Context

The Cartesian Plane was created by the French philosopher and mathematician René Descartes, hence the name 'Cartesian'. He developed a coordinate system in which each point on the plane is represented by an ordered pair of real numbers, allowing a geometric interpretation of pairs of numbers and, thus, the graphical representation of equations and functions. This system, extremely useful, has become fundamental in many areas of mathematics and exact sciences.

The idea behind the Cartesian Plane is quite simple, yet very powerful. Through it, it is possible to represent any point in space using only two numbers: the first coordinate indicates the horizontal distance, and the second one, the vertical distance. Each point on the plane is unique and has an ordered pair of numbers associated with it.

Introduction

This project is designed to help you better understand the concept of the Cartesian Plane. You will learn how to mark points on the plane and recognize the marked points, two important skills in various areas of study. And by working in groups, you will also have the opportunity to improve your socio-emotional skills, such as communication, time management, problem-solving, and creative thinking.

The Cartesian Plane is a basic concept in mathematics that has a wide range of real-world applications. Whether in physics, designing scientific experiments, developing video games, or creating graphics in business reports, the ability to use and interpret Cartesian planes is a valuable skill.

Practical Activity: Cartesian Treasure Hunt

1. Project Objectives

The objective of this project is to use the Cartesian Plane in a fun and engaging way to solidify the theoretical concepts learned in the classroom. The concepts will be applied in practice through the creation and solution of a 'Treasure Hunt' based on Cartesian coordinates.

2. Detailed Project Description

Students will be divided into groups of 3 to 5 members. Each group will be responsible for creating a 'treasure map', which is actually a Cartesian Plane, and a series of clues that will lead to a hidden 'treasure'. Each clue must indicate a coordinate on the Cartesian Plane.

Groups should create maps and clues that are challenging enough, but not impossible to solve. They should also ensure that all clues have a solution and lead to a single point on the map.

Once the maps and clues have been created, the groups will exchange their work with each other and try to locate the 'treasure' of other groups using the provided clues.

3. Necessary Materials

• Graph paper or grid paper to create the Cartesian Plane (map).
• Pencils, erasers, and colored pens.
• Prize/Surprise (the 'treasure').
• Computer and internet access for additional research, if necessary.

4. Detailed Step-by-Step

1. Each group should start by drawing a Cartesian Plane on paper. They should decide on the size and scale of the plane.

2. Next, they should decide where the 'treasure' will be and mark this point on the plane.

3. Then, the group should create a series of clues that, when solved, point to the location of the 'treasure'. Each clue should be linked to a specific point on the Cartesian Plane, and the solution should be an ordered pair of numbers.

4. Once the maps and clues have been created, the groups should exchange their work with each other.

5. Now, each group should try to solve the clues provided by the other group and find the location of the 'treasure' on the Cartesian Plane.

6. Finally, the groups should present their solutions and explain how they arrived at the location of the treasure.

5. Project Delivery and Written Document

After completing the practical activity, the groups should prepare a written document with the following sections:

1. Introduction: In this section, the groups should contextualize the theme of the Cartesian Plane, its relevance and practical application, in addition to the objective of this activity. It is important that in this part, the students explain the idea behind the 'Cartesian Treasure Hunt' and how this activity helps to understand and apply the concept of the Cartesian Plane.

2. Development: Here, the groups should detail the theory behind the Cartesian Plane, present a detailed explanation of the activity, the methodology used, and finally, present and discuss the results. They should explain about the creation of the map (Cartesian Plane), the choice of the 'treasure' location, the elaboration of the clues, and how the process of solving the other group's clues took place. It is essential that students explain the process of marking points on the Cartesian Plane and how they interpreted the coordinates given by the clues.

3. Conclusion: This section should summarize the main points of the project, the lessons learned, and the conclusions about the activity. Here, students should reflect on what they learned from the activity regarding the Cartesian Plane, how they applied the concept in practice, and how this activity helped develop socio-emotional skills such as communication, time management, problem-solving, and creative thinking.

4. Bibliography: Finally, the groups should indicate the sources used for the project. It is important to cite the books, videos, websites, or any other resources they used to learn and apply the concept of the Cartesian Plane.

This project, if done correctly, will not only help students better understand the Cartesian Plane but also encourage creative thinking, problem-solving, teamwork, and communication - essential skills for life.