Contextualization

Area is one of the fundamental concepts in geometry, and one of the first ones we learn in school. This project is specifically based on the idea of area by unit squares, a key concept that runs all the way from the basics of geometry to its more complex branches.

Area, in simple terms, is the space within a two-dimensional shape or contour. This can be as simple as the interior of a square or a circle, or as complicated as the space within an irregular shape with multiple sides. By now, we are sure you are quite familiar with calculating the area of simple shapes like squares or rectangles, by multiplying their vertical and horizontal dimensions. However, the question remains: How can we calculate the area of more complex shapes?

The answer lies in unit squares. A unit square, as the name suggests, is a square whose side is one unit of measurement. This provides an easy way to measure the area of more complex shapes: simply count how many unit squares fit inside that shape! We will delve deeply into this concept in this project.

The concept of area by unit squares is incredibly useful and relevant in the real world. In the field of engineering and architecture, it is used to calculate the area of building project plans. In the world of art, it is used to create complex mosaics. In computer graphics, it is used to model complex shapes. The importance of this concept cannot be underestimated.

Furthermore, learning and understanding the concept of area by unit squares is a fundamental step towards mastering more advanced topics in mathematics. This concept is at the foundation of other topics such as calculating volumes, surfaces, and integrals. Learning this now will open many doors for you in the future!

To enhance your knowledge, we suggest the following sources:

• Khan Academy: Area and Perimeter (link)
• Só Matemática: Area of Flat Figures (link)
• Mundo Educação: How to Calculate Area and Perimeter (link)

Practical Activity

Activity Title: "Building Knowledge: Area by Unit Squares"

Project Objective

The objective of this project is to deepen students' understanding of the concept of area by unit squares through a practical activity based on real-world situations. The project also aims to develop teamwork, time management, communication, conflict resolution, and critical thinking skills.

Detailed Project Description

Students, divided into groups of three to five people, will be tasked with planning and building a two-dimensional "garden" using graph paper, containing at least four different geometric shapes: a square, a rectangle, a triangle, and a circle. Each group must calculate the area of each shape in their garden using the method of unit squares.

Students should also consider the economic value of their "garden," assigning imaginary prices to each unit square (representing, for example, the cost of planting and maintaining different types of plants). Therefore, in addition to calculating the areas, students should use basic financial and economic concepts to determine the total cost of their garden.

The project should be completed over two weeks, with work both at home and in the classroom.

Required Materials

• Graph paper
• Colored pencils
• Ruler
• Compass
• Calculator (optional)

Step-by-Step

1. Divide the class into groups of three to five students.

2. Each group should design a two-dimensional layout for their "garden" on graph paper, including their four geometric shapes (square, rectangle, triangle, circle).

3. Using the method of unit squares, students must calculate the area of each shape in their garden.

4. Determine a value for each unit square in your garden, representing the cost of planting and maintaining different types of plants.

5. Calculate the total cost of your garden by adding up the prices of all unit squares.

6. Students should prepare a detailed project report, following the proposed report structure: introduction, development, conclusions, and bibliography.

Project Deliverables

Groups must submit the following materials at the end of the project:

1. The "garden" drawn on graph paper, with all shapes clearly identified and colored.

2. A table with each shape, its calculated area, and its total cost.

3. A written report, containing:

   • Introduction: explanation of the project and its relevance.

   • Development: detailing the steps taken, explaining the method of unit squares and how to calculate the area and cost of each shape in the garden.

   • Conclusions: What students learned from the project, what difficulties were encountered and how they were overcome, and what are the practical applications of what was learned.

   • Bibliography: all resources (books, websites, videos) used to understand and apply the concepts of area and finance in the project.

Students should pay special attention to the writing of the report, as it will be evaluated in terms of clarity, quality of writing, and the depth of their understanding of the concepts of area and finance.