Context

Introduction

Mathematics is a discipline that is present in our daily lives, in various contexts. The concept of a prism, in particular, is a fundamental part of our understanding of three-dimensional geometric shapes and their properties. In this project, we will explore in depth the metric relationships in a prism, including how to calculate the height and the distance between vertices that are not on the same face.

A prism is a solid figure bounded by flat faces, with two of them, called bases, being congruent polygons situated in parallel planes. The other faces, called lateral faces, are parallelograms. There are several forms of prisms, based on the shape of their base, including rectangular prisms, triangular prisms, pentagonal prisms, among others.

The metric relationships in a prism involve a set of formulas and equations that allow calculating the properties of the prism, such as its sides, volumes, areas, and much more. This includes, for example, calculating the diagonal of a lateral face, the distance between non-adjacent vertices, among other calculations.

The Importance of Prisms and their Metric Relationships in the Real World

Prisms are present in many parts of our daily lives and the world around us. They are the shape of many objects we use every day, including boxes, cans, pencils, and many others. In addition, prisms are used in various areas of science and engineering, such as in the construction of buildings and bridges, in the design of machines, among others.

The concepts and calculations related to the prism are also fundamental for a series of professions and fields of study, including architecture, civil engineering, interior design, physics, and many others. By learning about prisms and their metric relationships, you will be gaining the necessary tools to solve complex problems in various areas of knowledge.

Practical Activity

Activity Title: Construction and Analysis of Prisms

Project Objective

This project aims to provide students with the opportunity to:

• Better understand the structure and properties of a prism through the construction of physical models.
• Apply mathematical concepts and formulas to calculate metric relationships in prisms.
• Develop collaboration, communication, and time management skills while working in a team.

Detailed Project Description

Each group of 3 to 5 students will be tasked with building physical models of three different types of prisms: a triangular prism, a quadrangular prism, and a hexagonal prism. After construction, students should measure and calculate the different metric relationships of the prisms, including the height, the distance between non-adjacent vertices, the volume, the area of the faces, among others.

Required Materials

• Cardboard or cardstock.
• Ruler or tape measure.
• Pencil.
• Scissors.
• Glue.

Detailed Step-by-Step for Activity Execution

1. Each group of students should decide on the dimensions of their prisms and draw the shapes on cardboard or cardstock. Remember that all sides of the base and the heights of the prisms must be equal for each specific type of prism.

2. Students will cut out the drawn shapes and assemble the prisms, using glue to join the edges.

3. Next, each group will measure the different parts of the prisms: sides, height, diagonals, etc.

4. Based on the measurements, students will calculate different metric relationships of the prisms: volume, area of the faces, distance between non-adjacent vertices, etc.

5. Finally, each group will write a report on the project, including an introduction to the concept of the prism and its importance, the development of the project, the conclusions obtained, and the bibliography used.

Project Delivery

The project delivery will consist of two main components:

1. Physical models of the prisms: Each group will deliver the physical models of the constructed prisms. These will be used to demonstrate the students' understanding of the structure and properties of the prism.

2. Project Report: The report should be structured as follows:

   • Introduction: Students will contextualize the concept of the prism, its importance and applicability in the real world, in addition to the project's objective.
   • Development: Students will discuss the theory behind the metric relationships in the prism and explain, in detail, the activities carried out, the methodology used, and the results obtained.
   • Conclusions: Students will express their learnings and conclusions about the project.
   • Bibliography: Students will indicate the sources consulted during the work.

This practical activity will allow students to apply theoretical concepts in a practical context, reinforcing understanding and memorization. In addition, the project will assess students' ability to collaborate in a group, manage time, and solve problems.