Objectives (5 - 7 minutes)

• Main Objective: Understand and be able to apply the formula to calculate the surface area of a cone. Also, identify and describe the variables present in the formula.

  • Secondary Objective 1: Differentiate the surface area of a cone from the area of other three-dimensional figures such as a sphere and a cylinder.
  • Secondary Objective 2: Solve practical problems involving the calculation of the surface area of a cone in mathematical contexts and in real-world applications.

• Main Objective: Develop the ability to recognize and interpret problem situations that require the calculation of the surface area of a cone. Correctly apply the formula and arrive at precise solutions.

  • Secondary Objective 1: Identify relevant information in a problem and apply the appropriate formula to find the answer.
  • Secondary Objective 2: Use critical thinking and mathematical logic to solve complex problems involving the calculation of the surface area of a cone.

• Main Objective: Foster an understanding of the importance of the surface area of a cone in diverse fields of science and engineering. This promotes appreciation for and respect of mathematics.

  • Secondary Objective 1: Explore examples of real-world applications for calculating the surface area of a cone such as in constructing architectural structures and modeling natural phenomena.
  • Secondary Objective 2: Encourage students' curiosity and interest in mathematics by demonstrating how concepts learned in the discipline can be applied in practical and meaningful ways.

Introduction (10 - 12 minutes)

1. Review of Previous Content (3 - 4 minutes):

   • The teacher should start by reviewing the concepts of three-dimensional figures, especially the cone.
   • Students should be encouraged to recall the characteristics of a cone such as its base, vertex, and generatrix.
   • The teacher could also quickly review how to calculate the volume of a cone since the surface area of a cone is closely related to the volume.

2. Problem Situations (3 - 4 minutes):

   • The teacher could present two situations that require calculating the surface area of a cone but not immediately give the solution. For example, the first situation could involve calculating the area of a soda can and the second could involve calculating the area of a cone-shaped hat.
   • Students should be challenged to think about how they could calculate the surface area of these objects.

3. Contextualization (2 - 3 minutes):

   • The teacher should then contextualize the importance of calculating the surface area of a cone. They should highlight its practical applications in various areas such as architecture, engineering, cooking, and others.
   • For example, the teacher could mention how the surface area of a cone is used to determine the amount of paint needed to cover a soda can. Or how it is used in constructing iconic architectural structures like the Space Needle in Seattle.

4. Introduction to the Topic (2 - 3 minutes):

   • Finally, the teacher should introduce the topic of the class - calculating the surface area of a cone. They should explain that the surface area of a cone is the sum of the areas of the base circle and the circular sector generated by the generatrix.
   • The teacher could also show images of everyday objects that are representations of cones such as light bulbs, funnels, hats, etc. This helps students visualize the concept.

This Introduction phase is crucial to spark students' interest in the topic. It demonstrates its relevance and practical applications. It also reviews concepts necessary to understand the new material.

Development (20 - 25 minutes)

1. Explaining the Formula for Calculating the Surface Area of a Cone (5 - 7 minutes):

   • The teacher should begin by explaining that the formula for calculating the surface area of a cone is A = πr(r + g), where A is the surface area, r is the base radius of the cone, and g is the generatrix of the cone.
   • The teacher should clarify that the term πr², which represents the area of the cone's base circle, is added to the product πrg, which represents the area of the circular sector generated by the generatrix. This gives the total surface area of the cone.
   • The teacher should demonstrate how the formula was derived, for example, through a graphic representation of the development of the cone's surface.

2. Discussion and Examples of Applying the Formula (7 - 9 minutes):

   • The teacher should discuss the importance of each term in the formula and how they contribute to the total surface area of the cone.
   • The teacher should present examples of applying the formula using practical problems that students could encounter in everyday life. For example, they could calculate the surface area of an ice cream cone or a cone-shaped hat.
   • The teacher should solve the examples step-by-step explaining each stage of the reasoning and how it relates to the formula.

3. Practical Activity to Calculate the Surface Area of a Cone (5 - 7 minutes):

   • The teacher should propose a practical activity where students must calculate the surface area of an actual cone.
   • The teacher could provide cones of different sizes and ask students to measure the base radius and the generatrix, and then calculate the surface area using the formula.
   • This activity allows students to solidify their understanding of the formula and practice calculating the surface area of a cone in a concrete way.

4. Discussion on the Importance of Calculating the Surface Area of a Cone (3 - 4 minutes):

   • To conclude the Development phase, the teacher should lead a discussion on the importance of calculating the surface area of a cone.
   • The teacher could revisit the practical applications discussed in the Introduction. They could show how calculating the surface area of a cone is essential in diverse fields from architecture to cooking.
   • The teacher should encourage students to think about other possible applications for calculating the surface area of a cone and share their ideas with the class.

This Development phase is the core of the class because this is where students will acquire the knowledge necessary to solve problems involving the calculation of the surface area of a cone. The teacher should ensure that the explanation is clear and that the examples are varied and relevant to the students' lives. Additionally, the practical activity and the final discussion will help consolidate learning and stimulate students' critical thinking.

Review (8 - 10 minutes)

1. Review of Concepts Learned (3 - 4 minutes):

   • The teacher should begin this phase by reviewing the main concepts covered in the class.
   • They should revisit the formula for calculating the surface area of a cone (A = πr(r + g)) and the importance of each term in the formula.
   • The teacher could ask students to explain the formula in their own words to check their understanding of the concept.
   • Additionally, the teacher should reinforce the relationship between the surface area of a cone and the volume of a cone. The teacher can remind them that the surface area is used to calculate the volume.

2. Connection between Theory and Practice (2 - 3 minutes):

   • The teacher should then connect the theory presented in class with practice. They should revisit the activities done and how they helped illustrate and apply the theoretical concepts.
   • For example, the teacher could highlight how the activity to calculate the surface area of an actual cone allowed students to apply the formula and understand how it relates to the shape of the cone.
   • The teacher could also mention how the examples of applying the formula, such as calculating the area of a soda can, helped contextualize the concept and demonstrate its practical relevance.

3. Reflecting on Learning (2 - 3 minutes):

   • The teacher should ask students to reflect on what they learned in the class.
   • They could ask questions like: "What was the most important concept you learned today?" and "What questions do you still have about calculating the surface area of a cone?".
   • The teacher should encourage students to share their answers with the class to exchange ideas and consolidate their learning.
   • Additionally, the teacher could make a note of any questions students have to address in the next class or in future review sessions.

4. Feedback and Evaluation (1 minute):

   • Finally, the teacher should give students feedback on their performance in the class. The teacher can compliment what was done well and indicate areas that need improvement.
   • The teacher could also evaluate students' understanding of the topic with a brief review activity such as a quick quiz or a problem to solve.
   • The feedback and evaluation help students understand their strengths and areas for improvement. This allows the teacher to adjust the lesson plan as needed to ensure effective learning.

This Review phase is essential to consolidate learning and verify whether the Objectives of the class were achieved. The teacher should ensure that all important concepts have been understood and that students feel confident applying them in real situations. Additionally, reflecting on the learning and the feedback allows the teacher to adjust the teaching approach as necessary to meet students' individual needs.

Conclusion (5 - 7 minutes)

1. Summary of Content (2 - 3 minutes):

   • The teacher should recap the main points covered during the class. They should reiterate the definition of surface area of a cone, the formula to calculate it (A = πr(r + g)), and the importance of each term in the formula.
   • The teacher should also emphasize how the surface area of a cone differs from the volume of a cone, and how the two concepts are interrelated.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes):

   • The teacher should emphasize how the class connected theory, practice, and applications.
   • For example, the teacher could mention how the formula for calculating the surface area of a cone was introduced theoretically, applied in practice through examples and activities, and contextualized through its applications in real-world situations.
   • The teacher should reinforce that understanding the theory is fundamental to practical application and appreciating the applications.

3. Suggestion of Complementary Materials (1 minute):

   • The teacher could suggest additional study materials for students who wish to delve deeper into calculating the surface area of a cone.
   • These materials could include educational websites, explanatory videos, textbooks, and others.
   • The teacher should emphasize that using these materials is optional but could be useful for students who want to review the content at home or explore the topic in more depth.

4. Relevance of the Topic for Everyday Life (1 - 2 minutes):

   • Finally, the teacher should highlight the importance of calculating the surface area of a cone for everyday life.
   • The teacher could once again mention some of the practical applications discussed in class such as calculating the area of a soda can or a cone-shaped hat.
   • The teacher could also remind students that the ability to solve problems involving the calculation of the surface area of a cone could be valuable in various careers from engineering and architecture to cooking and design.

The Conclusion phase is essential for consolidating learning, reinforcing the relevance of the concepts presented, and motivating students to continue studying the subject. The teacher should ensure that students have a clear understanding of the concepts and know where they can find additional resources to deepen their knowledge. Additionally, the teacher should reinforce the applicability of calculating the surface area of a cone in the real world. This encourages students to value and use the concepts learned.