Contextualization

Welcome, dear students, to the amazing world of Geometry! In this project, we will focus on one of the most fundamental shapes in Geometry - the Triangle. Have you ever noticed how triangles are present in everything around us? They are in homes, buildings, toys, artworks, and even in nature.

Triangles are flat geometric figures formed by three non-collinear points connected by line segments. These line segments are called the sides of the triangle, and the points where these sides meet are called vertices. A peculiarity of triangles is that the sum of the internal angles is always equal to 180˚. No matter the size of the triangle, this rule never changes!

Triangles can be classified in two ways: by their sides and by their angles. Regarding the sides, we have: scalene (all sides different), isosceles (two sides equal), and equilateral (all sides equal). Regarding the angles, we have: acute-angled (all angles smaller than 90˚), right-angled (one angle of 90˚), and obtuse-angled (one angle greater than 90˚). Each has its peculiarities and applications.

Importance of Triangles

Triangles have many important applications in the real world. They are often used in engineering and architecture for their structural stability. Additionally, triangles are the basis for trigonometry, a branch of mathematics that we study more in-depth in high school and that allows the resolution of numerous practical situations, from measuring inaccessible heights to air and sea navigation.

Triangles also have a cultural and aesthetic significance. You can find them in fabric patterns, designs, paintings, and even in logos. They are also used in diagrams and charts to represent relationships and connections. Therefore, learning about triangles will help you understand and appreciate the world around you in a new way.

For our learning journey, I recommend the following sources as study and research bases:

1. Very Easy Mathematics - Triangles: An excellent online resource that offers a detailed introduction to triangle concepts.
2. Just Mathematics - Triangles: A useful online resource that covers the various types of triangles and their angles.
3. World Education - Triangles: This article delves into the classification of triangles.

Practical Activity: Building and Classifying Triangles

This activity will start in the classroom but will soon expand beyond it. You will work in groups of 3 to 5 students, and the project will have a total of 4 hours of execution.

Activity Objective

The main objective of this project is for you to be able to identify, build, and classify different types of triangles. Additionally, we will work as a team, develop time management skills, stimulate creativity, and communication.

Project Description

Each group must create three types of triangles (equilateral, isosceles, and scalene) and three types of triangles in terms of angles (acute-angled, right-angled, and obtuse-angled) using popsicle sticks. Then, they will make an exhibition, explaining the classification of each triangle and its characteristics.

Necessary Materials

• Popsicle sticks
• Glue
• Colored pens
• Cardboard
• Ruler
• Protractor

Step by Step

1. Divide into groups of 3 to 5 students.
2. Each group member should research about a specific type of triangle.
3. With the popsicle sticks, assemble the six different triangles.
4. On the cardboard, write the name of each triangle and its main characteristics.
5. Use the protractor to measure the angles of each triangle and the ruler to measure the sides. Write down this information on the cardboard.
6. Prepare a presentation about the classification of triangles and their characteristics for the rest of the class.
7. Finally, write a report on the activity, containing the sections: Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

Groups must deliver the following items:

1. Exhibition of the triangles: Each triangle must be displayed on a flat surface, such as a table or panel, containing information about its characteristics (sides and angles). Presentations will be made to the entire class.

2. Project report: Each group must produce a report that should have four sections:

   • Introduction: Provide context for the project theme, the importance of triangles in our daily lives, and the project's objective.
   • Development: Explain the theory about triangles, how you carried out the activity (triangle construction), and what the results were (measurements of sides and angles).
   • Conclusions: Summarize the main points of the project, describe what you learned from the experience, and what conclusions your group drew about the classification of triangles.
   • Bibliography: List the sources your group used to research the project.

This activity involves not only mathematical theory but also practical and communicative skills, as you will be building something with your hands and then sharing your findings with others.

I am looking forward to seeing the amazing work you will produce!