Lesson Plan | Technical Methodology | Spatial Geometry: Metric Relations of Prisms

Objectives

Duration: 10 - 15 minutes

The purpose of this stage of the lesson plan is to ensure that students understand the metric relationships in prisms, developing skills that are vital for both academic success and practical applications in the job market. The focus on practical and experimental activities will allow students to see the direct relevance of the studied content in real contexts, fostering a more meaningful and engaging learning experience.

Main Objectives

1. Understand the fundamental metric relationships of a prism, including the calculation of height and distances between vertices that are not on the same face.

2. Develop practical skills to solve real problems related to prisms in academic and professional contexts.

Side Objectives

1. Promote critical thinking and the ability to apply geometric concepts in everyday situations.

Introduction

Duration: (15 - 20 minutes)

Purpose:

The purpose of this stage of the lesson plan is to engage the students by demonstrating the practical relevance of studying the metric relationships of prisms. The contextualization and curiosities help to spark students' interest and curiosity, while the initial activity serves to connect theoretical content to everyday reality and the job market.

Contextualization

Contextualization:

Spatial geometry is a fundamental part of mathematics that finds practical applications in various areas of our daily lives. Prisms, for example, are geometric shapes present in many structures we use daily, such as buildings, boxes, and even in optical instruments like light-dispersing prisms. Understanding the metric relationships of prisms allows not only to solve academic problems but also to apply this knowledge in engineering, architecture, and design projects.

Curiosities and Market Connection

Curiosities and Market Connection:

Civil Engineering: Precise calculations of prism dimensions are essential for constructing safe and efficient buildings. Architecture: Architects use prisms to design innovative and aesthetically pleasing structures. Optics: Prisms are used in optical instruments to manipulate light, such as in binoculars and telescopes. Packaging and Logistics: Knowing how to calculate the volume and dimensions of prismatic boxes aids in optimizing space during the transportation of goods.

Initial Activity

Initial Activity:

Provocative Question: Ask the students, “Have you ever wondered how buildings are designed to bear weight and weather conditions?” Allow them to briefly discuss their answers. Short Video: Present a short video (3-5 minutes) that shows the application of prisms in civil engineering and architecture projects. Suggest a YouTube video about skyscraper construction or the use of prisms in interior design.

Development

Duration: 60 - 65 minutes

The purpose of this stage of the lesson plan is to provide students with a practical and interactive experience, allowing them to apply theoretical concepts in concrete situations. Through building models and problem-solving, students develop essential skills for the job market, such as precision, teamwork, and critical thinking. Additionally, the fixation exercises help consolidate the knowledge acquired, ensuring a deep understanding of the topic.

Covered Topics

1. Definition of prisms and their properties.
2. Metric relationships in prisms: height, edges, vertices, and faces.
3. Calculation of distances between non-adjacent vertices.
4. Practical applications of the metric relationships of prisms.

Reflections on the Theme

Guide the students to reflect on the importance of precision in geometric calculations in civil engineering and architecture. Facilitate a discussion on how small errors in calculations can lead to significant problems in real structures, such as buildings and bridges. Encourage them to think about the responsibility of professionals who work with these measurements and how the knowledge acquired in class can be applied in their future careers.

Mini Challenge

Building a Prism Model

Students will be challenged to build a physical model of a prism using simple materials (skewers, modeling clay, cardboard, etc.) and then calculate the metric relationships of this prism, such as height, distances between vertices, and areas of the faces.

Instructions

1. Divide the class into groups of 3-4 students.
2. Distribute the necessary materials for each group.
3. Ask the students to choose a type of prism (triangular, quadrangular, etc.) and build the model following the provided instructions.
4. After construction, each group should measure and calculate the height of the prism, the distances between non-adjacent vertices, and the areas of the faces.
5. Facilitate the presentation of each group's results, encouraging discussion about the methods used and the challenges encountered.
6. Conclude the activity by highlighting the importance of these measurements in real applications, such as in civil construction.

Objective: Develop practical skills in building and measuring prisms, as well as promote teamwork and the application of theoretical concepts in a real context.

Duration: 40 - 45 minutes

Evaluation Exercises

1. Calculate the height of a triangular prism whose base has sides of 5 cm, 6 cm, and 7 cm, and whose volume is 210 cm³.
2. Determine the distance between two opposite vertices of a rectangular prism with dimensions 10 cm x 15 cm x 20 cm.
3. A regular hexagonal prism has lateral edges of 12 cm and base edges of 5 cm. Calculate the total surface area.
4. Explain how you would apply the calculation of the metric relationships of a prism in the construction of a bridge.

Conclusion

Duration: 15 - 20 minutes

📝 Purpose:

The purpose of this stage of the lesson plan is to consolidate the knowledge acquired by the students, promoting critical reflection on the content and its practical applications. The discussion and summary help reinforce the concepts covered, while the closing highlights the relevance of the topic to everyday life and future professional careers. In this way, students are encouraged to see mathematics as an essential and applicable tool in various contexts.

Discussion

💬 Discussion:

Guide a discussion among the students about the different stages of the lesson. Ask what the main challenges faced during the building of the prism model were and how they solved these problems. Facilitate reflection on how the metric relationships of prisms are applied in different professional areas, such as civil engineering and architecture. Encourage students to share their own perceptions about the importance of precision in geometric calculations and how this affects the safety and efficiency of constructions and projects.

Summary

📚 Summary:

Recap the main content covered in the lesson, including the definition and properties of prisms, the metric relationships (height, edges, vertices, and faces), and the calculation of distances between non-adjacent vertices. Emphasize how the lesson integrated theory, practice, and real applications, highlighting the building of the prism model and the calculations performed by the students.

Closing

🔚 Closing:

Explain that understanding the metric relationships of prisms is fundamental not only for academic success but also for various practical applications in the job market. Emphasize how the knowledge acquired can be utilized in the construction of buildings, in interior design, in bridge engineering, and other structures. Thank the students for their participation and reinforce the importance of precision and practical application of mathematical concepts.