Context

Introduction

The perimeter of a geometric figure is fundamentally the measure of the outline of that figure. For example, if we want to fence a garden that has the shape of a rectangle or edge a square tablecloth, the amount of material needed will be the perimeter of these shapes. Mathematically speaking, for polygons (geometric figures with straight sides) such as triangles, squares, and pentagons, the perimeter is the sum of the lengths of all their sides. For other types of figures, such as circles, the perimeter is sometimes called circumference and can be calculated through a specific formula.

Like many other mathematical concepts, the perimeter has not only theoretical relevance but also numerous practical applications. We can use the concept of perimeter to determine the amount of paint needed to paint the edge of a door, the length of the fence needed to enclose a park, or even the length of the line that separates a soccer field.

Context

Understanding how to calculate and apply the concept of perimeter is a useful skill in many different fields and careers. Architects may need to calculate the perimeter of a room to determine the length of the necessary baseboard. Engineers can use the perimeter to calculate the amount of material needed to build a structure. Even in everyday life, the perimeter has its applications. If we want to frame a picture, we need to calculate the perimeter of the frame to know the length of the frame we will need.

To deepen your knowledge on the subject, we suggest the following sources for study:

1. Book: "Elementary Mathematics: plane geometry" by Elon Lages Lima. Available in libraries and bookstores.
2. Brazil School Portal: Perimeter.
3. YouTube Channel "Matemática Rio with Prof. Rafael Procopio": Flat Geometry Playlist.

Practical Activity

Title: Building and Calculating Perimeters in Scale Models

Project Objective:

This project aims to enhance the understanding of perimeter calculation by applying it in a real context. Students will learn to calculate the perimeter of various geometric figures and apply these concepts by creating scale models of parks. Additionally, they will work on collaboration skills, time management, problem-solving, and creative thinking.

Project Description:

In groups of 3 to 5 students, each team will design and build a scale model of a park. The park must contain at least three different geometric figures (for example, triangle, square, pentagon, etc.) that the students will calculate the perimeter of. Each park space (represented by the geometric figures) must be surrounded by a material chosen by the group, representing the perimeter fence. Additionally, students will calculate the cost of the material needed to enclose each figure, based on a fictitious price per unit of measure provided by the teacher.

Required Materials:

• Cardboard for the base of the scale model
• Modeling clay or colored paper to create the geometric shapes
• Various materials to represent the fence (wool, wire, masking tape, etc.)
• Ruler or measuring tape
• Calculator
• Materials for decorating the scale model (optional)

Step by Step:

1. In your group, discuss and sketch a layout of the park. Determine which geometric figures will be used and where they will be located.

2. Use modeling clay or colored paper to create the geometric figures on the cardboard base.

3. Measure the sides of each figure and record the measurements. Use these measurements to calculate the perimeter of each figure. Remember, the perimeter is the sum of the sides of a figure!

4. Based on the price per unit of measure provided by the teacher, calculate the cost of the materials needed to enclose each figure.

5. Use the chosen materials to create the fences around each figure in the scale model.

6. Decorate the scale model as desired, representing a park.

Project Delivery:

The project presentation will be in two parts:

1. The Scale Model: Each group will present their scale model, explaining the choices of geometric figures, showing perimeter calculations, and explaining the calculation of material costs.

2. The Report: Each group will write a report, which should include:

   • Introduction: The report should start with a paragraph introducing the project, discussing the importance and application of the perimeter concept in the real world, and describing the objective of the work done.

   • Development: In this part, the group should explain in detail how the project was done, including the choice and creation of the figures, the measurement of the sides, the calculation of the perimeter, and the calculation of material costs. The group should also discuss any challenges encountered and how they overcame them.

   • Conclusion: Here, the group should summarize the main points of the project, state the learnings obtained, and draw conclusions from the work done.

   • Bibliography: Finally, the group should indicate the sources consulted to carry out the practical activity.