Objectives (5 - 7 minutes)

1. Understand the concept of multiplication of fractions: The goal is for students to understand the operation of multiplication between fractions, realizing that the multiplication of two fractions is done by multiplying the numerators and denominators.

2. Solve problems involving multiplication of fractions: Students should be able to apply the concept of multiplication of fractions in solving various problems, both in visual representation and in numerical form.

3. Develop division skills with fractions: The goal is for students to understand how to perform division between fractions, realizing that dividing one fraction by another is equal to multiplying the first by the inverse of the second.

4. Apply the concept of division of fractions in problem solving: Students should be able to apply the concept of division of fractions in problem solving, both in visual representation and in numerical form.

Secondary Objectives:

1. Develop critical and analytical thinking: Through problem solving involving fractions, students will have the opportunity to develop critical and analytical thinking skills, necessary for mathematics and everyday situations.

2. Promote collaboration and communication: The use of group activities and class discussions will encourage collaboration among students, as well as enhance their communication skills.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing previous concepts that are fundamental to understanding the multiplication and division of fractions. These concepts include what fractions are, the terms numerator and denominator, and how to simplify fractions. This review can be done through targeted questions to the students or through a brief quiz. (3 - 5 minutes)

2. Problem-solving situations: The teacher should present two problem-solving situations involving the multiplication and division of fractions. For example, "If you have 1/2 of a pizza and multiply that by 3, how many pizzas will you have in total?" and "If you have 3/4 of a pizza and divide that by 2, how much pizza will each person have?" The teacher should ask students to think about how to solve these problems, but should not explain the solution yet. (3 - 5 minutes)

3. Contextualization: The teacher should explain the importance of fractions in everyday life, providing examples of situations where fractions are used, such as in cooking, construction, medicine, etc. This will help students understand why it is important to learn how to multiply and divide fractions. (2 - 3 minutes)

4. Engage students' attention: To spark students' interest, the teacher can share some fun facts about fractions. For example, "Did you know that the word 'fraction' comes from the Latin 'fractus', which means broken? This is because a fraction represents a part of a whole, which can be broken into smaller parts." Another curiosity could be, "Did you know that the ancient Egyptians were the first to use fractions? They used them to divide the land during the annual floods of the Nile River." The teacher can then ask students if they can think of other interesting facts or uses for fractions. (2 - 3 minutes)

Development (20 - 25 minutes)

1. "Pizza Party" Activity (10 - 12 minutes): The teacher should divide the students into groups of 3 to 4. Each group will receive a large, colorful piece of paper to draw a pizza. Then, the teacher will distribute smaller blank pieces of paper to each group and ask them to write a fraction on the paper, representing the amount of pizza each group member would like to eat. For example, one group may choose 2/8, another 3/8, and so on. Next, the teacher will provide each group with a random number to multiply their fraction by. For example, if the random number is 4, the group that chose 2/8 will multiply 2/8 by 4. The students must then calculate the new fraction and draw the corresponding amount on their pizza. The group that can draw the largest amount of pizza correctly will be the winner of the "Pizza Party". This activity will engage students in a playful and contextualized way, allowing them to apply the concept of multiplication of fractions in a fun and practical manner.

2. "M&M's Division" Activity (10 - 12 minutes): In this activity, the teacher will distribute a pack of colored M&M's to each group. Students should pour all the M&M's onto a plate and then divide the quantity of each color of M&M's into a fraction of the total. For example, if there are 10 red M&M's, the group can write the fraction as 10/50, since there are a total of 50 M&M's. Next, the teacher will provide each group with a new fraction, and the students must divide their quantity of each color of M&M's by this new fraction. For example, if the new fraction is 1/5, the group must divide 10 by 5 to get 2, so they would have 2 red M&M's. The students should continue this process until they have divided all their M&M's. This activity will help students understand the concept of division of fractions, allowing them to apply it in a concrete and tasty way.

3. "Cake Challenge" Activity (5 - 8 minutes): For this activity, the teacher will project an image of a cake divided into several irregular slices. Each slice will be labeled with a fraction. Working in their groups, students will have to identify the fractions that represent each slice of the cake. After identification, the teacher will ask students to solve a fraction division problem. For example, "If each slice of cake represents 1/8 of the whole cake, and we have 3/4 of the cake, how many cake slices do we have?" Students will have to use the concept of fraction division to solve the problem. This activity will allow students to apply the concept of fraction division in a visual and challenging context.

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should encourage each group to share their solutions and strategies found during the "Pizza Party", "M&M's Division", and "Cake Challenge" activities. Each group will have up to 3 minutes to present to the rest of the class. During the presentations, the teacher should observe the different approaches used by the groups to solve the proposed problems, highlighting the most efficient and creative strategies. The teacher should also correct any conceptual errors that may arise, ensuring that all students understand the concepts of multiplication and division of fractions correctly.

2. Connection to Theory (2 - 3 minutes): After the group discussion, the teacher should make the connection between the practical activities and the theory presented in the Introduction of the lesson. For example, the teacher can show how the "Pizza Party" activity illustrated the concept of multiplication of fractions, and how the "M&M's Division" and "Cake Challenge" activities demonstrated fraction division. This step is essential to consolidate students' learning, allowing them to see the applicability of mathematical concepts in everyday situations.

3. Individual Reflection (2 - 3 minutes): Finally, the teacher should propose that students reflect individually on what they learned in the lesson. The teacher can ask questions like: "What was the most important concept you learned today?", "What questions have not been answered yet?", and "How can you apply what you learned today in your everyday life?" Students will have a minute to think about their answers. After this time, the teacher can ask some students to share their reflections with the class. This step will help students consolidate their learning and identify any areas that may still need further study or practice.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should recap the main points covered during the lesson, emphasizing the concept of multiplication and division of fractions, as well as the strategies for solving problems involving these operations. The teacher can use slides or a whiteboard to highlight the main points and reinforce students' memorization.

2. Connection between Theory and Practice (1 - 2 minutes): The teacher should emphasize how the lesson connected theory to practice. He can mention the practical activities carried out during the lesson, such as the "Pizza Party" and the "Cake Challenge", and how they helped students understand and apply the theoretical concepts of multiplication and division of fractions. The teacher should also reinforce the relevance of these concepts in everyday life, mentioning examples of real situations where knowledge of fractions is useful.

3. Extra Materials (1 - 2 minutes): The teacher should suggest additional materials for students who wish to deepen their understanding of multiplication and division of fractions. These materials may include online educational videos, interactive math games, online practice exercises, math books, among others. The teacher should encourage students to explore these resources at their own pace, reinforcing the importance of autonomous learning and constant practice.

4. Importance of the Subject (1 minute): Finally, the teacher should emphasize the importance of the subject learned for everyday life. The teacher can mention how knowledge of fractions is used in different areas, such as finance, cooking, construction, arts, among others. Additionally, the teacher can highlight how the ability to solve complex mathematical problems, such as those involving fractions, can develop valuable skills, such as critical thinking, problem-solving, and perseverance.