Objectives (5 - 7 minutes)

1. Understand the concept of parallel lines and transversals:

   • Identify parallel lines and transversals in different situations, such as drawings, everyday objects, and constructions.
   • Differentiate between parallel lines and intersecting lines.

2. Develop the ability to identify and calculate angles formed by parallel lines and transversals:

   • Identify the different types of angles (alternate interior, alternate exterior, corresponding, and consecutive) and how they are formed.
   • Apply angle calculation rules to solve problems involving parallel lines and transversals.

3. Apply the acquired knowledge to solve practical problems:

   • Solve problems involving the identification of angles formed by parallel lines and transversals.
   • Apply the knowledge of parallel lines and transversals in everyday situations and in other disciplines.

Secondary objectives:

• Develop logical thinking and problem-solving skills.
• Encourage teamwork and communication among students through group activities.
• Encourage the application of mathematical knowledge in practical situations, promoting meaningful learning.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher starts the lesson by briefly reviewing mathematical concepts that have already been studied and are necessary for understanding the lesson's topic. These concepts may include the definition of a line, angle, sum of the interior angles of a triangle, among others. (3 - 5 minutes)

2. Problem situations:

   • The teacher presents two figures: one with two parallel lines cut by a transversal and another with two intersecting lines. The challenge is to identify which figures represent parallel lines and which represent intersecting lines. (2 - 3 minutes)

   • Next, the teacher presents a real-life situation, such as the construction of a bridge, and asks: 'How do engineers ensure that the bridge beams are parallel and do not intersect?' (2 - 3 minutes)

3. Contextualization: The teacher explains that the study of parallel lines and transversals is fundamental in various areas, such as architecture, engineering, industrial design, and even in computer programming. The teacher may cite examples of how these concepts are applied in practice, such as in road construction, computer game programming, among others. (2 - 4 minutes)

4. Introduction to the topic:

   • The teacher introduces the topic of parallel lines and transversals by telling the story of the Greek mathematician Thales of Miletus, who is considered the 'father of geometry' and is said to have been the first to study this type of configuration. (1 - 2 minutes)

   • Then, the teacher presents the importance of the theme through a curiosity: 'Did you know that the expression 'walking the line' comes from the fact that when two lines are parallel, they never meet, that is, they 'walk in the same line'?' (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity 1: 'Space Mission' (10 - 12 minutes)

   • Description: Students are divided into groups of up to 5 people. Each group receives a 'cosmic board' (a large sheet of paper) representing 'outer space.' The goal is to 'build a space station' (draw a figure composed of two parallel lines cut by a transversal) on their 'cosmic board.'

   • Necessary materials: Large paper, colored pens.

   • Step by step:

     1. The teacher explains the activity and the Objectives.
     2. The groups receive the necessary materials.
     3. Each group draws their 'space station' on the 'cosmic board.'
     4. Then, the groups must identify and mark the different types of angles formed by the 'transversal' and the 'parallel lines' (alternate interior, alternate exterior, corresponding, and consecutive angles).
     5. Finally, the groups must calculate the measure of each of the identified angles.
     6. The teacher circulates around the room, assisting the groups and clarifying doubts.

2. Activity 2: 'Race Track' (10 - 12 minutes)

   • Description: Still in groups, students receive a large sheet of paper representing a 'race track.' The challenge is to 'build a grandstand' (draw a figure composed of two parallel lines cut by a transversal) on their 'race track.'

   • Necessary materials: Large paper, colored pens.

   • Step by step:

     1. The teacher explains the activity and the Objectives.
     2. The groups receive the necessary materials.
     3. Each group draws their 'grandstand' on the 'race track.'
     4. Then, the groups must identify and mark the different types of angles formed by the 'transversal' and the 'parallel lines' (alternate interior, alternate exterior, corresponding, and consecutive angles).
     5. Finally, the groups must calculate the measure of each of the identified angles.
     6. The teacher circulates around the room, assisting the groups and clarifying doubts.

3. Activity 3: 'Engineer's Challenge' (5 - 6 minutes)

   • Description: The teacher presents a problem situation: 'You are an engineer responsible for building a bridge and need to ensure that the beams are parallel. How would you do that?' Each group must propose a solution, applying the concepts learned.

   • Step by step:

     1. The teacher presents the problem situation.
     2. The groups discuss the situation and propose a solution.
     3. Each group presents its solution to the class.
     4. The teacher leads a final discussion, highlighting the different solutions proposed and emphasizing the importance of the concepts of parallel lines and transversals in solving the problem.

At the end of the activities, the teacher reviews the concepts covered, highlighting the main learnings and clarifying any possible doubts. The teacher may also suggest that students record the main conclusions of the lesson in their notebooks.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher invites each group to share the solutions or conclusions found during the activities. Each group has a maximum of 2 minutes to present.
   • During the presentations, the teacher should encourage active participation from all students, asking questions to verify if they have correctly understood the concepts and applications.
   • The teacher should also promote interaction between groups, encouraging the exchange of ideas and respect for different approaches to the problem.

2. Connection to Theory (2 - 3 minutes)

   • After the presentations, the teacher reviews the theoretical concepts, relating them to the solutions or conclusions presented by the groups.
   • The teacher highlights how the concepts of parallel lines and transversals, and the different types of angles formed, were applied to solve the proposed problem situations.
   • The teacher may also reinforce the more difficult concepts or those that were less understood by students during the activities, clarifying any doubts.

3. Final Reflection (3 - 4 minutes)

   • The teacher proposes that students reflect individually for one minute on the following questions:
     1. What was the most important concept learned today?
     2. What questions have not been answered yet?
   • After the minute of reflection, the teacher asks students to share their answers.
   • The teacher should value all answers, clarify any doubts, and emphasize the importance of continuing to study and practice the concepts learned.
   • The teacher may also suggest that students record their answers to the reflection questions in their notebooks as a way to review the content and identify possible gaps in understanding.

4. Feedback and Closure (1 minute)

   • The teacher concludes the lesson by thanking everyone for their participation and effort.
   • The teacher may also request quick feedback from students, asking what they liked most about the lesson and what could be improved.
   • The teacher encourages students to continue studying and practicing the concepts learned and makes themselves available to clarify future doubts.

Conclusion (5 - 7 minutes)

1. Summary and Recap (2 - 3 minutes)

   • The teacher revisits the main points discussed during the lesson, reinforcing the concepts of parallel lines, transversals, and the angles formed.
   • The teacher gives a brief summary of the activities carried out, highlighting the main conclusions of the students and how they applied theory in practice.
   • The teacher reiterates the importance of understanding and being able to identify and calculate the angles formed by parallel lines and transversals, emphasizing that these concepts are fundamental not only in mathematics but also in various other areas of knowledge and everyday life.

2. Connection to Theory and Practice (1 - 2 minutes)

   • The teacher emphasizes how the lesson connected theory and practice, explaining that by working with playful activities and real-life situations, students were able to understand and apply theoretical concepts concretely.
   • The teacher highlights how group activities allowed students to develop skills such as teamwork, communication, and problem-solving, in addition to reinforcing mathematical concepts.

3. Additional Materials (1 minute)

   • The teacher suggests additional study materials for students who wish to deepen their knowledge on the subject. These materials may include explanatory videos, educational games, online exercises, among others.
   • The teacher may also recommend extra readings, such as math books, math education websites, and scientific articles.

4. Applications in Daily Life (1 minute)

   • Finally, the teacher reinforces the importance of the topic studied for daily life, citing examples of real-life situations where knowledge of parallel lines, transversals, and their angles is useful, such as in architecture, engineering, industrial design, computer programming, among others.
   • The teacher encourages students to observe these situations in their daily lives, reinforcing the idea that mathematics is not only in books but all around us.