Contextualization

Introduction and Theory

Parallelograms are important two-dimensional geometric figures in the world of mathematics. They have unique properties that set them apart from other shapes and are essential for certain calculations and problems. The word 'parallelogram' comes from the Greek 'parallelogrammon', which means 'drawn parallel'. And that's exactly what they are - two sets of opposite parallel lines drawn in a way that forms a four-sided figure.

If you draw a parallelogram, you will see that opposite sides and angles are equal. This means that if you know the measurement of one side, you can calculate the other. The same goes for the angles. Furthermore, the sum of the interior angles of a parallelogram is always 360 degrees, another property that can help us solve complex problems.

The parallelogram has an even more interesting property: if you draw diagonals inside the parallelogram, these diagonals will divide each other exactly in half. This means that the diagonals of a parallelogram are bisectors of each other. These are just some of the properties that make the parallelogram a powerful tool in geometry.

Contextualization

But why should we care about parallelograms? Is there any practical application for them? The answer is a resounding yes. Parallelograms are used in various areas, from engineering to art.

For example, engineers use parallelograms when designing structures such as bridges and skyscrapers. They use the property of equal sides and angles to ensure that the structure is stable and safe. In physics, the concept of a parallelogram is used to represent the sum of two vector forces, known as the 'parallelogram rule'.

Furthermore, parallelograms are often used in designs and patterns in art, fashion, and architecture. They can be used to create the illusion of depth and three-dimensionality in a two-dimensional work. You have probably seen patterns of parallelograms in wallpaper, fabrics, and architectural structures.

Practical Activity

Activity Title: Building and Exploring Parallelograms

Project Objective

This project aims to provide students with an in-depth and practical understanding of what a parallelogram is, its properties, and how they can be applied in the real world.

Detailed Project Description

This project will be carried out by groups of 3 to 5 students and has an estimated completion time of over 15 hours. Students will build their own parallelograms using various materials. Subsequently, students will work on developing an original project that involves the practical application of parallelograms in real-world contexts. This may include, but is not limited to, architectural projects, physical models, artistic projects, among others. Finally, students will reflect on and write about their experience and learning.

Required Materials

1. Ruler
2. Pencil
3. Paper
4. Scissors
5. Compass
6. Various materials for project construction (such as cardboard, construction paper, fabrics, etc.)
7. Computer with internet access for research and report elaboration.

Detailed Step-by-Step for Activity Execution

1. Understand the Theory: The first step is to understand the theory of parallelograms. Use the provided resources and do your own research to deepen your understanding of parallelograms.

2. Build Parallelograms: Using the mentioned materials, each student should build their own parallelogram. Try creating different types of parallelograms, such as rectangles and rhombuses, and observe their properties.

3. Properties Analysis: Each group should analyze the properties of the parallelogram and prove these properties based on their own models.

4. Project Development: Now that you understand parallelograms, it's time to apply them! Develop an original project that involves the application of parallelograms. It can be an architectural model of a building, a design pattern for a fabric, a physical model demonstrating the parallelogram rule, an art project, etc.

5. Report Elaboration: After completing the practical project, the team should elaborate a report on the experience. This report should contain an introduction (relevance of the topic, project objective), development (explanation of the theory, activity description, methodology used, results obtained), conclusions, and the bibliography used.

Project Deliverables

At the end of the project, each group must present the following:

1. Constructed Parallelograms: The parallelograms that the students built and analyzed during the project.

2. The Original Project: The original project developed by the group involving the practical application of parallelograms.

3. Written Report: A comprehensive report that includes sections on introduction, development, conclusion, and bibliography. The report must have a minimum of 2000 words and must detail each step of the project, including reflections on what was learned.

The report should be clear, well-written, and contain all relevant information about the project. It should also demonstrate the student's understanding of parallelograms and how they were applied. The report is also expected to reflect on teamwork, time management, problem-solving, as well as any other socio-emotional skills developed during the project.