Objectives (5 - 7 minutes)

1. Understand the concept of angles in the context of clocks, relating the position of the hours and minutes to the value of the formed angle.
2. Develop the ability to calculate the value of the angle formed by the hands of a clock at a specific time.
3. Apply the acquired knowledge to solve practical problems involving angles on clocks.

Secondary Objectives:

• Promote interaction and collaboration among students through practical activities and group discussions.
• Stimulate critical thinking and problem-solving through the application of the concept of angles in real situations.
• Encourage autonomy and responsibility for their own learning through classroom activities.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher should start the lesson with a brief review of the concept of angles, reminding students about the definition of an angle, the different types of angles (acute, right, obtuse, straight), and how to measure an angle with a protractor. This will prepare students to understand the new concept that will be introduced.

2. Problem situation: The teacher can propose two problem situations to pique the students' curiosity. The first one could be: 'If a clock is showing 6 o'clock, what is the angle formed between the hour and minute hands?' The second problem situation can be more complex: 'If the clock is showing 2:30, what is the angle formed between the hands?' Students should be encouraged to think about how to solve these problems.

3. Contextualization: The teacher should explain the importance of studying angles on clocks, showing that this knowledge is useful to understand how time is measured and how clocks work. Additionally, it can be mentioned that the ability to calculate angles on clocks can be useful in various practical situations, such as navigation, physics, and engineering.

4. Engaging students' attention: To spark students' interest, the teacher can share some curiosities about clocks. For example, it can be mentioned that the sundial, one of the earliest time-measuring devices, works based on the position of the Sun in the sky, which can be seen as a large hand. Another curiosity is that the world's oldest clock, called the 'Water Clock of Ctesibius,' was built in ancient Greece over 2,200 years ago and used water to move its hands.

With these strategies, the teacher should be able to capture students' attention, arouse their curiosity, and prepare them for the new content that will be presented.

Development (20 - 25 minutes)

1. 'Paper Clock' Activity: The teacher should divide the class into groups of 4 to 5 students. Each group will receive a paper clock model drawn on a sheet of paper and a protractor. The objective of the activity is for students to assemble the paper clock, position the hands correctly for a specific time, and then use the protractor to measure the formed angle. The teacher should propose different times for each group, varying between full hours and half hours. After measuring the angle, students should record the value on the sheet and then compare it with the measurements of other groups. This will allow them to notice the regularity of the angles formed at different times. (10 - 12 minutes)

2. 'Solving Practical Problems' Activity: After the 'Paper Clock' activity, the teacher should propose some problem situations for the students to solve in their groups. The situations may involve questions like: 'If the clock is showing 9:45, what is the angle formed?' or 'If the clock is showing 3:20, what is the angle formed?' Students should use what they learned in the previous activity to solve these problems. The teacher should move around the classroom, observing the groups' work, clarifying doubts, and providing guidance if necessary. (10 - 12 minutes)

3. Group Discussion: After solving the problem situations, the teacher should promote a group discussion where each group will present their solutions and strategies used. This will allow students to share and compare their ideas, promoting collaborative learning. The teacher should guide the discussion by asking questions to expand students' thinking and clarify concepts. (5 - 6 minutes)

These practical and playful activities will help students understand the concept of angles on clocks in a meaningful and fun way. Additionally, they promote interaction among students, collaboration, and problem-solving skills, important for the development of mathematical thinking.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should promote a group discussion so that each team can share their solutions and conclusions about the activities carried out. Each group will have a maximum of 3 minutes to present. During the presentations, the teacher should encourage other groups to ask questions and share their own experiences and strategies. The goal is to promote a rich and meaningful discussion where students can learn from each other and reflect on what was learned.

2. Connection with Theory (2 - 3 minutes): After the presentations, the teacher should make the connection between the practical activities carried out and the theory presented in the Introduction of the lesson. The teacher should reinforce the idea that the position of a clock's hands can be seen as an angle, and that this angle varies according to the time. The teacher should also emphasize that it is possible to measure this angle with a protractor. This connection is important for students to understand the relevance of what was learned and feel motivated to continue learning about the topic.

3. Individual Reflection (2 - 3 minutes): To conclude the lesson, the teacher should suggest that students make a brief individual reflection on what was learned. The teacher can ask questions like: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?' Students should have a minute to reflect, and then the teacher can ask some students to share their answers with the class. This reflection is an opportunity for students to consolidate what was learned, identify possible gaps in their knowledge, and express their doubts and curiosities.

4. Teacher Feedback (1 minute): The teacher should end the lesson by giving overall feedback on the class's performance and the lesson's progress. The teacher should praise strengths, point out areas for improvement, and reinforce the importance of the subject for daily life. Additionally, the teacher should encourage students to continue studying the topic and to ask questions in the next lesson.

By the end of the Return, students should have a clear understanding of what was learned, what still needs to be learned, and how they can continue learning about the topic. Additionally, they should feel motivated and confident to apply what they learned in practical situations.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered in the lesson. It should remind students about the concept of angles, the different types of angles, and how to measure an angle with a protractor. Then, it should emphasize the concept of angles on clocks, how the position of the hands can be seen as an angle, and how this angle varies according to the time. The teacher can use the whiteboard or a slide presentation to reinforce these concepts.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should explain how the lesson connected theory, practice, and applications. It should highlight that the 'Paper Clock' activity allowed students to visualize and measure the angles formed by a clock's hands, making the concept more concrete and understandable. Additionally, the teacher should reinforce that solving problem situations allowed students to apply what they learned in a practical and contextualized way. The teacher can also mention some real-world applications of the concept of angles on clocks, such as in navigation, physics, and engineering.

3. Extra Materials (1 minute): The teacher should suggest some extra materials for students who wish to deepen their understanding of the topic. These materials may include explanatory videos, online games, printable activities, and interactive websites. The teacher should write down these suggestions on the whiteboard or on a sheet of paper so that students can take notes in their notebooks.

4. Importance of the Subject (1 minute): Finally, the teacher should emphasize the importance of the subject for students' daily lives. It should explain that the ability to calculate angles on clocks can be useful in various practical situations, such as interpreting schedules, scheduling events, understanding natural phenomena (such as the apparent movement of the Sun and the Moon), and in various professions that involve time measurement. The teacher should emphasize that the knowledge of angles on clocks is not just a mathematical skill, but also a useful and relevant skill for everyday life.

With the Conclusion, students should have a clear and comprehensive view of what was learned in the lesson, the importance of the subject, and how they can continue learning about the topic. Additionally, they should feel motivated and confident to apply what they learned in their daily lives and in future studies.