Contextualization

Mathematics is a universal language that permeates our daily lives, even when we are not aware of it. A large part of the daily decisions we make involves, consciously or unconsciously, some kind of mathematical reasoning. It is a discipline that helps us understand the world we live in and make informed decisions. In this project, we will delve into the universe of squares and explore the concepts of geometric expansion and reduction.

Theoretical Introduction

The square is a flat figure formed by four equal sides and four right angles. It is an important figure in geometry because it is regular: all its measurements are equal. The measurement of the side of a square is called an 'edge'. The perimeter of a square is calculated by adding the length of all its sides, that is, four times the measurement of the side (4side). The area of a square is calculated by multiplying the measurement of the side by itself (sideside).

When it comes to expanding or reducing a square, things get a little more interesting. Expansion occurs by multiplying the measurements of the sides of the square by a number greater than one, while reduction occurs by multiplying the measurements of the sides by a number less than one. What intrigues is how these changes affect the area and the perimeter.

Importance and Practical Applications

The concepts of expansion and reduction are used in various practical situations. Architects and engineers, for example, often need to expand or reduce the measurements of house or building plans. In our daily lives, we also face situations where we have to expand or reduce something, whether it's a photo, a decorative object, or even a cooking recipe.

Furthermore, understanding how expansion and reduction affect the area and perimeter of a square can help develop important skills, such as critical thinking and spatial reasoning. These are essential resources that help us solve everyday problems and are skills often sought after in the job market.

Activity: 'Expanding and Reducing Squares'

Project Objective

This project aims to apply the concepts learned about expanding and reducing geometric figures, specifically the square, in a practical way. By the end of this project, it is expected that students will be able to understand and explain how expansion and reduction affect the area and perimeter of a square.

Detailed Project Description

Each group will be responsible for choosing a square-shaped object from the school environment or their homes. The object will serve as the basis for the practical study of expanding and reducing squares. For each phase of the project, students will expand and reduce this square in different proportions, calculating, at each step, the new perimeter and area and comparing them with the original values.

Required Materials

To carry out the activity, the following materials will be needed:

• Square object (e.g., matchbox, whiteboard, tile, etc.)
• Graph paper
• Ruler
• Calculator
• Pencil and eraser

Detailed Step-by-Step for Carrying Out the Activity

1. Gather with your group mates and choose a square object that will serve as the basis for your study. Measure the side of the square (with millimeter precision) and write down this value.

2. Using the graph paper, draw the square with the obtained measurements.

3. Calculate the perimeter and area of the original square and write down the values.

4. Now, you will expand the square. Choose an expansion factor (for example, 2, 3, etc.). Draw the new square on the graph paper.

5. Calculate the perimeter and area of the expanded square and compare them with the values of the original square.

6. Now, it's time to reduce the square. Choose a reduction factor (for example, 0.5, 0.3, etc.). Draw the new square on the graph paper.

7. Calculate the perimeter and area of the reduced square and compare them with the values of the original square.

8. Perform steps 4 to 7 with at least two different expansion/reduction factors.

9. After completing the expansion and reduction steps, students should gather all the collected information and write a report. This report will cover the following topics:

   • Introduction: In this section, students should describe the project's objective, the relevance of the topic, and its real-life applications.
   • Development: Here, students should explain the theory about expanding and reducing squares, describe in detail the activities carried out, the methodology used, and discuss the results obtained.
   • Conclusion: In this part, students should review the main points of the project, highlight the learnings obtained, and the conclusions drawn on the topic.
   • Bibliography: Finally, students should list the research sources used during the project development.

It is important that, in the report, students explain their reasonings and observations at each stage of the practical experiment. Additionally, they should also highlight the socio-emotional skills developed throughout the project, such as time management, communication, problem-solving, creative thinking, and proactivity.