Contextualization

Theoretical Introduction

Prisms are three-dimensional geometric figures that have significant applications in various disciplines such as engineering, architecture, graphic design, and many others. They are characterized by two parallel and equal bases connected by lateral faces, each being a parallelogram. Depending on the shape of the bases, prisms can be rectangular, triangular, square, among others.

The metric relationships in a prism refer to the calculation of its main characteristics, such as height, base area, lateral face area, and volume. The height of a prism is the distance between its two bases. The base area depends on the shape of that base. The area of the lateral faces is calculated by the product of the prism's height by the sum of the lengths of the base sides. The volume is given by the product of the base area by the height.

In this project, we will specifically focus on the rectangular prism, a type of prism in which the bases and lateral faces are all rectangles. We will explore the metric relationships in this prism - how to calculate the height, determine the distance between vertices that are not on the same face, and discover the area of the faces and the volume of the prism itself.

Applied Contextualization

Geometry is a fundamental part of mathematics that has applications in almost every aspect of the real world. Prisms, in particular, are used in interior design to calculate the amount of material needed to cover an object or space, in civil engineering when designing a building's structure, and in physics when studying the propagation of light through a prism.

Therefore, understanding the metric relationships of a prism and the ability to calculate these relationships is a vital skill. Furthermore, this knowledge is also important for improving problem-solving skills, critical thinking, and logic.

Atividade Prática

Activity Title: "Exploring Prisms: A Journey through Metric Relationships"

Project Objective:

The objective of this project is to build a rectangular prism using recyclable materials and explore its metric relationships. The project also aims to develop observation, measurement, calculation, and problem-solving skills, as well as apply theoretical concepts in practice.

Detailed Project Description:

Groups will consist of 3 to 5 students, and the project should be completed within one week. Each group will be responsible for building a rectangular prism using recyclable materials, measuring its dimensions, calculating its metric relationships, and writing a detailed report.

Required Materials:

• Recyclable materials (juice or milk cartons, cardboard, etc.)
• Ruler
• Scissors
• Glue
• Colored pens or pencils
• Calculator

Detailed Step-by-Step:

1. Each group should collect recyclable materials that can be used to build a rectangular prism.
2. Using the ruler and scissors, students should cut the materials in the shape of a rectangular prism and assemble the structure with glue.
3. After constructing the prism, students should measure the dimensions of its faces and its height.
4. With these measurements in hand, students should calculate the prism's main metric relationships: face areas, total area, and volume.
5. Students should also calculate the distances between vertices that are not on the same face.
6. Finally, each group should write a report detailing the prism construction process, the measurements, the calculations performed, and their conclusions.

Project Deliverables:

1. Photos of the constructed prism.

2. Written document:

   • Introduction: Brief description of the project, its real-world applicability, and the activity's objective.

   • Development: Details of the material collection process, prism construction, measurement methodology, and calculations performed. Also include a discussion of the results, highlighting whether they align with the theory and why.

   • Conclusions: Reflect on the difficulties faced, how they were overcome, and what was learned throughout the project. Relate the obtained results to the studied theory and discuss how essential the ability to calculate metric relationships in a prism is for various areas of life.

   • Bibliography: List the sources used for the work, such as books, websites, videos, among others.

By the end of the project, students should have a deeper understanding of the metric relationships in a prism, as well as have developed their measurement, calculation, problem-solving, and teamwork skills.