Context

Theoretical Introduction

In mathematics, one of the geometric structures we encounter is the parallelogram. This is a quadrilateral (a four-sided shape) where the opposite sides are parallel. Due to this parallelism, a series of interesting properties are formed, such as the opposite sides and angles being equal. These properties allow us to perform a series of mathematical calculations and analyses, from simple to complex, using parallelograms.

In addition, parallelograms are a special subset of polygons, which are geometric shapes that play a crucial role in the foundations of geometry. From architecture to graphic design, from land mapping to astronomy, geometry is fundamental to understanding and navigating our world. In particular, by understanding parallelograms, we gain tools to understand and model a range of phenomena.

Another important characteristic of parallelograms is their relation to the concept of area. The area of a parallelogram is calculated by multiplying the base by the height. This concept is essential in mathematics and has many practical applications, from determining the amount of paint needed to cover a wall to calculating the size of a piece of land.

Contextualization

Parallelograms are all around us, from everyday objects like a sheet of paper to architectural constructions and natural patterns. They are also present in many disciplines beyond mathematics, such as physics, engineering, architecture, and design.

For instance, in civil engineering, parallelograms are used to calculate the force needed to support a beam. In physics, they are used in the graphical representation of vectors and in the decomposition of forces. And in design, they are used to create interesting patterns and shapes.

Recognizing and manipulating parallelograms is an essential skill not only for advancing in mathematics but also for applying these concepts in many aspects of the real world. Through this project, we expect you to create a solid understanding of parallelograms and how they can be used in practice.

Hands-on Activity: "Parallelograms in Action!"

Project Objective

To apply, in a practical and collaborative way, the concept of parallelograms, exploring their properties and understanding their usefulness and applicability in the real world.

Project Description

Students will be divided into groups of 3 to 5 people. Each group will be tasked with:

1. Identifying Parallelograms in Real Life: Students should search for and identify examples of parallelograms in their local environment (home, school, neighborhood).

2. Measuring and Calculating: Measure the sides and angles of the parallelograms identified, calculate their perimeters, areas, and the angles between the sides.

3. Creating a Virtual Parallelogram: Use a 2D drawing software of your choice to create a parallelogram. You can use tools such as Geogebra, AutoCAD, SketchUp, or any other that allows you to create geometric figures.

4. Presenting: Document your findings, calculations, creations, and reflections in a report to be delivered at the end of the project.

Required Materials

• Measuring tape or ruler.
• Protractor (to measure angles).
• Paper and pencil for notes and calculations.
• Access to a computer with 2D drawing software.
• Camera or smartphone to record the parallelograms found.

Step-by-Step Project

1. Research and identification: Go out and look for parallelograms around you. When you find one, record it with a photo.

2. Measurement: Use the measuring tape or ruler to measure the sides of the parallelogram. Use the protractor to measure its angles.

3. Calculating perimeter and area: Use the collected measurements to calculate the perimeter and area of the parallelograms found.

4. 2D drawing software: Use the chosen software to draw a parallelogram, incorporating what you have learned about the properties of parallelograms.

5. Documentation: Document the whole process in a report, including images of the parallelograms found, descriptions of the measurements, calculations performed, image of the parallelogram created in the drawing software, and reflections on the learning that took place during the project.

Project Submission

At the end of the week, each group will submit a written report that should contain:

1. Introduction: Contextualization of the theme, its relevance, and real-world application, as well as the objective of this project.

2. Development: Detailed explanation of the theory about parallelograms and their properties, description of the methodology adopted for the development of the project, presentation of the results obtained (photos, measurements, calculations, and 2D drawing), and discussion of the results.

3. Conclusion: Conclusions about the project, learning achieved, summary of the main points, and practical application of the concept of parallelograms.

4. Bibliography: Indication of the sources used for the elaboration of the report and for the realization of the project.

Each member of the group must actively participate in the project, collaborating in the discussions, in the data collection, in the elaboration of the 2D drawing, and in the final report. Remember that teamwork is a fundamental skill and is as important as the theoretical knowledge about parallelograms.