Lesson plan of Angles: Classification

Objectives (5 - 7 minutes)

1. To provide students with a clear understanding of the concept of angles and their importance in the real world. This includes the definition of angles, understanding how they are formed, and the ability to identify and draw angles in different contexts.

2. To develop students' ability to classify angles. This involves the ability to identify whether an angle is acute, obtuse, right, or straight, and to justify their chosen classification based on its measurement.

3. To stimulate students' critical thinking by challenging them to apply their learning about angle classification to solve practical problems. This includes the ability to identify the classification of angles in complex shapes and the skill to justify their answers.

Secondary Objectives:

• To promote active student participation in the lesson by encouraging them to ask questions, participate in discussions, and solve problems in groups.
• To foster student autonomy by encouraging them to seek additional resources to enhance their understanding of the topic.
• To assess students' progress throughout the lesson, through formative feedback and assessment activities.

The objectives should be shared with students by the teacher at the beginning of the lesson, so that they are aware of what is expected of them and can prepare adequately. Additionally, the teacher should reiterate these objectives throughout the lesson, to ensure that students are focused on what is most important.

Introduction (10 - 15 minutes)

1. Review of relevant concepts: The teacher should begin the lesson by reviewing with students fundamental mathematical concepts that are the basis for the study of angles. This may include the concept of a point, line, ray, and line segment, as well as the understanding that a circle is made up of 360 degrees. This review can be done in an interactive way, by asking students to draw examples of these concepts on their notebooks.

2. Presentation of problem situations: Next, the teacher should present two problem situations that involve the use of angles. For example, the teacher could ask students how they could calculate the angle formed by the hands of a clock at a certain time or how they could determine the classification of an angle in a complex shape. These problem situations will serve to spark students' interest in the topic and to demonstrate the practical relevance of angles.

3. Contextualization of the importance of the subject: The teacher should then contextualize the importance of studying angles, explaining that they are widely used in diverse fields such as architecture, engineering, game design, computer programming, and even sports. For example, the teacher could mention that angles are used to design safe bridges, to create graphics in computer games, and to calculate the trajectory of a ball in a football game.

4. Introduction of the topic with curiosities and applications: To capture students' attention, the teacher can share some curiosities about angles. For example, the teacher could mention that the term "angle" comes from the Greek word "ankylos", which means "bent". Additionally, the teacher can show some interesting applications of angles, such as the use of angles in Islamic art and in the construction of the pyramids of Egypt.

5. Introduction of the topic in a playful way: Finally, the teacher can introduce the topic in a playful way, by presenting a game or activity that involves the measurement and classification of angles. For example, the teacher could ask students to play "Angry Birds", a popular computer game that uses physics and geometry, including the measurement and classification of angles.

The aim of this Introduction is to spark students' interest in the topic, to show the practical relevance of angles, and to prepare them for the more in-depth study that will follow. Additionally, the Introduction should establish a positive and engaging learning environment, which encourages active student participation.

Development (20 - 25 minutes)

1. Theory (10 - 15 minutes):

   1.1. Definition of angle: The teacher should start the theoretical part of the lesson by explaining that an angle is the figure formed by two rays that share a common endpoint, the vertex.

   1.2. Unit of angle measurement: Next, the teacher should address the unit of angle measurement, the degree (°), which is based on the division of a circumference into 360 equal parts.

   1.3. Types of angles: The teacher should then introduce the different types of angles that will be studied: acute, right, obtuse, and straight. For each type of angle, the teacher should provide the definition, characteristics, and examples.

   1.4. Acute angles: The teacher should explain that an angle is acute when it measures less than 90°. Examples of acute angles include the angle formed by two sides of an equilateral triangle or the angle formed by two sides of a square.

   1.5. Right angles: The teacher should then introduce right angles, which are those that measure exactly 90°. The teacher can explain that right angles are very common in everyday life, appearing, for example, in the corners of walls and tables.

   1.6. Obtuse angles: The teacher should then introduce obtuse angles, which are those that measure more than 90° but less than 180°. The teacher can use a protractor to demonstrate the measurement of an obtuse angle.

   1.7. Straight angles: Finally, the teacher should explain the concept of a straight angle, which is one that measures exactly 180°. The teacher can show examples of straight angles in nature, such as the angle formed by the side and the diagonal of a sheet of paper.

2. Practice (10 - 15 minutes): After the theoretical explanation, the teacher should move on to the practice of the content.

   2.1. Angle classification exercises: The teacher should provide students with a series of exercises in which they have to classify the type of angle (acute, right, obtuse, or straight) given its measurement. The exercises should be progressively more challenging, starting with well-defined angles and moving on to shapes where the angles are less obvious.

   2.2. Angle drawing exercises: The teacher should then ask students to draw angles of different types (acute, right, obtuse, straight) based on their descriptions. This will help students visualize the different types of angles and to better understand their characteristics.

   2.3. Angle identification exercises in figures: Finally, the teacher should present students with a series of complex shapes and ask them to identify and classify the angles present. This will help students apply what they have learned in a practical way and to develop their critical thinking skills.

The aim of this Development stage is to ensure that students have a clear understanding of the concept of angles and are able to classify them correctly. In addition, the content practice will allow students to apply what they have learned in a practical way and to develop their problem-solving skills.

Conclusion (8 - 10 minutes)

1. Group discussion (3 - 4 minutes): The teacher should start the Conclusion stage by promoting a group discussion. He or she can ask students to share their answers and solutions to the angle classification and identification exercises that were carried out. During the discussion, the teacher should encourage students to explain the reasoning behind their answers and to justify their choices. This will allow students to learn from each other and to develop their mathematical communication skills.

2. Connection with theory (2 - 3 minutes): After the group discussion, the teacher should make the connection between the practice carried out and the theory presented. He or she can, for example, ask students how they applied the definition and characteristics of each type of angle to classify them correctly. The teacher can also ask students to identify the theoretical concepts that were most useful to them in solving the exercises. This will help to reinforce the learning of theoretical concepts and to show students the importance of theory for practice.

3. Individual reflection (2 - 3 minutes): Finally, the teacher should propose that students make an individual reflection on what they have learned in the lesson. The teacher can ask questions such as:

   3.1. What was the most important concept that you learned today? 3.2. What questions have not yet been answered? 3.3. How would you apply what you learned today to everyday situations?

   Students should be given a minute to think about these questions and then the teacher should ask some volunteers to share their answers with the class. This will allow the teacher to assess the effectiveness of the lesson and to identify any areas that may need reinforcement in future lessons.

The Conclusion aims to consolidate students' learning, promote reflection on what has been learned, and identify any areas that may need reinforcement. In addition, the group discussion and individual reflection will help develop students' ability to communicate and justify their answers, as well as their ability to apply what they have learned to everyday situations.

Wrap-up (5 - 7 minutes)

1. Summary of the content (2 - 3 minutes): The teacher should begin the Wrap-up stage by summarizing the main points covered during the lesson. This includes the definition of angle, the unit of angle measurement (degrees), and the different types of angles (acute, right, obtuse, and straight). The teacher can ask students to share what they found to be the most important concepts, thus reinforcing learning.

2. Connection between theory, practice, and applications (1 - 2 minutes): Next, the teacher should explain how the lesson connected theory, practice, and applications of angles. The teacher can highlight how the theory of angles was applied in practice, through the angle classification and drawing exercises. In addition, the teacher can reinforce the practical applications of angles, such as in architecture, engineering, game design, among others.

3. Extra materials (1 minute): The teacher should suggest some extra materials for students who wish to deepen their knowledge on the topic. This could include mathematics books, math education websites, explanatory videos on YouTube, among others. For example, the teacher could suggest that students watch a video on angles on Khan Academy, or that they read a chapter on angles in a mathematics textbook.

4. Relevance of the topic (1 - 2 minutes): Finally, the teacher should summarize the relevance of the topic presented for everyday life and for other disciplines. For example, the teacher could mention that understanding angles is fundamental in many everyday activities, such as cooking, driving, or even playing a football game. In addition, the teacher could highlight how geometry, and in particular the study of angles, is related to other disciplines, such as physics and art.

The Wrap-up aims to consolidate students' learning, reinforce the importance and relevance of the topic studied, and motivate students to continue learning about the subject. In addition, the suggestion of extra materials and the connection with other disciplines will help promote a more comprehensive and interdisciplinary view of the topic.