Objectives (5 - 7 minutes)

1. Understand the definition of a parallelogram and its main characteristics, such as opposite parallel sides and congruent opposite angles.

2. Identify and differentiate types of parallelograms, such as rectangle, square, and rhombus, based on their specific properties.

3. Apply the acquired knowledge to solve practical problems involving parallelograms, such as calculating area and perimeter.

Secondary Objectives:

• Develop logical thinking skills and spatial visualization when working with complex geometric shapes.

• Encourage collaboration and group discussion through practical activities and contextualized problems.

Introduction (10 - 15 minutes)

1. Review of previous concepts:

   • The teacher should review basic concepts of plane geometry, especially about quadrilaterals, angles, and parallelism. This can be done through quick and interactive questions to activate students' prior knowledge. (3 - 5 minutes)

2. Problem situations:

   • The teacher can present two problem situations to motivate the Introduction of the topic. For example, "How can we prove that a rectangle is a parallelogram?" and "How can we determine the area of a square?" (3 - 5 minutes)

3. Contextualization:

   • The teacher should explain the importance of parallelograms in the real world, such as in architecture and design, where these shapes are frequently used. Additionally, they can mention that many games and toys, like tangram, use parallelograms to create shapes and figures. (2 - 3 minutes)

4. Introduction to the topic:

   • The teacher should introduce the topic of parallelograms, explaining that it is a special category of quadrilateral with interesting properties. They can mention that the study of parallelograms is fundamental for understanding other geometric shapes, such as trapezoids and triangles. (2 - 3 minutes)

5. Curiosities:

   • To spark students' interest, the teacher can share some curiosities about parallelograms. For example, they can mention that the term "parallelogram" comes from the Greek "parallēlogrammon," which means "parallel line." Another curiosity is that the sum of the interior angles of any parallelogram is always 360 degrees. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity "Building Parallelograms" (10 - 12 minutes)

   • Required materials: Ruler, pencil, cardboard paper.
   • Divide students into groups of 4 or 5. Each group will receive a sheet of cardboard paper, a pencil, and a ruler.
   • The teacher will explain that the activity consists of building different types of parallelograms: rectangle, square, and rhombus.
   • Students should start by drawing a straight line on the cardboard paper. Then, they should use the ruler to draw a line parallel to the first line, at a determined distance. This will form the parallel sides of the parallelogram.
   • To build a square, students must ensure that all sides of the parallelogram have the same length. To build a rectangle, they must ensure that the internal angles of the parallelogram are all right angles. To build a rhombus, they must ensure that all internal angles of the parallelogram are equal.
   • After construction, students should compare their parallelograms and discuss the differences and similarities between them.
   • To conclude the activity, each group must present their parallelogram to the class and explain how they ensured it fit into the specific category.

2. Activity "Perimeter and Area of Parallelograms" (10 - 13 minutes)

   • Required materials: Graph paper, colored pens.
   • Still in their groups, students will receive graph paper and a colored pen.
   • The teacher will explain that the activity consists of calculating the perimeter and area of each of the parallelograms built in the previous activity.
   • First, students should use the colored pen to mark the sides of their parallelograms on the graph paper. This will help visualize the calculations better.
   • Next, they should count the number of squares that make up the perimeter of each parallelogram and write down the result.
   • To calculate the area, they should count the total number of squares that make up the parallelogram and write down the result.
   • Students should compare the results obtained with the properties they observed in the previous activity. For example, they should realize that, for the square, the perimeter is equal to four times the length of one side, and the area is equal to the square of the length of one side.
   • To conclude the activity, students should present their calculations and conclusions to the class.

Return (10 - 12 minutes)

1. Group Discussion (4 - 5 minutes)

   • The teacher should promote a group discussion where each group shares their solutions and conclusions from the activities carried out.
   • Each group will have a maximum of 2 minutes to present. At this point, the teacher should encourage students to explain how they arrived at their answers and justify their conclusions.
   • During the presentations, the teacher should intervene, if necessary, to clarify doubts, correct misconceptions, and reinforce the main concepts.
   • The objective of this discussion is to allow students to learn from each other, developing their communication and argumentation skills, as well as strengthening their understanding of the content.

2. Connection with Theory (3 - 4 minutes)

   • After all presentations, the teacher should review the theoretical concepts, reinforcing the definition of a parallelogram, its main characteristics, and the different types (rectangle, square, rhombus).
   • The teacher should connect the theory with the practical activities, highlighting how students applied the concepts to build and identify the parallelograms, as well as to calculate the perimeter and area.
   • Additionally, the teacher should emphasize the importance of logical reasoning and spatial visualization in problem-solving, reinforcing the goal of developing these skills.

3. Individual Reflection (3 - 4 minutes)

   • To conclude the lesson, the teacher should propose a moment of individual reflection. The teacher will ask some questions, and students will have a minute to think and mentally respond.
   • Questions may include: "What was the most important concept you learned today?", "What questions have not been answered yet?", and "How can you apply what you learned today in everyday situations?".
   • After the minute of reflection, the teacher may ask some students to share their answers with the class, if they feel comfortable. This can lead to a final discussion and clarify any doubts.
   • The goal of this moment is to allow students to consolidate what they have learned, identify their knowledge gaps, and realize the relevance of the studied content.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (2 - 3 minutes)

   • The teacher should start the Conclusion by recalling the main points discussed during the lesson. They can give a brief summary of the definitions of parallelogram, rectangle, square, and rhombus, and recap the characteristics and properties that differentiate them.
   • Next, the teacher should highlight the main conclusions from the practical activities, such as the importance of parallelism and angle congruence for the classification of parallelograms, and how to calculate the perimeter and area of these figures.
   • Finally, the teacher should reinforce the relevance of the subject, emphasizing that the study of parallelograms is fundamental for understanding other geometric shapes and for solving practical problems.

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

   • The teacher should explain how the lesson connected the theory, practice, and applications of the content. They can mention examples from the practical activities, such as building the parallelograms and calculating their perimeter and area, to illustrate how theoretical concepts were applied and how they relate to real situations.
   • Additionally, the teacher can mention again the practical applications of parallelograms, such as in architecture and design, to show students the relevance of what they have learned.

3. Extra Materials (1 - 2 minutes)

   • The teacher should suggest extra materials for students who wish to deepen their understanding of the topic. These materials may include books, websites, videos, and educational games that address the topic of parallelograms in a playful and interactive way.
   • For example, the teacher may recommend the use of geometry apps, such as GeoGebra, that allow students to explore and manipulate geometric figures virtually.
   • Additionally, the teacher may indicate additional exercises from textbooks or math websites, so that students can practice and deepen what they have learned.

4. Relevance of the Topic (1 minute)

   • To conclude, the teacher should reinforce the relevance of the topic to students' daily lives. They can mention, for example, that knowledge about parallelograms can be useful in solving practical problems, such as calculating land areas, building furniture, or interpreting architectural plans.
   • Furthermore, the teacher can remind students that the study of geometry is not limited to the classroom but is present in many aspects of our lives, from nature to art and technology.