Objectives (5 - 10 minutes)

The teacher should start the lesson by establishing the Learning Objectives. This includes:

1. Understand the concept of lines, line segments, and rays: Students should be able to differentiate between lines, line segments, and rays, understanding their definitions and characteristics. They should understand that lines are infinite and have no beginning or end, while line segments and rays have a beginning and end or just a beginning, respectively.

2. Identify lines, line segments, and rays in real situations and geometric figures: Students should be able to apply the acquired knowledge to identify lines, line segments, and rays in practical situations and geometric figures. They should be able to identify these elements on maps, diagrams, drawings, and other contexts.

3. Solve problems involving lines, line segments, and rays: Students should be able to apply the concept of lines, line segments, and rays to solve math problems. This may include determining intersection points, calculating segment lengths, among others.

The Objectives should be presented clearly and concisely, so that students know what is expected of them by the end of the lesson. The teacher can share the Objectives in writing on the board or in a slide presentation, and should also verbally explain each objective to ensure that all students understand them.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing previously studied geometry concepts, such as points, lines, and planes. This review is crucial for students to understand the new concepts that will be presented. The teacher can ask quick questions to assess the level of understanding of the students and clarify any remaining doubts.

2. Problem situations: The teacher should present two problem situations involving lines, line segments, and rays. For example:

   • "Imagine you are looking at a map of the city and need to draw the shortest path between two points. How could you use the concept of line segments and lines to do this?"
   • "Have you ever seen a line that goes on forever? What would happen if we cut a small part of that line? What would we have?"

3. Contextualization: The teacher should explain the importance of the concepts to be studied, demonstrating how they are used in everyday life and in various areas of knowledge. For example, in architecture, engineering, interior design, navigation, among others.

4. Introduction of the topic: The teacher should then introduce the topic of lines, line segments, and rays. This can be done by telling an interesting fact, such as:

   • "Did you know that the concept of a line is so fundamental in mathematics that it cannot be defined? That is, the line is one of the primitive ideas of mathematics, which does not need to be explained in terms of more basic concepts."

5. Capturing students' attention: To spark students' interest, the teacher can:

   • Share a historical curiosity: "Did you know that the study of lines, line segments, and rays dates back to Ancient Greece? Greek mathematicians, such as Euclid, were some of the first to study these concepts and establish the foundations of the geometry we use today."
   • Propose a challenge: "Whoever can describe to me the difference between a line and a line segment clearly and concisely will earn an extra point on the next test!"

By the end of this stage, students should be curious and motivated to learn more about lines, line segments, and rays.

Development (20 - 25 minutes)

1. "Geometric Treasure Hunt" Activity (10 - 15 minutes):

   • Objective: Apply the concept of lines, line segments, and rays in a playful and practical context.
   • Activity Description: The teacher should divide the class into groups of 3 to 4 students. Each group will receive a sheet of paper with a complex geometric drawing, which contains several lines, line segments, and rays. The task for the students is to identify and color each of these elements in the drawing. The first group to finish correctly wins.
   • Development: The teacher should provide colored pencils and markers to the groups. During the activity, the teacher should circulate around the room, assisting groups that are having difficulties and clarifying doubts. At the end of the activity, the teacher should review the solution with the whole class, highlighting the main points.

2. "Creation of a Geometric Scenario" Activity (10 - 15 minutes):

   • Objective: Apply the concept of lines, line segments, and rays in creating a realistic scenario.
   • Activity Description: Still in groups, students will receive a cardboard, colored pencils, ruler, and compass. The teacher will ask them to create a scenario, such as a city, a park, a classroom, etc. In this scenario, students should draw and identify lines, line segments, and rays. Additionally, they should write a short text explaining where and why they chose to draw these elements.
   • Development: Students will have time to discuss and plan the scenario. Then, they will start drawing and identifying the lines, line segments, and rays. The teacher should circulate around the room, assisting groups when necessary and encouraging discussion about the choice of drawing the geometric elements in the indicated locations.

Both activities are designed to be interactive and engaging, allowing students to apply what they have learned about lines, line segments, and rays in a practical way. Additionally, they promote collaboration among students, problem-solving, and critical thinking.

Feedback (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   • Objective: Facilitate reflection and consolidation of the knowledge acquired during the group activities.
   • Activity Description: The teacher should gather all students and promote a collective discussion. Each group will have a maximum of 3 minutes to share their solutions or conclusions from the "Geometric Treasure Hunt" and "Creation of a Geometric Scenario" activities. During the presentations, students should explain how they applied the concept of lines, line segments, and rays, and what they learned from the activity.
   • Development: The teacher should guide the discussion, asking questions to deepen students' understanding, correcting possible misinterpretations, and reinforcing key concepts. It is important that all students actively participate in the discussion, whether by presenting, asking, or answering.

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

   • Objective: Reinforce the applicability of the theoretical concepts presented and the resolution of practical problems.
   • Activity Description: After the discussion, the teacher should revisit the concepts of lines, line segments, and rays and make the connection with the activities carried out. For example, how did the theoretical definition of lines, line segments, and rays apply in the "Geometric Treasure Hunt" and the "Creation of a Geometric Scenario"? The teacher can also ask students to cite real-world examples where these concepts are applied.
   • Development: The teacher should lead this discussion, allowing students to express their opinions and ideas. It is important that the teacher makes the necessary connections between theory and practice in order to consolidate students' learning.

3. Individual Reflection (3 - 5 minutes):

   • Objective: Provide a moment of individual reflection on what was learned.
   • Activity Description: The teacher should propose that students reflect silently on the following questions:
     1. What was the most important concept you learned today?
     2. What questions have not been answered yet?
   • Development: After a minute of reflection, students should write down their answers on a piece of paper. Then, the teacher can ask for volunteers to share their answers with the class. The teacher should reinforce that all questions are valid and that any concepts that have not been understood will be reviewed in the upcoming lessons.

By the end of this stage, students should have a solid understanding of the concept of lines, line segments, and rays, and be able to apply it in practical situations. Additionally, they should have had the opportunity to reflect on what they have learned and identify any areas that still need clarification.

Conclusion (5 - 10 minutes)

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

   • The teacher should review the main points covered in the lesson, reinforcing the difference between lines, line segments, and rays, and highlighting the importance of being able to identify them in real situations and geometric figures.
   • Students should be reminded that lines are infinite, line segments have a beginning and end, and rays have a beginning but no end. Additionally, the teacher should reinforce the applicability of these concepts in problem-solving and in interpreting maps, diagrams, drawings, among others.

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

   • The teacher should explain how the activities carried out in the lesson connected theory, practice, and application. For example, how the "Geometric Treasure Hunt" allowed students to apply the concept of lines, line segments, and rays in a practical context, and how the "Creation of a Geometric Scenario" made them reflect on the applicability of these concepts in everyday situations.
   • It should be emphasized that mathematics is not only a theoretical discipline, but also a practical and powerful tool that can be applied in various everyday situations.

3. Additional Materials (1 - 2 minutes):

   • The teacher should suggest some extra materials for students to deepen their knowledge on the subject. This may include math books, educational websites, YouTube videos, among others.
   • For example, the teacher may recommend the book "Introduction to Geometry" by Harold Jacobs, which offers a detailed and accessible introduction to geometry concepts, including lines, line segments, and rays.
   • Additionally, the teacher may suggest that students watch educational videos on YouTube that explain these concepts visually and interactively, such as those from the channel "Math Antics".

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

   • Finally, the teacher should reinforce the importance of the subject presented for real life. It should be explained that knowledge about lines, line segments, and rays is fundamental in various areas, such as architecture, engineering, interior design, navigation, among others.
   • The teacher can also highlight that the ability to identify and work with these geometric elements helps develop logical thinking, problem-solving skills, and aptitude for abstraction, skills that are useful not only in mathematics, but in many other aspects of life.