Objectives (5 - 7 minutes)

1. Understanding the concept of volume and area of the cylinder, including the formula for its calculation. Students should be able to explain what a cylinder is in mathematical and physical terms, and understand how the area of a cylinder differs from the volume.
2. Develop calculation skills to determine the volume and area of a cylinder, using the appropriate formula and given measurements. This includes the ability to substitute the appropriate values into the formula and solve the equation.
3. Apply the acquired knowledge to solve real-world problems involving cylinders, such as calculating the capacity of a cylinder, or calculating the materials needed to cover a cylindrical surface.

Secondary Objectives:

• Promote critical thinking and problem-solving, encouraging students to think about how and where cylinder formulas can be applied.
• Develop communication and collaboration skills, through group activities and classroom discussions.
• Foster curiosity and interest in mathematics, showing students how mathematical concepts apply to the real world.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts: The teacher should start the lesson by reviewing the concepts of area and volume, which were studied in previous classes. It is important that students have a solid understanding of these concepts, as they will be the basis for the study of the cylinder. The teacher can ask quick questions to check students' understanding and correct any misunderstandings. (3 - 5 minutes)

2. Initial Problem Situations: Next, the teacher can present two problem situations related to the theme of the lesson. For example, he can ask students how to calculate the volume of water that fits in a gas cylinder, or how to determine the amount of paint needed to paint the surface of a metal cylinder. These problem situations serve to arouse students' interest and show the relevance of the subject. (3 - 5 minutes)

3. Subject Contextualization: The teacher should then contextualize the importance of studying the volume and area of the cylinder. He can mention some practical applications, such as the use of cylinders in engineering, architecture, cooking, and even in our daily lives, such as in soda cans. The teacher can also highlight how calculating the volume and area of the cylinder can be useful in real situations, such as in the industry to calculate storage capacity or in design to plan the amount of material needed. (2 - 3 minutes)

4. Introduction to the Topic: To introduce the topic in an interesting and engaging way, the teacher can share some curiosities about the cylinder. For example, he can mention that the cylinder is one of the oldest geometric shapes to be studied, with evidence of its use in ancient Mesopotamia and Egypt. The teacher can also talk about how the cylinder is a very efficient shape, as it has the highest ratio between volume and area of all three-dimensional shapes. These curiosities can help capture students' attention and motivate them to learn more about the subject. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory - Cylinder Definition (5 - 7 minutes): The teacher should start by explaining the theory necessary to understand the calculation of the volume and area of the cylinder. He should begin by defining what a cylinder is, emphasizing that it is a geometric solid that has two parallel bases and a curved lateral surface. The teacher can use a three-dimensional model of a cylinder to illustrate the definition and help students visualize the shape. The teacher should also mention that the height of the cylinder is the distance between the two parallel bases.

2. Theory - Cylinder Volume (5 - 7 minutes): Next, the teacher should explain how to calculate the volume of a cylinder. He should start by showing the formula for the volume of the cylinder (V = πr²h), where V is the volume, π is a constant (approximately 3.14), r is the radius of one of the bases, and h is the height of the cylinder. The teacher should explain that the radius is the distance from the center of a base along its circumference, and that the height is the distance between the two parallel bases. The teacher can then provide a step-by-step example of how to calculate the volume of a cylinder, substituting the values into the formula and solving the equation.

3. Theory - Cylinder Area (5 - 7 minutes): The teacher should then explain how to calculate the area of the cylinder. He should start by showing the formula for the area of the cylinder (A = 2πrh + 2πr²), where A is the area, π is the constant, r is the radius of one of the bases, and h is the height of the cylinder. The teacher should explain that the area of a cylinder is the sum of the areas of its two bases (2πr²) and the area of its lateral surface (2πrh). The teacher can then provide a step-by-step example of how to calculate the area of a cylinder, substituting the values into the formula and solving the equation.

4. Practice - Application Exercises (5 - 7 minutes): After explaining the theory, the teacher should provide students with a series of exercises to practice calculating the volume and area of the cylinder. The exercises should vary in difficulty and include problems that require the application of concepts to real-world situations. The teacher should move around the classroom, providing help and clarifying doubts as needed.

5. Discussion - Review and Clarification (3 - 5 minutes): At the end of the Development, the teacher should review the main concepts and clarify any remaining doubts. The teacher can take this opportunity to reinforce the application of cylinder concepts in real-world situations, helping students see the relevance of what they are learning.

Return (8 - 10 minutes)

1. Lesson Review (3 - 4 minutes): The teacher should start the Return stage by recapping the main points covered during the lesson. He can ask students to remember and summarize the definitions of a cylinder, as well as the formulas for calculating the volume and area. This is an opportunity to reinforce learning and correct any misunderstandings.

2. Connection to Practice (2 - 3 minutes): The teacher should then help students connect the theory learned with practice. He can do this by bringing back the initial problem situations and showing how the concepts of volume and area of the cylinder can be applied to solve them. The teacher can also present other examples of cylinder application in real life, such as calculating the capacity of a gas cylinder or determining the amount of paint needed to cover the surface of a cylinder. This will help students see the relevance of what they are learning and appreciate mathematics as a practical tool.

3. Learning Reflection (2 - 3 minutes): The teacher should then ask students to reflect on what they learned during the lesson. He can ask questions like: What was the most important concept you learned today? What questions have not been answered yet? What did you find most interesting or challenging about the volume and area of the cylinder? Students should be encouraged to think deeply about the answers to these questions and express their reflections. The teacher can take note of students' answers for future reference.

4. Feedback and Questions (1 - 2 minutes): Finally, the teacher should ask for feedback from students about the lesson. He can ask if students feel they understood the concepts covered and if they think the lesson was effective. The teacher should also encourage students to express any doubts or difficulties they may still have. This will allow the teacher to make necessary adjustments in future lessons and ensure that all students are keeping up with the content.

The Return stage is a crucial part of the lesson, as it allows the teacher to assess the effectiveness of his instruction, reinforce students' learning, and correct any misunderstandings. In addition, reflecting on learning helps students consolidate what they have learned and build connections between theory and practice.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered during the lesson. He can recap the definition of a cylinder, the formulas for calculating the volume and area, and the practical applications of these concepts. The teacher should do this concisely and clearly, reinforcing what students have learned.

2. Connection to Theory and Practice (1 - 2 minutes): The teacher should then reiterate how the lesson connected theory and practice. He can mention again the problem situations presented at the beginning of the lesson and how students used the concepts learned to solve them. The teacher can also repeat some of the examples of cylinder application in real life, reinforcing the relevance and usefulness of these concepts.

3. Extra Materials (1 - 2 minutes): The teacher should suggest extra materials for students who want to deepen their understanding of the topic. This may include math books, educational websites, explanatory videos, and learning apps. The teacher can also provide some additional exercises for students who want to practice more.

4. Importance of the Cylinder (1 minute): Finally, the teacher should highlight the importance of the cylinder in the real world. He can reinforce how the cylinder is a common and useful shape, found in various everyday applications. The teacher can mention again some of the practical applications discussed during the lesson, emphasizing how knowledge of the volume and area of the cylinder can be useful in various situations.

The Conclusion is a crucial part of the lesson, as it allows the teacher to reinforce students' learning, make connections between theory and practice, and encourage continuous study. In addition, by highlighting the importance of the topic, the teacher helps motivate students and show the relevance of mathematics in their lives.