Objectives (5 minutes)

1. Understand what a parallelogram is: Students should be able to define what a parallelogram is, identifying its main characteristics and properties.
2. Recognize the fundamental properties of a parallelogram: Students should be able to identify and apply the basic properties of a parallelogram, such as opposite sides being parallel, opposite angles being congruent, and diagonals bisecting each other.
3. Solve problems involving parallelograms: Students should be able to apply the properties of parallelograms to solve problems involving measurements of sides and angles, areas, and perimeters.

Secondary Objectives:

• Stimulate critical and analytical thinking: Through problem-solving, students will be encouraged to develop critical and analytical thinking skills.
• Promote collaboration and teamwork: Group activities will promote collaboration and teamwork, essential skills in the real world.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher starts the lesson by reviewing the concepts of polygons and their classifications, with an emphasis on quadrilaterals. It may also be useful to review the definition of parallel lines and congruent angles. This review can be done through interactive questions, such as 'What are the characteristics of a quadrilateral? What are the properties of parallel lines and congruent angles?' (5 minutes)

2. Problem-solving situations: The teacher presents two problem-solving situations to arouse students' interest and contextualize the subject. For example, 'How can we prove that a quadrilateral is a parallelogram?' and 'Can we find the area of a parallelogram without knowing the height?'. (5 minutes)

3. Contextualization: The teacher explains that the study of parallelograms is fundamental in various areas, such as engineering (for building stable structures) and architecture (for drawing plans and projects). Additionally, it highlights that knowledge about parallelograms is applied in various everyday situations, such as solving geometry problems and interpreting maps and house plans. (2 minutes)

4. Introduction to the topic: The teacher introduces the topic of parallelograms, explaining that they are special quadrilaterals with unique properties. To capture students' attention, the teacher can tell the origin of the term 'parallelogram,' which comes from Greek and means 'parallel to the sides.' Additionally, interesting facts can be shared, such as the fact that many animals, like tigers and zebras, have skin patterns that resemble parallelograms. (3 minutes)

Development (20 - 25 minutes)

1. Activity 'Building Parallelograms': (10 - 12 minutes)

   • Materials needed: Ruler, compass, pencil, and cardboard paper (or thicker paper).
   • Procedure: Students, divided into groups, receive a kit with the necessary materials. The activity consists of building parallelograms using the ruler and compass. Each group should build at least three parallelograms of different sizes. After construction, students should measure the sides and angles of each parallelogram and record the values. Then, students should verify if the properties of the parallelogram (opposite sides being parallel, opposite angles being congruent, and diagonals bisecting each other) are satisfied. Finally, the groups should present their parallelograms to the class, explaining how they verified the properties.

2. Activity 'Problems with Parallelograms': (10 - 12 minutes)

   • Materials needed: Sheets of paper with problems involving parallelograms.
   • Procedure: Each group receives a sheet of paper with problems involving parallelograms. The problems may involve calculating areas, perimeters, identifying parallelograms in complex figures, among others. Students should solve the problems in groups, applying the properties of parallelograms. The teacher circulates around the room, assisting groups that encounter difficulties. In the end, each group should present their solutions to the class.

3. Activity 'Parallelograms Game': (5 - 8 minutes)

   • Materials needed: Cards with images of different geometric figures (squares, rectangles, rhombuses, trapezoids, and parallelograms).
   • Procedure: The teacher divides the class into groups and distributes the cards. Each group should separate the parallelogram cards from the others. Then, a representative from each group goes to the board and organizes the parallelogram cards according to their properties (opposite sides being parallel, opposite angles being congruent, and diagonals bisecting each other). The group that organizes the cards correctly first wins the round. The game continues until all cards are organized. This activity aims to reinforce the recognition of the properties of a parallelogram and the identification of figures that have these properties.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • Procedure: The teacher gathers all students and promotes a group discussion about the solutions or conclusions found by each team during the activities. At this moment, each group will have the opportunity to share their discoveries, difficulties, and strategies used. The teacher should encourage students to explain the reasoning behind their solutions, promoting the exchange of ideas and collaborative learning. The teacher should also clarify possible doubts and correct possible conceptual errors.

2. Connection to Theory (3 - 5 minutes):

   • Procedure: After the group discussion, the teacher should make the connection between the practical activities carried out and the theory presented at the beginning of the lesson. The teacher should highlight how the activities allowed students to experiment and explore the properties of parallelograms concretely, reinforcing the understanding and application of theoretical concepts. Additionally, the teacher can take the opportunity to introduce or review other related concepts, such as calculating areas and perimeters, identifying geometric figures, and solving geometry problems.

3. Individual Reflection (2 - 3 minutes):

   • Procedure: To conclude the lesson, the teacher proposes that students reflect for a minute on the following questions: 'What was the most important concept learned today? What questions have not been answered yet?'. After reflection, students are invited to share their answers with the class. The teacher should be open to listening to students' reflections and should encourage them to express their doubts and difficulties, reinforcing the importance of critical thinking and continuous learning.

4. Feedback (2 - 3 minutes):

   • Procedure: Finally, the teacher should provide overall feedback on the lesson, highlighting the positive points and areas that still need improvement. The teacher should praise the effort and participation of the students and reinforce the most important concepts learned. Additionally, the teacher should remind students about the importance of reviewing and practicing the concepts learned at home to consolidate learning. The teacher's feedback is crucial to motivate students and guide the planning of future lessons.

Conclusion (5 - 7 minutes)

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

   • Procedure: The teacher should give a brief summary of the main points covered during the lesson. This includes the definition of a parallelogram, its fundamental properties (opposite sides being parallel, opposite angles being congruent, and diagonals bisecting each other), and how to apply these properties to solve problems involving parallelograms. The teacher can use the board or slides to reinforce the concepts, making notes or drawings.

2. Connection to Practice (1 - 2 minutes):

   • Procedure: The teacher should emphasize how the lesson connected theory with practice. They can mention the activities carried out, such as building parallelograms and solving problems, and how these activities allowed students to experiment and explore the properties of parallelograms concretely. The teacher can also highlight the importance of understanding the properties of parallelograms for various practical applications, such as in engineering, architecture, and solving geometry problems.

3. Extra Materials (1 - 2 minutes):

   • Procedure: The teacher should suggest extra materials for students who wish to deepen their knowledge about parallelograms. This may include math books, educational websites, online videos, interactive games, and printable activities. For example, the teacher can suggest using geometric drawing apps to virtually build parallelograms or reading articles or books about the history of parallelograms and their real-world applications.

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

   • Procedure: Finally, the teacher should emphasize the importance of the subject presented for students' daily lives. They can mention how knowledge about parallelograms is applied in various everyday situations, such as interpreting maps and house plans, solving geometry problems, and understanding more advanced concepts in math and physics. The teacher can also emphasize the importance of developing critical and analytical thinking skills, which are essential not only for mathematics but for life.