Contextualization

Theoretical Introduction

Geometry is a branch of mathematics that studies the shapes and dimensions of objects. Within this study, we have very interesting concepts such as symmetry and reflection, which are the focus of our project 'Reflections 1'.

Symmetry occurs when we can divide a figure into parts that fit perfectly, that is, they are identical. These parts, called symmetrical, can be obtained in various ways, including Reflection Symmetry, where the image mirrors the original exactly, as if we were looking at it in a mirror.

On the other hand, Reflection in Geometry is a type of transformation that uses a line (or a point) as a mirror to reflect a figure. Thus, each point of the original figure is reflected through this line (or point), creating a mirrored image.

Contextualization

Have you ever noticed that there are many forms of symmetry and reflection around us? They are present in various elements, from plant leaves to buildings and works of art that we see around us.

Imagine, for example, the facade of a house or a building. Have you noticed that usually one half is the mirror image of the other? That's symmetry! And in works of art, such as paintings and sculptures, this concept is also widely used to create harmony and beauty in the pieces.

Understanding these concepts and knowing how to apply them not only helps us to better understand the world around us, but also to create our own works, whether artistic or practical, such as building an object or solving a complex problem.

Practical Activity

Activity Title: 'Mirroring the World: A Mathematical Perspective through Symmetry and Reflection.'

Project Objective

Investigate the presence and applicability of reflection symmetry in our daily lives, through the identification, reproduction, and creation of symmetrical images present in geometric figures, objects, architecture, and works of art.

Detailed Project Description

Groups should start by conducting research, identifying practical examples of reflection symmetry in their surroundings and reflecting them in a notebook or in a dynamic geometry software of their choice. Then, they should create their own images with reflection symmetry, using drawing tools or geometry software.

Required Materials

1. Notebook or sheets of paper
2. Pencil, eraser, ruler, set square, and compass
3. Smartphone or digital camera (optional)
4. Computer with Internet access
5. Dynamic geometry software (optional)

Step-by-Step for Activity Execution

1. Research: Each group should start by identifying at least five examples of reflection symmetry in their home, school, or community (they can also be found in pictures and photos on the internet). The group can photograph or draw these examples.

2. Reflection of Images: Next, the group should draw the symmetry line for each example found and reflect the image around that line, using drawing tools or a dynamic geometry software.

3. Creation: After analyzing the examples, students should create their own images using reflection symmetry. These images should be original and represent figures, objects, works of art, or architecture. The images should be accompanied by a brief description, explaining the motivation and creation.

Report

After completing the practical part, students should prepare a project report, containing the following topics:

1. Introduction: Contextualization of the theme and project objective.
2. Development: Explanation of the theory of reflection symmetry, detailed description of the activities carried out, including photos or drawings of the figures and objects found and created, methodology used, and discussion of the results.
3. Conclusions: Recap of the main points, lessons learned, and conclusions about the study of reflection symmetry.
4. Bibliography: References to resources used during the project.

The report should be clear, concise, and precise, reflecting collaboration and group learning. By the end of the project, students will have not only learned about symmetry and reflection but also developed essential skills such as teamwork, time management, and creative thinking.