Contextualization

Mathematics is a universe of numerous practical applications in our daily lives, and among its various branches we have Geometry, a fascinating field that allows us to understand and interact with shapes and figures around us. In this project, we will focus on a fundamental concept of geometry: the area of shapes.

Area is a concept that allows us to understand how much space a shape or figure occupies in a plane. Whether it's a square, a triangle, a circle, or any other shape, each one has a specific area. The area is calculated through mathematical formulas that take into account the characteristics of each shape. For example, the area of a square is determined by multiplying the length of one of its sides by itself, while the area of a circle is calculated using the radius and the mathematical constant Pi.

In practical context, understanding areas is critical in various fields. In the field of architecture, for example, the area of a plot of land is a physical limit for the project, and understanding this measure can significantly impact the development of an architectural project. Additionally, when painting a house or an object, we need to know the area to be painted to calculate the amount of paint needed, saving resources and avoiding waste.

In addition to its practical application, the study of areas also contributes to the development of skills such as logical and analytical thinking, important skills required in the 21st century. This, combined with the practice of collaboration and teamwork, makes the study of areas a rich and relevant educational activity.

References for further study on the topic:

1. Khan Academy: Area and Perimeter
2. Só Matemática: Area of Plane Figures
3. Brasil Escola: Area Calculation

Practical Activity

Activity Title: The Modeler of the Area

Project Objective:

This project aims to provide students with the opportunity to deepen their understanding of the concept of area of different geometric shapes (quadrilaterals, triangles, and circles) through the creation of a model of a city that includes different structures such as houses, parks, and roads. Additionally, it aims to encourage collaboration and time management among students.

Detailed Project Description:

Students, divided into groups of 3 to 5, must plan and build a model of a city. Each element of the city (buildings, parks, roads) must be represented by a geometric shape selected by the students.

The first step will be planning the city, in this plan, students will have to define what type of geometric shapes will represent each element of the city and calculate the areas of these shapes. Subsequently, students will move on to the construction phase of the model using the chosen materials.

At the end of the project, each group must present a written report, explaining the theory about the area of geometric shapes, detailing the calculation of the areas of these shapes in their model, and discussing the results obtained.

Additionally, each group must also give a brief oral presentation about the project developed and the learnings acquired.

Required Materials:

• Cardboard, kraft paper, or cardboard for the base of the model;
• Construction materials for the model such as sticks, clay, small boxes, styrofoam, etc;
• Ruler, compass, protractor;
• Paper and pencil for sketches;
• Calculator.

Detailed Step-by-Step:

Step 1: Formation of groups of 3 to 5 students. One month will be given for the completion of the project.

Step 2: Study and research on the area of quadrilaterals, triangles, and circles. Each group must take notes and have group discussions to ensure understanding of the topic.

Step 3: City planning. Each group must draw a sketch of how their city will be, deciding which geometric shape will be used to represent each element. The measurements of each shape should be included in the plan.

Step 4: Calculation of the area of the chosen geometric shapes. Students must show all calculations performed.

Step 5: Construction of the model. Following the sketch drawn in Step 3, each group must build their model.

Step 6: Preparation of the report. The report should include an introduction to the topic, the area calculations, the description of the city and its shapes, and a conclusion. The bibliography used should be listed at the end of the report.

Step 7: Oral presentation. Each group must present their model to the class, explain the area calculations of the shapes used, and the conclusions reached about the project.

Project Delivery:

Students will be evaluated based on their written reports, models, and oral presentations. The report should be structured around key topics: Introduction, Development, Conclusions, and Bibliography.

Introduction: Students must contextualize the concept of area, explain its importance, and describe the relevance of the project.

Development: Students must discuss the theory of the area of geometric shapes, explain the process of building their cities, and present all area calculations performed. The method of calculating the area for each shape used should be detailed.

Conclusions: Groups must list the main learnings acquired, both in technical terms and in socio-emotional skills. The experiences of collaboration and time management within the group should be discussed.

Bibliography: Groups must list all sources of information used, whether books, websites, videos, etc.

Groups must ensure that both the model and the report are clearly connected and complement each other.