Objectives (5 - 7 minutes)

1. Understand the concept of volume and its application in spatial geometry, specifically in the cylinder.
2. Develop skills to calculate the volume of a cylinder, using the appropriate formulas, both with the measurements of the radius and height and with the area of the base and the height.
3. Solve practical problems involving the calculation of the volume of a cylinder, applying the acquired knowledge efficiently.

Secondary Objectives:

• Foster critical thinking and problem-solving skills in students.
• Encourage active participation of students in the class, promoting discussions and clarifying doubts.
• Apply the acquired knowledge in everyday situations, reinforcing the relevance of the content.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the class by reviewing the concepts of spatial geometry already studied, such as the characteristics and properties of the cylinder. It is important to recall the formula for calculating the area of the base of the cylinder, which will be used in the class. Additionally, it is necessary to reinforce the concept of volume and its relationship with the capacity of a solid, bringing examples of other solids whose volume has already been calculated. This review allows students to connect the new content with what has already been learned, facilitating understanding. (3 - 5 minutes)

2. Problem Situations: The teacher should present two problem situations involving the calculation of the volume of a cylinder. For example, one can question what is the maximum amount of water that a cylindrical glass of certain dimensions can hold, or what is the volume of a cylinder that is twice the height and three times the radius of another cylinder of known volume. These situations should stimulate students' curiosity and prepare them for the content that will be covered. (2 - 3 minutes)

3. Contextualization: The teacher should then contextualize the importance of the theme, emphasizing its application in everyday situations, such as in the calculation of volumes of cylindrical containers (cans, bottles, glasses, etc.), in engineering (calculation of volumes of ducts, pipelines, etc.) and in architecture (calculation of volumes of columns, pillars, etc.). This contextualization demonstrates the relevance of the subject and motivates students to engage more in the class. (2 - 3 minutes)

4. Introduction to the Topic: To arouse students' interest, the teacher can present curiosities or applications of calculating the volume of a cylinder. For example, it can be mentioned that the formula for calculating the volume of a cylinder was discovered by Archimedes, one of the greatest mathematicians of Antiquity, or that the formula for the volume of the cylinder is the same for the volume of a prism, which demonstrates an interesting connection between these two solids. Another curiosity is that the formula for calculating the volume of a cylinder can be deduced from the formula for calculating the area of the base and the height, which allows students to perceive the logic behind the formulas. (3 - 5 minutes)

Development (20 - 25 minutes)

1. Practical Activity with Cylinder Models (10 - 15 minutes)

   • The teacher should divide the class into groups of up to five students and provide each group with a set of materials for building cylinder models. These materials may include cardboard, scissors, glue, ruler, and string.
   • The teacher should instruct the students to build the cylinder models, varying the dimensions (radius and height). Each model should be labeled with the dimensions used.
   • After building the models, the teacher should guide the students to measure the height and radius of each cylinder and calculate the volume using the cylinder volume formula. The results should be recorded in a table.
   • Finally, the teacher should facilitate a classroom discussion where each group presents their models and the calculations performed. Students should be encouraged to compare the volumes obtained and identify patterns. This activity allows students to visualize the relationship between the dimensions of the cylinder and its volume, reinforcing the concept of volume and the formula for its calculation.

2. Problem-Solving Activity (10 - 15 minutes)

   • After the practical activity, the teacher should propose a series of problems involving the calculation of the volume of a cylinder. These problems should vary in difficulty and complexity, allowing students to apply the acquired knowledge progressively.
   • The problems can be presented on a worksheet or projected on the board, one at a time. Students should solve the problems in their groups, discussing problem-solving strategies and performing calculations.
   • The teacher should circulate around the classroom, assisting groups that encounter difficulties and guiding the discussion. After a set time, the teacher should gather the class and discuss the solutions to the problems, clarifying doubts and highlighting key points. This activity allows students to apply knowledge autonomously, developing their problem-solving skills.

3. Group Discussion Activity (5 - 10 minutes)

   • Finally, the teacher should propose a group discussion on the importance of calculating the volume of a cylinder in daily life, in engineering, architecture, and other areas. Students should be encouraged to share their insights and experiences, promoting reflection on the applicability of the content.
   • The teacher should guide the discussion by asking questions that stimulate critical thinking and students' argumentation. The objective of this activity is to consolidate learning, reinforce the relevance of the content, and develop communication and collaboration skills.

These activities allow students to explore the content in a playful and contextualized way, applying knowledge practically and developing essential skills for the 21st century.

Return (10 - 12 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher should gather the whole class for a collective discussion on the solutions found by the groups for the proposed problems. Each group should share their findings and problem-solving strategies, and other students are encouraged to ask questions and make comments.
   • The teacher should guide the discussion, highlighting key points, clarifying doubts, and correcting possible misconceptions. This discussion allows students to learn from each other, develop argumentation and communication skills, and see different approaches to problem-solving.

2. Connection with Theory (2 - 3 minutes)

   • After the discussion, the teacher should make the connection between the practical activities carried out and the theory presented at the beginning of the class. The teacher should reinforce the concept of volume, the formula for calculating the volume of a cylinder, and the importance of considering units of measurement.
   • The teacher should also review the problem-solving strategies used by students, emphasizing the importance of understanding the problem, identifying relevant information, planning the solution, and verifying the answer. This connection helps consolidate learning and reinforce understanding of the content.

3. Final Reflection (3 - 4 minutes)

   • To conclude the class, the teacher should propose that students reflect for one minute on the following questions:
     1. What was the most important concept learned today?
     2. What questions have not been answered yet?
   • After the reflection time, the teacher should invite students to share their answers. This reflection allows students to assess their own learning, identify possible doubts or difficulties, and express their opinions.
   • The teacher should value students' answers, clarify doubts that are possible, and note down the questions that have not been answered yet to be addressed in future classes.

The Return is a crucial stage in the learning process, as it allows students to consolidate what they have learned, connect theory with practice, and reflect on their own learning. Additionally, the teacher has the opportunity to assess students' understanding, identify possible gaps in learning, and plan appropriate pedagogical interventions.

Conclusion (8 - 10 minutes)

1. Summary and Recapitulation (2 - 3 minutes)

   • The teacher should start the Conclusion by recalling the main points covered in the class, such as the concept of volume, the formula for calculating the volume of a cylinder, and its relationship with the area of the base and the height.
   • The problem-solving strategies used should also be highlighted, emphasizing the importance of understanding the problem, identifying relevant information, planning the solution, and verifying the answer.
   • The teacher can ask students to retell, in their own words, what they have learned, thus reinforcing the understanding of the content.

2. Connection of Theory, Practice, and Applications (2 - 3 minutes)

   • The teacher should emphasize how the class connected theory, practice, and applications. Students should be reminded that the theory, presented at the beginning of the class, provides the necessary tools for solving practical problems, such as those proposed.
   • Additionally, it should be highlighted how calculating the volume of a cylinder, which may seem abstract at first, has numerous practical applications in daily life, engineering, architecture, and other areas.
   • The teacher can reinforce this connection by asking students to mention some of the applications discussed during the class, ensuring that the relevance of the content has been understood.

3. Additional Materials (1 - 2 minutes)

   • The teacher should suggest some additional study materials for students to deepen their understanding of cylinder volume. These materials may include explanatory videos, educational websites, math books, and extra exercises.
   • For example, the teacher can suggest that students watch an animated video that explains the formula for cylinder volume visually and intuitively, or visit a website that has an online cylinder volume calculator, so they can practice the calculation at home.
   • These additional materials allow students to review the content autonomously, at their own pace, thus reinforcing learning.

4. Importance of the Subject (1 - 2 minutes)

   • Finally, the teacher should reinforce the importance of the subject presented for daily life, other disciplines, and professional life.
   • The teacher can remind students that calculating the volume of a cylinder is a fundamental mathematical skill, with applications in various areas of knowledge and practical life.
   • Additionally, the teacher can emphasize that problem-solving, a skill developed during the class, is an essential competence for life, both personal and professional.

The Conclusion of the class is the perfect moment for the teacher to consolidate learning, reinforce the relevance of the content, and encourage students to continue studying and exploring the topic. Additionally, it allows students to reflect on what they have learned and how they can apply this knowledge in their lives.