Objectives (5 - 10 minutes)

1. Understanding the concept of angles on the clock: The teacher must ensure that students understand how the clock is divided into 12 equal parts, representing 360 degrees, and that each hour is equal to 30 degrees. In addition, students must understand that one minute is equal to 6 degrees on the clock.

2. Identification and measurement of angles on the clock: Students should be able to identify and measure angles on the clock, using the information provided, such as the position of the hands or the difference between the angles formed by the hands.

3. Calculating time from angles on the clock: Students should be able to calculate the time from a given angle on the clock. This objective requires the application of previous knowledge about the relationship between the position of the hands and time.

Secondary Objectives:

• Developing problem-solving skills: By working with the concept of angles on the clock, students will have the opportunity to develop their problem-solving skills, as they will need to apply their mathematical knowledge to solve complex issues.

• Promoting autonomy in learning: The inverted classroom allows students to learn at their own pace, review the content as many times as necessary, and seek help from the teacher and peers when needed, thus promoting autonomy in learning.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing previous concepts that are fundamental to understanding the topic of the lesson. This includes reviewing the concepts of angles, degrees, and how they are measured. The teacher can do this through a quick classroom discussion or an interactive activity that involves students in reviewing these concepts. (3 - 5 minutes)

2. Problem-solving situations: The teacher can then present two problem-solving situations involving the use of angles on the clock:

   a. "If the minute hand is pointing to the number 3 and the hour hand is pointing to the number 12, what is the angle formed by these two hands?" (3 - 5 minutes)

   b. "If the hour hand is between the numbers 4 and 5 and the minute hand is on the number 12, how much time is left until the clock marks the next hour?" (3 - 5 minutes)

3. Contextualization: The teacher should then contextualize the importance of the subject, showing how understanding angles on the clock is useful in everyday life. Examples may include the ability to estimate time accurately, the importance of being aware of time in various life situations (e.g., arriving on time for appointments, managing time during a test, etc.), and how analog clocks are used in a variety of contexts (e.g., in many electronic devices, at train stations and airports, etc.). (2 - 3 minutes)

4. Capturing students' attention: To capture students' attention, the teacher can share some curiosities about clocks. For example:

   a. "Did you know that the first clocks, used by the ancient Egyptians, were sundials that used the position of the sun to indicate time, instead of hands like we use today?"

   b. "And that the oldest working clock in the world is the Prague Astronomical Clock, in the Czech Republic, which was built in 1410?" (2 - 3 minutes)

Development (20 - 25 minutes)

1. Practical Activity 1: "Walking in Time" (10 - 15 minutes)

   • Description: The teacher will divide the class into groups of 4 to 5 students. Each group will receive a large circle on the floor, representing a clock. The teacher will provide each group with a pair of "hour hand" and "minute hand" (can be a piece of cardboard attached to a barbecue stick). The teacher will then make a series of statements, such as "Place the hour hand on the number 3 and the minute hand on the number 12" or "Rotate the minute hand 90 degrees clockwise." The students will then have to position their hands correctly on the cardboard clock according to the teacher's statements.

   • Objective: This activity aims to allow students to manipulate and visualize angles on the clock in a practical and fun way. They will have the opportunity to experiment and test different hand configurations, which will help solidify the concept of angles on the clock.

   • Materials: Cardboard, barbecue sticks, glue, scissors.

2. Practical Activity 2: "Solving the Clock Mystery" (10 - 15 minutes)

   • Description: The teacher will present students with a mystery scenario: "The detective needs to find out what time the thief stole the jewelry store, based on the position of the clock hands he left behind." The teacher will provide each group with an image of the crime clock, with the hands in a specific position, and a list of possible robbery times. Students will have to use their knowledge of angles on the clock to determine the time of the robbery.

   • Objective: This activity aims to challenge students to apply their knowledge of angles on the clock in a real-world scenario. They will have to use their problem-solving skills to determine the time of the robbery based on the position of the clock hands.

   • Materials: Images of clocks with hands in different positions, list of possible robbery times.

3. Discussion and Reflection: After completing the activities, the teacher should promote a classroom discussion about the solutions found by the groups. The teacher should guide the discussion by asking questions that lead students to reflect on the process they used to solve the problems and how angles on the clock were applied. This discussion will help consolidate students' learning and identify any areas that may still be confusing. (5 - 10 minutes)

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes): The teacher should gather all students and promote a group discussion. Each group will have up to 3 minutes to share their solutions or conclusions from the practical activities carried out. During the presentations, other students should be encouraged to ask questions and make comments. The teacher should guide the discussion, ensuring that all relevant aspects of the topic are addressed.

   • Objective: This group discussion allows students to learn from each other, share different approaches to the same problem, and practice their communication and argumentation skills.

2. Learning Verification (3 - 5 minutes): After the group presentations, the teacher should quickly review the main conclusions or solutions presented. The teacher should highlight the key points, clarify any misunderstandings, and reinforce essential concepts.

   • Objective: This learning verification step helps ensure that all students have understood the key concepts of the lesson and are ready to move on to the next topic.

3. Connection to Theory (2 - 3 minutes): The teacher should then connect the practical activities carried out with the theory presented at the beginning of the lesson. The teacher can do this through a quick review of key concepts, highlighting how they were applied in the practical activities. The teacher can also ask students how they think understanding angles on the clock can be useful in everyday situations.

   • Objective: This connection to theory step helps consolidate students' learning, showing the relevance and applicability of the concepts presented.

4. Final Reflection (2 - 3 minutes): Finally, the teacher should propose that students reflect on what they learned in the lesson. 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 think about the answers and then have the opportunity to share them with the class, if they wish.

   • Objective: This final reflection helps students consolidate their learning, identify any gaps in their understanding, and develop a plan to fill those gaps. It also provides valuable feedback to the teacher on the effectiveness of the lesson and any areas that may need review or reinforcement in future classes.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should summarize the main points covered during the lesson, reinforcing the concept of angles on the clock, the relationship between the position of the hands and time, and the importance of knowing how to measure and calculate angles on the clock. This is the moment to ensure that all students have understood the fundamental concepts of the lesson.

2. Connecting Theory with Practice (1 - 2 minutes): Next, the teacher should reiterate how the practical activities carried out during the lesson helped to illustrate and apply the presented theory. The teacher can highlight specific examples from the activities that demonstrate the application of theoretical concepts, reminding students that mathematics is not just about numbers and formulas, but also about the practical application of these concepts.

3. Extra Materials (1 minute): The teacher can suggest some extra materials for students who wish to deepen their knowledge on the subject. This may include websites, online videos, practice exercises, or math books that cover the topic of angles on the clock in more detail. The teacher should encourage students to explore these resources in their own time, as part of the autonomous learning process promoted by the inverted classroom.

4. Relevance of the Subject (1 - 2 minutes): Finally, the teacher should reinforce the importance of the subject for students' daily lives. The teacher can mention again examples of situations where understanding angles on the clock can be useful, such as calculating the remaining time on a task, understanding TV or bus schedules, or even interpreting the position of the sun in the sky to determine the time.

   • Objective: This Conclusion stage helps consolidate students' learning, reinforcing the key concepts of the lesson, encouraging continuous learning, and demonstrating the relevance of the subject to the real world.