Introduction

Three-dimensional geometric figures, also called spatial figures, are shapes that have three dimensions: length, width, and height. These figures, which are part of Spatial Geometry, have volume and can be classified according to their characteristics, such as the number of faces, edges, and vertices. Some of these figures are: cube, parallelepiped, sphere, cone, pyramid, among others.

Unlike flat (or two-dimensional) figures, spatial figures have volume, meaning they occupy a space in three-dimensionality, just like the objects we see around us. If you look around you now, you can probably identify some of these figures forming objects that you use in your daily life, such as a ball (sphere), a pencil (cylinder), etc.

Knowing and differentiating these figures is essential not only for the discipline of Mathematics but for various areas of knowledge and daily activities. Spatial Geometry is a branch of mathematics that studies these figures, their properties and relationships, and is a fundamental area for Physics, Engineering, Architecture, among others.

Contextualization

Spatial figures are present in many aspects of our lives, from the architecture of houses, buildings, and structures that surround us, to product design and space organization. Knowing these figures and their characteristics allows us to better understand and interact with the world around us. For example, to organize a space (like a room, for instance), it is necessary to consider the volume of objects - this is a direct application of knowledge about spatial figures!

Furthermore, understanding spatial figures is not only relevant for pure mathematics. Engineers, architects, designers, and many other professionals regularly use these concepts in their work. Even for those who would like to become astronauts, understanding spatial shapes and how they behave in three-dimensional space is crucial!

Practical Activity: 'Construction and Exploration of Spatial Figures'

Project Objective:

The objective of this project is to provide students with a practical and concrete understanding of spatial figures, their properties, and differences between them. Additionally, it aims to stimulate students' ability to work in groups, improve time management, and enhance communication and problem-solving skills.

Project Description:

Students, in groups of 3 to 5, should construct 4 different types of spatial figures: a cube, a pyramid, a cylinder, and a sphere, using recyclable materials. During the process, students should measure and record the properties of each figure (number of faces, vertices, edges, etc.). At the end of the project, students should present their figures, discuss the difficulties they encountered, the solutions they created, and how they would apply the knowledge of spatial figures in everyday situations.

Required Materials:

• Cardboard or sturdy paper
• Ruler
• Pencil
• Scissors
• Glue
• String
• Balloons
• Papier-mâché

Step by Step:

1. Study of Figures - Students should start by researching and studying the concepts and properties of each spatial figure to be constructed.

2. Planning - Next, they should plan how they will construct each figure, deciding on the size, materials, and task division within the group.

3. Construction - Next, each group should construct the spatial figures, recording the process and measurements taken. For the sphere, the use of balloons and papier-mâché is suggested.

4. Presentation - Finally, the groups should present their figures, discussing their construction process, the properties of the figures, and possible applications.

Final Product:

After completing the practical part, students should prepare a detailed report of the project, containing:

1. Introduction: Contextualization of the theme, its relevance and real-world application, as well as the project's objective.

2. Development: Explanation of the theory about spatial figures, detailing the activity, methodology used, and discussion of the results obtained.

3. Conclusion: Recap of the main points, explanation of the learnings obtained, and final reflections on the project.

4. Bibliography: Indication of the sources consulted in the project development, both for the theoretical part and the practical part.

The report should be submitted to the teacher in digital or printed format, as instructed. The project presentation should demonstrate the students' understanding of spatial figures, their learnings from the project, and reflection on their developed socio-emotional skills.