Context

Cartesian coordinates are a way to indicate the position of a point or object in a two-dimensional or three-dimensional space. This technique was developed by the French philosopher and mathematician René Descartes. In Cartesian coordinates, each point is represented by a pair of numbers (x, y), which defines its position along two perpendicular axes, usually called the X-axis and Y-axis.

In a two-dimensional space (like a sheet of paper or a computer screen), the coordinates (x, y) of a point represent the horizontal (x) and vertical (y) distance of that point from the origin. The origin is the point (0, 0), where the two axes intersect. In a three-dimensional space, a third number (z) is added to represent the distance above or below the plane formed by the X and Y axes.

Learning about Cartesian coordinates may seem distant from your daily life, but in fact, they are used in many aspects of our modern world. For example, GPS systems use a form of Cartesian coordinates to show your location on Earth. Scientists and engineers use Cartesian coordinates to design and build everything from houses to space satellites. And spreadsheets, which are used in all kinds of work, use Cartesian coordinates to reference cells.

To delve deeper into the topic of Cartesian coordinates and assist in the project implementation, we recommend the following resources:

1. "Mathematics - Cartesian Coordinates" (YouTube): https://www.youtube.com/watch?v=68B1y3f4Um4
2. "Cartesian Coordinate System" (Just Mathematics): https://www.somatematica.com.br/fundam/coordenadas.php
3. "Cartesian Coordinates" (Khan Academy): https://pt.khanacademy.org/math/basic-geo/basic-geo-coord-plane

Practical Activity

Activity Title: "The City of Coordinates"

Project Objective:

The project aims to enhance students' understanding and ability to use Cartesian coordinates efficiently, through teamwork collaboration and practical application of these concepts.

Detailed Project Description:

Students will be assigned to groups of 3 to 5 members. Each group will have the task of building a miniature city on a grid board, which will be the Cartesian plane. Each building, house, or point of interest (such as a school, a bakery, a square, etc.) will be associated with a pair of coordinates on the board.

At the end, students should write a guide to their city, describing the locations of points of interest using Cartesian coordinates. They will also create routes between different locations using coordinates to direct the way.

Required Materials:

1. Chess or grid boards
2. Cardboard, scissors, and glue for building structures
3. Colored pens or markers

Step by Step:

1. Divide students into groups of 3 to 5.

2. Provide each group with a grid board, which will be their Cartesian plane.

3. Students should decide which structures/locations their city will have (for example: houses, school, market, hospital, etc.) and build them with cardboard.

4. Each structure should be glued to a specific cell on the chessboard, which will be referenced by a pair of Cartesian coordinates.

5. Students should write a city guide, describing each structure and giving its location in the form of a pair of Cartesian coordinates.

6. Each group should also create and describe at least three routes between different points of interest in the city, using Cartesian coordinates to indicate the path taken.

7. The project should be completed in two to four hours per student, and the deadline for submission is one week.

Project Deliverables and Connection to Suggested Activities:

At the end of the project, each group must submit the board with the miniature city and the written city guide. The city guide should follow the structure of a report, with the following topics:

1. Introduction: Students should introduce the city, contextualize the use of Cartesian coordinates in the project, and explain the relevance of this concept in the real world.

2. Development: Students should explain about Cartesian coordinates, the activity in detail, the methodology used (i.e., how they organized the work, the construction of the city, how they decided where to place each structure, etc.), and present the routes created indicating the path through the coordinates.

3. Conclusions: Students should conclude by summarizing the main points of the project, explaining the learnings and conclusions drawn from collaborative work and the application of Cartesian coordinates.

4. Bibliography: Students should indicate the sources from which they obtained the information for the project. It can be the material provided by the teacher, books, websites, videos, etc.

This project helps students understand and apply the concept of Cartesian coordinates in a practical and realistic way, as well as encouraging skills such as teamwork, time management, problem-solving, and creative thinking.