Contextualization

What are polygons?

Polygons are closed geometric figures formed by line segments that touch each other at their ends, but do not intersect. The word 'polygon' comes from Greek and means 'many angles'. In fact, a polygon has as many angles as it has sides.

Polygons are classified according to the number of their sides. A polygon with three sides is a triangle, with four sides is a square, and so on. In addition, polygons can also be classified according to their regularity. Regular polygons are those in which all sides and angles are equal. Irregular polygons, on the other hand, do not have all sides and angles equal.

When we refer to the measurements of the sides and angles in a polygon, we are dealing with concepts such as perimeter and area, which are fundamental for the understanding of geometry and, by extension, the world around us.

Why learn about polygons?

Learning about polygons presents an incredible opportunity for students to see mathematics applied in the real world. From architecture to art, science, and engineering, polygons are used to solve problems and create beautiful designs.

For example, engineers use the understanding of polygons to design structures with specific shapes that can withstand certain loads and forces. Artists, on the other hand, can use polygons to create complex patterns and designs in their works.

Mastering the fundamental concepts of geometry, such as understanding the properties of polygons, is essential for problem-solving in various areas of knowledge.

Activity

Activity Title: 'Creating and Deconstructing Polygons'

Project Objective:

The objective of this project is for students to develop a deep understanding of polygons, particularly equilateral triangles and squares, through the creation of physical models, their deconstruction, and the development of algorithms/flowcharts that indicate this process.

Project Description:

Students will be divided into groups of 3 to 5 people. Each group must build models of regular polygons (here we will focus on squares and equilateral triangles) using popsicle sticks and glue, knowing the measure of the sides beforehand. The idea is for them to explore their properties, number of sides, angles, etc. during construction.

After building the polygons, the groups will need to deconstruct them in an orderly manner, recording each step. The deconstruction process will represent the creation of an algorithm/flowchart.

Required Materials:

• Popsicle sticks
• Ruler
• Glue
• Paper and colored pens for drawing
• Camera or cell phone to record each step of the process

Step by Step:

1. Using the popsicle sticks, measure and mark the length that will correspond to the sides of the polygons to be built. (Important: all sides of the polygons must have the same measure.)

2. Glue the popsicle sticks together to form the polygons: a square and an equilateral triangle. Make sure all sides have the same measure.

3. After building the polygons, start the deconstruction process of these figures, recording each step, both through written notes and photographs.

4. Based on these notes and photographic records, create an algorithm or a flowchart that represents the steps of the deconstruction. This flowchart will be a visual way to represent the steps to create a polygon.

5. Finally, students should write a report detailing the entire process, from the construction of the polygons and the deconstruction to the creation of the flowchart or algorithm.

Project Delivery:

The project delivery will consist of two parts:

1. The flowchart or algorithm that students created representing the deconstruction of the square and the equilateral triangle.

2. A written report containing:

   • Introduction: In this topic, students must contextualize the theme, explain the relevance of polygons in daily life and in various fields of knowledge. Additionally, they should detail the origin and purpose of the project.

   • Development: Students must describe the theory behind polygons, explain in detail the activity they carried out (the construction and deconstruction of polygons and the creation of the deconstruction algorithm), indicate the methodology used, and finally present and discuss the results obtained.

   • Conclusion: Students must conclude the work by highlighting key points, explaining the learning obtained, and drawing conclusions about the project.

   • Bibliography: Students must indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.