Contextualization

Volume is a quantity that measures the space occupied by a body or its capacity to hold some substance. In mathematics, it is especially important when studying spatial geometry, as it allows us to quantify spheres, cylinders, cones, and specifically for our project, rectangular prisms.

Rectangular prisms, also known as parallelepipeds, are three-dimensional solid figures bounded by six rectangular faces. In them, the volume can be calculated relatively simply: just multiply the measure of the height, width, and length.

Volume measurements are used in various situations in our daily lives. At home, for example, they define the space a piece of furniture will occupy or the capacity of a storage box. In cooking, they determine the amount of ingredients that will fit in a pot. In engineering and architecture, they are essential for planning and building structures.

For industry, determining the volume of their products or the packaging that will be used to contain them is essentially important. Furthermore, volume also plays a significant role in areas such as logistics, transportation, and goods storage, as it allows evaluating the space needed to accommodate a certain quantity of products in a vehicle or warehouse.

It is possible to delve deeper into the study of volume and rectangular prisms through online resources such as the OBMEP Mathematics Portal, which offers detailed explanations and practical exercises on the subject, and the video Calculating the volume of the rectangular prism, available on YouTube, which presents the volume calculation in a didactic and dynamic way, using practical examples.

Practical Activity

Activity Title: Building and exploring rectangular prisms

Project Objective

This project aims to enhance students' knowledge about rectangular prisms and the calculation of their volume through a practical, collaborative, and playful activity.

Detailed Project Description

Groups, composed of 3 to 5 students, will build rectangular prisms using cardboard or cardstock and adhesive tape. Each group will receive a set of dimensions (height, width, and length) different from the other teams. They will then calculate the volume of the constructed figures.

Working together not only in construction but also in solving the proposed problems aims to develop teamwork, communication, and creative thinking skills. The project should be carried out over a month, with an estimated dedication of 5 to 10 hours per student.

Required Materials

• Cardboard or Cardstock
• Adhesive tape
• Ruler
• Pencil
• Calculator

Step-by-Step for Activity Execution

1. Form groups of 3 to 5 students.
2. Each group will receive a tuple of three numbers (height, width, and length).
3. With the received dimensions, the groups must build their own rectangular prism using cardboard or cardstock and adhesive tape.
4. After building the prisms, each group must calculate the volume of their figure. This should be done by multiplying the dimensions (height, width, and length).
5. The groups should prepare a presentation, explaining how they built the prism and how they calculated its volume.
6. Finally, each team must prepare a detailed written report containing the following topics: Introduction, Development, Conclusions, and Bibliography.

Project Deliverables

• Rectangular Prism: Each group must deliver their constructed rectangular prism.

• Presentation: Each group must present their work, explaining the prism's construction and volume calculation.

• Written Report:

  • Introduction: The student must contextualize the theme, its relevance and real-world application, as well as the objective of this project.
  • Development: The student must explain the theory behind volume and the rectangular prism, detail the activity, indicate the methodology used, and finally present and discuss the results obtained.
  • Conclusion: The student must conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.
  • Bibliography: The student must indicate the sources they relied on to work on the project such as books, web pages, videos, etc.