Contextualization
Mathematics is a science that uses logic and strategic thinking to solve everyday problems. One of the main concepts used in mathematics is that of the Cartesian plane. The Cartesian plane, named after René Descartes, is a two-dimensional representation formed by two perpendicular numerical lines, one horizontal and one vertical, intersecting at a point. The points within the plane are denoted by ordered pairs (x, y).
The concept of distance between two points in the Cartesian plane is fundamental to understanding many concepts in mathematics and related fields, such as physics and engineering. In mathematics, particularly in geometry, it is used to calculate the distance between two points, which forms the basis for calculating perimeters and areas of flat figures.
In the real world, the notion of distance between two points can be seen in various contexts. When we use a GPS to navigate, for example, it uses the concept of distance between two points to calculate the shortest route. In civil construction, engineers and architects use the notion of distance to design and build structures effectively and safely.
This project aims to deeply explore the concept of distance between two points through a practical activity involving teamwork, strategic thinking, and the application of mathematical concepts.
To prepare for the project, I suggest that students explore the following resources:
- Khan Academy: 8th-grade math course that includes an extensive section on the Cartesian plane and distance between points (available at https://pt.khanacademy.org/math/cc-eighth-grade-math).
- GeoGebra: An interactive online tool that allows students to explore geometry concepts, including distance between points and the Cartesian plane (https://www.geogebra.org/m/dYvK7G3Z).
The above resources provide an excellent foundation for students to begin understanding and applying the project's concepts.
Practical Activity
Activity Title: Unraveling the Maze
Project Objective:
The objective of this project is to allow students to enhance their understanding of the concept of distance between points in the Cartesian plane, applying this knowledge in a practical and playful context: creating and solving a maze.
Detailed Project Description:
In this project, students, grouped in teams of 3 to 5 members, will create a maze on a Cartesian plane.
Teams must draw a maze on graph paper, clearly defining a starting point and an endpoint. Next, students will apply the concept of 'distance between points' to calculate the minimum path to exit the maze.
Additionally, teams will write a report detailing the maze creation process, the theory involved, and the conclusions drawn, as well as a reflection on teamwork.
Required Materials:
- Graph paper
- Colored pens or pencils
- Rulers
- Calculator (optional)
Detailed Step-by-Step for Activity Execution:
- Form groups of 3 to 5 students.
- Each group should create a maze on a sheet of graph paper. Define a starting point and an endpoint.
- With the maze drawn, each group member must calculate the distance of the minimum path to exit the maze. This calculation should be based on the concepts of distance between points and the midpoint of a line segment.
- After all group members have calculated the path distance, they should discuss the results among themselves and choose the most suitable one.
- Each group must prepare a report detailing the maze creation process, the calculations made, and the conclusions drawn. The report should include:
- Introduction: Should include a contextualization of the concept of distance between points and its real-world application;
- Development: Should detail the theory behind the distance between points, explain the maze creation and the calculations made, and present the results obtained;
- Conclusion: The team summarizes the main points of the project, highlighting what was learned and concluding about the activity;
- Bibliography: Include the sources consulted to elaborate the project.
- The group must present the maze, explain the calculation of the minimum distance, and discuss their report in a presentation to the class.
It is expected that for the complete realization of the project, including the creation of the maze, the calculations, and the elaboration of the report, each student dedicates between five to ten hours over the course of a one-month deadline.
