Contextualization

Mathematics, one of the oldest disciplines known to humanity, presents a vast array of concepts, ideas, and properties that can help us understand the universe around us. One of these fundamental concepts is angles.

Angles are a measure of rotation or curvature between two intersecting lines. You can find angles everywhere, from the drawing of a triangle to the structure of a skyscraper. The classification of angles is very important for the understanding of many mathematical and physical concepts and has several practical applications.

To understand the importance of classifying angles, imagine this: You are an architect and you are designing a building. The angle you choose for the windows, the shape of the structure, the courtyards, and many other aspects of your project can significantly affect the appearance, functionality, and even the safety of the building. Now, think about how difficult it would be without knowing what an angle is, or how to classify them.

The study of angles is fundamental in various areas such as engineering, architecture, arts, and even in sports. The correct classification and measurement of angles allow the construction of various objects in our daily lives, from the formation of a simple ladder to the construction of a gigantic bridge. In sports, the correct angle of kicking a soccer ball can determine whether the team scores a goal or not.

Now that you understand the importance of classifying angles, let's delve a little deeper into this fascinating subject. To do so, you can use the following resources to delve deeper and research more on the topic:

• Book: "Mathematics - A New Approach" by James Stewart. (This book can be found in the school library).
• YouTube Video: "Angle Classification".
• Website: "Didactic Mathematics", a site full of mathematical content in a simple and didactic way.

Practical Activity

Activity Title: Creating and Classifying Angles in the Real World

Project Objective

The objective of this project is to develop students' ability to identify and classify the types of angles present in real-world objects, through the creation of a three-dimensional model.

Detailed Project Description

This project will challenge students to research, plan, and build a three-dimensional model that contains a series of different angles, including acute, right, and obtuse angles.

To make the project more interesting and applicable to the real world, the models must be based on a real building or architectural structure.

Additionally, as part of the work, students should document the entire process in a report, which will include:

• Introduction (contextualization, application of angles in the real world, project objective)
• Development (theory, detailed project description, methodology, results)
• Conclusion (summary of main points, learnings, and conclusions)
• Bibliography.

Required Materials

• Cardboard
• Ruler
• Pencil
• Colored pens
• Glue
• Scissors

Detailed Activity Steps

1. Research (2 hours)

Start with research on buildings that have a variety of different angles. Select the building that will serve as inspiration for the model.

2. Model Sketch (2 hours)

Sketch a drawing of the building, highlighting where the acute, right, and obtuse angles are located.

3. Model Construction (4-5 hours)

Build the model of the building from the sketch, making sure that all angles are represented correctly.

4. Project Documentation (1-2 hours)

Document the entire process in a report. Include images of the final model and highlight where each type of angle is located and why it was used in that specific part of the building design.

5. Presentation (1 hour)

Prepare a project presentation to present to the class, including an explanation of your model and the mathematical concepts it incorporates.

Project Deliverables

• Three-dimensional model of a building that incorporates different types of angles.
• Detailed project report, including: Introduction, Development, Conclusion, and Bibliography.
• Oral presentation of the project to the class.

In the written document, students should complement the practical work with theoretical concepts and real-world applications of angles. It is important that, in addition to describing the project and methodology used, students comment on the results obtained and discuss what they learned from the experience.