Lesson plan of Spatial Geometry: Surface Area of the Prism

Objectives (5 - 7 minutes)

1. Understand the concept of surface area of a prism: Students should be able to understand what the surface area of a prism is and how it is calculated. They should be able to identify the parts of a prism that make up its surface area and understand that the total surface area is the sum of the areas of the lateral faces and the bases.

2. Apply the concept of surface area of a prism to real-world problems: Students should be able to apply the concept of surface area of a prism to real-world problems. They should be able to interpret the problem, identify the prism and its faces, and calculate the surface area of the prism accurately.

3. Solve problems involving the surface area of a prism: Students should be able to solve problems that involve calculating the surface area of a prism. They should be able to use the appropriate formulas, perform the necessary calculations, and provide the correct answer.

   Secondary Objectives:

   • Develop logical and analytical thinking skills: Solving problems involving the surface area of a prism requires students to apply logical and analytical thinking. They must be able to analyze the problem, identify the steps needed to solve it, and apply the correct formulas.

• Promote collaboration and teamwork: Group or pair activities can be incorporated to promote collaboration and teamwork. This will allow students to share ideas, discuss solutions, and learn from one another.

Introduction (10 - 15 minutes)

1. Review of prior knowledge: The teacher should begin the lesson by reviewing the prior knowledge that is necessary for understanding the current topic. In this case, the concept of a prism, its characteristics, types, and elements should be reviewed. It is also important to review the formula for calculating the area of plane figures, such as squares and rectangles, as these concepts will be fundamental for calculating the surface area of a prism.
2. Problem situations: Next, the teacher should pose two problem situations that will be the focus of the lesson. For example, a rectangular prism could be presented and students could be asked to calculate its surface area, or a scenario could be presented where the surface area of a prism represents a challenge to be solved. These situations will help to contextualize the content and spark students' interest.
3. Contextualization: The teacher should then contextualize the importance of the topic, explaining that calculating the surface area of a prism is a fundamental mathematical skill and that it has practical applications in various fields, such as architecture, engineering, design, and construction. For example, when designing a package, it is necessary to calculate the surface area of the prism to determine the amount of material needed.
4. Introduction to the topic: To capture students' attention, the teacher could share fun facts or stories related to the topic. For example, the story of the Greek mathematician Euclid, who was one of the first to study the properties of prisms, could be told, or images of famous buildings that are shaped like prisms, such as the Louvre Pyramid in Paris, could be shown and students could be challenged to calculate the surface area of these buildings.
5. Motivation: Finally, the teacher should motivate students for the lesson, explaining that they will have the opportunity to solve challenging problems, apply mathematics in a practical way, and develop important skills, such as logical and analytical thinking. In addition, the teacher should emphasize that the lesson will be interactive and that they will have the chance to work in groups, which can make learning more enjoyable and effective.

Development (20 - 25 minutes)

1. Activity "Constructing Prisms":
   • Materials needed: Colored cardstock, scissors, ruler, glue.
   • Activity description: Students will be divided into groups of four. Each group will receive materials to construct a prism, which can be rectangular or triangular. They will have to assemble the prism following the instructions provided by the teacher. Then, they must measure the area of each face of the prism and the total surface area. The teacher should circulate around the room, assisting groups that are struggling and asking questions to encourage reflection.
   • Objective: This activity aims to allow students to visualize the concept of a prism and its surface area, and to understand that the surface area is the sum of the areas of the faces. In addition, it promotes collaboration and teamwork.
2. Activity "The Prism in Real Life":
   • Materials needed: Images of everyday objects that are shaped like a prism, such as a juice box, a gift box, a pencil.
   • Activity description: Still in their groups, students should choose one of the images provided and then measure the dimensions of the object (length, width, and height) to calculate the surface area of the prism represented by the image. They should also discuss and write down possible applications for calculating the surface area of the prism in the situation presented. The teacher should circulate around the room, assisting groups and asking questions to encourage reflection.
   • Objective: This activity aims to provoke students to apply the concept of surface area of a prism to real-world situations. In addition, it helps to develop problem-solving skills and to understand the relevance of the topic.
3. Activity "Prism Area Challenge":
   • Materials needed: Printed activity sheets with problems involving the calculation of the surface area of a prism.
   • Activity description: Each student will receive an activity sheet with problems to solve. The problems should vary in difficulty and complexity, so that all students are challenged. The teacher should circulate around the room, assisting students who are struggling and providing feedback. At the end of the activity, the teacher should review the answers with the class, clarifying doubts and reinforcing the concepts learned.
   • Objective: This activity aims to provide students with the opportunity to practice calculating the surface area of a prism and to develop problem-solving skills. In addition, it allows the teacher to assess students' understanding and to identify areas that need reinforcement.

Debrief (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):
   • The teacher should gather all students and promote a group discussion about the solutions or conclusions found by each team during the activities.
   • Each group should briefly share what they discovered, the challenges they faced, and how they solved the problems.
   • The teacher should ask questions to encourage students' reflection and ensure that the concept of surface area of a prism has been understood.
2. Connection to Theory (2 - 3 minutes):
   • The teacher should then make the connection between the activities carried out and the theory presented at the beginning of the lesson.
   • They should highlight how the activities allowed students to visualize and apply the concept of surface area of a prism in a practical way.
   • The teacher should also reinforce the importance of calculating the surface area of a prism in everyday situations, such as in architecture, engineering, design, and construction.
3. Individual Reflection (2 - 3 minutes):
   • To consolidate learning, the teacher should propose that students do a one-minute individual reflection.
   • The teacher could ask questions like: "What was the most important concept learned today?" and "What questions are still unanswered?"
   • Students should write down their reflections and, if they have any unanswered questions, they can share them with the teacher or with the class.
4. Feedback and Closure (1 minute):
   • Finally, the teacher should ask students for feedback on the lesson, asking what they liked the most and what they found most challenging.
   • The teacher should thank everyone for their participation and effort, and end the lesson by reinforcing the importance of calculating the surface area of a prism and the need for practice to improve the skill.

Conclusion (5 - 7 minutes)

1. Summary and Recap (2 - 3 minutes):
   • The teacher should begin the Conclusion by reviewing the main points covered in the lesson. They should summarize the concept of surface area of a prism, the formula for its calculation, and how to apply this concept to practical problems.
   • In addition, the teacher should recap the activities carried out, highlighting the main learnings and the skills developed.
2. Connection between Theory, Practice, and Applications (1 - 2 minutes):
   • Next, the teacher should reinforce the connection between the theory presented, the practical activities carried out, and the applications of the content in the real world.
   • They should explain that the lesson sought to provide students with a deep understanding of the concept of surface area of a prism, through activities that allowed for the practical application of this concept and reflection on its applications in everyday life.
3. Extra Materials (1 - 2 minutes):
   • The teacher should suggest extra materials for students who wish to deepen their knowledge on the topic. These materials could include explanatory videos, interactive math websites, online games, and textbooks.
   • For example, the teacher could indicate a video that shows the construction of a rectangular prism, a website that allows students to virtually manipulate a prism and calculate its surface area, and a book that presents challenging problems on the topic.
4. Importance of the Topic (1 minute):
   • Finally, the teacher should emphasize the importance of the topic for everyday life and for the development of essential skills.
   • They should explain that calculating the surface area of a prism has practical applications in various fields, such as architecture, engineering, design, and construction.
   • In addition, the teacher should highlight that the lesson not only taught a mathematical concept, but also helped to develop important skills, such as logical reasoning, problem solving, and teamwork.