Objectives (5 - 7 minutes)

Main Objectives:

1. Understand the concept of angles and their measurement in degrees and radians

   • Students must be able to define what an angle is and understand that it is a measure of rotation between two radii.
   • They must also understand that angles can be measured in degrees or radians, with degrees being the most commonly used measurement.

2. Convert angles between degrees and radians

   • Students must be able to convert angles from degrees to radians and vice versa.
   • They must understand that a complete circumference corresponds to 360 degrees or 2π radians, and be able to use this information to convert between the two units of measurement.

Secondary Objectives:

1. Identify angles in everyday situations

   • In addition to understanding the theory, students must be able to apply this knowledge in practice, identifying and measuring angles in everyday situations.

2. Solve problems involving angles and their measurements

   • Students must be able to solve problems that involve applying the concepts learned, such as calculating the measure of an unknown angle in a triangle.

Secondary objectives can be achieved through practical activities and problem-solving during the lesson. The teacher should encourage active student participation and provide constant feedback to promote understanding and learning.

Introduction (10 - 15 minutes)

1. Review of Previous Content:

   • The teacher should begin the lesson by reminding students of the mathematical concepts that are fundamental to understanding the current topic, such as the definition of a circle, radius, and diameter, as well as the notion of fractions and proportions. This review can be done through interactive questions and answers to engage students and activate prior knowledge. (3 - 5 minutes)

2. Problem Situation:

   • The teacher can then present two problem situations to arouse students' curiosity and interest:
     • Situation 1: "Imagine that you are in a park and see a Ferris wheel spinning. How could you measure how much the wheel has turned? Does this have anything to do with angles?"
     • Situation 2: "Have you ever heard of geographic coordinates? They are used to determine the exact location of a point on Earth. But how are they related to angles?" (3 - 5 minutes)

3. Contextualization:

   • The teacher should then contextualize the importance of the topic, explaining that the measurement of angles is applied in many areas of daily life and in various professions, such as architecture, engineering, astronomy, among others. Real-life examples can be mentioned where understanding and the ability to work with angles are essential, such as in the construction of structures, in maritime or air navigation, and in the study of the movement of planets and stars. (2 - 3 minutes)

4. Introduction of the Topic:

   • Finally, the teacher should introduce the topic of angles and their measurement, presenting the definition of an angle and emphasizing that angles are measured in degrees or radians. Visual examples can be used, such as the minute hand on a clock (which travels 360 degrees in one hour), to illustrate the concept. The teacher can also tell a curiosity about the topic, such as the fact that the measure of an angle in radians is the ratio between the length of the corresponding arc and the radius of the circumference. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory: Definition of Angle and Measurement in Degrees and Radians (10 - 12 minutes)

   • The teacher should begin the theoretical part by explaining the definition of an angle, which is the measure of the rotation required to move from one side of the angle to the other, with the vertex as the point of rotation.
   • The two main units of angle measurement should then be introduced: Degrees and Radians.
   • The teacher should explain that the degree is a unit of measurement that divides a complete turn (a circumference) into 360 equal parts.
   • The radian should then be introduced as the unit of measurement that divides the length of the arc of the circle by the radius. A radian is the angle that, when placed at the center of a circumference, intercepts an arc whose length is equal to the radius of the circumference.
   • The teacher should emphasize that the radian is a more natural unit for measuring angles, as it is directly related to the length of the arc, while the degree is an arbitrary unit that has no direct relationship to the geometry of the circumference.
   • To facilitate students' understanding, the teacher can use a slide presentation with images and animations, or drawings on a whiteboard, to illustrate the concepts and the differences between the two units of measurement.

2. Practice: Conversion between Degrees and Radians (5 - 7 minutes)

   • After explaining the theory, the teacher should move on to the practice, teaching students how to convert between degrees and radians.
   • The teacher should start by reinforcing that a complete turn (a circumference) corresponds to 360 degrees or 2π radians.
   • It should then be shown how to convert angles from degrees to radians, by dividing the measure in degrees by 180 and multiplying the result by π.
   • For example, to convert 45 degrees to radians, we divide 45 by 180 (0.25) and multiply by π, obtaining 0.25π radians.
   • It should then be shown how to convert angles from radians to degrees, by multiplying the measure in radians by 180 and dividing the result by π.
   • For example, to convert 0.5π radians to degrees, we multiply 0.5 by 180 (90) and divide by π, obtaining 90 degrees.
   • The teacher should provide several examples and allow students to practice converting in exercises.

3. Theory: Practical Applications of Angles and their Measurements (5 - 6 minutes)

   • To reinforce the importance of the topic, the teacher should present several practical applications of angles and their measurements.
   • For example, in geometry, angles are used to describe the shape and position of figures, and to calculate areas and volumes.
   • In physics, the measurement of angles is fundamental to the study of motion, both linear and rotational.
   • In engineering, angles are used to design and build structures, and to determine the force and direction of motion in machines and equipment.
   • The teacher can present other examples relevant to the students' reality, such as in navigation, astrology, computer science (graphics and games), etc.
   • For each example, the teacher should explain how angles are used and why the measurement in degrees or radians is appropriate.
   • The teacher should encourage students to think of more examples and to discuss their own observations and experiences.

4. Practice: Solving Problems Involving Angles and their Measurements (5 - 7 minutes)

   • To consolidate learning, the teacher should propose some problems for the students to solve.
   • The problems should involve the application of the concepts learned, such as the conversion of angles, the identification of angles in figures and real situations, and the calculation of the measure of unknown angles.
   • The teacher should provide guidance and tips for solving the problems, and should be available to clarify doubts and give feedback.
   • The students should work in groups to solve the problems, promoting collaboration and discussion.
   • The teacher should encourage the students to explain their solutions and justify their reasoning, so that they can develop a deeper and more meaningful understanding of the topic.
   • The teacher should correct the problems together with the students, highlighting the important points and the resolution strategies.

The Development of the class should be planned in a way that balances theory and practice, providing students with the opportunity to understand the theoretical concepts and to apply them in practical situations. The teacher should promote active student participation, stimulating critical thinking and problem-solving.

Return (8 - 10 minutes)

1. Content Review (3 - 4 minutes)

   • The teacher should begin the Return stage by reviewing the main points covered during the lesson.
   • He should recap the definition of angle, the difference between degrees and radians, and how to convert between the two units of measurement.
   • He should also reinforce the practical applications of angles and their measurements, and how they are used in various fields of science and technology.
   • The teacher can use direct questions to check students' understanding and encourage active participation.

2. Connection of Theory with Practice (2 - 3 minutes)

   • Next, the teacher should help students make the connection between the theory presented and the practical activities performed during the lesson.
   • He should explain how the theory of angles and their measurements was applied in solving the proposed problems, and how understanding these concepts facilitated the understanding and solution of the problems.
   • The teacher can ask students to share their experiences and observations, and to explain how they applied the theory in practice. This not only helps to consolidate learning, but also promotes reflection and critical thinking.

3. Reflection on Learning (2 - 3 minutes)

   • The teacher should then ask the students to reflect on what they have learned during the lesson.
   • He can ask questions such as: "What was the most important concept you learned today?" and "What questions have not yet been answered?"
   • The teacher should give a moment of silence so that the students can think about the questions, and then encourage them to share their answers.
   • The teacher should be open to hearing the students' doubts and questions, and should respond in a clear and concise manner. He should also encourage students to seek answers on their own, for example by searching the Internet, consulting textbooks, or asking a classmate for help.

4. Feedback on the Lesson (1 minute)

   • Finally, the teacher should ask the students to provide feedback on the lesson. He can ask: "What did you find most interesting or useful in today's lesson?" and "What could be improved?"
   • Students' feedback is important for the teacher to evaluate the effectiveness of his teaching approach and to make necessary adjustments for the next lessons.

The Return is a crucial part of the lesson, as it allows the teacher to assess students' progress and identify areas that need more attention. It also helps students to consolidate what they have learned, to make connections with the real world and to develop critical thinking and metacognitive skills.

Conclusion (5 - 7 minutes)

1. Summary of Main Content (2 - 3 minutes):

   • The teacher should begin the Conclusion of the lesson by summarizing the main content covered.
   • He should recap the definition of angle, the difference between degrees and radians, and how to convert between the two units of measurement.
   • The teacher should recall the practical applications of angles and their measurements, and how they are used in various fields of science and technology.

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

   • Next, the teacher should reinforce the connection between the theory presented, the practice performed, and the practical applications of angles and their measurements.
   • He should explain how the theory was applied in solving the practical problems, and how understanding these concepts facilitated the understanding and solution of the problems.
   • The teacher should emphasize that mathematics is not just a set of abstract rules, but a powerful tool for understanding and describing the world around us.

3. Suggestion of Supplementary Materials (1 minute):

   • The teacher should suggest some supplementary study materials for students who wish to deepen their understanding of the topic.
   • He can recommend textbooks, mathematics websites, YouTube videos, mobile apps, among others.
   • The teacher should emphasize that regular practice and review of the concepts are fundamental for the consolidation of learning.

4. Importance of the Topic for Everyday Life (1 - 2 minutes):

   • Finally, the teacher should reinforce the importance of angles and their measurements for everyday life.
   • He should present more examples of real-life situations where understanding and the ability to work with angles are essential, such as in navigation, architecture, engineering, astronomy, among others.
   • The teacher should emphasize that, although it may seem abstract at first, mathematical knowledge is a powerful tool that helps us understand and interact with the world around us.

The Conclusion is an essential part of the lesson, as it allows the teacher to reinforce the key concepts, make the connection between theory and practice, and highlight the relevance of the topic for everyday life. In addition, by suggesting supplementary study materials, the teacher encourages students to continue learning independently and in depth.