Contextualization

The study of shapes and their areas is essential in various aspects of life and human knowledge. Mathematics, specifically Geometry, is a discipline that provides insight into understanding and describing the physical world around us. Whether it is figuring out the amount of paint needed to paint a wall or designing a building, geometric principles and the ability to calculate areas are of great help.

The understanding of the area of flat shapes such as quadrilaterals, triangles, and circles is a foundational concept in Geometry. Thus, learning to calculate the area of these shapes helps develop logical and spatial reasoning, skills that are imperative in preparing for the increasing number of technology and data-driven careers in our society.

With this in mind, the project "Area of Shapes" aims to apply these concepts in a practical and challenging environment, fostering teamwork, effective communication, and time management. Throughout the project, students will have the opportunity to deepen theoretical knowledge, apply it practically, evaluate the effectiveness of their solutions, and reflect upon the outcomes.

Theoretical Introduction

Area is a measure that expresses the extent of a surface. In mathematics, the calculation of the area of a flat shape is done based on its linear dimensions. To calculate the area of different shapes, there are different formulas. For quadrilaterals like rectangles and squares, the formula is based on the product of the base and height. In a triangle, it is the product of the base and height divided by two. In the case of a circle, the formula involves the mathematical constant Pi, and the area is calculated using the formula Pi multiplied by the square of the radius.

It is important to note, however, that not all areas can be easily calculated using these basic formulas. Often, more complex shapes need to be decomposed into smaller, simpler shapes whose areas can be easily calculated. This technique is called decomposition into simpler figures.

This project will involve not only mathematics but also art, since the creation of forms and the visualization of areas are inherent to artistic and constructive thinking.

Practical Activity

Title: "Unveiling Areas through Art"

Project Goal:

To apply the concepts of calculating the areas of different geometric shapes (quadrilaterals, triangles, and circles) to create a collaborative artwork using colored paper, which must be planned and constructed by the group.

Detailed Project Description:

Divided into groups of 3 to 5 students, each team will be tasked with designing and creating a two-dimensional artistic representation using only colored paper. The challenge is that each piece of paper used in the artwork must have its area correctly calculated and recorded, building up to a final report that will be a central piece in the assessment of the project.

The project will be divided into three phases: Planning and Design, Execution, and Documentation. The total duration of the project is approximately 12 hours per student.

Required Materials:

• Colored papers of various sizes and colors
• Ruler or measuring tape
• Scissors
• Glue
• Pencils and erasers
• Paper for drafting and planning
• Computer with internet access for research and final report preparation

Step by Step:

Phase 1: Planning and Design

1. Discuss as a group and choose a theme for the artistic representation.
2. Make a sketch of how the representation will look, identifying the different geometric shapes to be used.
3. Calculate the area of each shape that will be used in the artwork and make an estimate of the amount of paper needed for each color.

Phase 2: Execution

1. Using the measurements and calculated area from the planning, cut out the geometric shapes from the colored paper.
2. Assemble the artistic representation according to the plan, gluing the pieces of paper in the appropriate place.

Phase 3: Documentation

1. Develop a detailed report describing the planning and execution process of the project, indicating the formulas used to calculate the areas and how these values were obtained.
2. Include images of the project at different stages of execution.
3. Include a section on the difficulties encountered and how the group overcame them, as well as the learning acquired from the project.
4. Conclude with a general overview of the project and the lessons learned.
5. Correctly cite all references used.

Project Deliverables:

The final project deliverables include the finished artwork and the written report. The artwork should be presented in the classroom, accompanied by a brief presentation explaining the design choice, area calculations, and project execution.

The written report should contain all the area calculations done, as well as a detailed description of how the artwork was planned and executed. The writing of the report should be a collaborative effort, where all members of the group contribute to its elaboration. The report should clearly and objectively connect all the practical parts of the project to the theories on calculating the area of different geometric shapes.

The report should be divided into the following sections: introduction, development, conclusions, and references used. In the introduction, the project and its objectives should be contextualized. In the development, the students should describe all the steps, from the planning to the finalization of the project, explaining how the areas were calculated. In the conclusions, the students must make a critical analysis of the project, the challenges faced, the results obtained, and what they learned during the process. Finally, in the references, all the sources consulted to carry out the project must be included.