Context

Mathematics is an abstract science that, however, finds real applications in our daily lives. Every shape we see around us, whether in natural objects or human constructions, can be understood through basic geometric shapes.

Basic shapes include flat figures such as the square, rectangle, circle, triangle, etc., and also spatial figures such as the cube, cylinder, sphere, cone, and many others. They are the foundation upon which we build our understanding of space and how objects fit into it.

The ability to understand and recognize these shapes allows us to describe the world in a more structured way. These skills also assist in areas such as motor skills, reading, and even more advanced thinking skills.

Knowledge of basic shapes is not only useful in mathematics but also in disciplines like art, where the use of geometric shapes can help create more complex drawings and paintings. In sciences, flat and spatial figures are used to explain concepts such as crystal structures or planetary orbits.

Therefore, understanding basic shapes is crucial for building a solid foundation in mathematics and other disciplines, allowing students to advance to more complex concepts in the future.

Here are some reliable sources that can assist in exploring this theme:

1. Book: 'Discovering Geometry' by David Brannan, Matthew Esplen, Jeremy Gray
2. Book: 'Fun and Delirious Mathematics' by Yakov Perelman
3. Video: TED-Ed - The Art of Geometry
4. Website: Just Mathematics - Spatial and Flat Geometry

Practical Activity

Activity Title: City of Basic Shapes

Project Objective:

This project consists of building a city, using basic shapes as the basis for constructions. The goal is to reinforce the understanding and recognition of basic geometric shapes, encourage the creative use of these shapes in problem-solving, and foster effective collaboration in team environments.

With this project, it is intended that students introduce the main concepts of flat and spatial geometry, recognize and distinguish the main geometric shapes, use these shapes creatively and collaboratively to create a city, applying these concepts in mathematics as well as in disciplines such as arts and sciences.

Detailed Project Description:

Students will work in groups of 3 to 5 people. Each group will be responsible for building a sector of the city. For example, one group may be in charge of building the residential part, another group the commercial/industrial part, and another the recreation sector (parks, squares, etc.). The estimated time for the project is over 12 hours per student and should be carried out over several weeks.

During the project, students should research and study flat and spatial geometric shapes, identifying them in the architecture and design of real buildings existing in their city or those they observe in videos and images on the internet.

Required Materials:

• Cardboard, colored paper, glue, scissors
• Colored pencils, markers, and/or paints
• Ruler, compass, and square
• Books and online resources on basic shapes and architecture.

Detailed Step-by-Step for Activity Execution:

1. Planning: Each group, with the help of the teacher, decides which sector of the city will be responsible for the construction. They should brainstorm to decide which types of buildings are present in their sector and make a general sketch of their building designs using the studied basic shapes.

2. Research: Students will research and study flat and spatial geometric shapes, identifying them in the architecture and design of real buildings.

3. Drawing: Students draw their buildings on a large piece of paper, representing the shapes they plan to use. They should be as detailed as possible.

4. Construction: Using the provided materials, students build their buildings in 3D. They can use cardboard for the bases and structures, and colored paper for decoration.

5. City Assembly: Once all buildings are ready, the teacher and students assemble the city, connecting all sectors. They can use cardboard to build roads and public spaces.

6. Report: Each group then writes a report detailing their design choices, the shapes used, the difficulties encountered, and how these were overcome. They should also reflect on what they learned from the project, and how collaboration skills affected the process and the outcome.

Project Deliverables:

At the end of the project, students must deliver:

1. The constructed city, with all buildings and structures built.

2. The original drawing planned by them.

3. A written report:

   • Introduction: Project context, the importance of studying basic shapes, and the activity's objective.
   • Development: Detailed description of the activities carried out, justification of the shape choices for constructions, challenges encountered and how they were overcome, and a discussion on the use of spatial and flat shapes in the city's construction.
   • Conclusion: Reflections on what was learned during the project, how geometric shapes were applied, and how collaboration skills contributed to the project's completion.
   • Bibliography: References to books, web pages, and videos used for research and project execution.

Students need to work on their reports in parallel with the city construction. The report and the city are integral parts of the project and complement each other.