Context

Understanding the concepts of area and perimeter is fundamental in the study of mathematics and applies to a variety of real-world scenarios. The perimeter is the measurement of the outline of a geometric figure, representing the distance around the figure, while the area is the measurement of the space within a figure.

To better understand, imagine a path around a park, the distance you would walk on that path would be equivalent to the perimeter. On the other hand, if you wanted to paint the entire floor of the park, the amount of paint needed would be determined by the area of the park.

Often, people confuse area with perimeter, believing that figures with equal areas have equal perimeters, or vice versa. However, this is not true. Figures with the same perimeter can have different areas and figures with equal areas can have different perimeters. Through this project, you will have the opportunity to explore these concepts more deeply and gain a better understanding.

By understanding these concepts, you will be able to apply this knowledge in real-life situations, whether to calculate the amount of material needed to build a fence or paint a wall, or even to understand the layout of fields and courts in various sports.

This project offers a collaborative and practical learning environment. The goal is for you to investigate, through practical activities and group discussions, the concepts related to area and perimeter and how they relate.

Resources for studying and reviewing the concepts can be found at:

• Mathematics Portal on perimeter and area
• Mathematics Zup - area and perimeter concepts
• World Education - difference between area and perimeter

Both concepts will be applied throughout the project, providing a deeper understanding and significant learning of these topics.

Practical Activity: Shapes and Figures

Project Objective

This project aims to investigate and explore the concepts of perimeter and area. Students will create various figures with equal perimeters but different areas, and vice versa, using construction paper and strings.

Detailed Project Description

This is a project that involves the creation of physical models to investigate the concepts of area and perimeter. Groups of students will create figures with equal perimeters but different areas, and other figures with equal areas but different perimeters.

Although the concepts are related, when carrying out this project, students should understand that figures with the same perimeter do not necessarily have the same area and that figures with the same area can have different perimeters.

Materials Needed

The materials needed for this project are:

• String or twine of known length (1 meter, for example)
• Construction paper
• Ruler or measuring tape
• Scissors
• Pens or markers

Detailed Step-by-Step for Activity

1. Form groups of 3 to 5 students. Each group will receive a piece of string or twine of known length. Ensure that each group has the same length of string or twine.

2. Each group must now create several different figures (square, rectangle, triangle, circle, etc.) in such a way that each figure has the same perimeter (the length of the string or twine).

3. Using construction paper, students will create physical models of these figures. The models should reflect the dimensions of the figure's perimeter.

4. After making the figures, each group must measure and record the area of each of the figures.

5. Next, students should create several different figures that have the same area but different perimeters. Again, they will use construction paper to create physical models of each figure.

6. Students must measure and record the perimeter of each figure that has the same area.

7. Finally, each group will present their findings to the class. They will compare their figures, discussing why figures with the same perimeter have different areas and why figures with the same area have different perimeters.

Final Project Product and Delivery Format

At the end of the project, each group must produce a written report that reflects their understanding of the concepts and documents their findings. The report should follow this format:

1. Introduction: Provide context to the problem, explain the relevance of studying area and perimeter, and the project's objective.

2. Development: This section should contain two parts. The first should present the theory of the concepts of area and perimeter. In the second part, the group should describe in detail the process of the activity, including the methodology used to create the figures, how the measurements were taken, and the results of the measurements. This section should contain visual evidence (such as photos or drawings) of the created figures, as well as tables with measurements and calculations for the area and perimeter.

3. Conclusion: In this part, students should summarize the main points of the introduction and development, explaining what they learned from the activity. They should discuss their results, especially the differences in the areas of figures with the same perimeter and the differences in the perimeters of figures with the same area.

4. Bibliography: Cite all sources that were used to understand the concepts and develop the project.