Contextualization

Reflection is a geometric transformation that is based on a point or axis of reflection. This means that if we take a figure and reproduce it as a reflected image through a point or a line, we are working with reflections. In mathematics, this is a way to move figures in the plane. For example, just one reflection movement is enough to transform a 'b' into a 'p'.

But what makes reflections more than just a simple game of mirrors? And did you know that reflections are not only fundamental to mathematics, but also to other disciplines, such as physics and computer science?

Studying reflections and their impact on our daily lives is where the beauty of mathematics is revealed. Whether in a mirror, a puddle of water, or the reflection in a pair of glasses, reflections are everywhere.

Introduction

Although it may seem abstract, reflection is a mathematical concept with practical applications. For example, did you know that reflections are fundamental to creating computer games?

Game developers use reflections to create symmetries and perspectives, making game environments more realistic. In addition, reflection is also used in other fields, such as physics, where it is used to understand phenomena like the reflection of light.

Working with reflections not only deepens our geometric understanding, but also develops critical thinking skills, problem-solving abilities, and collaboration. Can you predict the result of a series of reflections before making them? How do you work as a team to solve challenging problems?

Practical Activity: 'Mathematical Mirrors: Exploring Reflections and Symmetries'

Project Objective:

This project aims to explore the concept of reflections in the study of geometry, as well as their application in everyday contexts and in different disciplines, such as physics. In addition, students must develop teamwork skills, time management, problem-solving, and critical thinking.

Detailed Project Description:

The group of students (3 to 5 students) will be challenged to create a 'Mirrored World'. This world will be a board where the pieces are geometric figures that will undergo reflections, rotations, and translations and must be placed in the correct position according to the game rules created by the students themselves.

In addition, the team will have to prepare a presentation showing the importance of reflection and geometric transformations in different areas (physics, computer science, art, etc.)

Required Materials:

1. Cardboard for the board.
2. Colored paper to create the geometric pieces.
3. Ruler, compass, and square.
4. Pens and markers.
5. Reflection and rotation software (such as GeoGebra).
6. Books and online resources on reflections and geometric transformations.

Detailed Step-by-Step:

1. Study reflection and other geometric transformations using online resources and recommended books.
2. Discuss as a group to fully understand the concepts studied.
3. Plan the 'Mirrored World', including the game rules, and draw a sketch.
4. Build the board and pieces using the listed materials.
5. Test the game by playing several rounds to ensure the rules work and are challenging.
6. Prepare a presentation, showing the application of reflection and geometric transformations in different fields.
7. Present the game and the presentation to the class and the teacher.

Project Delivery:

Students must deliver the board of the 'Mirrored World' game, the geometric pieces of the game, and a written documentation.

The documentation should be written with the following topics:

1. Introduction: Contextualization of reflection and its relevance in everyday life and in different fields. The project's objective should also be explained.
2. Development: Detailed explanation of the theory studied and how it was applied in the project. Describe the activity (building the game and preparing the presentation) and the methodology used. Finally, discuss the challenges encountered and how they were overcome by the team.
3. Conclusion: Review of the main points of the project, lessons learned, applications of reflection and geometric transformations better understood. Personal reflection on the experience.
4. Bibliography: Indicate all sources used to learn about the subject and work on the project.

The documentation should be written carefully and reflectively, demonstrating the students' understanding of the topic and the depth of the work done.