Objectives (5 - 10 minutes)

1. Introduce the concept of Divisors and Multiples: The teacher must ensure that students clearly understand what divisors and multiples of a number are. This includes the mathematical definition as well as the practical application of these concepts.

2. Develop skills to identify Divisors and Multiples: The teacher should teach students techniques and strategies to identify the divisors and multiples of a number. This may include teaching students to calculate mentally, as well as using factoring techniques.

3. Apply the acquired knowledge in problem-solving: The teacher should provide students with various problem-solving situations that involve identifying divisors and multiples. Students should then apply the knowledge learned to solve these problems.

Secondary Objectives:

• Foster classroom participation: The teacher should actively encourage student participation during the lesson by asking questions, promoting discussions, and requesting feedback.

• Develop critical thinking skills: The teacher should design the lesson to challenge students to think critically about the concepts presented and apply them to solve complex problems.

• Promote collaborative learning: The teacher should encourage students to work in groups, fostering collaboration and discussion among them. This not only promotes active learning but also helps students develop teamwork skills.

Introduction (10 - 15 minutes)

1. Review of related content: The teacher should start the lesson by reminding students of the concepts of multiple and divisor of a number, which were studied in previous classes. This can be done through a brief classroom discussion or a quick review activity. This step is crucial to ensure that students have a solid knowledge base before moving on to new material.

2. Presentation of initial problem-solving situations: The teacher can then present two problem-solving situations to stimulate curiosity and critical thinking among students. For example, 'If I have 8 balls and want to divide them equally between 2 boxes, how many balls should I put in each box?' and 'If I want to find the smallest number that is a multiple of 3 and 4, which number should I choose?'

3. Contextualization of the subject's importance: The teacher should then explain to students the practical importance of divisors and multiples. This can be done through everyday examples, such as dividing tasks equally among a group of people or determining the least common multiple to calculate when two events will occur together.

4. Presentation of the topic with curiosities or stories: To spark students' interest, the teacher can share some curiosities or stories related to the topic. For example, he can mention that the divisors of a number are always smaller or equal to the number itself, or that if a number has only two divisors (1 and itself), it is considered a prime number.

5. Introduction of the topic with the theory and the lesson's objective: Finally, the teacher should introduce the lesson's topic - Divisors and Multiples - and clearly explain the learning objectives. For example, 'Today, we will learn what divisors and multiples of a number are, how to identify them, and how to apply them to solve complex problems. Our goal is that, by the end of the lesson, you feel comfortable working with divisors and multiples and are able to apply this knowledge to solve everyday and mathematical problems.'

This Introduction aims to capture students' attention, contextualize the lesson's theme, establish learning objectives, and create an environment conducive to active and engaged learning.

Development (20 - 25 minutes)

1. Theory and Concepts (10 - 12 minutes)

1.1. Divisors of a number: The teacher should begin by explaining the concept of divisors of a number, clarifying that they are the numbers that divide the number in question exactly. For example, the divisors of 10 are 1, 2, 5, and 10. The teacher can then show students how to check if one number is a divisor of another by performing the division and observing if the remainder is zero.

1.2. Multiples of a number: The teacher should then introduce the idea of multiples of a number, which are the numbers that can be obtained by multiplying the number in question by any integer. For example, the multiples of 3 are 3, 6, 9, 12, ... The teacher should emphasize that all numbers are multiples of 1, and that the number itself is always a multiple of itself.

1.3. Relationship between divisors and multiples: The teacher should then explain that the divisors and multiples of a number are closely related. For example, if one number is a divisor of another, then all the multiples of that first number are also multiples of the second number. The teacher can illustrate this idea with concrete examples.

1.4. Prime numbers: Finally, the teacher should introduce the concept of prime numbers, which are those that have exactly two divisors: 1 and the number itself. The teacher can list some examples of prime numbers and explain that identifying prime numbers is an important and challenging mathematical problem.

2. Practical Activities (10 - 12 minutes)

2.1. Identification Exercises: The teacher should provide students with a list of numbers and ask them to identify the divisors and multiples of each. This activity will help reinforce the concepts presented in theory and develop students' identification skills.

2.2. Application Problems: The teacher should then present students with a series of problems that involve applying the concepts of divisors and multiples. For example, 'If I have 12 balls and want to divide them equally among 3 boxes, how many balls should I put in each box?' and 'If I want to find the smallest number that is a multiple of 5 and 7, which number should I choose?'. The teacher should encourage students to use their skills in identifying divisors and multiples to solve these problems.

2.3. Group Discussion: The teacher should then divide the class into small groups and ask them to discuss the solutions to the problems. This not only promotes collaborative learning but also helps students enhance their critical thinking skills.

2.4. Feedback and Correction: Finally, the teacher should provide feedback to the groups and correct the solutions to the problems in the classroom. This will help reinforce the concepts learned and correct any misunderstandings.

Return (10 - 15 minutes)

1. Comprehension Check: The teacher should start the Return by checking students' understanding of the concepts covered. This can be done through a brief review of the lesson's content and some verification questions. For example, 'What are the divisors of a number?' or 'How can we find the divisors of a number?'. The teacher should encourage all students to participate and share their answers and thoughts.

2. Connection to the Real World: The teacher should then make the connection between the concepts learned and the real world. This can be done through practical examples and everyday situations. For example, he can ask students how they can use the concept of divisors and multiples to solve everyday problems, such as dividing a pizza equally among a group of people, or to understand more advanced mathematical concepts, such as fractions and proportions.

3. Individual Reflection: The teacher should then ask students to reflect individually on what they learned in the lesson. This can be done through reflective questions, such as 'What was the most important concept you learned today?' or 'What questions have not been answered yet?'. Students should have a minute to think about these questions and then they can share their answers with the class, if they feel comfortable.

4. Teacher's Feedback: Finally, the teacher should provide feedback to the students. He should praise the students' effort and participation, and point out strengths and areas that need improvement. He should also reinforce the importance of the concepts learned and how they connect with other topics in mathematics. The teacher should encourage students to continue practicing and applying what they have learned in everyday situations.

This Return aims to consolidate students' learning, reinforce the connection between theory and practice, and provide constructive feedback to students. Additionally, it gives the teacher the opportunity to assess the effectiveness of the lesson and make any necessary adjustments for future classes.

Conclusion (5 - 10 minutes)

1. Recap of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered in the lesson. This can be done through a brief review of the concepts of divisors and multiples, their relationship, and the identification of prime numbers. This recap aims to consolidate the knowledge acquired by students and reinforce the most important concepts.

2. Connection between Theory and Practice (1 - 2 minutes): The teacher should then highlight how the lesson connected theory and practice. He can mention the practical activities carried out, such as identifying divisors and multiples and solving problems, and how they helped illustrate and apply the theoretical concepts presented. The teacher should emphasize that mathematics is not just about learning formulas and theorems, but also about understanding how to apply them to solve real problems.

3. Supplementary Materials (1 - 2 minutes): The teacher should then suggest some complementary study materials for students. This may include math books, educational websites, instructional videos, and math games. For example, the teacher can suggest that students practice identifying divisors and multiples of different numbers at home, or watch a video explaining the concept of prime numbers. These materials will help students consolidate what they have learned in the lesson and expand their understanding of the topic.

4. Relevance of the Subject (1 - 2 minutes): Finally, the teacher should explain the importance of the subject for everyday life. He can mention, for example, how the ability to identify divisors and multiples can be useful for solving practical problems, such as dividing a pizza equally among a group of people, or for understanding more advanced mathematical concepts, such as fractions and proportions. The teacher should also emphasize that mathematics, despite being an abstract discipline, has practical applications in various areas of knowledge and life.

This Conclusion aims to consolidate students' learning, reinforce the connection between theory and practice, and motivate students to continue studying and applying the concepts learned. Additionally, it gives the teacher the opportunity to reinforce the importance of the topic and highlight its relevance to everyday life and to the learning of mathematics.