Contextualization

Mathematics is a universal language that permeates various aspects of our daily lives, and one of its fundamental topics is the study of angles. Like numbers, angles are a way to represent quantity, but instead of representing a count of objects, they represent the measure of differences between directions. That's why, without angles, we would be unable to navigate the world, build solid structures, or understand the patterns formed by light, sound, and other types of waves.

Angles are an integral part of geometry, a branch of mathematics that studies the sizes, shapes, and properties of space. In addition, angles are also essential for trigonometry, which deals with the relationships between angles and the sides of triangles. Trigonometry, in turn, has applications in diverse areas such as engineering, physics, computer graphics, and even hobbies like music and photography.

Perhaps the most obvious application of angles is in navigation. From the time of ancient navigators, who used sextants to measure angles in the stars and thus determine their direction and position, to the present day, with GPS systems that use spherical trigonometry to calculate our position on Earth based on satellite signals, angles are fundamental to our ability to travel the world. But angles are also used to build buildings, design machines, analyze weather patterns, and many other things.

To delve deeper into the study of angles, we recommend the following sources:

• Book: "Fundamentos de Matemática Elementar - Vol. 3 - Trigonometria" by Gelson Iezzi and Carlos Murakami. This book, which is part of a well-known high school mathematics series, offers a solid introduction to trigonometry, with many exercises for practice.
• Website: Khan Academy - This educational website has a series of videos and interactive exercises to help understand the basic concepts about angles.
• Video: "Ângulos - Matemática Rio com Prof Rafael Procopio" - This video provides an overview of the most basic concepts related to angles in an easy-to-understand way.

Practical Activity

Activity Title: "Architect Angle - A Geometry Project"

Project Objective:

The project aims to enhance students' understanding of angles, their classifications, properties, and practical applications, especially in the field of architecture.

Detailed Project Description:

Students, divided into groups of 3 to 5, will be challenged to design a model of a building, park, or any other architectural structure. This structure must incorporate and highlight the different types of angles (acute, right, obtuse, straight). Students will have the freedom to choose the scale, materials, and complexity of the model, as long as the different types of angles can be clearly identified.

Required Materials:

Students will need materials to build the models such as cardboard, colored papers, glue, scissors, ruler, protractor, and any other items they deem necessary for their model.

Step by Step:

1. Group Organization: Students will be divided into groups of 3 to 5 people.
2. Project Selection: Each group must decide on the type of model they will create.
3. Project Drawing: Groups must then create a schematic drawing of their model identifying the angles used.
4. Model Construction: Groups must then build the model using the available materials.
5. Angle Analysis: Using a protractor, the angles present in the model must be measured and classified.
6. Report Preparation: Each group must produce a report that includes project details, angles used and their measurements, the justification for the choice of these angles, as well as any difficulties encountered and how they were resolved.

Deliverables and Connections:

Each group will present, at the end of the project, the created model and a written report. The report should be divided into introduction, development, conclusions, and used references.

1. In the introduction, students should provide a summary of the project, its objectives, and the relevance of studying angles. They should also indicate the chosen structure for the model and its justification.
2. In the development, students should mention theories and concepts related to angles, classifying them, presenting their activity, and the results obtained (angle measurements). Here students can explain how each type of angle was incorporated into the model and what its function is in the structure in question (aesthetic, functionality, etc.).
3. In the conclusion, students should discuss the results obtained, the skills acquired, the difficulties faced, and how they were overcome.
4. In the bibliography, all research sources used in the project should be listed.

By the end of the process, students should have gained a deeper understanding of the classification and application of angles in real-world situations, as well as developed skills in teamwork, time management, creative thinking, and problem-solving.