Contextualization

Perimeter and area are two fundamental concepts in geometry and mathematics in general. Understanding these concepts will allow you to explore and solve real-world problems involving spaces and shapes.

Introduction

In mathematics, the perimeter of a flat figure is the sum of the lengths of its sides, that is, it is the measure of the figure's contour. If we imagine a figure as a field, the perimeter would be the measure of the fence surrounding it. In the case of a square or rectangle, for example, the perimeter can be found by adding the lengths of all four sides.

Area, on the other hand, is the measure of the extension of a surface. Continuing with the field analogy, the area would be the space inside the fence. In a square or rectangle, the area can be calculated by multiplying the length of one of its bases by the height.

Why is it important?

Understanding the concepts of area and perimeter is essential in a variety of fields, including engineering, architecture, urban planning, and even agriculture. For example, an architect needs to know the area of a room to plan its design and the perimeter to calculate the amount of material needed for floor and ceiling finishes. Similarly, a farmer needs to know the area of his land to estimate the amount of seeds or fertilizers he will need, while the perimeter may be important for planning fences or access paths.

Furthermore, understanding the relationship between area and perimeter allows us to understand that two shapes can have the same area but different perimeters, and vice versa. This discovery can be surprising and exciting, opening doors to the exploration of new mathematical concepts.

Practical Activity: "Exploring Area and Perimeter"

Project Objective

The objective of this project is to explore the concepts of area and perimeter through the creation and analysis of geometric shapes. Students will learn to calculate the area and perimeter of various figures and understand the relationship between these two measures.

Project Description

In this project, students will work in groups of three to five members to create a variety of geometric shapes using ropes and pins. They will calculate the perimeter and area of each shape and record their results. Then, they will compare the collected data and discuss their findings.

Required Materials

• Ropes of different lengths
• Pins
• Measuring tape
• Paper and pencil for notes
• Calculator (optional)

Step by Step

1. Group Formation: Students will be divided into groups of 3 to 5 participants.
2. Definition of Figures: Each group must choose at least three different geometric shapes to create: a square, a rectangle, and a triangle.
3. Creation of Figures: Using the rope and pins, students will create their geometric shapes on a flat surface.
4. Measurement: Students will measure the sides of their shapes using the measuring tape and calculate the perimeter of each shape.
5. Area Calculation: Students will calculate the area of each shape and record their results.
6. Analysis: Students will compare and discuss their results, trying to find relationships between the area and perimeter of the shapes.
7. Documentation: Each group must prepare a report documenting their findings.

Project Delivery

After completing the practical part of the project, student groups must write a report documenting their findings and learnings. The report should include the following sections:

1. Introduction: Students should contextualize the problem they were trying to solve, the relevance and application of the concepts of area and perimeter in the real world, and the objective of this project.
2. Development: Students should describe in detail the shapes they created, how they measured the sides and calculated the perimeter and area of each shape. They should present the results obtained and discuss them, noting any relationship or pattern observed between the area and perimeter of the shapes.
3. Conclusions: Students should conclude the project by summarizing their main points, explaining the learnings obtained, and drawing conclusions about the project.
4. Bibliography: Students should indicate the sources of information used for the project, whether books, web pages, videos, etc.

Reports should be submitted one week after the practical activity, allowing students enough time to reflect on their findings, prepare their report, and effectively collaborate as a group.