Contextualization

A rhombus, like other elements of Geometry, is a mathematical object that has practical application in our daily lives. It is a flat figure, a quadrilateral (four-sided shape) in which all sides are equal in length. Although all sides are equal, the angles do not necessarily need to be equal, unless the rhombus is also a square.

In the real world, rhombuses appear in various forms and contexts. They are found in tile patterns, in jewelry, and in art. In architecture, rhombuses are used to create four-sided roofs, known as mansard roofs, which are particularly common in areas with heavy snowfall. In many sports, the playing field (such as baseball and softball) has the shape of a rhombus. Therefore, understanding a rhombus and its properties is not only interesting but also very useful!

In this project, we will explore the mathematical properties of rhombuses, working together to solve problems involving the angles and sides of rhombuses. We will also understand how rhombuses connect with other aspects of mathematics, such as Trigonometry and Algebra, and also with Physics. Additionally, we will see how rhombuses are used and applied in real life.

Atividade Prática - Projeto "Construindo e explorando losangos"

1. Project Objective:

The objective of this project is to develop, through practical activities and problem-solving, a complete understanding of the geometric figure rhombus. Students should investigate its characteristics, the relationships between its sides and angles, and its real-world applications. This task should be carried out in groups of 3 to 5 members and should take more than 12 hours per participating student to complete.

2. Project Description:

To understand a rhombus and its properties, students will carry out a series of activities, including creating a rhombus model, performing geometric transformations, and solving applied physical problems.

Students will need to work together to create a model of a rhombus using resources such as cardboard, ruler, pencil, and scissors. They will measure and document the properties of the rhombus, including its sides, diagonals, and angles.

Students will be challenged to solve mathematical and physical problems involving the use of rhombuses. This may include applying the Pythagorean Theorem, using the rhombus in Trigonometry problems, and calculating the area of a rhombus.

Students will also explore the relevance of the rhombus in Physics, for example, how the shape is used in the construction of a mansard roof, or how the figure appears in some laws of light reflection and refraction.

3. Required Materials:

• Cardboard or cardstock
• Ruler
• Pencil
• Scissors
• Calculator

4. Step-by-Step for Activity Completion:

1. Initial Research: Each group member should conduct independent research on the rhombus, its properties, and real-world applications. Use the provided resources and others you find. Hold group meetings to share and discuss the information found.
2. Model Making: Using cardboard or cardstock, create a rhombus and record all its measurements (sides, angles, and diagonals).
3. Model Exploration: Each group member should propose at least one mathematical and one physical problem involving a rhombus. Share and solve these problems as a group.
4. Practical Application: Research an application of the rhombus in Physics and everyday life (for example, the construction of a mansard roof). Explain these applications in detail in the final report.
5. Report Writing: Finally, work together to write a project report, which should include sections on Introduction, Development, Conclusions, and Bibliography.

Project Deliverables:

Students must deliver the constructed rhombus, the proposed and solved problems, and the final report. The report will be used to assess the project's progress and the students' learning. It should be a written document that reflects the work done, the discoveries made, and the skills developed.

In the "Introduction" section, students should present the object of study (rhombus), its relevance and application in the real world, as well as the objective of this project. In the "Development" section, students should explain the theory behind the rhombus, the activities carried out, the methodology used, and the results obtained. In the "Conclusions" section, students should outline the learnings acquired and the conclusions drawn from the project. Finally, in the "Bibliography" section, students should indicate all sources used in the work.