Objectives (5 - 10 minutes)

1. Understanding the fundamental concepts of spatial geometry: Students should be able to understand the basic concepts of spatial geometry, such as points, lines, planes, polyhedra, round bodies, among others. This includes the ability to differentiate between them and recognize them in practical examples.

2. Application of concepts in real situations: Students should be able to apply the knowledge acquired in concrete situations. This may involve identifying geometric shapes in everyday objects, or solving problems that involve the use of spatial geometry concepts.

3. Development of logical-mathematical reasoning: Through the study of spatial geometry, students will improve their logical-mathematical reasoning skills. They will learn to think abstractly, to analyze problems systematically, and to apply problem-solving strategies.

Secondary objectives:

• Stimulate teamwork: The proposed practical activities should encourage collaboration among students, promoting teamwork and the exchange of ideas.

• Foster curiosity and interest in Mathematics: The lesson plan should be structured to arouse students' curiosity and interest in the subject, demonstrating the relevance and applicability of Mathematics in everyday life.

Introduction (10 - 15 minutes)

1. Review of basic concepts: The teacher starts the lesson by quickly reviewing the basic concepts of plane geometry, which have already been studied before. This includes the definition of points, lines, and planes, as well as the basic properties of these elements. This review is essential for understanding the concepts that will be introduced in the spatial geometry lesson.

2. Problem situations: Next, the teacher presents two problem situations that will serve as the basis for the topic Introduction. The first one could be: 'How would you describe the shape of a ball? And an ice cube?'. The second situation could be: 'How would you determine the distance between two points on a sphere?'.

3. Contextualization: The teacher explains that spatial geometry is an important tool in various areas of knowledge, including physics, engineering, architecture, and biology. He also highlights that spatial geometry has practical applications in everyday life, such as in the design of three-dimensional objects, in the construction of buildings, and in navigation.

4. Introduction to the topic: To arouse students' interest, the teacher presents two curiosities related to spatial geometry. The first one is that spatial geometry is not a human invention, but rather a fundamental characteristic of the universe. The second curiosity is that many of the shapes found in nature, such as snail shells and ice crystals, follow principles of spatial geometry.

5. History of spatial geometry: Finally, the teacher can briefly talk about the history of spatial geometry, highlighting the main contributors and discoveries. He may mention, for example, the Greek mathematician Euclid, who is considered the 'father' of geometry, and the German mathematician Carl Friedrich Gauss, who made important contributions to spatial geometry in the 19th century.

Development (20 - 25 minutes)

1. Activity 'Building Space': The teacher divides the class into small groups and provides each group with a cardboard box, scissors, and tape. The students' task is to build a three-dimensional object using only the materials provided. The object should be composed of various polyhedra, such as cubes, prisms, and pyramids, which will be glued together to form a unique structure. During the construction, students should discuss in their groups the best assembly strategies, taking into account the geometric characteristics of each polyhedron. At the end of the activity, each group presents their object to the class, explaining the choice of polyhedra and the geometric characteristics involved. (10 - 15 minutes)

2. Activity 'Everyday Sphere': The teacher proposes a challenge to the class: determine the volume of a tennis ball. For this, students must work in their groups and use the acquired knowledge of spatial geometry. They should measure the diameter of the tennis ball and then calculate its volume. During the problem-solving process, the teacher circulates around the room, assisting groups that encounter difficulties. At the end of the activity, each group presents their calculation to the class, and the teacher verifies the accuracy of the results. (10 minutes)

3. Activity 'Identifying Shapes in Space': To conclude the Development stage, the teacher distributes to each group a selection of images of everyday objects, such as a shoebox, a die, a glass pyramid, among others. The students' task is to identify and name the three-dimensional geometric shapes present in each object. They should also discuss in their groups the geometric characteristics of each shape. At the end of the activity, each group presents their conclusions to the class. (5 - 10 minutes)

During the activities, the teacher should encourage the participation of all students, promoting the exchange of ideas and discussion within the groups. He should also circulate around the room, monitoring the progress of the groups and clarifying doubts. At the end of the activities, the teacher leads a class discussion, highlighting the main points learned and clarifying any doubts.

Return (10 - 15 minutes)

1. Group Discussion: The teacher should start a group discussion, where each team shares their solutions or conclusions from the activities carried out. Each group will have up to 5 minutes to present. This allows students to learn from each other and see different approaches to problem-solving. The teacher should encourage students to ask questions and provide constructive feedback to their peers.

2. Connection with Theory: After the group presentations, the teacher should recap the theoretical concepts discussed at the beginning of the lesson and how they were applied in the practical activities. This helps reinforce the connection between theory and practice, and allows students to see how the acquired knowledge can be applied in real situations.

3. Individual Reflection: The teacher proposes that students make an individual reflection on what was learned. He can ask questions like: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'. Students should write down their answers on a piece of paper or in their notebooks. This activity helps students consolidate what they have learned and identify any gaps in their understanding.

4. Teacher's Feedback: The teacher collects the papers with the students' answers and reads some of them out loud. He also provides general feedback to the class, highlighting strengths and areas that need improvement. The teacher can also take this opportunity to clarify any misunderstandings or doubts that arose during the lesson.

5. Preparation for the Next Lesson: Finally, the teacher should briefly introduce the topic of the next lesson and explain what students should do to prepare. This may include reading a chapter from a textbook, solving some practice exercises, or researching a specific concept. The teacher should remind students that proper preparation is essential for success in the following lesson.

Conclusion (5 - 10 minutes)

1. Summary of Contents: The teacher should summarize the main contents covered in the lesson, reinforcing the concepts of spatial geometry, the definitions of points, lines, planes, polyhedra, and round bodies, as well as highlighting the main characteristics of each. This allows students to review and consolidate what they have learned.

2. Connection between Theory, Practice, and Applications: The teacher should reiterate how the lesson connected theory, practice, and the applications of spatial geometry concepts. He can, for example, mention the practical activities carried out and how they allowed students to apply theoretical concepts concretely. Additionally, the teacher can emphasize how spatial geometry is used in real situations, such as in building construction, in the design of three-dimensional objects, and in navigation.

3. Additional Materials: The teacher should suggest some complementary study materials, such as textbooks, math websites, educational videos, and interactive games. These resources can help students deepen their understanding of spatial geometry and practice the learned concepts in a fun and interactive way. For example, the teacher may recommend a YouTube video that clearly and visually explains the definition and properties of a polyhedron.

4. Relevance of the Subject: Finally, the teacher should emphasize the importance of the subject for everyday life. He can mention, for example, how the ability to visualize and manipulate three-dimensional objects is useful in many everyday situations, such as packing a suitcase, assembling furniture, or calculating the space needed to accommodate an object in a closet. Additionally, the teacher can highlight how the logical-mathematical reasoning developed through the study of spatial geometry is a valuable skill in many areas of life, not only in Mathematics, but also in science, technology, engineering, and many other fields.