Objectives (5 - 10 minutes)

1. Understand the concept of grouping and highlighting in factoring algebraic expressions: The teacher should establish the foundation for the lesson, clearly explaining what grouping and highlighting are in factoring algebraic expressions. They should ensure that students understand the idea of grouping terms and highlighting a common factor.

2. Develop the ability to factor algebraic expressions using the grouping method: The teacher should guide students step by step, showing how to group terms and factor an expression. Students should practice the method with examples provided by the teacher.

3. Apply the concept of grouping and highlighting in practical problems: The teacher should promote the application of the concept and method through problem situations that require the use of grouping and highlighting to factor algebraic expressions.

Secondary Objectives:

• Encourage active participation of students during the lesson: The teacher should encourage students to ask questions and participate in discussions, in order to promote an active and collaborative learning environment.

• Develop critical thinking and problem-solving skills: By working on problems that require factoring algebraic expressions, students will have the opportunity to develop their critical thinking and problem-solving skills.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing previous concepts that are fundamental for understanding the current topic. This includes the definition of algebraic expressions, similar terms, common factors, and multiples. The teacher can do this through a brief quiz or class discussion. (3 - 5 minutes)

2. Problem situation: Next, the teacher should present two situations that require the use of grouping and highlighting for factoring algebraic expressions. For example:

   • "If you had to factor the expression 3x + 3y + 2x + 2y, how would you do it?"
   • "And if you had to factor the expression 4x² - 12xy + 5x - 15y, what would be your first step?" (3 - 5 minutes)

3. Contextualization: The teacher should then explain the importance of the topic, showing how factoring algebraic expressions is used in various areas such as algebra, physics, engineering, and economics. They can give concrete examples of situations where factoring is used to solve real-world problems. (2 - 3 minutes)

4. Introduction to the topic: Finally, the teacher should introduce the topic of the day - factoring: grouping and highlighting - in a way that sparks students' interest. They can do this in several ways, for example:

   • Telling a curiosity: "Did you know that the Indian mathematician Srinivasa Ramanujan discovered an unusual factoring method known as 'Ramanujan's factoring'? He used this method to factor algebraic expressions in a way that no one had done before!"
   • Relating the topic to students' daily lives: "Have you ever wondered how engineers design such strong and safe bridges? One of the tools they use is factoring algebraic expressions! They use this method to simplify the equations that describe the forces acting on the bridge, which facilitates the design and construction."
   • Presenting a challenge: "Do you think you can factor the expression 6x² - 11xy + 4y²? Let's see who can factor it more quickly!" (2 - 3 minutes)

Development (20 - 25 minutes)

1. Grouping and highlighting activity with colored cubes: The teacher should distribute a set of colored cubes to each group of students. Each color will represent a term of an algebraic expression. For example, if the expression is 2x + 3y + 4z, the red cubes can represent 2x, the blue ones 3y, and the green ones 4z. Students should then group the cubes in a way that maximizes the number of cubes of each color in each group. They should then highlight the common factor of each group and write the factored expression. This activity will allow students to visualize the concept of grouping and highlighting in factoring in a playful and concrete way. (10 - 12 minutes)

2. Problem-solving activity: The teacher should present students with a series of problems that require the use of grouping and highlighting for factoring. Students should work in their groups to solve the problems. The teacher should move around the room, assisting groups that are struggling and encouraging discussion and reasoning. (8 - 10 minutes)

3. Board game activity: To reinforce the concept and practice of grouping and highlighting, the teacher can propose a board game where students advance according to the color of the cube they were able to group and highlight correctly. The game can be a fun way to review the lesson content and to stimulate participation and teamwork. (2 - 3 minutes)

By the end of these activities, students should have developed a solid understanding of the concept of grouping and highlighting in factoring algebraic expressions, as well as had the opportunity to practice applying this concept in real problems. They will also have had the chance to work in teams, develop their critical thinking and problem-solving skills, and learn in a playful and enjoyable way.

Feedback (10 - 15 minutes)

1. Group discussion: The teacher should gather all students and promote a discussion about the solutions or conclusions found by each group. Each group should share the expression they factored and how they arrived at it. The teacher should encourage students to explain the reasoning behind their solutions, in order to promote mutual understanding and learning. They should also correct any errors or misunderstandings that may have arisen during the activities. (5 - 7 minutes)

2. Connection to theory: After the group discussion, the teacher should make the connection between the practical activities and the theory presented at the beginning of the lesson. They should explain how the concept of grouping and highlighting was applied in the activities and how it helped in factoring the expressions. The teacher can use examples from the activities to illustrate theoretical points. (3 - 5 minutes)

3. Individual reflection: The teacher should then ask students to reflect individually on what they learned during the lesson. They can do this by asking questions such as:

   1. "What was the most important concept you learned today?"
   2. "What questions have not been answered yet?"
   3. "How can you apply what you learned today in real situations or in other disciplines?"

   Students should write down their answers and, if they wish, can share them with the class. The teacher should reinforce the importance of reflection as a means of consolidating learning and identifying areas that still need to be worked on. (2 - 3 minutes)

4. Teacher feedback: Finally, the teacher should provide overall feedback on the class's participation and performance during the lesson. They can praise students' efforts, highlight strengths, and point out areas that need more practice. The teacher should encourage students to continue studying the topic and to ask questions in the next lesson. (1 - 2 minutes)

With this Feedback stage, students will have the opportunity to consolidate what they have learned, reflect on the learning process, and receive constructive feedback from the teacher. This will help ensure that they have understood the concept of grouping and highlighting in factoring algebraic expressions and are ready to apply it in other situations.

Conclusion (5 - 10 minutes)

1. Content summary: The teacher should start the Conclusion of the lesson by summarizing the main points covered. They should review the concept of grouping and highlighting in factoring algebraic expressions, briefly explaining how these methods are applied. They should also highlight the importance of factoring in simplifying expressions and solving mathematical problems. (2 - 3 minutes)

2. Connection between theory, practice, and applications: Next, the teacher should reinforce how the lesson connected theory, practice, and applications of the topic. For example, they can mention how the practical activities with colored cubes helped visualize and understand the concept of grouping and highlighting, and how the applied problems helped practice the application of these methods. The teacher should also reiterate the practical applications of factoring algebraic expressions, showing how this skill can be used in various areas of knowledge. (2 - 3 minutes)

3. Additional materials: The teacher should then suggest additional materials for students who wish to deepen their studies on the topic. These materials may include books, websites, videos, games, and math apps that offer explanations and exercises on grouping and highlighting in factoring. The teacher should encourage students to explore these resources at their own pace and to bring their questions and discoveries to the next lesson. (1 - 2 minutes)

4. Importance of the topic for daily life: Finally, the teacher should briefly explain how the lesson topic is relevant to students' daily lives. For example, they can mention how factoring algebraic expressions is used in various everyday situations, such as solving mathematical problems, understanding scientific models, and making financial decisions. The teacher should emphasize that, although mathematics may seem abstract, many of its concepts and methods have practical and useful applications. (1 - 2 minutes)

At the end of the Conclusion, students should have a clear understanding of the lesson content, its importance, and opportunities to deepen their studies. They should also be motivated to continue learning and applying what they have learned in their daily lives and in other disciplines.