everyday situations. For example, in geography, Cartesian coordinates are used to indicate the location of places on a map. In engineering and architecture, Cartesian coordinates are used to design and build complex structures.

In mathematics, Cartesian coordinates are fundamental to understand and solve problems in geometry and algebra. Furthermore, Cartesian coordinates are an essential tool for the development of spatial thinking, a skill indispensable in many areas.

The resources we recommend for students to consult are:

• Textbook: 'Mathematics and Reality', by authors Gelson Iezzi, Carlos Murakami. Published by Editora Atual. This book has a simple and direct language, as well as various examples and exercises.
• Website: Just Mathematics. This site presents a detailed explanation of Cartesian coordinates, with interactive examples and exercises.
• Video: The Cartesian Coordinate System - Matemática Rio Channel. This video provides a visual explanation of Cartesian coordinates, facilitating understanding.

Practical Activity

Activity Title: 'Exploring the World with Cartesian Coordinates'

Project Objectives

The objective of the project is to apply the concept of Cartesian coordinates to solve everyday problems, promoting a better understanding of the topic and developing teamwork and time management skills.

Project Description

In this activity, students will create a 'board game' in the form of a map, which will be filled with drawings of objects or animals of their choice. Then, they will create 'missions' or 'tasks' that must be carried out on the board by moving using Cartesian coordinates. Each group will present their game and rules to the class.

Required Materials

• Large sheets of paper
• Colored pens
• Ruler

Step by Step

1. Divide the class into groups of 3 to 5 students.

2. Each group should draw the Cartesian plane on a large sheet of paper, with a grid of at least 10 x 10 squares.

3. Then, the students should fill the map with drawings of their choice (objects, animals, etc), assigning each drawing a coordinate on the Cartesian plane.

4. Next, the students should create 'missions' or 'tasks'. For example, a task could be 'Go from the object at coordinate (1,2) to the object at coordinate (5,8)'.

5. Once the map and tasks are ready, each group will have the opportunity to present their game to the class. Other groups can try to complete the proposed missions.

Project Deliverables

1. The board game created by the group, with the drawings and their respective coordinates clearly identified.

2. A list of the 'missions' or 'tasks' created.

3. A written report containing:

   3.1. Introduction: Students should write about the concept of Cartesian coordinates, their importance, and applications. They should also explain the project's objective.

   3.2. Development: Students should describe in detail the process of creating the game, explaining how they applied the concept of Cartesian coordinates. They should also report on the experience of presenting the game to the class.

   3.3. Conclusions: Students should reflect on what they learned from the project, the challenges they faced, and how they overcame them. They should also comment on the skills they developed throughout the project, such as teamwork, time management, etc.

   3.4. Bibliography: Students should list the sources they used to learn about the topic and to assist in the project's creation.

The project should be delivered after a month of work, and each student should dedicate between 5 to 10 hours to the project.