Introduction

Cartesian coordinates are one of the most widely used tools in mathematics and various other areas of knowledge for representing position and movement in space. They were created by René Descartes, a French philosopher and mathematician. With the introduction of this system, Descartes revolutionized mathematics by creating analytical geometry, which allows solving geometry problems through algebraic calculations.

To understand Cartesian coordinates, it is important to first grasp the concept of the Cartesian plane. The Cartesian plane is divided into four quadrants by two axes: the x-axis, which is horizontal, and the y-axis, which is vertical. Each point on the plane can be identified by a pair of numbers, which are the Cartesian coordinates. The first coordinate indicates the position of the point along the x-axis and the second along the y-axis.

Cartesian coordinates are widely used to represent data in graphs and are a foundation for developing skills in geometry, algebra, and trigonometry. It is a concept that opens the door to a wide range of mathematical applications, ranging from mapping geographic locations to data analysis in science and industry.

Contextualization

The application of Cartesian coordinates is present in various daily and professional activities. In geography, for example, Cartesian coordinates are used to map the Earth's surface, using longitude and latitude systems. In architecture and engineering, coordinates are essential for creating plans and projects. In the field of computer science, Cartesian coordinates are used for graphical representation of data and for creating games and computer programs.

In the modern world, Cartesian coordinates are also widely used in making strategic decisions in companies. For example, a retail company can use Cartesian coordinate graphs to identify sales trends and predict future stock needs. In summary, knowledge of Cartesian coordinates opens up a wide range of opportunities for students and can be applied to various professions and daily activities.

Practical Activity

Project "Navigating Cartesian City"

Project Objective

The objective of the "Navigating Cartesian City" project is to develop students' understanding of Cartesian coordinates and apply them practically. Students will be able to use digital tools, manual drawing skills, and work in teams to create, understand, and navigate through a "map" of a fictional city using the rules of Cartesian coordinates.

Project Description

Each group of 3 to 5 students will create a fictional city on the Cartesian plane. The city should have different types of buildings (e.g., schools, hospitals, parks, supermarkets, etc.), and each building will be represented by a point on the Cartesian plane.

Students must also create a "travel guide" that includes several "trips" within the city. Each trip is a set of instructions on how to move from one point to another using Cartesian coordinates.

The project involves the disciplines of mathematics, for understanding and applying Cartesian coordinates, and Arts, for creating the city and the travel guide.

Required Materials

• Large grid paper
• Colored pencils
• Ruler
• Computer with internet access

Step by Step

1. Understand the Concept of Cartesian Coordinates: Students must study and understand the concept of Cartesian coordinates using the recommended resources and other sources of information.

2. Plan the City: Students must plan their fictional city, determining the location of each type of building on the Cartesian plane. Each building will be a point with its respective coordinate.

3. Draw the City: Using grid paper, colored pencils, and a ruler, students must draw their fictional city, representing each building as a point on the Cartesian plane.

4. Create the Travel Guide: Students must create a "travel guide" that includes several "trips" within the city. Each trip is a set of instructions in Cartesian coordinates on how to move from one point to another.

5. Navigate the City: Students must then follow the travel instructions and move from one location to another in the fictional city using Cartesian coordinates.

6. Document the Process: The group must document the entire creation process, from the conception of the city to the execution of the trips. This should be done in a report format, following the guidelines below.

Project Deliverables

The group must deliver:

• The fictional city drawn on the Cartesian plane;
• The created travel guide;
• A report documenting the process.

The report should contain an introduction to the theory of Cartesian coordinates, a detailed description of the activity including the methodology used and results obtained, the conclusions drawn from the project, and the bibliography used. This report should be written to complement the practical work carried out.

Groups have a deadline of four weeks to complete the project. The expected workload is over twelve hours per student.