Objectives (5 - 7 minutes)

1. Understand the concept of arithmetic mean and its application in everyday situations.
2. Develop the ability to calculate the arithmetic mean of a set of numbers.
3. Apply the acquired knowledge to solve practical problems involving arithmetic mean.

Secondary Objectives:

• Foster critical thinking skills when analyzing and interpreting statistical data.
• Promote the practice of mathematical calculations using arithmetic mean.
• Encourage active student participation through discussions and group problem-solving.

Introduction (10 - 15 minutes)

1. Review of previous contents:

   • The teacher starts the lesson by briefly reviewing basic statistics concepts, such as data collection and organization, and the importance of central measures to represent a set of data. (3 - 5 minutes)

2. Problem situations:

   • The teacher presents two problem situations to arouse students' interest and contextualize the subject of the lesson:
     • Situation 1: 'In a class of 30 students, test scores ranged from 0 to 10. The arithmetic mean of the scores was 6. What is the possibility of a student scoring higher than the mean, if the maximum score is 10?'
     • Situation 2: 'In a company, employees' salaries range from R$ 1,000.00 to R$ 10,000.00. If the average salary is R$ 5,000.00, what is the chance of an employee earning more than the average salary?' (5 - 7 minutes)

3. Subject contextualization:

   • The teacher explains that the arithmetic mean is a widely used tool in various everyday situations, such as calculating school grades averages, salary averages, temperature averages, among others. Emphasizes that understanding and knowing how to calculate the arithmetic mean is essential to interpret and make decisions based on statistical data. (2 - 3 minutes)

4. Attention-grabber:

   • To arouse students' curiosity, the teacher can share some curiosities about the arithmetic mean, such as:
     • Curiosity 1: 'Did you know that the arithmetic mean was known by the ancient Greeks as 'aleph', which means 'a whole' or 'totality'?'
     • Curiosity 2: 'And that the arithmetic mean is used in many board games to calculate the average score of the players?' (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 'Students' Mean':

   • The teacher divides the class into groups of five students and gives each group a list of 30 fictitious grades (ranging from 0 to 10), representing the grades of a class of students in a test.
   • The challenge is to calculate the arithmetic mean of the grades and then each group must discuss and decide the possibility of a student scoring higher than the mean, if the maximum score is 10.
   • After the discussion, each group must present their answer and the reasoning used. The teacher should guide the discussion and clarify doubts. (10 - 12 minutes)

2. Activity 'Salaries in the Company':

   • The teacher proposes a new challenge: each group must imagine they are managers of a company and need to decide whether to give a raise to an employee who currently earns below the average salary.
   • The teacher provides each group with a list of fictitious salaries (ranging from R$ 1,000.00 to R$ 10,000.00) in the company, and the current average salary.
   • The challenge is to calculate the chance of an employee earning more than the average, if they decide to give the raise.
   • Again, students must discuss and present their answers, considering the impact of the raise on the average salary. The teacher should guide the discussion and clarify doubts. (10 - 12 minutes)

3. Discussion and Reflection:

   • After the conclusion of the group activities, the teacher leads a classroom discussion about the solutions found by the students.
   • The teacher emphasizes the importance of understanding and correctly applying the arithmetic mean, and how it can be useful for making decisions based on statistical data.
   • The teacher can also address the issue of the limitations of the arithmetic mean, such as the fact that it can be influenced by extreme values (outliers) and does not necessarily represent the situation of all individuals or elements in the set.
   • Finally, the teacher makes a connection between the activities carried out and the theory, reinforcing the concepts learned. (5 - 7 minutes)

Return (8 - 10 minutes)

1. Group Discussion (3 - 5 minutes):

   • The teacher asks each group to share their conclusions and solutions from the practical activities carried out.
   • Each group will have a maximum of 3 minutes to present, encouraging synthesis and clarity in the exposition of ideas.
   • During the presentations, the teacher should ask questions to stimulate students' reflection and ensure that everyone is understanding the content.

2. Connection with Theory (2 - 3 minutes):

   • After the presentations, the teacher summarizes the activities and connects the results obtained by the students with the theory presented at the beginning of the lesson.
   • The teacher highlights how the arithmetic mean was applied in the problem situations, reinforcing the concept and the importance of this statistical measure.
   • Additionally, the teacher can take the opportunity to correct any errors or misunderstandings in the application of arithmetic mean calculation, reinforcing the correct way to perform the operation.

3. Individual Reflection (2 - 3 minutes):

   • To conclude the lesson, the teacher proposes that students make an individual reflection on what they have learned.
   • The teacher can ask questions such as: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'.
   • Students should write down their answers in a notebook or piece of paper, which will be reviewed and discussed at the beginning of the next lesson.

4. Teacher's Feedback (1 minute):

   • Finally, the teacher thanks everyone for their participation and effort, and reinforces the importance of continuous study and practice for learning mathematics.
   • The teacher can also give general feedback on the lesson, highlighting the positive aspects and areas that still need improvement.
   • The teacher encourages students to ask questions and seek help whenever necessary, reminding them that the learning process is gradual and that everyone is constantly evolving.

This Return is essential to consolidate students' learning, as it allows them to reflect on what they have learned, identify possible doubts or difficulties, and receive feedback from the teacher. In addition, group discussion and connection with theory help reinforce the concepts learned and the practical application of the arithmetic mean.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes):

   • The teacher gives a brief summary of the main points covered in the lesson, reinforcing the concept of arithmetic mean, its importance, and how it is calculated.
   • Also highlights the practical activities carried out and how they demonstrated the application of arithmetic mean in everyday situations, such as analyzing a class's grades or deciding on a salary increase.
   • The teacher can use a whiteboard or a slide presentation to visualize the calculations performed and the conclusions reached.

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

   • The teacher reinforces how the lesson connected theory, practice, and the application of arithmetic mean.
   • Emphasizes how understanding the concept of arithmetic mean allowed students to solve the proposed problem situations, and how the discussion and reflection after the practical activities helped consolidate learning.

3. Extra Materials (1 minute):

   • The teacher suggests extra materials for students who wish to deepen their knowledge of arithmetic mean.
   • It could be a math book, an explanatory video, a website with interactive exercises, among others.
   • The teacher can make these materials available on the school's teaching platform, or indicate where students can find these resources.

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

   • Finally, the teacher emphasizes the importance of the subject presented for students' daily lives.
   • Explains that arithmetic mean is an essential tool to interpret and make decisions based on statistical data, and that it is present in various everyday situations, such as calculating school grades averages, salary averages, temperature averages, among others.
   • The teacher reinforces that the goal of mathematics is not only to learn how to do calculations, but also to develop critical thinking skills and problem-solving skills, which are fundamental for students' academic and professional success.