Context

Introduction

Mathematics is present in many aspects of our daily lives, and having a clear understanding of its fundamentals allows us to solve practical problems in creative and efficient ways. One of these fundamentals is the concept of area, which allows us to quantify the space occupied by a flat figure. This becomes even more interesting when dealing with so-called composite figures, which are sets formed by two or more basic flat figures, such as triangles, squares, and rectangles.

Acquiring the ability to calculate the area of composite figures is a fundamental skill that facilitates various activities in everyday life - for example, when we need to calculate the amount of paint needed to paint an irregularly shaped wall, or decide the amount of grass needed to cover a garden with various shapes. In addition, this skill is also essential in various professions, such as architecture, design, engineering, among others.

Contextualization of the Theme

It is easy to understand the importance of calculating the area when thinking about real situations. Imagine, for example, that you are architects and need to design and calculate the amount of flooring needed to cover different rooms in a house. Or if you were farmers and needed to calculate the area of a field with various shapes to determine the amount of seeds you will need to buy.

To help visualize these theoretical concepts in a practical way, in this project we will propose a challenge of calculating areas that will involve not only mathematics but also arts, creativity, and, of course, teamwork.

Activity

Activity Title:

"Artistic Area: Discovering and Creating with Composite Figures"

Project Objective

Develop technical knowledge about calculating areas of composite figures and stimulate socio-emotional skills such as time management, teamwork, and creativity.

Project Description

In this project, students will be divided into groups of 3 to 5 members and will create an artistic mural. This mural must be composed of geometric figures that, when put together, form a composite figure. The challenge of the project is to calculate the total area of the mural and the images created, using the concepts of calculating the area of composite figures acquired in the classroom. After the construction of the mural, students will write a report detailing the process.

Required Materials

• Cardboard, cardboard, or any similar material that can be used as a base for the mural.
• Colored paper for the construction of the figures that will compose the mural.
• Ruler, square, compass.
• Scissors and glue.
• Pens, pencils, and eraser.

Step by Step

1. Planning: students must gather to define the theme of the mural and sketch which geometric figures will be used in the composition.
2. Initial Calculations: each chosen figure must have its area calculated and documented before it is even built.
3. Mural Construction: using the planned geometric figures, students will assemble the mural.
4. Total Area Calculation: after assembly, students must calculate the total area of the mural, mathematically proving the measurements that were previously planned.
5. Final Report: with the mural built and the calculations completed, students must prepare a report containing: Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

The project will be divided into two parts: the physical delivery and the written delivery.

Physical Part

Students will deliver the mural built with the geometric figures. Each figure used in the mural must have a label with the corresponding area calculation.

Written Part

A written report with the following topics:

• Introduction: a contextualization of the theme, its relevance and application in the real world, in addition to the work's objective.
• Development: the theory behind calculating the area of composite figures, the description of the mural construction process, the methodology used to calculate the area of the mural and the figures used, and the presentation and discussion of the results obtained.
• Conclusion: summarize the main points of the project, mention the learnings and experiences acquired during the development, and draw conclusions from the project.
• Bibliography: cite the sources of information used to carry out the project.

The report will be the fundamental part of the project, as it is where students will demonstrate the knowledge acquired and the practical application of these concepts. Therefore, in addition to technical rigor in executing the calculations, clarity in communicating ideas will be valued.