Contextualization

The Cartesian plane is a geometric representation of an ordered pair of real numbers. The first, called 'x' (abscissa), tracks the distance along the horizontal axis (x-axis) and the second, called 'y' (ordinate), tracks the distance along the vertical axis (y-axis). The point where the two axes intersect is called the origin.

The Cartesian plane is divided into four quadrants, the first quadrant being the one where both 'x' and 'y' are positive values. Due to its simplicity and ease of understanding, the first quadrant is usually the first that students learn when being introduced to the concept of the Cartesian plane.

Learning how to use the Cartesian plane is fundamental in many disciplines, including mathematics, physics, engineering, geography, and even economics. It is used, among other things, to represent mathematical functions, track movements, represent geographical spaces, and represent economic relationships.

The importance of the Cartesian plane lies in the fact that it offers a visual way to explore and understand mathematical relationships. Additionally, in many professions and fields of knowledge, the ability to comprehend and utilize the Cartesian plane is an essential skill.

A few useful resources for deepening the study of the Cartesian plane include the website Só Matemática, the channel Matemática Rio com Prof. Rafael Procopio on YouTube and the book "Plano Cartesiano e Funções" by professor Victhor Gabriel de Oliveira.

Practical Activity: "Create Your City on the Cartesian Plane"

Project Objective

This project aims to lead students to understand and apply in practice the concepts of the Cartesian plane in the first quadrant. To this end, each group of 3 to 5 students will be responsible for creating a city on the Cartesian plane.

Detailed Project Description

Each city should be represented by a set of points on the plane, where each point represents a building, a house, a park, among others. Additionally, the city streets should be represented by the lines that connect the points.

Each element of the city should be represented by an ordered pair (x,y), where x is the horizontal coordinate and y is the vertical coordinate. The group needs to define the meaning of these ordered pairs in their city.

Students will be responsible for creating a map of the city on the Cartesian plane, captioning it with the coordinates of the representative points and explaining how the coordinates were chosen, associating these decisions with the theory learned in the classroom.

Required Materials

• Graph paper;
• Colored pencils or markers;
• Ruler.

Project Step-by-Step

1. Divide into groups of 3 to 5 students.

2. On the graph paper, draw the first quadrant of the Cartesian plane.

3. Discuss within the group and decide what elements your city will have (houses, buildings, parks, etc.).

4. Assign each element an ordered pair (x,y) and mark this point on the Cartesian plane.

5. Draw the lines that represent the city streets to connect the points.

6. Create a legend identifying each point with its respective ordered pair and what it represents in the city.

7. Write a report (1. Introduction, 2. Development, 3. Conclusion, 4. Bibliography) detailing the city creation process, the logic used for the distribution of elements on the Cartesian plane, and how the concepts of mathematics were applied.

Project Deliverables

In addition to the city drawn on the Cartesian plane, each group must deliver a report with the following structure:

1. Introduction: Should contain a brief explanation about the Cartesian plane and a description of the city created by the group.

2. Development: Should contain the theory behind the creation of the city, a detailed explanation of each element of the city and its location (ordered pairs), as well as the discussion on the methodology used to create the city.

3. Conclusion: Should contain a critical evaluation of the work, what was learned, and conclusions drawn about the project.

4. Bibliography: Should contain the references of the resources consulted for the project.

After submitting the project, students should be able to associate ordered pairs with points in the first quadrant of the Cartesian plane and understand their applications in the real world, in addition to developing socioemotional skills such as teamwork, time management, problem solving, and creative thinking.