Contextualization

The area of an object is the amount of space it occupies in a two-dimensional plane. It is a mathematical measure used in a wide variety of disciplines, including mathematics, physics, engineering, and even art. The area can be expressed in various units of measurement, such as square meters, square centimeters, square millimeters, etc.

The formula for calculating the area varies depending on the shape of the object. For example, the area of a square is calculated by multiplying the length of one side by the other side, while the area of a triangle is calculated by multiplying the base by the height and dividing the result by two. The area of a circle is calculated by multiplying the square of the radius by the number pi (which is approximately 3.14159).

The concepts of area are enormously useful not only in mathematics but also in many other areas and everyday situations. For example, in architecture and civil construction, area measurements are fundamental to determine the amount of materials needed for a construction, such as bricks, cement, paint, etc. Additionally, area measurement is essential for real estate appraisal, agriculture, urban planning, among many other activities.

To delve deeper into the topic, we recommend the following resources:

• Article "How to calculate the area" on the Mundo Educação portal (link here).
• Video "How to calculate the area of the main geometric figures" on the Matemática Rio channel (link here).
• Book "Geometry and measurements" by Eduardo Wagner, available in the school library.

Practical Activity

Activity Title: "Calculating Areas in Our School"

Project Objective

The objective of this project is to apply the concepts of area calculation to real objects, in a real-world scenario, specifically, our school. Students will work in groups of 3 to 5 and should be able to calculate the area of various parts of the school, as well as prepare a final report documenting the process and results.

Detailed Project Description

This project is a student-led investigation that involves physical measurements, area calculations, problem-solving, and report writing. Each group will be responsible for measuring and calculating the areas of three environments: a classroom, the gymnasium, and the school sports court. Students will need to divide each area into smaller, more manageable shapes (squares, rectangles, circles, and/or triangles) and then calculate the area of each shape. Finally, they will sum all the sub-areas to obtain the total area of each environment.

Necessary Materials

• Measuring tape
• Paper and pencil
• Calculator

Step-by-step for the activity

1. Divide the group into teams of 3 to 5 students.

2. Each group will choose a classroom, the gymnasium, and the sports court to measure.

3. Students will use the measuring tape to collect the necessary measurements for their designated areas.

4. They will need to divide each area into smaller, more manageable geometric shapes (squares, rectangles, triangles, and/or circles) to facilitate the calculation.

5. Using the collected measurements and the appropriate area formulas, the groups will calculate the area of each sub-shape.

6. The groups will then sum all the sub-areas together to find the total area of each environment.

7. Finally, each group will document the entire process in a final report.

Project Submission

Final Report

Each group will be responsible for submitting a final report at the end of the project. This report, which can be handwritten or typed, should address the following topics:

1. Introduction: Here, students should contextualize the importance and application of area calculation in the real world and the objective of this project.

2. Development: Students should explain the theory behind area calculation, detail the activity carried out, discuss the methodology used, and finally present and discuss the results obtained.

3. Conclusion: Students should revisit the main points of the project, discuss what they learned, and conclude about the experience as a whole.

4. Bibliography: Students should indicate the sources they relied on to work on the project, such as books, web pages, videos, etc.

This final report will be used not only to evaluate the result of the area calculation done by the students but also to assess group collaboration, time management, and communication skills.