Contextualization

Introduction

The rhombus is a flat geometric figure that belongs to the group of quadrilaterals, just like the square, rectangle, and trapezoid. This family of figures has some fundamental characteristics in common, such as the sum of internal angles equal to 360º. But the rhombus has some peculiarities that make it special. The four sides of a rhombus have the same measure, and this brings some interesting implications, such as the existence of two pairs of equal opposite angles.

To deeply understand a rhombus means to discuss and explore important geometry concepts. By exploring these properties, the ability to visualize and manipulate geometric figures mentally is developed.

Furthermore, understanding the rhombus provides tools for solving various mathematical problems. Topics such as similarity of figures, area of flat figures, and trigonometry are just a few examples where rhombuses frequently appear.

Relevance in the Real World

The world is full of rhombuses! This geometric figure is everywhere, from the shape of some crystals to the structure of certain molecules. It is used in design and architecture for being a simple and harmonious shape. In nature, the rhombus shape is seen in leaves, flowers, and even in the shape of some animals. Knowing the geometry of the rhombus and its properties can help us better understand the world around us.

Rhombuses are also widely used in industry. For example, in civil engineering, rhombus shapes are used to maximize strength and minimize the weight of steel structures. In graphic design, the rhombus shape is used to create attractive visual patterns. In sports, the rhombus shape is used in baseball diamonds and soccer fields.

Atividade Prática

Activity Title: "Building Rhombuses in the Real World"

Project Objective

In this project, the group of students will be challenged to find and analyze rhombuses in real life and to create a rhombus using various materials available in the school environment or at home. Through the analysis and construction of the rhombus, students will explore and understand the properties of this geometric figure in a practical and participatory way.

Detailed Project Description

This project will be carried out by groups of 3 to 5 students and will last for one month. It will be divided into four phases: Identification, Documentation, Construction, and Analysis and Report.

Phase 1 - Identification:

Students must search for examples of rhombuses in the surrounding environment, whether at school, in the city, or at home. The goal is to find and record at least five examples of rhombuses in real life.

Phase 2 - Documentation:

Students must document each example found, recording the location, the measurements of the rhombus (if possible), and taking a photo or drawing of it. If possible, they should also try to identify the reason for the presence of the rhombus in the observed location (tile layout, product design, etc.).

Phase 3 - Construction:

Students must build a rhombus using various materials such as ruler, compass, paper, cardboard, rope, etc. Students must document the construction process and take measurements of the sides and angles of the rhombus.

Phase 4 - Analysis and Report:

Students must analyze the documented examples and the constructed rhombus, relating them to the theoretical concepts studied. A report must be written containing the following sections: Introduction, Development, Conclusions, and Bibliography.

Required Materials

1. Notebook for notes.
2. Digital camera or cell phone with a camera.
3. Ruler, compass, protractor.
4. Materials for rhombus construction (paper, cardboard, rope, etc.).

Detailed Step-by-Step

1. Form groups of 3 to 5 students and discuss the concepts of rhombus learned in class.
2. Go in search of examples of rhombuses in the surrounding environment.
3. Document each example found with photos or drawings, note the location and measurements of the rhombus, if possible.
4. Back in the classroom or at home, build a rhombus with the available materials. Document the construction process and the measurements of the constructed rhombus.
5. Analyze the examples found and the constructed rhombus in relation to the theoretical concepts studied.
6. Write a report containing the following sections: Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

The final result of the project will be a report containing all the details of the project, including observations of the rhombuses found, the process of constructing the rhombus, the analyses made, and the connection with the theoretical concepts. The report should be written clearly and precisely, depicting all stages of the project, from forming the groups to the final analysis of the rhombuses.

Additionally, the constructed rhombus must be presented along with the photographic mapping of the rhombuses found in real life. It is important that the analysis of the rhombuses is present in the report, with a detailed description of how each rhombus fits into the studied theoretical concepts.

The introduction section in the report should contextualize the theme and its relevance, while in the development section, students should report on the practical application of rhombus concepts. The conclusion should contain the observations and learnings obtained throughout the project, ending with a bibliography of the sources consulted during the project development.