Contextualization

Geometric shapes are fundamental in mathematics and are present in everything around us, from everyday objects to grand architectural constructions. Spatial Geometry is a branch of Mathematics that studies figures in space, that is, those that have more than two dimensions. Here, we will be introduced to spatial figures such as spheres, cubes, cylinders, pyramids and cones, among many others, which are a complex and fascinating expansion of the flat shapes that we already know.

Connecting with these shapes, learning to identify them and understanding their properties is important not only for mathematical studies but also for better understanding the world around us. After all, we live in a three-dimensional environment filled with spatial geometric figures. When we look at, for example, a juice box, a glass of water or a soccer ball, we are in contact with different spatial geometric shapes: parallelepipeds, cylinders, spheres.

Also, don’t be fooled into thinking that this is a subject restricted to Mathematics. It also connects with Art, Physics, Engineering and many other fields. Understanding spatial geometry is a way to better understand the shapes and volumes, the objects that surround us, the works of art, the architectural constructions, and even the movement of bodies in space.

To help students understand the subject in a dynamic way, I suggest using the Khan Academy platform, which has a section dedicated to Spatial Geometry with videos and exercises that can be done online: Khan Academy - Spatial Geometry

In the Só Matemática portal, students can find detailed explanations and examples that help to visualize and understand the concepts: Só Matemática - Spatial Geometry.

I also suggest reading the book "Spatial Geometry: Metric and Descriptive", by José Barroso, which presents the concepts in a detailed way and has exercises solved: Spatial Geometry: Metric and Descriptive - José Barroso .

Remembering that these resources are only suggestions and do not replace the research and individual involvement of each student in the learning process.

Practical Activity: Scale Spatial Model and Artistic Exhibition

Project Goal

The project aims to provide an understanding of the concepts of spatial figures, their characteristics, properties and everyday applications, developing technical and socio-emotional skills, uniting not only mathematics and spatial geometry, but also art and writing.

Detailed Project Description

The students, divided into groups of 3 to 5, should choose a spatial figure of interest, which can be a sphere, cube, pyramid, cylinder, cone, among others, and create a scale model of that figure using recyclable materials.

Each group, after building the model, should make an exhibition for the class, presenting the chosen spatial figure, its properties, the process of building the model and its everyday application. In addition, the group should explore the artistic side of the project, painting and decorating the model in a creative way.

Finally, each group should produce a written report detailing the entire project, from choosing the spatial figure, building the model, the exhibition, to the conclusions and lessons learned.

Necessary materials

• Recyclable materials (milk cartons, pet bottles, toilet paper rolls, etc.)
• Cardboard
• Scissors
• Glue
• Paper strips
• Gouache paint
• Brushes

Step by Step to Carry Out the Activity

1. Form the groups and define which spatial figure each one will work with.
2. Research the chosen spatial figure and its everyday applications.
3. Make a drawing or sketch of the spatial figure, observing its characteristics and properties (edges, vertices, faces).
4. Plan how to build the scale model of the spatial figure with the available recyclable materials.
5. Build the model.
6. Paint and decorate the model creatively.
7. Prepare the exhibition, which should include the presentation of the spatial figure, its properties, the process of building the model, its everyday application and the artistic side of the project.
8. Make the exhibition for the class.
9. Write the report, detailing the entire process, from choosing the spatial figure, the research carried out, the construction of the model, the preparation and carrying out of the exhibition, to the conclusions and lessons learned.

Project Deliverables

1. Scale model of the spatial figure: The model should be built with recyclable materials, be faithful to the shape of the chosen spatial figure and be duly painted and decorated.

2. Exhibition for the class: The exhibition should be well prepared and planned, presenting the spatial figure, its properties, the process of building the model, its everyday application and the artistic side of the project.

3. Written report: The report should follow the format of introduction, development, conclusion and bibliography. In the introduction, the student should contextualize the chosen spatial figure and justify the choice. In the development, it should explain the theory behind the spatial figure, detail the construction of the model and the preparation of the exhibition. In the conclusion, it should present the lessons learned, the difficulties encountered and how they were overcome. In the bibliography, it should list the sources used to carry out the project.