Contextualization

Theoretical Introduction

Planning is the two-dimensional representation (a sheet of paper, for example) of a three-dimensional object, which in Mathematics, we call a spatial figure. This activity is essential to develop students' spatial vision and understand how three-dimensional objects are constructed. Working with plans allows exploring geometric properties of spatial figures, such as prisms, pyramids, cylinders, and cones.

In our daily lives, several objects are assembled from plans. Imagine the packaging of a chocolate, a perfume box, or even a soda can. All these objects go through a planning stage before being assembled.

The ability to visualize three-dimensional objects from their two-dimensional representation is very useful in various professional careers, such as architecture, engineering, product design, among others.

Contextualization

Understanding what a spatial figure is and how it can be represented in a plan is of great importance not only for geometry but for mathematics in general. This knowledge allows you to better visualize and understand the space around you.

For example, companies that work in packaging production use this concept to create efficient transport boxes that save space. In construction, plans are used to create building plans and complex structures. Even in the fashion industry, designers create flat patterns that, when sewn together, form a three-dimensional piece of clothing.

Spatial figures and planning are useful tools that play a crucial role in solving everyday problems and making decisions in various areas.

Activity: Building and Planning Spatial Figures

Project Objective

Students will, in groups, build models of spatial figures (prisms, pyramids, cylinders, and cones) using various materials. They will then deconstruct these models, turning them back into plans. The objective of this project is to associate spatial figures with their plans and verify the planning of these figures through the practice of construction, deconstruction, and analysis of spatial figures.

Detailed Project Description

Each group of 3 to 5 students will choose a spatial figure to represent (prisms, pyramids, cylinders, or cones). The group will build a model of the chosen spatial figure using the available materials and then deconstruct this model, turning it into a plan. Through this activity, students will learn to associate spatial figures with their plans and verify the planning of these figures.

The project should be completed in one week, and it is estimated that each student will spend two to four hours on the activity.

Required Materials

• Cardboard or cardstock sheets (for building the models);
• Scissors;
• Tape or glue;
• Ruler and compass (optional, to help draw the shapes);
• Pencil and eraser;
• Colored pens or colored pencils (for coloring and identifying the different parts of the figure).

Step-by-Step for Activity Execution

1. Choosing the Spatial Figure: Each group must choose a spatial figure to work on (prism, pyramid, cylinder, or cone).

2. Building the Model: With the chosen figure, the group will build the model of the spatial figure using cardboard or cardstock.

3. Deconstruction of the Model: Once the model is ready, the group will deconstruct the model, turning it into a plan.

4. Analysis of the Plan: The group will analyze the obtained plan and discuss how the different parts of the spatial figure are represented in it.

5. Document Writing: Finally, the group will write a project report on the construction, deconstruction, and analysis of the spatial figure.

Project Delivery

At the end of the project, each group must deliver:

1. The deconstructed plan of the spatial figure on cardboard or cardstock.

2. A written document, also as a group, containing:

   • Introduction: Description of the chosen spatial figure, its relevance and real-world application, and the objective of this project.
   • Development: Explanation of the theory about the chosen spatial figure, detailed description of the activities carried out, methodology used, presentation, and discussion of the results obtained in the practical activity.
   • Conclusion: Conclusions drawn about the project, lessons learned, and the importance of studying spatial figures and their plans.
   • Bibliography: Indication of the research sources and support materials used during the project.

Students must ensure that the delivery is in line with the project's objective, that is, to demonstrate an understanding of spatial figures and their plans and apply this knowledge through the practical activity carried out.