Lesson Plan | Active Learning | Volume and Area: Cylinder

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is crucial to establish the focus of the lesson and ensure that both the teacher and students have a clear understanding of what will be covered. By defining specific objectives, students can better direct their prior study efforts and classroom activities, maximizing the effectiveness of learning. In this stage, the teacher will guide students on what is expected for them to learn and how to apply this knowledge in real contexts.

Main Objectives:

1. Empower students to calculate the volume of a cylinder, understanding the mathematical formula and its practical application in everyday situations.

2. Develop the skill to calculate the lateral and total surface area of a cylinder, using practical examples to reinforce learning.

Side Objectives:

1. Encourage logical reasoning and the application of mathematical concepts to everyday problems.
2. Promote collaboration and debate among students during practical activities to reinforce learning.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and remind them of previously studied concepts, using problem situations that stimulate critical thinking and the practical application of mathematical knowledge. Additionally, contextualizing the topic with everyday examples helps to recognize the relevance of mathematical studies in real life, increasing student interest and motivation.

Problem-Based Situations

1. Imagine you are responsible for organizing an event in a cylindrical space, such as a party tent. How would you calculate the volume of the space to ensure that all guests are comfortably accommodated?

2. Think of a kitchen remodeling situation in an industrial setting, where ingredient storage tanks are cylindrical. How would you calculate the external surface area of these tanks to ensure that the necessary coating is adequate?

Contextualization

The cylinder is a common shape found in many practical applications, from soda cans to storage silos in industries. Understanding how to calculate the volume and surface area of a cylinder is crucial not only for mathematics but also for various everyday situations, such as packaging design, architecture, and engineering. Knowing how to apply these concepts allows for optimizing the use of materials, space, and resources, making it a valuable skill in various professions and daily tasks.

Development

Duration: (70 - 75 minutes)

The Development stage is designed to allow students to apply the concepts of volume and surface area calculation of cylinders they studied previously in a practical and contextualized manner. Through playful and collaborative activities, they can explore different scenarios and challenges, solidifying their understanding and mathematical skills while developing teamwork and communication abilities.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Mathematical Festival of Cylinders

> Duration: (60 - 70 minutes)

- Objective: Apply the knowledge of volume calculation in a practical and collaborative context, developing teamwork and communication skills.

- Description: In this activity, students are challenged to design a festival using cylinders as a basis for the structures. The scenario consists of them being part of a team of event organizers and needing to plan the layout of booths, stages, and resting areas in a field shaped like a cylinder. Each group receives the dimensions of the field and must calculate the volume needed for each structure according to its intended use.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the dimensions of the cylindrical field and the functions of each structure (stage, booth, restrooms, etc.).

• Ask each group to calculate the volume needed for each structure, considering the capacity of people and equipment each must accommodate.

• Students should present a layout plan, including the dimensions of each structure and the total volume calculation of all components.

• Facilitate a class discussion where each group justifies its decisions based on the calculations made.

Activity 2 - Mini-City Architects

> Duration: (60 - 70 minutes)

- Objective: Encourage the practical application of volume calculation and promote critical and creative thinking in solving urban design problems.

- Description: Students, organized into groups, take on the role of architects who need to design a mini-city within a cylindrical space. They must calculate the total available volume and decide how to distribute different types of buildings (residential, commercial, green areas) to maximize land use. This challenge involves not only volume calculation but also creativity in devising a functional urban plan.

- Instructions:

• Form groups of up to 5 students and provide the dimensions of the cylindrical space.

• Explain that each group must calculate the total volume of the space and plan the city to optimize land use.

• Students must calculate the volume of each type of building and green area they wish to include, ensuring that the sum of the volumes does not exceed the total volume of the cylinder.

• Each group must draw the city plan on graph paper and present its project, explaining the decisions made during planning.

• Conduct a vote among the projects to choose the most creative one that best utilized the available space.

Activity 3 - Cylinders in Space: An Interplanetary Adventure

> Duration: (60 - 70 minutes)

- Objective: Develop skills in volume and surface area calculation in an interdisciplinary context of science and engineering, stimulating critical thinking and collaboration.

- Description: In this activity, students become space scientists who need to design a space station with cylindrical sections that serve as living areas, laboratories, and food production areas. Each group must calculate the volume and surface area needed for each section, considering the astronauts' needs and the limitations of the available space in their spacecraft.

- Instructions:

• Divide the class into groups of up to 5 students and assign each group a type of section to design (living area, laboratory, food production).

• Provide the dimensions of the spacecraft and the cylinders they need to design.

• Students must calculate the volume and surface area of each section, considering specific needs (such as the number of astronauts, equipment, and plants).

• Each group must draw a technical sketch of its section and present it to the class, discussing the implications of their calculations and design decisions.

• Conduct a simulation of the 'launch' of the spacecraft, where each group presents its section and how it fits into the overall spaceship design.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate learning by allowing students to reflect on the work done and articulate the knowledge acquired in a collective discussion. This stage also serves for the teacher to evaluate students' understanding of the concepts of volume and surface area of cylinders, in addition to promoting communication and argumentation skills. By sharing experiences and hearing colleagues' solutions, students can gain new perspectives and insights, enriching their learning.

Group Discussion

To initiate the group discussion, the teacher may ask each group to share a brief description of the project they developed, focusing on the challenges encountered and the creative solutions applied. Next, encourage students to discuss the differences between the projects and how each group approached the calculations and design in distinct ways. Use questions such as: 'What were the biggest challenges in calculating volumes and areas?', 'How did you decide to distribute the different structures in the cylindrical space?' and 'Was there any idea from another group that you wish you had thought of first?' to guide the conversation.

Key Questions

1. What are the main practical applications you can envision for the concepts of volume and surface area of cylinders after this activity?

2. How can the ability to visualize and calculate volumes help in other studies or everyday situations?

3. What mathematical and non-mathematical skills do you believe were most important for successfully completing the project?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage serves to reinforce and synthesize the lessons learned in class, ensuring that students can consolidate the knowledge acquired. Additionally, it helps to establish a clear connection between the mathematical theory studied and its practical applications, highlighting the relevance of the topic for everyday situations and the students' future careers. This recap also prepares students for long-term information retention and for effectively utilizing knowledge in non-academic contexts.

Summary

To wrap up today's lesson, let's recap the main points discussed about the volume and surface area of cylinders. We reviewed the formula for calculating volume and the importance of understanding the applicability of these calculations in real situations, such as event design, urban planning, and even in space projects.

Theory Connection

During the lesson, we observed how the theory of volume calculation directly connects with practical activities, like planning a festival or designing a mini-city. This hands-on approach not only facilitates the understanding of mathematical concepts but also demonstrates their relevance in everyday life and various professions.

Closing

Finally, it is important to emphasize that the knowledge acquired about volume and surface area calculation of cylinders has significant applications in daily life, helping to optimize resources, plan spaces, and solve practical problems in various areas. Students are prepared to recognize and apply these concepts in varied contexts, reinforcing the importance of mathematics in the real world.