Contextualization

Mathematics is a universal language that is part of virtually all areas of human knowledge, and among its most intriguing branches is geometry. In this fascinating world of shapes and figures, translation is one of the key subjects, and our journey will lead us to discover more about the topic 'Translations 2'.

Translations are geometric transformations that involve the movement of a point or figure on the Cartesian plane without altering its shape or orientation. In other words, a translation 'slides' the figure, keeping all its properties intact.

Within geometry, there are several forms of translations, and understanding these variations is essential to comprehend the relationship between shapes and the space in which they are embedded. This concept is one of the foundations for the development of essential skills in spatial visualization, problem-solving, and logical thinking.

But translation is not limited to the universe of geometry. In fact, it has practical applications in various areas of real life: translation is used in graphic design, computer animation, architecture, civil engineering, and even in video games. Understanding the concept of translation allows us to understand how these industries create and move digital objects in a three-dimensional environment.

The importance of translation is also evident in science. In the physical sciences, translation refers to the movement that changes the position of an object, such as a car moving along a road. In the field of biology, translation is a vital process that occurs in our cells where messenger RNA is 'translated' into proteins.

For this activity, we recommend the use of the following reliable resources for a deeper understanding of the topic:

1. Your Research - Translation
2. World Education - Translation
3. Brazil School - Translation
4. Book: Fundamentals of Elementary Mathematics - Vol 8 - Plane Geometry - Gelson Iezzi, Carlos Murakami.

Practical Activity

Activity Title: 'Translations 2: The Game of Geometric Transformation'

Project Objective

This activity aims to provide students with a playful and collaborative experience to explore the concept of translation in geometry in a practical, fun, and interactive way. Additionally, this project also aims to enhance teamwork skills, time management, and research and communication skills.

Detailed Project Description

Students will be divided into groups of 3 to 5 members and will create an educational board game. The goal of the game is to move geometric figures represented by game pieces across a board using the concept of translation. The figures should be translated according to the rules defined by the students, which should be based on mathematical concepts of translation.

Required Materials

1. Cardboard or cardboard for board construction.
2. Game pieces representing the geometric figures to be translated.
3. Ruler, compass, and protractor for creating translations.
4. Markers and materials for board decoration.
5. Writing material for the report: laptop or paper and pen.

Detailed Step-by-Step for Activity Execution

1. Divide the class into groups of 3 to 5 students.
2. With the available material, each group should make the board and game pieces.
3. Students should research and define the game rules, basing them on mathematical concepts of translation.
4. Test and adjust the game.
5. Write a report on the activity.
6. Present the game produced and explain its operation to the class.

The estimated time for project execution is two to four hours per student, and the delivery time is one week.

Project Delivery

As a project delivery, each group must present the created board game and a written report. The report should follow the structure: Introduction, Development, Conclusions, and Bibliographic References.

In the Introduction section, the student should contextualize the translation theme and the objective of the created game.

In the Development section, they should detail the game creation process, explaining the rules and how translation is applied, as well as presenting the theory behind the project's central theme.

In the Conclusion, students should discuss what they learned throughout the project, what challenges they faced, and how they overcame these challenges.

In the Bibliographic References section, students will indicate the resources they used to understand the theme and to design the game, such as books, websites, videos, etc.

At the end of the project, it is expected that students have improved their technical skills such as recognizing and constructing figures obtained by compositions of geometric transformations and identifying figures obtained by translation. Additionally, it is expected that they have developed socio-emotional skills such as time management, problem-solving, creative thinking, proactivity, among others.