Contextualization

Mathematics is present in everything around us and, many times, we don't even notice it. One of the interesting and widely applied concepts in the real world is related to the enlargement and reduction of figures. Knowing how these processes occur is essential to understanding aspects from the construction of buildings to the design of everyday objects.

In this project, we will focus on the enlargement and reduction of figures, an essential topic for learning Mathematics and Geometry. And don't think that this is restricted to these disciplines only. This is an interdisciplinary concept that interacts richly with Art, Architecture, Engineering, among other fields of knowledge.

Introduction

In mathematics, "enlarging" means making a figure bigger while keeping the same shape, that is, the proportions between the various elements of the image are maintained. This is what we call similarity. Enlarged figures are called similar figures. On the other hand, "reduction" is the process of making a figure smaller while maintaining the same shape.

The enlargement and reduction of figures are geometric processes based on proportions and scales. The scale is the proportion between the measurement of an object or place in the drawing or model and the corresponding measurement in reality. For example, on a map, one centimeter can represent one kilometer. In this case, the scale of the map is "1:100000" if we consider the measurements in centimeters and meters.

Mastering the knowledge of enlargement and reduction is crucial in many aspects of daily and professional life. Maps, models, 3D modeling, photographs, product design, arts, architecture, among others, are all based on concepts of enlargement and reduction of figures.

Hands-on Activity

Activity Title: Miniatures and Magnifications: Mathematics in Art and Architecture

Project Goal

Through a hands-on and collaborative activity, understand and apply the mathematical concepts of enlargement and reduction of figures, developing teamwork skills, time management, communication and creative thinking.

Project Description

The groups, with 3 to 5 students, will be responsible for choosing an everyday object or a famous architectural work and creating a miniature (reduction) and a giant version (enlargement) of it, using the mathematical concept of proportion.

Required Materials

• Graph paper
• Pencil, eraser
• Ruler
• Object construction materials (can be cardboard, clay, playdough, among others)
• Computer with internet access (for research and report preparation)

Activity Steps

1. Choice of Object: The group must choose an everyday object or an architectural work to be the focus of the project. This choice should be justified in the final report.

2. Study of Proportions: Students should study the proportions of the object, measuring the actual dimensions (in the case of an everyday object) or researching (in the case of an architectural work). The proportions should be calculated and recorded.

3. Creation of the Miniature and Giant Version: Based on the proportions studied, students should create a miniature and a giant version of the object. Both versions must maintain the proportions of the original object.

4. Preparation of the Report: In parallel with the practical activity, the groups should prepare a project report, including the following topics:

   • Introduction: Contextualization of the theme, explanation of the relevance and objective of the project.
   • Development: Theoretical explanation of the concept of enlargement and reduction of figures (with the proper bibliographic citations), detailing the methodology and stages of the project, presentation and discussion of the results.
   • Conclusion: Summary of the main points of the work, reflection on the learnings and final considerations about the project.
   • Bibliography: Indication of the sources used during the project.

The miniatures and giant versions created, together with the report, form the final deliverable for the project. In addition to applying mathematical concepts in real situations, the work focuses on collaboration and communication among group members, managing time and resources to complete the project.

It is expected that, in the end, the students will be able to create similar figures in situations of enlargement and reduction, using different materials and, of course, mathematics! Furthermore, students should develop valuable socio-emotional skills, such as teamwork, time management, communication, creative thinking and proactivity.