Objectives (5 - 10 minutes)

1. Understand the concept of arithmetic mean and its practical application. Students should be able to define the arithmetic mean, explain how it is calculated, and identify everyday situations where it is applied.

2. Develop skills to calculate the arithmetic mean. Students should be able to solve problems involving the calculation of the arithmetic mean, using both the formula and the strategy of summing the values and dividing by the total.

3. Apply the arithmetic mean to analyze data and draw conclusions. Students should be able to use the arithmetic mean as a tool to interpret data sets, identify patterns, and make predictions.

Secondary objectives:

• Foster critical thinking and problem-solving. Through the application of the arithmetic mean in real situations, students should be encouraged to think analytically and seek solutions independently.

• Promote active learning. Students should be encouraged to actively participate in the class, asking questions, discussing ideas, and solving problems together.

Introduction (10 - 15 minutes)

1. Review of Concepts: The teacher starts the class by recalling fundamental mathematical concepts such as addition, subtraction, multiplication, and division. This review is important for students to understand the calculation of the arithmetic mean, which involves summing and dividing. Additionally, the teacher can reinforce the idea that the mean is a value that represents a data set, and not necessarily a value present in the set.

2. Problem Situation: The teacher presents two problem situations to spark students' interest and contextualize the importance of the arithmetic mean:

   • Situation 1: Imagine you are in a bicycle race with your friends. Each friend has a different speed. How can you calculate the group's average speed?

   • Situation 2: Suppose in a class of 30 students, the test scores range from 0 to 10. How can you calculate the class's average score?

3. Contextualization: The teacher explains that the arithmetic mean is a widely used tool in various everyday situations and different fields, such as economics (to calculate the price index), medicine (to calculate a patient's average temperature during a day), and sports (to calculate a player's average points in a season, for example).

4. Initial Problem: To pique students' curiosity, the teacher proposes the following problem: "In the classroom, we have 30 students. The height of each student varies between 1.40 m and 1.80 m. How can we calculate the class's average height?".

5. Gaining Students' Attention: To make the Introduction more engaging, the teacher can share some curiosities about the arithmetic mean:

   • Curiosity 1: The term "mean" comes from the Latin "medius", which means "middle". This reflects the idea that the mean is a value that is in the middle of the other values in the set.

   • Curiosity 2: In music, the arithmetic mean is used to calculate the average note of a piece. This is done by assigning a numerical value to each musical note (for example, 1 for C, 2 for D, and so on) and then calculating the mean of these values.

Development (20 - 25 minutes)

1. Presentation of Theory (10 - 15 minutes)

   1.1. Definition and Concept (2 - 3 minutes): The teacher explains that the arithmetic mean is a measure of central tendency that represents the average value of a set of numbers. It is obtained by summing all the values in the set and dividing the total by the number of elements. The teacher can use the notation of mean with the symbol "x" with a bar on top to represent the mean of a data set.

   1.2. Calculation of the Mean (3 - 4 minutes): The teacher demonstrates how to calculate the arithmetic mean of a set of numbers. He should emphasize that all values in the set must be summed and that the total must be divided by the number of elements in the set.

   1.3. Application of the Mean (2 - 3 minutes): The teacher illustrates the application of the arithmetic mean in practical situations. He can use examples such as calculating the average grades of a class, the average speeds of a group in a race, the average prices of a product over a certain period, among others.

   1.4. Difference between Mean and Weighted Mean (1 - 2 minutes): The teacher explains that the weighted mean is a variation of the arithmetic mean where each value in the set has an associated "weight". He should emphasize that the weighted mean is different from the arithmetic mean because it takes into account not only the values in the set but also the weights of each value.

2. Practical Activities (10 - 15 minutes)

   2.1. Solving Examples (5 - 7 minutes): The teacher presents a series of examples of calculating the arithmetic mean for students to solve. He should start with simple examples and gradually increase the complexity. The teacher should circulate around the room, helping students who are having difficulties and providing constant feedback.

   2.2. Group Discussion (3 - 5 minutes): After students solve the examples, the teacher promotes a group discussion so they can share their answers and resolution strategies. This helps reinforce the understanding of the subject and promote critical thinking.

   2.3. Application in Everyday Situations (2 - 3 minutes): The teacher presents some everyday situations where the arithmetic mean can be applied and asks students to calculate the mean. This helps reinforce the relevance of the subject and show its practical utility.

3. Reinforcement of Learning (5 - 10 minutes)

   3.1. Summary of the Lesson (2 - 3 minutes): The teacher gives a brief summary of the main points covered in the lesson, reinforcing the definition and calculation of the arithmetic mean, and the differentiation between mean and weighted mean.

   3.2. Questions and Answers (3 - 5 minutes): The teacher opens a space for questions and answers, allowing students to clarify any doubts they may have. This is an important moment to assess students' understanding and identify any gaps in understanding that may need to be addressed in future lessons.

   3.3. Homework (1 - 2 minutes): The teacher assigns homework that consists of solving more examples of calculating the arithmetic mean. He should emphasize that practice is essential for content retention and the development of calculation skills.

Return (10 - 15 minutes)

1. Connection with Real Life (3 - 5 minutes): The teacher asks students to think about everyday situations where the arithmetic mean can be applied. They can consider examples such as calculating the average grades of a class, the average speeds of a group in a race, the average prices of a product over a certain period, the average heights of a family, among others. Students are encouraged to share their ideas with the class, promoting discussion and the exchange of experiences.

2. Reflection on Learning (3 - 5 minutes): The teacher then asks students to reflect on what they learned during the lesson. He can ask questions such as:

   2.1. What was the most important concept you learned today?

   2.2. What questions remain unanswered?

   2.3. How can you apply what you learned today in everyday situations?

   Students are encouraged to share their reflections with the class, promoting self-assessment and consolidation of learning.

3. Student Feedback (2 - 3 minutes): The teacher then asks students to provide feedback on the lesson. Students can be asked about what they liked most about the lesson, what they found most challenging, and what they would like to learn more about. This helps the teacher assess the effectiveness of their teaching strategies and make adjustments if necessary.

4. Class Closure (1 - 2 minutes): To close the lesson, the teacher reinforces the most important concepts covered and answers any final questions from students. He can also give a preview of what will be covered in the next lesson to maintain students' interest and encourage them to continue studying the topic.

Conclusion (5 - 10 minutes)

1. Summary of Content (2 - 3 minutes): The teacher summarizes the main points covered in the lesson, reinforcing the concept of arithmetic mean, the calculation of the mean, the difference between mean and weighted mean, and the practical applications of the arithmetic mean. He can use concrete examples to illustrate each of these points and reinforce students' understanding.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher highlights how the lesson connected theory (the concept and calculation of the arithmetic mean) with practice (solving examples and problems) and real applications (everyday situations where the arithmetic mean is applied). He emphasizes that understanding the theory is important, but the ability to apply this knowledge in practice is what makes learning meaningful.

3. Extra Materials (1 - 2 minutes): The teacher suggests some extra materials for students who want to deepen their understanding of the subject. These materials can include math books, educational websites, explanatory videos, among others. He should emphasize that exploring these materials is optional but can be useful for students who want to reinforce their learning.

4. Importance of the Subject (1 - 2 minutes): To close the lesson, the teacher emphasizes the importance of the arithmetic mean in everyday life. He can mention some situations where the arithmetic mean is applied, such as in evaluating a team's performance, analyzing economic data, measuring health indicators, among others. The teacher should emphasize that the ability to calculate and interpret the arithmetic mean is a valuable tool, not only for mathematics but for various fields of knowledge and for life in society.

5. Closure (1 minute): The teacher closes the lesson by thanking students for their participation and reinforcing the importance of continuous study. He can remind students about the homework and encourage them to review the lesson content. The teacher can also give a preview of what will be covered in the next lesson to maintain students' interest and encourage them to continue learning.