Objectives (5 - 7 minutes)

1. Understanding the concept of simple permutation: Students should understand what simple permutation is, how it is calculated, and when it should be applied. This includes the idea that the order of elements is important in permutation.

2. Skills in calculating simple permutations: Students should learn how to calculate simple permutations, either through formulas or practical techniques. This involves the ability to identify the number of possibilities in a permutation situation.

3. Application of knowledge in practical situations: Students should be able to apply the acquired knowledge in solving real problems. This may include gaming situations, event planning, among others.

Secondary objectives:

• Develop logical reasoning skills: The discipline of mathematics is an excellent tool for developing students' logical reasoning. Combinatorial analysis, in particular, helps promote the ability to think logically and systematically.

• Promote teamwork: During problem-solving, students will be encouraged to work in groups. This not only promotes collaboration but also helps improve communication skills and conflict resolution.

Introduction (10 - 15 minutes)

1. Review of previous content (3 - 5 minutes): The teacher starts the lesson by reviewing important concepts, such as factorial and arrangement, that were covered in previous classes. This review is crucial for students to understand simple permutation, which is the main focus of the lesson. The teacher may ask quick questions to ensure that these concepts have been properly reviewed and understood.

2. Problem Situations (5 - 7 minutes): The teacher presents two problem situations to the students involving simple permutations. The first could be a planning problem, for example, 'How many different ways can we organize a team of 6 people to form a committee of president, vice president, and secretary?'. The second situation could be a gaming problem, for example, 'If we have 5 cards numbered from 1 to 5, how many different ways can we arrange them so that the sequence is in ascending order?'. These problem situations serve to arouse students' interest and demonstrate the relevance of the content to be studied.

3. Contextualization of the theme (2 - 3 minutes): The teacher explains to the students that simple permutation is a concept widely used in various areas of knowledge, such as statistics, computer science, economics, among others. He can give practical examples, such as in cryptography, where the order of symbols is changed to ensure information security.

4. Introduction to the subject (3 - 5 minutes): The teacher introduces the topic of the lesson, explaining that simple permutation consists of calculating the number of possible arrangements of a set of elements without repetition, where the order of the elements matters. He can give a simple example, such as the number of different ways to arrange the letters of the word 'MAT' or the students in a classroom in a line. The teacher can also mention curiosities, such as the fact that the number of possible permutations of a deck of cards is approximately 8x10^67, a quantity greater than the estimated number of atoms in the universe.

Development (25 - 30 minutes)

1. Theoretical explanation (10 - 12 minutes): The teacher begins the explanation of the concept of simple permutation. He should emphasize that the order of elements is crucial in this type of permutation.

   1. Definition (2 - 3 minutes): The teacher defines simple permutation as the ordered arrangement of all elements of a set. He can give the example of the permutation of the letters of the word 'MAT', which can result in 'MAT', 'MTA', 'AMT', 'ATM', 'TMA', and 'TAM'.

   2. Calculation (3 - 4 minutes): The teacher explains how to calculate the number of simple permutations using the formula n! (factorial), where n is the number of elements in the set. He can give practical examples, such as calculating the number of possible permutations for the letters of the word 'MAT' (3!) and for the students in a classroom (n!).

   3. Differentiation between permutation and combination (2 - 3 minutes): The teacher clarifies the difference between permutation and combination, emphasizing that in permutation, the order of elements is important, while in combination, the order of elements is irrelevant. He can give practical examples, such as the difference in calculating the number of ways to choose 3 students from a class to form a committee (combination) versus the number of ways to arrange the 3 chosen students in a line (permutation).

2. Resolution of practical examples (10 - 12 minutes): The teacher then asks students to solve the problems of simple permutation that were presented in the Introduction of the lesson. He can do this in groups to promote collaboration among students.

   1. Problem 1: Formation of a committee (5 - 6 minutes): The teacher guides students to calculate the number of different ways to organize a team of 6 people into a committee of president, vice president, and secretary. He can give tips, such as starting by calculating the number of ways to choose the president (simple permutation) and then the number of ways to choose the vice president (simple permutation) and the secretary (simple permutation).

   2. Problem 2: Sequence of cards (5 - 6 minutes): The teacher asks students to calculate the number of different ways to arrange the 5 cards numbered from 1 to 5 so that the sequence is in ascending order. He can give tips, such as starting by calculating the number of ways to arrange the cards without worrying about the order (simple permutation) and then subtracting the number of ways to arrange the cards so that the sequence is not in ascending order (combination).

3. Discussion and clarification of doubts (5 - 6 minutes): After solving the examples, the teacher leads a discussion about the solutions. He can ask students to explain how they arrived at the results and clarify any doubts that may have arisen. This is important to ensure that students have understood the concept of simple permutation and are able to apply it in practical situations.

Return (8 - 10 minutes)

1. Review of concepts (3 - 4 minutes): The teacher starts the Return stage by recalling the main concepts covered in the lesson. He can do this through an oral recap of key points, such as the definition of simple permutation, the formula for calculating permutations, the difference between permutation and combination, and the importance of the order of elements in permutation. This recap is essential to reinforce learning and identify possible gaps in students' understanding.

2. Connection to practice (2 - 3 minutes): The teacher then connects theory with practice by revisiting the problem situations discussed at the beginning of the lesson. He can ask students to explain how the theory of simple permutation was applied to solve the problems. This exercise allows students to see the relevance of the studied content and how it can be applied in real situations.

3. Individual reflection (2 - 3 minutes): The teacher proposes that students reflect individually on what they learned in the lesson. He can ask questions like:

   1. 'What was the most important concept you learned today?'
   2. 'What questions have not been answered yet?'
   3. 'How can you apply what you learned today in everyday situations or in other disciplines?'

   Students will have a minute to think about these questions. This reflection helps consolidate learning and identify any areas that have not been fully understood.

4. Feedback and clarification of doubts (1 - 2 minutes): Finally, the teacher opens the floor for students to share their answers and doubts. He can ask some students to share their reflections with the class. The teacher should pay attention to any doubts or misunderstandings that may arise and clarify them immediately. This feedback exchange is essential to ensure that the lesson objective has been achieved and to prepare students for the next topic.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered during the lesson. This includes the definition of simple permutation, the formula for calculating permutations, the difference between permutation and combination, and the importance of the order of elements in permutation. The teacher can use graphs, diagrams, or practical examples to reinforce these concepts.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): Next, the teacher should explain how the lesson connected theory, practice, and applications. He can remind students of the problem situations presented at the beginning of the lesson and how the theory of simple permutation was applied to solve them. The teacher can also mention again the practical applications of this concept, such as in cryptography or in planning situations.

3. Additional Materials (1 - 2 minutes): The teacher should suggest some complementary study materials for students. This may include math books, educational websites, explanatory videos, online permutation games, among others. The teacher can also indicate extra exercises for students to practice more simple permutation calculations.

4. Importance of the Subject (1 minute): Finally, the teacher should emphasize the importance of the subject presented for students' daily lives. He can mention that simple permutation is a fundamental concept in various areas of knowledge, not only in mathematics but also in statistics, computer science, economics, among others. Additionally, the teacher can emphasize that studying this subject helps develop important skills, such as logical reasoning, problem-solving ability, and teamwork collaboration.