Objectives (5 - 7 minutes)

1. Understand multiplication and division as inverse operations: Students should be able to recognize that multiplication and division are inverse operations. This means that when solving a multiplication problem, they should be able to verify their answer by dividing the result by the original multiplication and vice versa.

2. Apply the commutative property in multiplication and division: Students should understand that in multiplication and division, the order of factors does not alter the product. They should be able to apply this property in different problematic situations.

3. Solve problems involving the multiplication and division of integers and decimals: Students should be able to solve practical problems involving the multiplication and division of integers and decimals. They should master the technique of multiplication and division, as well as the use of calculators to verify their answers.

   Secondary objectives:

   • Develop critical thinking skills and solve mathematical problems.
   • Promote collaboration among students through group activities.
   • Reinforce the importance of accuracy and answer verification in mathematics.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by briefly reviewing the concepts of multiplication and division that were previously studied. This can be done through a brief classroom discussion or a quick quiz. This will ensure that all students have a solid foundation before moving on to new concepts.

2. Problem-solving situations: The teacher can present two problem-solving situations involving multiplication and division. The first one can be a division problem that students need to solve, but without the answer. The second one can be a multiplication problem that students need to solve, but with the incorrect answer. This will provoke students' thinking and prepare them for the introduction of new concepts.

3. Contextualization: The teacher should explain the importance of multiplication and division in everyday life, presenting examples of real situations where these operations are used. For example, he can mention how multiplication is used to calculate the total price of various items in a store, or how division is used to divide a pizza equally among several people.

4. Introduction to the topic: The teacher should then introduce the topic of the lesson - multiplication and division as inverse operations. This can be done by presenting a curiosity or an interesting fact about the subject. For example, he can mention that the idea of inverse operations is used in many areas of mathematics and physics, and that it is one of the reasons why mathematics is considered the 'language of science'.

5. Capturing students' attention: To capture students' attention, the teacher can share a story or an intriguing problem related to multiplication and division. For example, he can tell the story of the Indian mathematician Srinivasa Ramanujan, who was famous for his incredible ability to multiply and divide large numbers in his head. Or he can present the 'problem of King Solomon', an ancient mathematical problem that involves dividing a treasure among several people fairly.

Development (20 - 25 minutes)

1. Simulation Activity - The Candy Store (10 - 12 minutes)

   • Scenario: Students will be divided into groups. Each group will be a 'Candy Store' and will receive a list of products and their unit prices. The task is to calculate the total price of each item by multiplying the unit price by the number of units and then dividing the total price by the number of customers to determine the price each customer will pay.

   • Materials needed: Lists of products and prices, calculators, paper, and pencils.

   • Step by step:

     1. The teacher should distribute the lists of products and prices to each group.
     2. The students, in their respective groups, should calculate the total price of each item on the list by multiplying the unit price by the number of units.
     3. Then, they should divide the total price by the number of customers to determine the price each customer will pay.
     4. Students should record their calculations on paper and share their answers with the rest of the class.

   • Objective: This activity aims to help students understand the practical application of multiplication and division. They will practice the skill of multiplying and dividing decimal numbers and verify their answers using calculators. Additionally, they will realize how the order of operations does not alter the final result.

2. Problem-Solving Activity - The Card Game (10 - 12 minutes)

   • Scenario: Still in groups, students will receive a set of cards numbered from 1 to 10. They must create their own multiplication and division problems using the cards and then solve the problems created by other groups.

   • Materials needed: Sets of cards numbered from 1 to 10, paper, and pencils.

   • Step by step:

     1. The teacher should distribute the sets of cards to each group.
     2. The students, in their respective groups, should create multiplication and division problems using the cards. For example, they can create the problem '3 x 4 =' using the cards 3 and 4, or the problem '12 ÷ 4 =' using the cards 12 and 4.
     3. Then, the students should exchange their problems with another group and solve the problems they received.
     4. Students should record their problems and answers on paper and share them with the rest of the class.

   • Objective: This activity aims to consolidate students' understanding of multiplication and division operations. They will practice creating and solving problems and verify their answers using the cards and, if necessary, a calculator. Additionally, they will realize that multiplication and division are inverse operations, as they need to reverse the original operation to verify their answers.

3. Group Discussion - Reflection and Connection (5 - 7 minutes)

   • The teacher should gather all students for a group discussion. He can ask questions like: 'How did you use multiplication and division to solve the problems in the Candy Store and Card Game activities?', 'How did you verify your answers?' and 'What did you learn about multiplication and division from these activities?'.
   • Students should be encouraged to share their experiences and reflections. The teacher should facilitate the discussion and make connections with the concepts discussed in the Introduction of the lesson.
   • Objective: This activity aims to promote students' reflection on what they have learned and how they have applied their knowledge. They will also have the opportunity to learn from other groups and see different ways of approaching problems.

Return (8 - 10 minutes)

1. Group Discussion - Reflection and Connection (3 - 5 minutes)

   • The teacher should gather all students for a group discussion. He can ask questions like: 'How did you use multiplication and division to solve the problems in the Candy Store and Card Game activities?', 'How did you verify your answers?' and 'What did you learn about multiplication and division from these activities?'.
   • Students should be encouraged to share their experiences and reflections. The teacher should facilitate the discussion and make connections with the concepts discussed in the Introduction of the lesson.
   • Objective: This activity aims to promote students' reflection on what they have learned and how they have applied their knowledge. They will also have the opportunity to learn from other groups and see different ways of approaching problems.

2. Connection with Theory (2 - 3 minutes)

   • The teacher should revisit the theoretical concepts discussed during the lesson and make connections with the practical activities. For example, he can recall the commutative property and how it was applied in the Candy Store activity, or discuss the inverse operation and how it was used to verify the answers in the Card Game activity.
   • Objective: This activity aims to reinforce students' understanding of theoretical concepts and their practical application. They will see how mathematics is not just a series of rules and formulas, but a useful tool for solving real-world problems.

3. Individual Reflection (2 minutes)

   • The teacher should propose that students reflect for a minute on the following questions: 'What was the most important concept you learned today?' and 'What questions have not been answered yet?'.
   • After a minute of reflection, students should be encouraged to share their answers with the class. The teacher should listen attentively and, if necessary, clarify any doubts or misunderstandings.
   • Objective: This activity aims to promote self-assessment and self-reflection among students. They will have the opportunity to identify their strengths and weaknesses and think about how they can improve their learning.

4. Feedback and Closure (1 minute)

   • To conclude the lesson, the teacher should provide brief feedback on the students' performance. He should praise the students' efforts, acknowledge their achievements, and encourage them to continue practicing. Additionally, he should reinforce the importance of the concepts learned and how they apply to everyday situations.
   • Objective: This activity aims to motivate students and reinforce learning. They will receive constructive feedback and feel encouraged to continue learning.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should give a brief summary of the main points discussed during the lesson. He should recall key concepts, such as multiplication and division as inverse operations, and the commutative property.
   • Additionally, he should emphasize the importance of verifying answers, whether using the inverse operation or a calculator, and how this helps ensure the accuracy of calculations.
   • Objective: This activity aims to reinforce the concepts learned and help students consolidate their knowledge.

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

   • The teacher should explain how the lesson connected theory, practice, and applications. For example, he can discuss how the Candy Store and Card Game activities applied the theoretical concepts of multiplication and division in a practical and realistic manner.
   • Additionally, he should reiterate the importance of these concepts in everyday life, mentioning examples of real situations where multiplication and division are used.
   • Objective: This activity aims to help students understand the relevance and applicability of what they have learned.

3. Additional Materials (1 minute)

   • The teacher should suggest additional materials for students who wish to deepen their understanding of the topic. This may include math books, educational websites, online games, explanatory videos, and practice exercises.
   • For example, he may recommend using calculators to practice answer verification, or board games involving multiplication and division.
   • Objective: This activity aims to promote autonomous learning and provide additional resources for students who wish to expand their knowledge.

4. Importance of the Subject (1 minute)

   • To conclude the lesson, the teacher should emphasize the importance of the topic learned. He should explain how the ability to multiply and divide is essential for a variety of everyday and professional tasks, from solving math and physics problems to managing personal finances.
   • Objective: This activity aims to motivate students to continue learning and apply their knowledge effectively and meaningfully in their daily lives.