Objectives (5 - 10 minutes)

1. Understanding the concept of angles in circles: The teacher should guide the students to understand the concept of angles in a circle, including the fact that the sum of the angles around a central point is always 360 degrees. This can be done through visual and practical examples, such as using a compass and a protractor.

2. Calculating angles in circles: After understanding the concept, the teacher should guide the students to calculate the angles in circles. This can be done through practical examples and exercises, where students should apply the formula correctly.

3. Applying the concept of angles in circles to real-world problems: Finally, the teacher should help the students apply what they have learned in real-life situations. This may include solving everyday problems, such as calculating the distance traveled in a circle based on the rotated angle.

   Secondary objectives:

   • Stimulate logical reasoning and problem-solving: Throughout the lesson, the teacher should encourage students to think logically and solve problems efficiently.

   • Promote collaboration and communication: The teacher should encourage active participation from students, promoting group discussions and clarifying doubts.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing the concepts of circle, radius, diameter, and circumference, as these are fundamental to understanding the topic of angles in circles. This can be done through direct questions to the students or through a quick quiz.

2. Problem situations: Next, the teacher should present two situations to the students that involve calculating angles in circles. For example:

   • Situation 1: "Imagine you are in a park and see a carousel spinning. You would like to know how far you are from the carousel, but you cannot approach it. However, you know that the diameter of the carousel is 5 meters and that it has rotated 45 degrees since you started observing it. How could you use this angle to calculate the distance between you and the carousel?"

   • Situation 2: "Imagine you are drawing a circle on a piece of paper and want to divide it into equal sectors. How could you use the concept of angles in circles to do this?"

3. Contextualization: The teacher should then contextualize the importance of angles in circles, showing how they are applied in various areas such as architecture, engineering, astronomy, and even in games and toys, like the carousel from the previous example.

4. Introduction of the topic: Finally, the teacher should introduce the topic of angles in circles, explaining that, just like in triangles and quadrilaterals, angles in circles also have specific properties and formulas. To spark students' interest, the teacher can share curiosities, such as the origin of the degree symbol (°) and the story of the Greek mathematician Thales of Miletus, who, according to legend, used the concept of angles in circles to measure the height of the pyramids in Egypt.

Development (20 - 25 minutes)

1. Theory - The concept of angle in a circle (5 - 7 minutes):

   • The teacher should start by explaining that in a circle, the sum of the angles around a central point is always 360 degrees. This can be visually demonstrated by drawing a central point and tracing several radii from it, which will form various angles.
   • The teacher should emphasize that in a circle, the right angle measures 90 degrees, the straight angle measures 180 degrees, and the obtuse angle measures more than 180 degrees but less than 360 degrees.
   • The concept of the central angle should be presented and explained. The teacher should make it clear that the central angle is formed by two radii emanating from the center of the circle and that it is used to measure the opening of a circular sector.

2. Theory - Measuring angles in circles (5 - 7 minutes):

   • The teacher should explain that to measure an angle in a circle, a protractor must be used. The protractor should be placed with the central point at the center of the circle and one side of the angle aligned with the radius of the circle.
   • The teacher should demonstrate the process of measuring an angle, using a circle drawn on the board and a protractor. The result should be compared to the value calculated by the formula for the sum of angles in a circle.
   • The teacher should reinforce the importance of measuring the angle correctly, as a small error in measurement can lead to a large error in calculation.

3. Practice - Calculating angles in circles (5 - 7 minutes):

   • The teacher should propose some exercises for calculating angles in circles, starting with simple examples and gradually increasing the difficulty. Students should be guided to use the formula for the sum of angles in a circle to calculate the angles.
   • The teacher should move around the classroom, observing and guiding students in solving the exercises. Doubts and difficulties should be clarified immediately.

4. Practice - Applying angles in circles (5 - 7 minutes):

   • The teacher should have students solve the problem situations presented in the Introduction of the lesson. Students should be guided to apply the concept of angles in circles to solve the situations.
   • The teacher should move around the classroom, observing and guiding students in solving the problem situations. Doubts and difficulties should be clarified immediately.
   • At the end of the activity, the teacher should promote a class discussion where students can share their solutions and strategies. This can help consolidate learning and promote collaborative learning.

Return (10 - 15 minutes)

1. Review of learned concepts (5 - 7 minutes):

   • The teacher should start this stage by asking students to summarize, in their own words, what they have learned about angles in circles. This can be done through a small classroom discussion where students can share their understandings and remaining doubts.
   • Next, the teacher should review the main points of the lesson, reinforcing the concept of angles in circles, the formula for the sum of angles in a circle, and the application of this concept in real-world problems.
   • The teacher should also clarify any remaining doubts and reinforce the importance of correctly using the protractor to measure angles.

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

   • The teacher should ask students to reflect on the practical application of what they have learned. This can be done through questions such as: "How are angles in circles used in the real world?" or "In which daily life situations can we find examples of angles in circles?"
   • Students should be encouraged to think of concrete examples and share their ideas with the class. The teacher should clarify and discuss each example, highlighting how angles in circles are used in practice.

3. Final reflection (2 - 3 minutes):

   • The teacher should ask students to individually reflect on what they have learned in the lesson. They should answer questions such as: "What was the most important concept learned today?" and "What questions have not been answered yet?"
   • Students should be encouraged to write down their answers and share them with the teacher. This reflection can help the teacher assess the effectiveness of the lesson and plan for future teaching sessions.

4. Preparation for the next lesson (2 - 3 minutes):

   • Finally, the teacher should introduce the topic of the next lesson, which will be related to angles in circles. This can be done through a brief introduction of the new concept or a reflection question. The teacher should then assign homework or a quiz for students to prepare for the next lesson.
   • The teacher should remind students to review the concepts learned and to study for the next lesson. Additionally, the teacher should encourage students to ask questions and seek help whenever needed.

Conclusion (5 - 10 minutes)

1. Summary of key points (2 - 3 minutes):

   • The teacher should start the Conclusion by summarizing the key points covered during the lesson. This includes the concept of angles in circles, the formula for the sum of angles in a circle, measuring angles in circles with a protractor, and applying this concept to real-world problems.
   • The teacher can do this interactively by asking students to recall each point and explain it in their own words. This helps reinforce learning and check students' understanding.

2. Connection between theory, practice, and applications (1 - 2 minutes):

   • The teacher should highlight how the lesson was able to connect theory, practice, and applications of angles in circles. It should be emphasized that the theory was presented clearly and understandably, that the concepts were practiced through exercises and problem situations, and that practical application was demonstrated through real-world examples.

3. Extra materials (1 - 2 minutes):

   • The teacher should suggest some extra materials for students who wish to deepen their knowledge of angles in circles. This may include textbooks, educational websites, online videos, and interactive games.
   • For example, the teacher may recommend a YouTube video that explains the concept of angles in circles visually and dynamically, or an online game that allows students to practice calculating angles in circles in a fun and interactive way.

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

   • Finally, the teacher should emphasize the importance of the topic of angles in circles for daily life and for various areas of knowledge. It should be explained that understanding this concept is essential for comprehending many natural phenomena, solving practical problems, and developing mathematical and logical skills.
   • For example, the teacher may mention how angles in circles are used in architecture and engineering for designing curves and arches, or how they are used in astronomy to measure the positions and movements of celestial bodies. This helps show students the relevance and applicability of what they learned in the lesson.