Contextualization

Theoretical Introduction

Geometry is one of the fields of mathematics that studies aspects of space, including concepts such as size, shape, distance, proportions, volume, among others. One of the fundamental concepts in geometry is the concept of area. In this project, we will focus specifically on determining the area of a specific geometric shape: the hexagon.

The hexagon is a flat geometric figure that has six sides. When these sides are all equal, we have what is called a regular hexagon. The regular hexagon has several interesting properties, and one of them is the ease with which we can determine its area.

To calculate the area of a regular hexagon, we use the formula A = (3√3/2)*s² where 's' is the length of any side. This formula allows us to calculate the area of the hexagon if we know the length of its sides.

Contextualization

The fascinating geometry of the hexagon can be found in various situations in our daily lives. From the cellular pattern of the honeycomb produced by bees, the shape of some snowflakes and basaltic rocks, to even the pattern of certain fabrics and architectural structures. Studying the area of a hexagon is not only a theoretical question but also of great practical relevance.

The relevance of studying the area of the hexagon transcends mathematics, finding applications in various areas of knowledge, such as biology, chemistry, engineering, and architecture. Furthermore, the ability to calculate the area of a hexagon is a fundamental skill in disciplines such as physics, geography, and computer science.

Practical Activity - "The Universe of the Hexagon: Mathematics and Art in Harmony"

Project Objectives:

1. Explore the geometry of the hexagon, with an emphasis on calculating its area.
2. Teach the application of mathematics in solving real-world problems.
3. Demonstrate the interrelationship between mathematics, art, and design.
4. Encourage teamwork and collaboration among students.
5. Develop research, writing, and presentation skills.

Project Description:

In this project, student groups will be challenged to create an artistic mural composed of different hexagons. Each hexagon will have a different size, and each group will be responsible for calculating the area of each hexagon that makes up the mural. In addition, students should research and include in the mural examples of where the hexagon is found in nature, art, and design.

The second part of the project will involve writing a detailed report explaining the process of creating the mural, the calculations involved, and the discovered applications of the hexagon in nature and in different fields of knowledge.

Required Materials:

1. Cardboard paper in various colors
2. Ruler
3. Pencil
4. Compass
5. Scissors
6. Glue
7. Computers with internet access for research.

Step by Step:

1. Group Formation: Students will be divided into groups of 3 to 5 members. Each group will receive a set of hexagons of different sizes to work on.

2. Research and Drawing: Each group should research examples of where hexagons are found in the real world. Based on the research, they will create geometric drawings inside the hexagons, representing their findings.

3. Area Calculation: Each group will be responsible for calculating the area of each hexagon that makes up their mural. They will document their calculations and how they arrived at them.

4. Mural Assembly: The groups will assemble their murals, joining the hexagons worked on in a harmonious way, forming a large artistic panel.

5. Report Elaboration: Each group will write a report explaining how they calculated the area of their hexagons, the discoveries made during the research, and how these findings were incorporated into the art created in their hexagons.

Project Deliverables:

• Artistic Mural: Each group will present the created mural, with an explanation of the drawings and the creative process.
• Written Report: Each group must submit a report explaining the theory used to calculate the area of the hexagons, the methodology used, the discoveries made during the research, and how these were applied in the creation of the mural. The report should follow the structure of: Introduction, Development, Conclusion, and Bibliography.

When writing the report, students should be encouraged to connect the theory learned with the practice carried out, making clear links between the calculations made and the real objects studied. Furthermore, students should be encouraged to reflect on the value of mathematics in the real world and on the teamwork processes that facilitated their discoveries and learning.