Objectives (5 - 7 minutes)

1. Understand the concept of GCD (Greatest Common Divisor) and how it is calculated.

   • Define GCD and explain its importance in mathematics.
   • Present examples of calculating the GCD of pairs of numbers.

2. Apply the concept of GCD in problem-solving.

   • Propose problems that involve the calculation of the GCD and its application in practical situations.
   • Encourage students to identify the need to calculate the GCD in different contexts.

3. Develop logical and mathematical reasoning skills through the study of GCD.

   • Stimulate reflection on how the GCD can be useful in solving mathematical problems.
   • Encourage the practice of calculating the GCD as a way to enhance students' mathematical skills.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts:

   • The teacher should start the lesson by reviewing previous mathematical concepts that are fundamental for understanding the GCD. Among these concepts are: prime factors, divisibility, products, and divisions. This review can be done through questions to students, encouraging active participation and connection with the new content.

2. Problem Situations:

   • The teacher can propose two problem situations to arouse students' interest in the topic. For example:

     i. Situation 1: 'Imagine you have 15 chocolates and want to divide them equally among 3 friends. How many chocolates will each receive?'

     ii. Situation 2: 'In your garden, you have 18 carrots and 12 beets. You want to equally divide these vegetables into baskets. How many vegetables of each type will each basket have?'

   • The teacher should encourage students to try to solve these problem situations, even if they don't know how initially. The goal is for them to realize the need for a calculation that allows finding the largest quantity of chocolates or vegetables that can be given to each one, without leftovers.

3. Contextualization:

   • The teacher should explain the importance of the GCD in everyday situations, such as in solving resource division problems, optimizing production processes, organizing tasks, among others.

4. Introduction to the Topic:

   • The teacher should then introduce the concept of GCD, explaining that it is a mathematical tool that allows finding the largest number that divides two or more numbers. It can also present the mathematical notation for the GCD: GCD(18, 12) = 6.

   • To capture students' attention, the teacher can tell the story of how the GCD was used in antiquity by Babylonian and Greek mathematicians to solve practical problems, such as land division.

5. Curiosities and Applications:

   • To reinforce students' interest, the teacher can share some curiosities about the GCD, such as the fact that it is used in cryptography to ensure the security of information transmitted over the internet.

   • Additionally, the teacher can mention some practical applications of the GCD, such as in optimizing logistical operations, scheduling tasks, solving division problems, among others.

With this Introduction, students should be prepared to deepen their knowledge in the study of GCD.

Development (20 - 25 minutes)

1. Theory: Concept, Calculation, and Properties of GCD (10 - 15 minutes)

   1.1. The teacher should start the theoretical part by explaining what the GCD (Greatest Common Divisor) is and how it is calculated. It should be emphasized that the GCD is the largest number that divides two or more numbers exactly.

   1.2. Next, the teacher should present the methods for calculating the GCD. Two strategies can be used:

    - Factorization method: Explain that the GCD can be calculated by factoring the numbers into their prime factors and looking for the common factors of both numbers. The GCD will be the product of these common factors.
    
    - Division method: Explain that the GCD can be calculated through successive division, dividing the larger number by the smaller one and then the divisor by the remainder. Repeat this process until the remainder is zero. The GCD will be the last non-zero divisor.
   

   1.3. After explaining the calculation methods, the teacher should demonstrate each of them with practical examples.

   1.4. Additionally, the teacher should present the properties of the GCD, such as the property that the GCD of a number by 1 is always the number itself, and the property that the GCD of a number by itself is the number itself.

2. Practice: GCD Calculation Exercises (10 - 12 minutes)

   2.1. The teacher should propose a series of GCD calculation exercises for students to practice the presented methods. The exercises should be varied, including small and large numbers, and should be contextualized, that is, related to real situations or everyday problems.

   2.2. The teacher should move around the classroom, assisting students who have difficulties and clarifying doubts. Students should be encouraged to discuss the strategies for solving the exercises among themselves, promoting collaboration and the exchange of ideas.

   2.3. After the exercises are completed, the teacher should correct them together with the class, highlighting the main points and possible pitfalls.

3. Application: Practical Examples of GCD Use (5 - 8 minutes)

   3.1. To consolidate the understanding of the GCD, the teacher should propose some practical examples of its use. These examples may include situations of resource division, process optimization, task organization, among others.

   3.2. The teacher should encourage students to identify the need to calculate the GCD in each example and explain how the GCD helps solve the problem.

   3.3. The teacher should discuss each example with the class, highlighting the resolution strategies and the benefits of using the GCD.

With this Development part, students will have the opportunity to consolidate their knowledge about the GCD, applying what they have learned in solving real problems. The teacher should encourage active student participation, promoting debate and reflection.

Return (5 - 7 minutes)

1. Review and Reflection (2 - 3 minutes)

   1.1. The teacher should start the Return stage by asking students to reflect on what they learned in the lesson. They should think about the GCD calculation strategies that were presented and how they can be applied in different contexts.

   1.2. The teacher should ask guiding questions to stimulate students' reflection, such as: 'Which GCD calculation method did you find most useful? Why?' 'How would you use the GCD to solve the problem of dividing chocolates among friends?'

2. Connection with Practice (1 - 2 minutes)

   2.1. Next, the teacher should ask students to identify practical examples of GCD use in their daily lives. They can think of situations where they needed to divide resources, organize tasks, optimize processes, among others.

   2.2. The teacher should encourage students to share their ideas and experiences, promoting the connection between the theory presented in the lesson and practice.

3. Self-assessment (1 - 2 minutes)

   3.1. Finally, the teacher should suggest that students self-assess what they have learned. They should think about what they consider most important to have learned in the lesson and about any questions they still have.

   3.2. The teacher should encourage students to express their opinions and doubts, ensuring that everyone feels comfortable participating.

   3.3. The teacher should thank the students for their participation and reinforce the importance of the GCD for mathematics and everyday life.

With this Return stage, students will have the opportunity to consolidate their learning, connect theory with practice, and express their opinions and doubts. The teacher, in turn, will be able to assess the effectiveness of the lesson and plan the next steps in teaching the GCD.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes)

   1.1. The teacher should start the Conclusion by summarizing the main points covered in the lesson. This includes the definition of GCD, the calculation methods (factorization and division), the properties of the GCD, and the practical applications.

   1.2. The teacher can recap the examples used during the lesson to illustrate the concepts and the practice exercises to consolidate students' understanding.

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

   2.1. Next, the teacher should explain how the lesson connected the theory, practice, and applications of the GCD. It should be highlighted how the calculation methods presented are fundamental for understanding the concept and how practical applications helped contextualize the use of the GCD.

   2.2. The teacher can reinforce the idea that mathematics is not just a theoretical discipline, but has real and practical applications in everyday life.

3. Suggestions for Additional Materials (1 - 2 minutes)

   3.1. The teacher should suggest additional materials for students to deepen their knowledge of the GCD. These materials may include textbooks, math websites, educational videos, math games, among others.

   3.2. For example, the teacher may suggest that students watch a video explaining the GCD in a playful way, or play an online game involving the application of the GCD.

4. Importance of GCD in Daily Life (1 minute)

   4.1. Finally, the teacher should reinforce the importance of the GCD in daily life. It should be emphasized that the GCD is a useful tool for solving practical problems, such as resource division, process optimization, task organization, among others.

   4.2. The teacher can encourage students to observe the use of the GCD in everyday situations, such as in card games, party planning, scheduling household tasks, among others.

With this Conclusion, students will have the opportunity to consolidate their learning, connect theory with practice, and explore the GCD beyond what was covered in the lesson. The teacher, in turn, will be confident that the main learning objectives have been achieved and that students are prepared for the next challenges in mathematics.