Contextualization

This project aims to understand the concept of area through the use of unit squares. We encounter the idea of area in various situations in our daily lives. For example, when we want to paint a wall, we need to know its area to buy the right amount of paint. When moving to a new apartment, it is important to know the area of the rooms to arrange furniture and decorative objects. In the industry, knowledge of area is crucial for the production and design of numerous products.

Area is a measure of surface, and in the case of flat shapes, such as squares and rectangles, this concept is particularly simple: it is the product of their dimensions. For example, the area of a square with a side of 1 is 1, just as the area of a rectangle with sides of 1 and 2 will be 2.

However, how can we calculate the area of more complex and irregular figures? The answer is to use unit squares. Essentially, it is enough to cover the surface of the figure with squares of side length 1 and count how many of them fit.

The use of unit squares is a practical and intuitive way to understand the concept of area and also facilitates the understanding of how area is calculated for different geometric figures. This approach also provides a visual way to understand the concept of area that can be especially useful for solving problems involving complex and irregular figures.

Atividade Prática

Activity Title: "Building Figures and Measuring Areas with Unit Squares"

Project Objective:

The objective of this project is for students to apply the concept of area through the use of unit squares to calculate the area of various geometric figures in a playful and collaborative environment.

Detailed Project Description:

This is a project aimed at groups of 3 to 5 students and has an approximate duration of two to four hours per student. The groups will be tasked with creating various flat geometric figures using unit squares and calculating their areas. They will also be challenged to create more complex figures by dividing the unit squares and calculating the area of the new figure. In addition, students will have the opportunity to become familiar with the format of the technical report, describing the project approach and its results.

Required Materials:

• Graph paper
• Colored pencils
• Ruler
• Scissors

Step by Step:

1. Each group should start by drawing different geometric figures such as squares, rectangles, and triangles on the graph paper. Colored pencils should be used to differentiate each figure.
2. Next, students should quantify the number of unit squares that fill each geometric figure, recording this number.
3. Students should repeat this process for each drawn geometric figure.
4. After quantification, students should create more complex geometric figures by dividing the unit squares and recording the amount needed to form the new figures.
5. The results should be clearly documented and presented in the report format.

Project Deliverables and Report:

Students will submit their drawn geometric figures along with a report that should include:

1. Introduction: contextualization of the theme, its relevance and real-world application, and the project's objective.
2. Development: explanation of the theory behind the project's central theme, detailed description of the activity, methodology used, and discussion of the results obtained.
3. Conclusions: recap of the main points, lessons learned, and conclusions about the project.
4. Bibliography: sources used for the project development.

In this document, students should connect the practical activities carried out with the theoretical concepts studied, explaining how the use of unit squares allowed the calculation of the area of the drawn geometric figures. Additionally, they should discuss the challenges encountered and how they were overcome, especially in the more complex figures.

The report is an important technical communication tool, and it is essential for students to learn how to organize their ideas and present their results clearly and concisely. Therefore, in addition to checking the area calculations, the quality of the writing and organization of the report will also be evaluated.