Objectives (5 - 7 minutes)

1. Understand the concept of fractions and their representation in multiplication and division: Students should be able to understand what fractions are, how they are represented, and how they are used in multiplication and division operations.

2. Apply the acquired knowledge in practical problems: Students should be able to apply the rules of multiplication and division of fractions in real situations, such as dividing a pizza among friends or multiplying a cake recipe.

3. Develop problem-solving skills: Through practicing problems involving the multiplication and division of fractions, students should be able to develop problem-solving skills, such as the ability to analyze the problem, identify the necessary operation, and execute it correctly.

Secondary objectives:

• Stimulate critical thinking and decision-making: By solving problems involving the multiplication and division of fractions, students will be encouraged to think critically and make decisions, thus developing these essential skills.

• Promote autonomous learning: Through problem-solving and the stimulation of critical thinking, students will be encouraged to seek answers on their own, thus promoting autonomous learning.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by reviewing the basic concepts of fractions, such as their definition, how they are represented, and the basic operations of addition and subtraction. This review will serve as a basis for the new content that will be presented. The teacher can ask students questions to assess their level of understanding of these concepts.

2. Problem situation: The teacher can present students with two problem situations involving the multiplication and division of fractions. For example, the teacher can propose the following question: "If a pizza is divided into 8 equal parts and each part is further divided into 4 equal parts, how many equal parts will we have in total?" or "If I have 3/4 of a cake and divide it equally among 5 people, how much will each person receive?".

3. Contextualization: The teacher should explain to students that fractions are widely used in everyday life, in situations such as dividing a pizza among friends, sharing a cake recipe, or calculating the percentage of discount in a store. Therefore, understanding how to multiply and divide fractions is an important skill for daily life.

4. Introduction to the topic: The teacher should introduce the topic of the lesson, explaining that students will learn how to multiply and divide fractions. To spark students' interest, the teacher can share fun facts about the subject. For example, the teacher can tell the story of how ancient Egyptians used fractions to measure the land during the construction of the pyramids or how fractions are used in music to represent rhythms and intervals.

Development (20 - 25 minutes)

1. Practical Activity 1 - "Dividing the Pizza": Students will be divided into groups of up to 5 people. The teacher should provide each group with a paper circle (representing the pizza) divided into 8 equal parts. Then, the teacher should propose the following problem: "If each part of the pizza is further divided into 4 equal parts, how many equal parts will we have in total?". Students should solve the problem by dividing the paper pizza and then representing the solution in the form of a fraction. This activity will allow students to visualize and understand the division of fractions.

   • Step by step:
     1. The teacher divides the class into groups and distributes the materials (paper circle and colored pencils).
     2. The teacher explains the problem and students discuss among themselves how they will solve it.
     3. Students draw the pizza and divide each part into 4, representing the total in the form of a fraction.
     4. Groups present their solutions to the class and the teacher corrects if necessary.

2. Practical Activity 2 - "Cake Recipe": Next, the teacher proposes the following problem: "If we have a cake recipe that yields 3/4 of a cake and we want to make half of the recipe, how much cake will we have?" Again, students should solve the problem, this time using multiplication of fractions. The teacher can provide real ingredients so that students can visualize the situation.

   • Step by step:
     1. The teacher presents the problem and provides the ingredients for the cake recipe.
     2. Students discuss in their groups how to solve the problem.
     3. Students perform the multiplication of fractions and calculate the final amount of cake.
     4. Groups present their solutions and the teacher corrects if necessary.

3. Reflection Activity: After solving the problems, the teacher should propose a reflection on the activities carried out. The teacher can ask questions such as: "How did the pizza activity help us understand the division of fractions?" and "How did the cake recipe activity help us understand the multiplication of fractions?". The objective of this reflection is to consolidate learning and help students relate theory to practice.

   • Step by step:
     1. The teacher presents the reflection questions.
     2. Students discuss in their groups and prepare their answers.
     3. Groups share their answers with the class and the teacher provides final comments.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should gather all students and promote a group discussion about the solutions found by each team in the practical activities. The teacher can ask a representative from each group to share how they solved the problems and how they arrived at their answers. During the discussion, the teacher should encourage students to ask questions and provide feedback to each other. This step is important to consolidate learning, allowing students to see different approaches to problem-solving and better understand the concepts.

2. Learning Verification (2 - 3 minutes): The teacher should then verify the students' learning by asking them to reflect on what they learned in the lesson. The teacher can ask questions such as: "What was the most important concept you learned today?" and "What questions have not been answered yet?". Students should answer these questions in writing and hand them to the teacher. This step will allow the teacher to assess the level of understanding of the students and identify any areas of confusion that need to be addressed in future lessons.

3. Connection to Real Life (2 - 3 minutes): Finally, the teacher should help students make the connection between what they learned in the lesson and their daily lives. The teacher can ask questions such as: "Where do you see fractions being used in everyday life?" and "How can the knowledge of how to multiply and divide fractions be useful in real situations?". Students should discuss these questions in their groups and share their answers with the class. This step will help students realize the relevance of what they have learned and apply it in different contexts.

   • Step by step:
     1. The teacher gathers all students and promotes the group discussion.
     2. The teacher asks questions to verify learning and students respond in writing.
     3. The teacher helps students make the connection to real life and students share their answers.
     4. The teacher concludes the lesson, reinforcing the main learning points and answering any final questions from students.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes): The teacher should summarize the main points covered during the lesson. This may include the definition of fractions, the representation of fractions in multiplication and division, and practical examples of how these operations are performed. The teacher can use this moment to reinforce the most important concepts and correct any misunderstandings that may have arisen during the lesson.

2. Connection Between Theory and Practice (1 - 2 minutes): The teacher should explain how the lesson connected theory (mathematical concepts) with practice (problem-solving activities). For example, the teacher can highlight how the "Pizza" activity helped students visualize the division of fractions, while the "Cake Recipe" activity demonstrated the application of multiplication of fractions. The teacher can emphasize that understanding these operations is essential for solving everyday problems involving fractions.

3. Extra Materials (1 minute): The teacher can suggest extra materials for students who wish to deepen their knowledge on the subject. This may include textbooks, math websites, educational videos, and online games involving the manipulation of fractions. The teacher should encourage students to explore these resources on their own, reinforcing the importance of autonomous learning.

4. Relevance of the Subject (1 minute): Finally, the teacher should explain the importance of the lesson topic for students' daily lives. The teacher can mention examples of real-life situations where fractions are used, such as dividing a pizza among friends or multiplying a cake recipe. The teacher should emphasize that the ability to multiply and divide fractions is a valuable tool that students can use to solve practical problems and better understand the world around them.

   • Step by step:
     1. The teacher summarizes the main points of the lesson.
     2. The teacher explains the connection between theory and practice.
     3. The teacher suggests extra materials for study.
     4. The teacher explains the relevance of the subject for daily life.
     5. The teacher concludes the lesson, encouraging students to continue studying and applying what they have learned.