Contextualization

Mathematics often seems like a set of numbers and equations without practical application or relevance to everyday life. However, when studying concepts such as enlarging and reducing squares, we can perceive the usefulness of this discipline in various aspects of our daily lives. The study of enlarging and reducing figures opens doors to a better understanding of the world we live in, as they are present from building houses to drawing maps.

Enlarging or reducing a square is more than just increasing or decreasing its size. It is essential to understand how these changes affect the perimeter and area of the figure. The perimeter, which is the measurement around the square, increases proportionally to the size of the side being altered. On the other hand, the area - which is the measure of the internal space of a figure - does not behave in the same way. When we double the size of one side of the square, the area increases fourfold, not twofold. This difference allows us to explore mathematical concepts such as scales, proportions, and quadratic relationships.

Enlarging and reducing squares is a concept that can be applied to various everyday situations. When we draw a map and represent a large area on a small piece of paper, we are reducing. Similarly, when we increase a cake recipe to serve more people, we are enlarging. Understanding these concepts is essential for dealing efficiently and correctly with situations in our daily lives.

For a better understanding of the topic, in addition to our classes, I suggest the following resources:

1. Enlarging and Reducing Figures - Brasil Escola
2. What is Scale - Mundo Educação
3. Video about scale - Matemática Zup

Practical Activity: Modeling Mathematics with Clay

Project Objective

This project aims to allow students to explore the concepts of enlarging and reducing squares and their implications on area and perimeter. Additionally, they will be challenged to apply these concepts in creating a 3D model, thus developing teamwork, time management, and problem-solving skills.

Detailed Project Description

Each group of 3 to 5 students will be involved in a project that will last approximately 12 hours. They will have to shape squares with clay, enlarge and reduce these squares, and then calculate and observe the variations in their areas and perimeters.

Required Materials

• Clay
• Ruler
• Calculator
• Graph paper
• Pencil and eraser

Detailed Step-by-Step for Activity Execution

1. Each group will start the project by modeling a clay square with a side of 10cm. They will measure and record the perimeter and area of this square.
2. The next step will be to enlarge the initial square by 2 times and then by 3 times, recording the perimeter and area of each enlarged square.
3. From the original square, they will also reduce it to half its size, again recording the perimeter and area.
4. The entire process will be documented by the students in a report, which will include an introduction to the subject, the methodology used, the results obtained, and the conclusion. In addition, photos of the different stages of the project will be attached to the report.
5. To answer the final question about the relationship between enlargement/reduction and the area and perimeter of the square, the students will plot a graph on graph paper, where the x-axis will represent the scale factor (side length) and the y-axis will represent both the area and the perimeter.

Project Deliverables

Each group will deliver a final report containing:

1. Introduction: An overview of the topic, explaining the concepts of enlarging and reducing squares, area, and perimeter, and how these concepts are useful in everyday life.
2. Development: A detailed explanation of how the project was carried out, including initial measurements, results of enlargements and reductions, and calculations performed.
3. Results: The results obtained throughout the project, including area and perimeter calculations for the enlarged and reduced squares, as well as graphs representing these changes.
4. Conclusions: A reflection on the results obtained, what they learned from the project, and how they relate to the theoretical concepts studied.
5. Bibliography: Sources consulted throughout the project.