Contextualization

We are surrounded by angles! They are everywhere: in the structures of buildings, in the objects in our homes, in nature, and even in the positions our bodies can assume. But what are angles? Why are they so important in mathematics and in real life? And how are they classified?

Angles are a measure of rotation or inclination between two lines that meet at a point. They are used in a wide range of practical applications, from engineering and architecture to sports and video games. The classification of angles is a basic concept in mathematics that helps to understand and solve complex problems.

Introduction

Angles can be classified based on the measurement of their degrees. An acute angle has less than 90 degrees, a right angle has exactly 90 degrees, an obtuse angle has more than 90 degrees but less than 180, and a straight angle is exactly 180 degrees. Understanding and correctly applying these concepts is fundamental to the study of geometry, trigonometry, and a series of other disciplines.

However, classifying angles is not just a matter of memorizing definitions. It is also a matter of understanding how these definitions relate to the world around us. For example, architects and engineers use the classification of angles to design buildings and bridges. Soccer players can use knowledge of angles to calculate the best way to kick a ball.

In this project, we will explore the classification of angles in a practical and engaging way. We will carry out activities that help visualize and understand angles and where they apply in our daily lives.

To provide a basis for you to deepen your understanding of the topic, we suggest you use the following resources:

1. Khan Academy - 'Angles: introduction and types'. Available at: Khan Academy

2. Só Matemática - 'Classification of Angles'. Available at: SoMatematica

3. YouTube - 'Matemática Rio with Prof. Rafael Procopio'. Available at: Matematica Rio

4. YouTube - 'Simple Mathematics - Classification of Angles'. Available at: Matematica Simples

Practical Activity

Activity Title: 'Angle Engineering'

Project Objective

This project aims to provide a practical and fun experience with the classification of angles using the construction of a mini city, where students need to design and build buildings, streets, and bridges, all with specific angles.

Detailed Project Description

Students will work in groups of 3 to 5 people to build a mini city on a large piece of cardboard. Each group will be responsible for drawing and building different aspects of the city, such as buildings, bridges, streets, and parks, all taking into account the classification of angles.

During the project, students will use not only their knowledge of mathematics but also arts and geometry skills to create the structures.

To make the challenge even more engaging, groups should develop a short story for their city, explaining why each element was designed the way it was and how angles were applied.

Required Materials

1. Large piece of cardboard (at least 1m x 1m)
2. Rulers and protractors
3. Pencils and markers
4. Colored paper
5. Scissors and glue

Detailed Step-by-Step

1. Each group should start by sketching the city's floor plan.
2. Then, they should begin to draw and build each building, street, bridge, and park, always taking into account the angles.
3. Each element of the city should be marked with the type of angle used in its creation.
4. The creation of the city's story should be developed in parallel to the project, with all elements of the story coherent with the city built.
5. At the end of the project, each group should present their city and the story they created to the class, explaining how angles were applied in each element.

Project Deliverables

At the end of the project, in addition to the practical work, students must produce a report containing:

1. Introduction: Description of the relevance and application of angles in the real world and a summary of the practical activity carried out.
2. Development: Theoretical discussion on the classification of angles and detailed description of the practical activity carried out, including the methodology used, detailed description of the city's construction, discussion, and analysis of the results obtained.
3. Conclusions: Reflection on the project experience, highlighting the learnings obtained, the skills developed, and the conclusions reached about the application and classification of angles.
4. Bibliography: References to the materials and research sources used for theoretical foundation and project implementation.

The report will be an essential part of the project deliverables, where students must demonstrate not only the theoretical understanding behind angles but also how they were able to apply this knowledge in practice, describe the challenges encountered, and the creative solutions found.

Each group must submit the report with the project development along with the mini city built.