Contextualization
The study of prisms is a fascinating and immensely pertinent topic in many disciplines, including mathematics, physics, and engineering. Simply put, a prism is a geometric solid with two identical bases and rectangular or parallelogram-shaped lateral faces. One significant property of prisms is their volume, which is the amount of space that a prism occupies. Understanding the concept of volume and how to calculate it is crucial, not only in solving mathematical problems but also in practical applications in various real-world scenarios.
The volume of a prism is calculated by multiplying the area of the base by the height. While the formula may seem simple, it is the understanding of what these measurements represent and how they interrelate that can be challenging. It is essential to grasp that the area of the base is the measure of the "space" occupied by the base, while the height is the "distance" from the top of the base to the top of the prism. By multiplying these two measurements, we obtain the volume, which is effectively the three-dimensional space that the prism occupies.
But why is this important? In many professions and everyday situations, it is necessary to know the volume of an object. An architect needs to calculate the volume of a building to determine the amount of materials needed for its construction. An engineer needs to know the volume of a reservoir to calculate its storage capacity. A student may need to calculate the volume of a box to determine whether their belongings will fit inside. Therefore, having a solid understanding of the concept of volume and how to calculate it can have very real and significant practical applications.
For further reading on the topic, we suggest the following resources:
- Book: "Matemática Volume Único - Ensino Médio" by Gelson Iezzi (Editora Atual)
- Professor Ferretto's Website: Prisms and Cylinders - Theory and Solved Exercises | Professor Ferretto
- Videos from the YouTube Channel Matemática Rio with Prof. Rafael Procópio: Matemática Rio with Prof. Rafael Procópio
Hands-on Activity – “Calculating Volume in Our Community”
Project Objective:
This project aims to apply the acquired knowledge about the volume of prisms in a practical and real-world context, fostering interaction with the community and collaboration among students.
Detailed project description:
In this project, groups of 3-5 students will identify, measure, and calculate the volume of different prisms present in the community, such as buildings, water reservoirs, boxes, among others. Additionally, students should delve into related topics, such as the importance of volume for certain professions (e.g., architecture, engineering) and how volume calculation can be useful in everyday situations. This project is interdisciplinary, involving mathematics (area and volume calculations) and geography (understanding scale and accurate measurements).
Materials required:
- Measuring tape
- Notebook
- Camera or smartphone to record the identified objects
- Library or internet for research
- Drawing applications to sketch the measured objects
- Presentation software (PowerPoint, Google Slides) for report preparation
Detailed step-by-step:
-
Identification of the study objects: Each group must identify and select at least three distinct prisms present in their community for study. Students should take pictures of the chosen objects, which will be included in their final report.
-
Measurement: Using the measuring tape, students should measure the dimensions of the chosen prisms (height, length, and width). These measurements should be carefully recorded.
-
Volume calculation: Applying the theory learned, students should calculate the volumes of the chosen prisms. They should discuss and explain in detail the calculations performed and the results obtained.
-
Practical applications: The groups should investigate and discuss the importance and applications of volume calculation in professional and everyday contexts. For example, they could interview professionals who use these calculations in their occupations (architects, engineers, etc.).
-
Report preparation: With the collected information and calculations, each group should prepare a report detailing the project process, findings, and conclusions. The report should include an Introduction contextualizing the theme and the project's objective; a Description of the practical activity, obtained results, and theoretical discussion; the Conclusion of the work, and finally, the Bibliography used.
This project should last approximately three weeks, allowing enough time for research, site visits, measurements, calculations, discussions, and report writing.
Project deliverables:
The project will culminate in the submission of a final report, where students will present the chosen study objects, the calculations they performed, and the results found. This report is not only the final product of the project but also the students' opportunity to tell the story of their project in detail, from the process of choosing the study objects to the challenges faced, the discoveries made, and the insights gained. This document will complement the hands-on experience, serving as a means of reflective journaling and consolidating the learning acquired.
The written report should follow the traditional research project structure, comprising:
- Introduction
- Development (methodology, practical activity, and discussion of results)
- Conclusions
- Bibliography used.
The report should also include photographs of the objects studied and schematic drawings of the measurements taken, as well as screenshots of the calculations performed, either manually or using computer programs.
This report will be the basis for the project's assessment. In addition to a command of the concepts studied, the quality of the presentation, accuracy of the measurements and calculations, the relevance and depth of the discussion made, and the correctness and appropriateness of the language use will be considered.
