Context

Theoretical Introduction

The three-dimensional world around us is filled with objects of various shapes. Among these, a very common one is the prism, a geometric solid defined by parallel and congruent bases and rectangular lateral faces. These objects are common in our reality, being present in boxes, soda cans, buildings, etc.

To better understand the space occupied by a prism, it is necessary to calculate its volume. This is a fundamental concept in mathematics and natural sciences, and it has a specific formula for prisms: the product of the base area by the height. It is a simple relationship, but it requires an understanding of the prism's dimensions and the ability to calculate areas.

The study of prism volumes is an integral part of the high school mathematics curriculum and is essential for the development of spatial reasoning and the understanding of measures of magnitude.

Context

Frequently, in daily life, we come across situations where understanding volumes is essential. Whether to determine the amount of paint needed to paint a room, calculate the amount of soil to fill a garden, or even to know how much a shipping box can accommodate, volume calculation is a valuable skill.

For students who intend to pursue careers in engineering, architecture, design, physics, chemistry, and many other areas, the ability to understand and calculate volumes is absolutely crucial. Similarly, understanding volumes is essential for active citizenship, allowing people to make informed choices about issues that affect their lives and those of their loved ones.

Practical Activity

Activity Title: "Prism Architects: A Practical Approach to Volume Calculation"

Project Objective

The objective of this activity is to apply the concepts of prism volumes in a creative and collaborative project, allowing students to experience mathematics in a concrete and relevant way to the real world.

Project Description

Students will be divided into groups of 3 to 5 people. Each group will be tasked with designing a building in the shape of a prism and calculating its volume. The groups must choose the type of prism (rectangular, triangular, hexagonal, etc) and draw a sketch of the building on graph paper, considering the real proportions.

The students will then build a model of the building using easy-to-find materials - such as cardboard, clay, glue, etc. The model must respect the scale defined for the project. Based on the model, the students will calculate the volume of the prism.

The project will culminate in a presentation by each group, where they will showcase their models, explain the construction process and volume calculation of their building, and discuss what they have learned throughout the project.

Required Materials

To carry out this activity, groups will need:

• Graph paper to draw the building sketch.
• Materials for building the model (cardboard, clay, glue, etc).
• Ruler, compass, and calculator for volume calculation.

Step by Step

1. Group Formation and Prism Selection: students form groups and choose the type of prism they will work with.

2. Project Sketch: groups draw the building sketch on graph paper, respecting the chosen scale.

3. Model Construction: the team builds a model of the building, respecting the proportions of the sketch.

4. Volume Calculation: groups calculate the volume of the prism based on the model measurements.

5. Report and Presentation: groups prepare a written report on the project and present their work to the class.

At the end of the project, each group must submit a detailed report with the following sections:

• Introduction: Contextualization of the project, justifying the choice of prism, the importance of volume calculation, and the purpose of the study.
• Development: detailed description of the model construction process, volume calculations performed, discussion of results, and methodology used.
• Conclusion: reflection on what was learned, challenges encountered, skills developed, and practical applications of what was studied.
• Bibliography: indication of the research sources used to support the project.

Reports should be written in a clear and concise manner, using appropriate technical vocabulary and highlighting the connection between practical work and theory. Students should make use of the suggested resources and any others they consider useful for the project.