Contextualization

In this project, we will explore a fascinating field of mathematics: the development of spatial figures. Spatial figures are objects that occupy a place in space, such as a cube, a sphere, a cylinder, or a pyramid. The development, in turn, deals with how these figures could be represented on a two-dimensional plane, such as a sheet of paper.

The concepts we will cover are fundamental to understanding the space around us and allow us to interpret and operationalize three-dimensional shapes in our environment. Having a good understanding of how these figures can be developed is essential for various professions and activities, from engineering and architecture to solving everyday problems.

You have probably come across some of these situations in your daily life without even realizing it. For example, the box of an appliance when disassembled becomes a flat figure, it is like the manufacturer produces it. Do you know that pizza box? Well, it was planned before it was assembled to deliver the pizza to you hot. And these are just a few examples.

The development of spatial figures is an important subject not only in mathematics but also in disciplines such as Arts and Geography. In this project, you will have the opportunity to delve into concepts that transcend mathematics and have practical applications in several other areas of knowledge.

To learn more about this topic, you can consult the following resources:

• Book "Mathematics and Reality", by Gelson Iezzi, which brings a chapter dedicated to Spatial Geometry.
• Videos from the "Matemática Rio" channel, by Professor Rafael Procópio, which brings explanations about Spatial Geometry and development.
• Website "Só Matemática", which has a section dedicated to Spatial Geometry.

Practical Activity: "Space Planning Around Us"

Project Goal

The goal of this project is for you to have fun learning through the construction of models of spatial figures and their respective developments. You will model the environment around you, identify the spatial figures present, develop these figures, and finally, build the models.

Detailed Project Description

1. Identification of Spatial Figures: First, as a group, you will choose a location within the school (it can be a classroom, the cafeteria, the sports court, etc.) and record all the spatial figures that you can identify in this environment.

2. Development of Spatial Figures: Next, you should develop the identified spatial figures. For each spatial figure, you must draw the corresponding development on a sheet of paper.

3. Model Construction: Finally, you will use these developments to build a model of the chosen environment, using recyclable materials.

4. Written Document: You should prepare a detailed report on the project, including the topics of introduction, development, conclusions, and bibliography used.

Necessary Materials

• Cardboard or poster board
• Scissors
• Glue
• Pencil
• Ruler
• Various recyclable materials (juice boxes, toilet paper rolls, etc.)

Step by Step

1. Identification of Spatial Figures: As a group, choose a location within the school and record the spatial figures that you can identify. You can take pictures of the place to help you remember later.

2. Development of Spatial Figures: For each of the identified spatial figures, draw the corresponding development on a sheet of paper. You must use the ruler to ensure that the measurements are correct.

3. Model Construction: Now, it's time to bring the spatial figures to life! Use the recyclable materials and developments as guides to build a model of the chosen environment.

4. Written Document: Throughout the process, remember to record what you are doing and take pictures. This material will be crucial for the preparation of the written document.

Project Deliverables

The project results should be presented as follows:

1. Model of the Chosen Environment: Present the model of the chosen environment with the spatial figures constructed from the developments.
2. Report: The report should contain:
   • Introduction: Contextualize the theme, its relevance, and application in the real world as well as the project's objective.
   • Development: Explain the activity in detail, indicate the methodology used, and finally present and discuss the results obtained (include images of the process and the final model).
   • Conclusion: Return to the main points, explaining the lessons learned and the conclusions drawn about the project.
   • Bibliography: Indicates sources of information such as books, web pages, videos, etc.

The report is a fundamental part of the project and should be written in an organized and clear manner, complementing the practical work carried out. Therefore, be sure to dedicate adequate time to this part of the project.