Contextualization

Mathematics is much more than just numbers, equations and formulas; it is a fundamental tool that allows us to understand and interact with the world around us. In every corner of our daily lives, mathematics is present, from the proportions of ingredients in a recipe to the scale of a map. It is in this context that we will discuss the topic of enlarging and reducing figures, a fundamental concept in geometry.

Enlarging and reducing figures is a common procedure in various fields, from art to building and product design, to navigation using maps and many others. When we change the size of a figure without altering its shape, we say that we are performing an enlargement or a reduction and this has a very practical purpose! It is thanks to this concept that we can, for example, understand the proportions of a building through a floor plan or follow a recipe that serves more people than the original.

Introduction

Before we delve into the practical activity, it is essential that we understand the theoretical concepts related to enlarging and reducing figures. In essence, these terms refer to the practice of changing the size of an object while maintaining its shape. This is achieved by maintaining the same ratio in all dimensions of the object - be it a flat figure or a three-dimensional object.

The process of enlarging and reducing is widely used in practical situations, where we need to change the size of an object, but maintain its proportions. For example, in industrial and product design, engineers and architects use these concepts to create scale models of buildings and objects.

Last but not least, it is important to understand that the ability to enlarge and reduce figures is an exercise that develops our spatial thinking, a valuable skill that is useful in many areas beyond mathematics.

Practical Activity: “Reshaping Figures”

Project Goal

This project aims to apply the concepts of enlarging and reducing figures in practice, allowing students to not only understand the theoretical principles but also visualize and experience its real-world applications.

Project Description

In this project, each group of 3 to 5 students will be responsible for creating a “set of shapes”. Initially, the group should choose a geometric figure from a book or the internet and then create enlarged and reduced variations of that figure. The challenge is to create these variations while maintaining the original proportions and shapes. They should then create an explanatory poster with all the figures and their respective proportions, highlighting the enlargement and reduction processes used.

Finally, the group should produce a detailed report on the process, discussing the theory behind enlarging and reducing, the methodology used, the challenges encountered, the solutions created and the conclusions drawn from the project.

Required Materials

1. Graph paper or a printout of a grid
2. Ruler
3. Pencil and eraser
4. Cardstock or poster board for the poster
5. Colored pens, markers or crayons
6. Computer with internet access for research and report writing

Step by Step

1. Gather the group and choose a geometric figure from a math book, a website, or create an original figure.
2. Using the grid paper, draw the chosen figure. This will be the base figure.
3. Discuss as a group and decide on an enlargement factor and a reduction factor to apply to the figure.
4. Use the grid paper to enlarge and reduce the base figure, according to the factors decided, maintaining the original proportions and shapes.
5. Compare the enlarged and reduced figures with the base figure to ensure the proportions have been maintained.
6. Prepare the poster, placing the base figure in the center and arranging the enlarged and reduced figures around it, detailing the proportions used and the enlargement and reduction processes.
7. Produce the report, addressing the teamwork process, the challenges encountered and how they were solved, the mathematics involved in the project and the importance of these concepts in the real world.

Project Submission

The group should submit the finished poster and the report. The report should be structured as follows: Introduction, Development, Conclusions and Bibliography.

1. Introduction: Provide context for the theme, its relevance, real-world applications and the project goal.
2. Development: Address the theory behind enlarging and reducing, the activity in detail, the methodology used and the results obtained.
3. Conclusion: Recap the main points, highlighting the lessons learned and the conclusions about the project.
4. Bibliography: Cite all research sources used for the project.

Remember, the focus here is not only on the final product, but also on the teamwork process, problem-solving and creative thinking involved.