Contextualization

The world is full of objects whose shapes can be represented by rectangular prisms, also known as parallelepipeds. Whether in architecture, with buildings and houses, in the packaging of a cereal or in the box of a smartphone, these objects are always around us. Understanding the properties of these shapes, particularly their volume, allows us to solve several practical problems of everyday life: for example, have you ever wondered how the amount of material needed to pack a box is calculated, or the amount of air inside a room?

The volume of a rectangular prism is calculated by multiplying the measures of its length, width, and height. This concept, although simple, is fundamental to many areas of science, from engineering to architecture, from physics to logistics.

Introduction

A prism is one of the most basic and versatile geometric shapes, used as a basis for the study of many other topics in mathematics and science. The rectangular prism, specifically, is a three-dimensional body consisting of six rectangular faces. Each face is a rectangle, and the opposite faces always have equal measurements.

The way we calculate the volume of a rectangular prism is by multiplying its length by its width and height. This formulation is quite intuitive: we are essentially counting how many 1x1x1 "cubes" fit inside our prism. Each of these "cubes" represents a unit of volume.

The study of the volume of rectangular prisms is crucial for various applications in the real world. Architects and engineers use this concept to calculate the internal space of buildings and the material needed to build them. In logistics, the volume of packages determines how they will be allocated for transport, and in cooking, the volume of containers used to store ingredients or prepare recipes.

Practical Activity: Building and Calculating the Volume of Rectangular Prisms

Project Objectives

1. Understand the theoretical concept of the volume of a rectangular prism and how to calculate it.
2. Apply the acquired knowledge in the construction of rectangular prisms with different dimensions.
3. Develop teamwork, time management, and critical thinking skills.

Detailed Project Description

The students, divided into groups of 3 to 5 people, will build rectangular prism models using cardboard or cardstock. These models should have different dimensions, defined by the group itself, and the students should calculate the volume for each one of them.

In addition to the construction and calculation of the volume, each group will be responsible for preparing a report containing theoretical information about the volume of a rectangular prism, the process of building the models, the calculations performed and the conclusions reached during the project.

In terms of duration, the project should take about two to four hours per student, and the maximum time for delivery of the completed project (models and report) will be one week.

Materials Required

1. Cardboard or cardstock
2. Ruler
3. Scissor
4. Glue
5. Pencil and eraser
6. Colored pens or markers (optional)

Detailed Step-by-Step

1. Research and study: Before starting the practical part, the students should research and study the volume of rectangular prisms, using the suggested resources and other sources they may find. Write down the important information, as it will be useful for the report.

2. Planning and division of tasks: Next, the groups should plan the activity, defining the dimensions of the prisms that will be built and dividing the tasks among the members.

3. Construction of the models: Each group will build their prisms using the cardboard or cardstock, following the previously defined dimensions. Remember to write down all the measurements used.

4. Volume calculation: Once built, the group must calculate the volume of each prism, remembering that the volume is obtained by multiplying the length by the width and by the height.

5. Report preparation: With the prisms built and the volumes calculated, the group should start writing the report. This document should contain four main topics: Introduction, Development, Conclusions and Bibliography used.

6. Project delivery: The activity will be completed with the delivery of the prism models and the written report.

Project Deliverables

The deliverables of this project will be:

1. Rectangular prism models: These will be the final products of the practical activity. Each model should have its measurements clearly annotated.

2. Report: This document should be well structured, with all sections clearly defined:

   a. Introduction: Students should contextualize the theme, explain its relevance and application in the real world, and indicate the purpose of the project.

   b. Development: The students should detail the process of building the models, explain the theory behind the volume calculation, present the calculations performed and discuss the results obtained.

   c. Conclusion: The students should highlight the main points of the work, explain the lessons learned and the conclusions drawn about the project.

   d. Bibliography: Students should indicate the sources used for the project.

Remember that, in addition to technical knowledge, this project aims to develop socio-emotional skills, such as time management, communication, problem solving, creative thinking, proactivity, among others.