Contextualization

Triangles are geometric figures formed by three straight lines that intersect at three different points. They are one of the most basic shapes in geometry and can be found in many places in the world around us, from architecture to art. In this project, we will deepen our knowledge about triangles and understand their properties and unique characteristics.

Triangles are quite useful in various areas of knowledge. In engineering and architecture, for example, they are used to calculate distances and angles, helping to build structures more efficiently. In art, triangles are also widely used, often being used in paintings and sculptures to create a sense of balance and stability.

Introduction

Triangles can be classified in different ways. They can be categorized based on the size of their angles (acute, right, or obtuse) or by the length of their sides (scalene, isosceles, or equilateral). Each of these types of triangles has its own unique properties, and understanding these aspects is fundamental to a good knowledge of geometry.

There are several theorems and postulates involving triangles that are crucial for understanding many aspects of mathematics. Some of them, such as the Pythagorean theorem and the properties of isosceles and equilateral triangles, will be the focus of this project. Additionally, we will understand how these concepts apply to real-world problems.

Triangles are also connected to other important mathematical concepts, such as calculating areas and perimeters. Algebra can also be applied to triangles to solve complex problems. In this project, we will have the opportunity to explore all these connections and deepen our understanding of these concepts.

Practical Activity

Activity Title: Building the World with Triangles

Project Objective

In this activity, each group must engage in an interdisciplinary practice involving Mathematics and Social Sciences, to understand the different types of triangles and apply them in a real-life scenario. The work aims to acquire a solid understanding of triangles and their properties, as well as develop skills in research, teamwork, time management, and presentation.

Detailed Project Description

The project is based on building a model of a city using only triangular shapes. Each group will be responsible for designing and constructing the model, considering the use of different types of triangles. This project will allow students to directly apply the knowledge acquired in the classroom, especially regarding the concepts of types of triangles, the Pythagorean theorem, and the calculation of area and perimeter.

Required Materials

1. Colored cardboard paper.
2. Ruler.
3. Protractor.
4. Scissors.
5. Glue.
6. Pencil and eraser.
7. Graph paper for project sketch.
8. Painting materials (optional).
9. Research materials - books, internet access, etc.

Detailed Step-by-Step for Activity Execution

Part 1: Research and Planning (3 hours)

1. Gather as a group and decide on the type of city that will be represented in the model.
2. Research the types of triangles and their practical uses in real life.
3. Discuss how different triangles can be applied in the construction of the city.
4. Develop a sketch of the model, indicating where each type of triangle will be applied.

Part 2: Model Construction (6 hours)

5. Based on the sketch, cut out the triangles on the cardboard paper using the ruler, protractor, and scissors.
6. Assemble the city structures by gluing the triangles.
7. Review the model to ensure it aligns with the sketch. Make necessary adjustments.

Part 3: Documentation and Presentation (3 hours)

8. Write the project report, describing the entire process from research to model completion.
9. Prepare an oral presentation to demonstrate the model and explain the decisions made during construction.
10. Review the report and presentation with the rest of the group to ensure all members contributed and are aware of the content.

Project Deliverables

The completion of the project will result in two main deliverables: the city model, meticulously constructed with triangular shapes, and a detailed written report.

The written report should address the four main topics: introduction, development, conclusions, and bibliography.

1. The introduction should contextualize the use of triangles in the city construction, the motivation behind the city choice, and the relevance of this concept in real life.
2. The development section should describe the theory of triangles, explain in detail the methodology of model construction, and present the results obtained, i.e., the model itself and the complexities faced and overcome during construction.
3. The conclusion should summarize the main points, highlight the learnings obtained, and the conclusions drawn from the project.
4. The bibliography should indicate all resources used during the research, such as books, websites, videos, etc.

Students must ensure that the application of each type of triangle is clearly demonstrated and explained in the model and report.

Remember, this is a group project. Therefore, teamwork, effective communication, and time management will be essential for the project's success.