Contextualization

Mathematics is a fascinating tool for deciphering the universe we live in. Among its various fields of study, Geometry stands out for allowing us to understand and represent the three-dimensional world we are part of. Through the study of triangles, one of the simplest and fundamental polygons, we can develop spatial vision, as well as apply it in various areas such as Architecture and Engineering, as they are the basis for the study of all other shapes.

In ancient times, triangles were used by the Egyptians and Greeks for calculations in the construction of pyramids and in the elaboration of theorems, respectively. Nowadays, the analysis of triangles is used in many everyday applications, such as GPS, video games, calculating inaccessible distances, and even predicting the financial market. Therefore, learning about triangles is not only an academic exercise but also an extremely useful skill in real life!

Introduction

The triangle is a flat geometric figure bounded by three sides. The points of intersection of the sides are called vertices and the angle formed by them, internal angles. The classification of triangles is basically based on two criteria: by the measurement of the sides and by the measurement of the angles. Regarding the sides, triangles can be classified as: Scalene (three sides with different measurements), Isosceles (two sides with the same measurement), and Equilateral (three sides with the same measurement).

Regarding the angles, we can classify them as: Acute-angled (three angles with measurements less than 90°), Right-angled (one angle with a measurement of 90°), and Obtuse-angled (one angle with a measurement greater than 90°). These concepts are the basis for our study and will allow us to explore the geometry of triangles more deeply.

In our project, we will explore the universe of triangles, classifying them, constructing them, and even finding them in the world around us!

Practical Activity

Activity Title: "Triangles Around the World"

Project Objective:

In this activity, the objective is to identify, analyze, and classify the different forms of triangles in our daily lives, fostering perception and understanding of their properties in geometry, thus enabling meaningful learning and the application of theoretical concepts in practice.

Detailed Project Description:

Students, in groups of 3 to 5, will have one month to develop this activity. It will be necessary for students to investigate, identify, and classify triangles present in everyday scenarios, such as in constructions, objects, logos, etc. Additionally, they must build a model representing a daily life scene with various applications of triangles.

Required Materials:

1. Camera (can be a cellphone camera)
2. Various paper materials (color paper, cardboard, etc.)
3. Glue
4. Scissors
5. Colored pens
6. Ruler and protractor

Detailed Step-by-Step of the Practical Activity:

1. Form a group with your classmates. Each group should have 3 to 5 students.
2. Discuss with your classmates where you can find triangles in the world around you (in architecture, nature, objects, etc.)
3. Take photos of the triangles you find and note where they were found.
4. Each group must choose at least 15 different triangles.
5. Classify each triangle found according to the sides and angles.
6. Create a model representing a daily life scene with various applications of triangles. Use the materials to build your model and make sure to represent all types of triangles studied.
7. Document the entire research, classification, and construction process in a report.

The report should contain the following elements:

• Introduction: Here you should contextualize the theme, present the importance of triangles in daily life, and the project's objective.
• Development: Theoretical explanation of triangle concepts, types, and characteristics. Additionally, detail the methodology used to find the triangles, how and where they were found, how they were classified, and the challenges encountered. Present photos of the identified triangles with their classifications. Also, explain in detail the construction of the model, which materials were used and why they were chosen. Describe the triangles present in the model and their classifications.
• Conclusions: In this part, reaffirm the main points addressed about triangles, explain what you learned from the activity, the importance of teamwork, and how the experience of discovering triangles applied in real life was.
• Bibliography: Cite the sources you used for research and to base the project's construction.

This practical activity will provide technical skills, such as triangle classification, and socio-emotional skills, such as time management, teamwork, communication, conflict resolution, critical thinking, among others.