Objectives (5 - 7 minutes)

1. Understand the concept of parallel lines and transversals, identifying and drawing them in practical situations.
2. Develop the ability to calculate angles formed by parallel lines and transversals, applying the corresponding properties correctly.
3. Apply the acquired knowledge to solve practical problems involving parallel lines and transversals.

Secondary Objectives:

• Promote interaction among students, encouraging collaborative learning through group activities.
• Develop critical thinking and the ability to solve mathematical problems by applying the properties of parallel lines and transversals.
• Stimulate students' curiosity and interest in mathematics, demonstrating its applicability in everyday situations.

Introduction (10 - 15 minutes)

1. Review of previous contents: The teacher should start the class by reviewing basic geometry concepts, such as what lines, angles, and their classification are. It is also important to review properties of plane figures, such as the sum of the interior angles of a triangle and the property of vertical angles. These reviews are essential for students to understand and apply the properties of parallel lines and transversals correctly.

2. Problem situations: The teacher can present two problem situations that will serve as context for the development of the subject. The first one may involve building a fence parallel to a street, and the second one may involve determining angles in a drawing representing the intersection of two lines.

   • Example 1: "If we want to build a fence that is parallel to a street, how can we ensure that it is truly parallel?"
   • Example 2: "If we have two intersecting lines, how can we determine the measure of the angles formed?"

3. Contextualization: The teacher should highlight the importance of the subject, showing examples of real situations where knowledge about parallel lines and transversals is fundamental. Examples could include the construction of roads, bridges, and buildings, where geometry is widely used. Additionally, the application of these concepts in solving math and physics problems can be mentioned.

4. Engaging students' attention: To spark students' interest, the teacher can share some curiosities or stories related to the subject. For example, the story of how ancient Egyptians used geometry to build the pyramids could be told, or how geometry was crucial for the navigation of ancient sailors. Furthermore, a mathematical challenge involving the use of parallel lines and transversals, such as the "Tower of Hanoi Problem," could be presented.

   • Curiosity 1: "Did you know that the word 'geometry' comes from Greek and means 'earth measurement'? This is because the first studies of geometry were done to measure lands and build buildings."
   • Curiosity 2: "What if I told you that with just two parallel lines and one transversal, we can prove that the sum of the interior angles of a triangle is always 180 degrees? Can you imagine how?"

By the end of this stage, students should have understood the importance of the subject, be motivated to learn more, and have their curiosity piqued.

Development (20 - 25 minutes)

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

   • Preparation: The teacher should divide the class into groups of 4 to 5 students. Then, provide each group with a large sheet of paper, pencils, and a ruler.
   • Description: The challenge is for each group to "build" a city on their sheet of paper, drawing roads, buildings, parks, etc. However, they must ensure that all roads are parallel or transversal to each other. Each road should be drawn with a different color for easy identification.
   • Execution: Students should work together to plan and draw the city, ensuring that all roads are correctly parallel or transversal. They should also calculate and note the angles formed by each intersection of roads.
   • Feedback: After completing the activity, the groups should present their cities to the class, explaining how they ensured that the roads were parallel or transversal and how they calculated the angles.

2. Activity 2 - "Solving the Mystery" (10 - 12 minutes)

   • Preparation: The teacher should provide each group with a set of cards. Each card should have a different drawing representing the intersection of two lines.
   • Description: The challenge is for the groups to use the cards to solve a "mystery." The mystery is to discover what rule determines if the lines in each drawing are parallel or transversal. The rule may involve the position of intersection points, the orientation of the lines, the presence of other elements in the drawing, etc.
   • Execution: Students should analyze the drawings, discuss in groups, and try to identify the rule. They should write down their hypotheses and justifications. Once most groups have identified the rule, they should share it with the class.
   • Feedback: The teacher should guide the discussion, confirm if the rule identified by the students is correct, and explain how it relates to the concept of parallel lines and transversals.

3. Activity 3 - "Angle Challenge" (5 - 8 minutes)

   • Preparation: The teacher should provide each group with a set of cards. Each card should have a drawing representing the intersection of two lines, but with one of the angles missing.
   • Description: The challenge is for the groups to calculate the value of the missing angle in each drawing. They should use the properties of parallel lines and transversals they learned to solve the problem.
   • Execution: Students should work together to calculate the missing angles in each drawing. They should write down their answers and justifications. Once most groups have completed the challenge, they should share their solutions with the class.
   • Feedback: The teacher should correct the students' solutions, explain any errors, and reinforce the correct problem-solving strategies.

These playful and contextualized activities are designed to engage students actively and meaningfully in the learning process. They will have the opportunity to apply the acquired knowledge, develop problem-solving skills, work in teams, and improve their understanding of the concept of parallel lines and transversals.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher should gather all students in a large circle and start a group discussion. Each group will have a maximum of 2 minutes to share their solutions, conclusions, and learnings from the activities carried out.
   • The teacher should ensure that all groups have the opportunity to speak. During the discussion, the teacher should ask questions to promote reflection and deepen students' understanding of the subject. For example: "Why do you think this strategy worked?" or "How would you apply what you learned today in other situations?"
   • The teacher should encourage students to make connections between the activities performed, the theory discussed in the Introduction, and the practical application of the concept of parallel lines and transversals.

2. Learning Verification (2 - 3 minutes)

   • After the group discussion, the teacher should conduct a quick learning verification. This can be done through oral questions or a small printed questionnaire.
   • The goal is to assess whether students were able to understand and apply the properties of parallel lines and transversals correctly, as well as to calculate angles in practical situations.
   • The teacher should correct students' answers on the spot and take the opportunity to clarify any remaining doubts.

3. Final Reflection (2 - 3 minutes)

   • To conclude the class, the teacher should propose that students make a brief reflection on what they have learned. The teacher can ask questions such as: "What was the most important concept you learned today?" and "What questions have not been answered yet?"
   • Students should have a minute to think and write down their answers. Then, they should share their reflections with the class. The teacher should listen carefully to students' answers, as they can reveal the level of understanding and possible learning gaps.
   • The teacher should end the class by reinforcing the main points discussed during the lesson, highlighting the importance of the subject, and encouraging students to continue studying and practicing at home.

By the end of this stage, students should have consolidated their understanding of the concept of parallel lines and transversals, developed skills in calculating angles and problem-solving, and be prepared to apply this knowledge in future situations. Additionally, the teacher should have a good understanding of the students' learning level and areas that may need reinforcement in future classes.

Conclusion (5 - 7 minutes)

1. Summary and Recapitulation (1 - 2 minutes)

   • The teacher should start the Conclusion by recalling the main points of the lesson. This includes the concept of parallel lines and transversals, the properties associated with these geometric figures, and how to calculate the angles formed.
   • A brief summary of the activities carried out, highlighting the main learnings obtained through them, can be made.
   • It is important for the teacher to make connections between the presented theory and the discussed practical applications, reinforcing the relevance of the subject for daily life and other disciplines.

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

   • The teacher should explain how the lesson connected theory, practice, and applications.
   • It should be emphasized that the main objective was for students not only to understand the concept of parallel lines and transversals but also to be able to apply it in practical situations and solve related problems.
   • The teacher can highlight the skills developed by students during the activities, such as the ability to work in teams, think critically, and solve problems creatively.

3. Extra Materials (1 minute)

   • The teacher should suggest extra materials for students who wish to deepen their knowledge on the subject. This may include math books, educational websites, YouTube videos, among others.
   • For example, the teacher could suggest that students watch a video explaining the properties of parallel lines and transversals in more detail or solve more problems on the subject.

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

   • To conclude the class, the teacher should emphasize the importance of the subject presented.
   • It can be mentioned how knowledge about parallel lines and transversals is fundamental in various areas of knowledge and daily life, such as in engineering, architecture, physics, and even in daily activities like following a map.
   • The teacher can encourage students to observe examples of parallel lines and transversals in their homes and schools, reinforcing the idea that mathematics is present in our daily lives in a much broader way than we imagine.

By the end of this stage, students should have consolidated their learning about parallel lines and transversals, understood the relevance of the subject, and felt motivated to continue exploring the topic. The teacher, in turn, should be confident that the learning objectives have been achieved and that students are prepared to advance to more complex topics.