Objectives (5 - 10 minutes)

1. Understand the concept of a cone: Students should be able to identify a cone and differentiate it from other geometric solids. They should also be able to describe the properties of a cone, such as the presence of a circular base and a single curved surface extending from the base to a point called the apex.

2. Learn the formula for calculating the volume of a cone: Students should be able to memorize and apply the formula for calculating the volume of a cone (Volume = 1/3 * π * r² * h), where "r" is the radius of the cone's base and "h" is the height of the cone.

3. Solve practical problems involving the volume of cones: After learning the formula, students should be able to apply it to solve real problems that involve calculating the volume of cones. They should be able to identify the necessary information in the problem, substitute it into the formula, and calculate the volume correctly.

Secondary Objectives:

• Develop critical thinking skills: When solving problems involving the volume of cones, students should be encouraged to think critically, identifying which information is relevant and how to apply the formula correctly.

• Promote active learning: Through practical activities, students will be encouraged to learn actively, seeking solutions to the proposed problems.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson with a brief review of concepts that are fundamental to understanding the lesson topic, such as the definition of geometric solids (specifically cones) and the formula for calculating the volume of cylinders and spheres. This review can be done through quick and interactive questions to assess students' prior knowledge and prepare them for the new content.

2. Presentation of problem situations: Next, the teacher should present two problem situations that serve as hooks for the Introduction of the topic. These may include, for example, the need to calculate the volume of a cone to fill an ice cream cone or to determine the amount of paint needed to paint a cone.

3. Contextualization of the topic's importance: The teacher should then contextualize the importance of the topic, explaining that calculating the volume of cones is used in many areas of everyday life and science, such as in architecture (to calculate the volume of domes, for example), in engineering (to calculate the volume of silos or storage tanks), and in cooking (to calculate the amount of ingredients needed to fill a cone-shaped cake pan, for example).

4. Introduction of the topic with curiosities: To spark students' interest, the teacher can introduce the topic with some curiosities or interesting applications. For example, they can mention that the famous Egyptian monument, the Great Pyramid of Giza, is essentially a cone with the top cut off, and that its volume can be calculated using the cone volume formula. Another curiosity is that the cone volume formula is one of the first mathematical formulas discovered and proven by ancient Greek mathematicians.

5. Presentation of the lesson objective: Finally, the teacher should present the lesson objective, which is to empower students to understand the concept of cone volume, memorize the formula for calculating this volume, and apply this formula to solve practical problems.

Development (20 - 25 minutes)

1. Cone construction activity (10 - 15 minutes): The teacher should divide the class into groups of 3 to 4 students and provide each group with a piece of cardboard, a ruler, a compass, scissors, and glue. The teacher will then instruct the students to construct a cone using the cardboard, following the provided measurements (base radius and height). During the activity, the teacher should move around the groups, guiding them and clarifying any doubts that may arise. This activity will not only help students visualize a three-dimensional cone but also understand how the cone volume formula is related to its shape.

   • Activity step by step:
     1. Each group receives the necessary materials.
     2. The teacher instructs the students to draw a circle on the cardboard with the compass, which will be the base of the cone.
     3. The students should cut out the circle and form a circular sector.
     4. The teacher instructs the students to roll up the circular sector to form the cone.
     5. The students should glue the ends of the sector to secure the cone.

2. Measurement and calculation of cone volume activity (10 - 15 minutes): After constructing the cones, the teacher will instruct the students to measure the base radius and the height of the cone they built. Then, the students should apply the cone volume formula (Volume = 1/3 * π * r² * h) to calculate the volume of their cone. This activity will allow students to experience the practical application of the cone volume formula and verify the relationship between the cone's dimensions and its volume.

   • Activity step by step:
     1. The students measure the base radius and the height of the cone they built.
     2. They substitute the values into the cone volume formula and perform the calculation.
     3. The students record the volume value of their cone.

3. Problem-solving activity (5 - 10 minutes): Finally, the teacher will provide the groups with a series of problems involving the calculation of cone volumes. The students, in their groups, should solve these problems by applying the cone volume formula. The teacher should move around the groups, assisting them and clarifying any doubts that may arise. This activity will allow students to consolidate their understanding of cone volume calculation and develop their problem-solving skills.

   • Activity step by step:
     1. The teacher provides the groups with a series of cone volume problems.
     2. The students, in their groups, solve the problems by applying the cone volume formula.
     3. The students record their solutions, and the teacher discusses them with the class, clarifying any doubts that may arise.

Return (10 - 15 minutes)

1. Group discussion (5 - 7 minutes): The teacher should draw the attention of all students and initiate a group discussion about the solutions or conclusions that each group found during the practical activities. Each group should have the opportunity to share their findings, difficulties, and strategies used to solve the problems. The teacher should moderate the discussion, encouraging the participation of all students and ensuring that the conversation remains focused on the lesson topic.

   • Step by step:
     1. The teacher asks a representative from each group to share the solution or conclusion that their group found during the activities.
     2. The teacher encourages other students to ask questions or make comments about the groups' presentations.
     3. The teacher highlights the effective strategies used by the groups and clarifies any misunderstandings that may have arisen during the presentations.

2. Connection with theory (3 - 5 minutes): After the group discussion, the teacher should provide a brief review of the theory presented at the beginning of the lesson, highlighting how the theory connects with the practical activities carried out by the students. The teacher should emphasize the importance of understanding the cone volume formula and how it can be applied to solve real problems. The teacher can also reinforce key concepts of the lesson by answering any questions students may have about the theory.

   • Step by step:
     1. The teacher reviews the cone volume formula and how it was used during the practical activities.
     2. The teacher emphasizes the importance of understanding the theory for solving practical problems.
     3. The teacher answers any questions students may have about the theory.

3. Individual reflection (2 - 3 minutes): To conclude the lesson, the teacher should ask students to reflect individually on what they have learned. The teacher can ask guiding questions, such as: "What was the most important concept you learned today?" and "What questions have not been answered yet?" The teacher should give students a minute to reflect and then open the discussion for students to share their reflections, if they are comfortable.

   • Step by step:
     1. The teacher asks students to reflect individually on what they have learned.
     2. The teacher asks guiding questions to help students in their reflection.
     3. The teacher gives time for students to reflect and then opens the discussion for students to share their reflections, if they are comfortable.
     4. The teacher ends the lesson, thanking the students for their participation and effort.

Conclusion (5 - 10 minutes)

1. Summary and Recap (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points discussed during the lesson. This includes the definition of a cone, the properties of a cone, the formula for calculating the volume of a cone (Volume = 1/3 * π * r² * h), and how this formula was applied to solve practical problems. The teacher should ensure that all students have understood these fundamental concepts, encouraging them to ask questions if necessary.

2. Connection between Theory and Practice (1 - 2 minutes): The teacher should then emphasize how the lesson managed to connect theory to practice. This can be done by highlighting the cone construction activity, which allowed students to visualize a three-dimensional cone and understand how the cone volume formula is related to its shape. The teacher can also mention the measurement and calculation activities of the cone volume, which helped students apply the cone volume formula in practice and verify the relationship between the cone's dimensions and its volume.

3. Suggestion of Extra Materials (1 - 2 minutes): The teacher should suggest some extra materials for students who wish to deepen their understanding of the topic. This may include math books that address spatial geometry, explanatory videos about cone volumes available on the internet, and math websites that offer interactive exercises on the topic. The teacher should encourage students to explore these resources at their own pace, emphasizing that continuous practice is essential for mastering the topic.

4. Importance of the Topic in Everyday Life (1 - 2 minutes): To conclude, the teacher should reinforce the importance of the topic in everyday life. This can be done by mentioning some practical applications of calculating cone volumes in different areas, such as architecture, engineering, cooking, among others. The teacher should emphasize that mathematics is a powerful tool that can be applied in various real-life situations, and that mastering mathematical concepts, such as calculating cone volumes, can open doors to a range of careers and interests.