Contextualization

The perimeter is one of the most basic concepts in geometry and is frequently used in everyday life. If you have ever measured a room before buying a carpet or wrapped a tape around a box to know how much wrapping paper you needed, you were calculating the perimeter. This is an extremely important and also very interesting concept!

The perimeter can be defined as the measurement of the outer boundary of a geometric shape. In other words, if you walk around a plot of land, a building, or an object, the distance you covered is the perimeter of that object. The perimeter is a measure of length and is usually expressed in units of measurement such as meters, centimeters, or kilometers.

But why is the perimeter so important? Imagine you want to build a fence around your garden to prevent animals from damaging your plants. The material you will need to build that fence is directly related to the perimeter of your garden. Similarly, if you want to put frames on all the windows of your house, the amount of material needed will be determined by the perimeter of the windows.

Now that we understand a little more about the perimeter, it's time to put our knowledge into practice. Through a practical activity, we will not only learn more about the perimeter but also develop important skills such as time management, communication, problem-solving, and creative thinking.

Some reliable resources that can help you deepen your understanding of the perimeter include the website Só Matemática, which has several explanations and examples on how to calculate the perimeter of various geometric shapes. Another resource is the YouTube channel Matemática Rio with Prof. Rafael Procopio, which provides a series of videos explaining perimeter calculation in a simple and fun way.

Practical Activity

Activity Title: "The Mission of the Perimeter"

Project Objective

The project aims to allow students to apply the concepts of perimeter in a practical way, through the creation of a city model, where they will need to calculate the perimeter of various structures. Students will be encouraged to work in teams, improve communication, practice time management, and develop problem-solving skills.

Detailed Project Description

Students, in groups of 3 to 5, should plan and build the model of a city that must contain at least five types of structures with different geometric shapes (for example, a square-shaped park, a circular track, a triangular-shaped building, etc.). Each structure must be properly planned beforehand, with perimeter calculations presented.

After the planning phase, students will build the structures in the model, applying the knowledge acquired in Arts for a better visual representation. The project's completion requires the presentation of the model and the delivery of the report with the perimeter calculations, where they will explain the construction process, the challenges encountered, and how they overcame them.

Finally, they will be challenged to calculate the construction cost of a fence around each structure, considering that each meter of fence costs a value X. They should present these calculations in the report.

Required Materials

1. Cardboard or other material for the model base (an approximate base of 1m x 1m would be ideal)
2. Construction materials for the model (paper, colored pencils, cardboard, glue, scissors, etc.)
3. Ruler or measuring tape
4. Pencils and erasers
5. Notebook or tablet for research
6. Cameras for documenting the process (can be a smartphone)

Detailed Step-by-Step for Activity Execution

1. Planning Phase: In this stage, students must decide which structures they will create and draw a plan for each of them, including measurements and perimeter calculations.
2. Construction Phase: In this phase, students must build the model following their plans, taking photos of the process for documentation and possibly including them in the report.
3. Calculating the Fence Cost: Using the measurements of the obtained perimeters, students must calculate the cost of the fences for each structure.
4. Writing the Report: Students will write the report, explaining the calculations, the model construction, the challenges encountered, and how they overcame them.
5. Model and Report Presentation: Groups will present the model to the class and discuss the report content.

Project Deliverables

• The complete model of the city, with all planned structures.
• The report containing the planning of the structures, the perimeter calculations, the fence cost calculation, and conclusions about the project experience.
• Photos of the model construction process for documentation.

Students should use the knowledge acquired in the development of the practical activity for writing the report. The document should fit and complement what was worked on in the project, expressing the learnings acquired and the experiences lived during the execution. The report should be clear and objective, making use of mathematical language when necessary, especially when showing the calculations.