Contextualization

Introduction to Key Theoretical Concepts

Location is a fundamental concept not only in mathematics, but in many areas of study. Since ancient times, people have been making maps and studying ways of orientation and location to explore unknown lands and navigate through large bodies of water. In mathematical terms, location is closely related to geometry and coordinate systems.

Location can be defined in different ways depending on the context. In the mathematical context, it refers to a specific point in space, which can be defined by a set of numerical coordinates in a coordinate system. The most common coordinate system is the Cartesian coordinate system, which uses two or three numbers to define the position of a point in 2D or 3D space.

Coordinate systems are mathematical tools that allow defining the position of a point in space uniquely and unambiguously. They are composed of axes that intersect at a point called the origin. Each point in space can be defined by a set of values, called coordinates, representing the distance from the point to the origin along the axes.

Contextualization and Importance of Location

Location is essential for human survival and development. It is the basis for the spatial organization of society and for activities such as navigation, urban and transportation planning, geolocation, and many more. Without an efficient location system, it would be very difficult for navigators, explorers, drivers, and even for us in our daily lives to find our way in a city or through unknown locations.

Furthermore, location is also fundamental for understanding many natural and social phenomena that are spatially distributed, such as the spread of diseases, weather patterns, population distribution, and migration behavior.

Activity: "Geometry Explorers"

Project Objective

The objective of this activity is to deepen students' understanding of location and Cartesian and geographic coordinate systems, and the application of these concepts in the real world. It also aims to promote skills such as teamwork, time management, and problem-solving.

Project Description

Groups (3 to 5 students) will have the task of creating a map of the neighborhood or city where they live, including landmarks and routes between these points. They will have to use scales to represent distances on the map proportionally and will need to define Cartesian and geographic coordinate systems for their maps. Subsequently, they will need to plan and execute a local expedition based on the created map, which will include following a route and writing step-by-step directions.

Required Materials

• Drawing paper (A3)
• Pencils and erasers
• Ruler
• Protractor
• Pen
• GPS or map application on the phone
• Camera or phone to record the expedition

Step by Step

1. Research the location to be mapped: Online tools can be used to study the location and identify landmarks. Make notes about the characteristics and important locations.

2. Draw the map: Use A3 paper to draw the map. Remember to include all landmarks and main streets. Use the ruler and protractor to keep the map proportional and accurate.

3. Define the coordinates: Establish a Cartesian coordinate system on your map. Define the origin (0,0) and the orientation of the axes. Also, identify the geographic coordinates of the landmarks.

4. Plan the expedition: Based on the map, plan a route that passes through at least three landmarks. Write step-by-step directions on how to get from one point to another in terms of location and coordinates.

5. Execute the expedition: Follow the planned route and check the accuracy of your map and directions. Take photos of the landmarks when you reach them.

6. Prepare the report: Document the entire process, from the initial research, map creation, coordinate definition, planning, and execution of the expedition. It should include an introduction, development, conclusions, and bibliography.

Project Deliverables

The deliverables of this project will be:

1. The map created by the group, with landmarks and the coordinate system clearly indicated.
2. Documentation of the directions of the planned route, written step by step.
3. Photos taken during the expedition.
4. The report documenting the project execution process, as indicated in step 6 above.

The report should complement the practical work. In the introduction, students should contextualize the theme of location, its relevance, and the motivation for the project. The development should detail the theory behind location and coordinate systems, a detailed description of the activities carried out, and the results obtained. The conclusion should summarize the main points, the learnings, and the discoveries made during the project. Finally, the bibliography should list all sources consulted during the project execution.

The estimated time for completing this project is approximately 12 hours per student.