Contextualization

Spatial Geometry or Solid Geometry, as it is also called, is a branch of Geometry that is dedicated to the study of three-dimensional figures, called solid figures or geometric solids. The main geometric solids that we will analyze during this project are prisms and pyramids.

Prisms are solids that have two identical and parallel bases. Pyramids, on the other hand, have a base and all other faces converge to the same point, called the apex. Both solids are widely used in various areas of science and engineering.

The property that we want to emphasize in this project is the relationship between the number of vertices, faces, and edges of these solids. For example, a prism that has a base in the shape of a pentagon has 5 faces, 5 vertices, and 10 edges. A pyramid that has a base in the shape of a triangle has 4 faces, 4 vertices, and 6 edges.

To better understand these relationships, we will dive into the world of Spatial Geometry, building our own geometric solids and exploring their properties.

Importance of Spatial Geometry

Have you ever stopped to think about how many objects in our daily lives have shapes that resemble geometric solids? Bottles, soda cans, juice boxes, pyramids, buildings, and even the Earth, which has the shape of a geoid - a solid that is almost a sphere. Thus, Spatial Geometry is essential for us to understand and relate to the world around us.

In addition, geometric solids are very important in various areas of knowledge. For example, in Architecture and Engineering, a deep understanding of these concepts is necessary for the planning and construction of structures. In Chemistry and Biology, the study of the shape and structure of molecules also involves Spatial Geometry.

Therefore, the understanding of Spatial Geometry and, specifically, geometric solids is fundamental for the development of all of us as citizens and future professionals.

Hands-on Activity: "Construction and Exploration of Geometric Solids"

Project Objective

Explore the properties of three-dimensional geometric solids through the construction of physical models. Students will learn to identify and quantify the faces, vertices, and edges of different geometric solids, in addition to understanding the relationships between these elements.

Project Description

The teams must build models of different geometric solids - one prism and one pyramid of each type, with bases of 3, 4, and 5 sides. After building the models, students should document the properties of each solid (number of faces, vertices, and edges) and explore the relationships between them.

Required Materials

• Wooden sticks or straws
• Modeling clay or gummy candies
• Cardstock or cardboard
• Ruler
• Colored pens
• Digital camera or cell phone with camera

Step by Step

1. Group Formation: Form groups of 3 to 5 students. Each group will be responsible for building and documenting the properties of the geometric solids mentioned above.

2. Construction Planning: Before starting to build, each group must plan how they will make each solid. They should determine the dimensions of the solids, the number of sticks or straws, and the amount of clay or candies that will be needed.

3. Construction of the Solids: The groups should then build their geometric solids, using the available materials.

4. Documentation of Properties: Once the solids are built, the groups should document their properties. They should count the number of faces, vertices, and edges of each solid, and write down this information.

5. Exploration of Relationships: The groups should explore the relationships between the number of faces, vertices, and edges. They should check if Euler's formula (F + V = A + 2) is valid for the solids they built.

6. Preparation of the Report: Finally, the groups should prepare a report detailing the process of constructing the solids, the documentation of their properties, and the exploration of the relationships between faces, vertices, and edges.

Project Deliverables

• Physical Models: Each group must deliver the geometric solids they built.
• Photos: Each group should take clear and sharp photos of each solid, from different angles, clearly showing all faces, vertices, and edges.
• Report: The report should be written in article format and should contain the following topics:
  1. Introduction: Contextualization of the project, justification of the relevance of the topic, and objectives of the project.
  2. Development: Detailed description of the process of building the solids, documentation of the properties of the solids (including tables with the number of faces, vertices, and edges of each solid), and discussion of the relationships found between these elements.
  3. Conclusion: Reflection on what was learned from the project, difficulties encountered and how they were overcome, and how the activity contributed to the understanding of the concepts of Spatial Geometry.
  4. Bibliography: List of sources that helped in the development of the project.

The report should be submitted in digital format and each member of the group should have contributed to its elaboration. In addition, students should demonstrate that they were able to work well as a team, manage their time, and solve problems that arose during the project.