Objectives (5 - 7 minutes)

1. Understand the multiplication of fractions:

   • Identify the basic rule of multiplying fractions.
   • Perform multiplication operations of fractions correctly and precisely.

2. Apply the multiplication of fractions in problem situations:

   • Solve problems involving the multiplication of fractions in the context of everyday situations.

3. Understand the division of fractions:

   • Recognize the relationship between multiplication and division of fractions.
   • Apply the rule of dividing fractions appropriately.

Secondary objectives:

• Develop critical thinking skills and problem-solving abilities.
• Foster active student participation through discussions and practical activities.
• Reinforce the importance of using fractions in daily life.

Introduction (10 - 15 minutes)

1. Review of previous concepts:

   • The teacher starts the lesson by reviewing the basic concepts of fractions, including what they are, how they are represented, and how they are added and subtracted. (3 - 5 minutes)

2. Initial problem situations:

   • To introduce the concepts of multiplication and division of fractions, the teacher proposes two problem situations:
     1. If a pizza is divided into 8 slices and you eat 3/8 of it, how much of the total did you eat?
     2. If 1/3 of a chocolate bar costs $2, how much does the whole bar cost? (4 - 5 minutes)

3. Contextualization of the subject's importance:

   • The teacher emphasizes the importance of fractions in daily life, citing examples such as: kitchen recipes, time measurements, financial calculations, among others. (2 - 3 minutes)

4. Introduction of the topic with curiosities:

   • To spark students' interest, the teacher presents two curiosities about fractions:
     1. The word 'fraction' comes from the Latin 'fractus', which means 'broken', and refers to the idea that a fraction is a part of a whole.
     2. Fractions were first used by the Egyptians, who used them to divide their food fairly. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory presentation:

   • The teacher explains that the multiplication of fractions is an operation that consists of multiplying the numerators (top numbers) and denominators (bottom numbers) of the fractions. For example, to multiply 2/3 by 3/5, you multiply 2 by 3 to get 6 in the numerator and 3 by 5 to get 15 in the denominator, resulting in 6/15. The teacher emphasizes that whenever possible, the resulting fraction should be simplified. (5 - 7 minutes)

2. Practical activity:

   • The teacher hands out worksheets with a variety of multiplication of fractions problems. Students are encouraged to solve the problems in small groups, discussing their approaches and solutions. The teacher circulates around the room, clarifying doubts and providing guidance as needed. (10 - 12 minutes)

3. Group discussion:

   • After the conclusion of the practical activity, the teacher leads a group discussion, asking students to share their problem-solving strategies and reflect on the difficulties encountered. The teacher may also propose challenging problems for the class to solve together, encouraging the participation of all students. (5 - 6 minutes)

4. Theory presentation:

   • The teacher introduces the concept of division of fractions, explaining that to divide one fraction by another, it is necessary to invert the second fraction (turning it into a multiplication) and then multiply the fractions as in the previous operation. For example, to divide 2/3 by 3/5, you invert 3/5 to 5/3 and multiply by 2/3, resulting in 2/1 or simply 2. The teacher reinforces that simplification is important and that if the resulting fraction can be simplified, students should do so. (5 - 7 minutes)

5. Practical activity:

   • The teacher hands out more worksheets, this time focusing on division of fractions problems. Students work in groups to solve them, discussing their strategies and solutions. The teacher circulates around the room, providing guidance and clarifying doubts. (10 - 12 minutes)

6. Group discussion:

   • The teacher leads a group discussion about the division of fractions activity, asking students to share their strategies and reflect on the difficulties encountered. The teacher may propose more complex problems for the class to solve together, encouraging the active participation of all students. (5 - 6 minutes)

Return (8 - 10 minutes)

1. Review of key concepts:

   • The teacher begins the Return stage by reviewing the main concepts of the lesson, reinforcing the idea that the multiplication of fractions involves multiplying the numerators and denominators, and the division of fractions involves inverting the second fraction and multiplying the fractions.
   • The teacher also reminds the importance of simplifying fractions whenever possible. (2 - 3 minutes)

2. Connection between theory and practice:

   • Next, the teacher discusses how the presented theory was applied in practice, referring to the activities carried out in the classroom.
   • The teacher highlights the problem-solving strategies used by students and how they relate to the rules of multiplication and division of fractions. (2 - 3 minutes)

3. Reflection on learning:

   • To promote reflection on learning, the teacher asks questions such as:
     1. What was the most important concept learned today?
     2. What questions have not been answered yet?
   • Students are encouraged to express their opinions and share any difficulties they may have faced.
   • The teacher listens carefully to the students' responses and notes any concerns or areas that may need additional review. (2 - 3 minutes)

4. Content synthesis:

   • Finally, the teacher synthesizes the content of the lesson, highlighting the main points and concepts covered.
   • The teacher also provides an overview of what will be covered in the next lesson, preparing students for the next topic. (1 - 2 minutes)

5. Encouragement for additional study:

   • Before ending the lesson, the teacher encourages students to review the lesson material at home and practice more multiplication and division of fractions problems.
   • The teacher may suggest additional study resources, such as textbooks, math websites, and educational videos. (1 minute)

Conclusion (5 - 7 minutes)

1. Recap of contents:

   • The teacher starts the Conclusion by recalling the main points covered during the lesson, highlighting the basic rule of multiplication and division of fractions, the need to simplify the resulting fractions, and the importance of applying these concepts in everyday situations.
   • The teacher also reinforces the relationship between the multiplication and division of fractions, emphasizing that dividing fractions is actually multiplying by the inverted fraction. (2 - 3 minutes)

2. Connection between theory, practice, and applications:

   • Next, the teacher reviews how the lesson connected the theory of multiplication and division of fractions with practice, through group activities and proposed problems.
   • The teacher highlights how these seemingly abstract concepts have practical applications in everyday life, such as in food sharing situations (pizza) or financial calculations (price of a chocolate bar).
   • The teacher reinforces the importance of understanding and applying these concepts to solve everyday problems. (1 - 2 minutes)

3. Suggestion of extra materials:

   • To complement learning, the teacher suggests some extra materials for students to study at home, such as multiplication and division of fractions exercises, explanatory online videos, and math textbooks.
   • The teacher may also recommend educational game websites that allow students to practice these skills interactively and in a fun way. (1 minute)

4. Importance of the subject for daily life:

   • Finally, the teacher emphasizes the relevance of the subject covered for daily life, reinforcing the importance of fractions in various everyday situations, such as in the kitchen, at the store, or even in a bike race (fraction of the distance traveled).
   • The teacher encourages students to be attentive to these situations in daily life, reinforcing the idea that mathematics is present in our daily lives in ways we may not always realize. (1 minute)