Contextualization

Mathematics is one of the most ancient disciplines in the world. Geometry, one of its branches, has played a fundamental role in the development of scientific knowledge since antiquity. Among the various geometric shapes, triangles have great value and an infinite number of practical and theoretical applications.

Introduction

Triangles are plane geometrical figures composed of three sides and three angles. The sum of the interior angles of a triangle is always equal to 180 degrees. Triangles can be classified based on their sides and their angles. In the first case, we have the equilateral triangle (all sides and angles are equal), the isosceles triangle (two equal sides and one different) and the scalene triangle (all sides and angles are different).

The classification of triangles is a fundamental topic in the teaching of mathematics because it is the basis for studying the properties of these figures and, consequently, for solving complex problems that involve areas and volumes, in addition to the application in several fields of exact sciences.

The Importance of Triangles

In our daily lives, triangles are present in many objects and structures that surround us, such as roofs of houses, bridges, statistical graphs, graphic design, architecture, physics, etc. They are also used in many scientific fields to solve complex problems, such as physics, engineering, computer science, among others.

In engineering, for example, the strength and stability of many structures, such as bridges and skyscrapers, depend directly on the correct understanding and application of the concepts associated with triangles. In physics, triangles are fundamental for studying vectors and solving problems that involve movement and forces. In geography and astronomy, they are used to calculate inaccessible distances.

Practical Activity: "Building and Classifying Triangles - A Multidisciplinary Approach"

Project Goal

This project aims to deepen students' knowledge about the classification of triangles, their properties and practical and theoretical applications in the real world. It also seeks to enhance students' teamwork, communication, research, writing, time management and critical thinking skills.

Detailed Project Description

This project will be carried out by groups of 3 to 5 students and should last approximately two weeks. It will be divided into two main parts: a research, discussion and theoretical study part and a practical application part.

Part 1: Research, Discussion and Theoretical Study

Students will research the following:

1. The theory behind the classification of triangles, the conditions for the existence of triangles and the resolution of metric problems of triangles.
2. Practical applications of triangles in different areas of knowledge, such as engineering, geography, physics and astronomy.
3. Examples of how the classification of triangles and their properties can influence the solution of everyday problems.

Students should discuss the information collected, raise hypotheses, question their conjectures and validate the information collected.

Part 2: Practical Application

Students will have to choose one of the practical applications of the triangles researched and plan a project that demonstrates the usefulness and importance of triangles and their classifications. The project can be a model, an experiment, software, a video, a presentation, a play, etc.

Required Materials

The necessary materials will depend on the type of practical project chosen by the students. However, in general, students will need access to the internet to search for information and materials to carry out the practical project.

Detailed Step-by-Step Guide for the Activity

1. Formation of groups and assignment of functions: each student will have a specific role in the group, such as researcher, writer, builder, presenter, etc.
2. Research and study: students should research the indicated topics and hold group discussions.
3. Planning of the practical project: students should choose a practical application of triangles and plan the execution of the project.
4. Execution of the practical project: students should execute the project according to the plan.
5. Writing the report: students should write a report on the project, containing introduction, development, conclusions and bibliography.
6. Project presentation: students should present the project to the class.

Project Deliverables

Students must deliver:

1. The practical project: a demonstration of a practical application of the classification of triangles.
2. The written report: a document in which students must contextualize the theme, its relevance and practical application, the theory behind the classification of triangles, the detailed description of the practical project, the methodology used and the conclusions that were drawn.
3. An oral presentation: where the group must present the practical project and explain the theory and conclusions drawn.

The report will be an opportunity for students to show their understanding of the concepts involved, applying them in practice and connecting them with the real world. They should also clearly show how they managed to work together as a group, how they managed their time and how they solved any problems that arose.

The report should also include a bibliography, where students will indicate the sources they used for the theoretical research, and the justification for the choice of the practical project.