Objectives (5 minutes)

1. Understand the concept of negative numbers and their representation in the numeric system. Students should be able to understand what negative numbers are, how they are represented, and where they fit in the numeric system. This includes understanding that negative numbers are less than zero and that they are represented with the minus sign (-) in front of the number.

2. Perform basic operations with negative numbers. Students should be able to add, subtract, multiply, and divide negative numbers. This includes understanding how the minus sign affects the operation and the result.

3. Apply the concept of negative numbers in everyday situations. Students should be able to identify and solve real-world problems that involve the use of negative numbers. This includes the ability to correctly interpret the problem, apply the appropriate operation, and interpret the result.

Secondary Objectives:

• Develop critical thinking and problem-solving skills. Using negative numbers can be challenging for some students, and the practice of solving problems with them can help develop these important skills.

• Promote active participation and student engagement. By planning interactive and engaging activities, the teacher can encourage students to actively engage with the material, thus increasing retention and understanding.

Introduction (10 - 15 minutes)

1. Review of Previous Concepts: The teacher should begin the class by reviewing the concepts of integers and the numeric system, emphasizing the idea that numbers can be classified as positive, negative, or zero. (2 - 3 minutes)

2. Problem Situations: The teacher can present two problem situations to arouse students' interest and contextualize the importance of negative numbers. For example:

   • "If you owe 5 dollars to a friend and he gives you 3 dollars, how much do you still owe him?"
   • "If you are 10 meters above sea level and go down 15 meters, what position will you be in relation to sea level?" (3 - 5 minutes)

3. Contextualization: The teacher should explain that negative numbers are widely used in various everyday life situations and in several disciplines, such as physics, economics, meteorology, etc. For example, in physics, negative numbers are used to represent the opposite direction to that of movement or a force. In economics, negative numbers are used to represent debts or losses. (2 - 3 minutes)

4. Curiosities and Applications:

   • The teacher can share the curiosity that the use of negative numbers was introduced in mathematics long after positive numbers, as it was difficult for people to understand what "minus something" meant. (1 - 2 minutes)
   • The teacher can mention some practical applications of negative numbers, such as in below-zero temperatures, altitude below sea level, negative financial results in companies, among others. (1 - 2 minutes)

5. Introduction to the Topic:

   • The teacher should introduce the topic of negative numbers, explaining that they represent values less than zero and that they will be used to solve the problem situations presented. (1 - 2 minutes)
   • The teacher can grab the students' attention by sharing that, although negative numbers may seem abstract, they are a powerful tool that allows us to describe and understand the world around us in ways that would not be possible with positive numbers alone. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Definition and Representation of Negative Numbers (5 - 7 minutes)

   • The teacher should begin by explaining the definition of negative numbers, emphasizing that they are less than zero. Then, they should show the representation of negative numbers in the numeric system, with the minus sign in front of the number.
   • To reinforce the idea, the teacher can use the example of the number line, showing that negative numbers are to the left of zero.
   • The teacher should provide several examples of negative numbers, both integers, and decimals, and ask students to identify them and represent them on the number line.

2. Operations with Negative Numbers (7 - 10 minutes)

   • The teacher should explain how to perform basic operations with negative numbers, starting with addition and subtraction. The focus should be on the rule that a negative number added to another negative number results in a more negative number.
   • To illustrate this, the teacher can use concrete examples, such as "If you owe 3 dollars to a friend and then owe another 2 dollars, how much do you owe now?" Or "If you have a debt of 5 dollars and pay 3 dollars, how much do you owe now?"
   • The teacher should then move on to multiplication and division, explaining that a negative number multiplied or divided by a positive number results in a negative number, and vice versa.
   • The teacher should provide several examples of operations with negative numbers and ask students to solve them, explaining step by step how to arrive at the answer.

3. Problem Solving with Negative Numbers (8 - 10 minutes)

   • The teacher should then show how to apply the concept of negative numbers to solve real-world problems. They should start with simple problems and gradually increase the complexity.
   • To do this, the teacher should use the problem situations presented in the Introduction of the class and ask students to solve them, guiding them in the process.
   • The teacher should encourage students to think critically and to justify their answers by explaining how they arrived at them.

This Development of the class allows students to gradually understand the concept of negative numbers, from their definition to their application in solving real-world problems. In addition, the teacher should be attentive to clarify any doubts that may arise and to ensure that all students are keeping up with the pace of the class.

Feedback (10 - 15 minutes)

1. Review of Concepts (5 - 7 minutes)

   • The teacher should begin the Feedback phase by recapping the key concepts covered in the class. This includes the definition of negative numbers, their representation in the numeric system, the rules for performing operations with negative numbers, and the application of these concepts in solving real-world problems.
   • The teacher can use practical examples to reinforce these concepts, such as below-zero temperatures, debts, position in relation to sea level, among others.
   • During this review, the teacher should ask students questions to check their understanding and clarify any misunderstandings that may arise.

2. Connection with Theory (3 - 5 minutes)

   • The teacher should then explain how the class connects to the theory. For example, they can mention that the addition and subtraction of negative numbers are similar to the addition and subtraction of positive numbers, but with the difference that two negative numbers always result in a more negative number.
   • The teacher can also make the connection with the number line, showing how negative numbers fit into this model.
   • The goal is for students to see the relationship between theory and practice, understanding that the theoretical concepts learned have useful practical applications.

3. Reflection on Learning (2 - 3 minutes)

   • The teacher should then ask students to reflect on what they learned in class. They can ask questions such as: "What was the most important concept you learned today?" and "What questions have not yet been answered?"
   • The teacher should encourage students to think about the answers to these questions, giving them a minute of silence to reflect. Then, they should allow some students to share their reflections with the class.
   • The goal of this activity is to make students internalize what they have learned and to identify any areas of confusion or uncertainty they may have.

4. Teacher Feedback (1 - 2 minutes)

   • Finally, the teacher should provide feedback to students on their performance in class. They should praise the students' efforts, acknowledge areas of improvement, and provide guidance for further study if needed.
   • The teacher should encourage students to continue practicing the concepts learned, as practice is essential for gaining fluency and confidence in using negative numbers.

This Feedback phase is essential for consolidating learning and ensuring that students have understood the concepts presented. In addition, it provides the teacher with an opportunity to evaluate the effectiveness of the class and to make any necessary adjustments for future classes.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should begin the Conclusion by summarizing the main points discussed during the class. This includes the definition of negative numbers, their representation in the numeric system, the rules for operations with negative numbers, and the application of these concepts in everyday situations.
   • The teacher can recall the practical activities carried out, the problem situations discussed, and the students' answers, highlighting the most important concepts.

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

   • The teacher should emphasize how the class connected the theory of negative numbers with practice, through examples and exercises.
   • In addition, the teacher should reinforce the relevance of negative numbers, showing once again how they are applied in various everyday situations and in different areas of knowledge.

3. Complementary Materials (1 - 2 minutes)

   • The teacher should suggest complementary study materials for students who wish to deepen their knowledge of negative numbers.
   • These materials may include textbooks, mathematics websites, educational videos, among others. The teacher can provide a list of these resources, along with a brief description of each and a recommendation of where students should start.

4. Importance of the Subject (1 - 2 minutes)

   • To conclude the class, the teacher should reiterate the importance of negative numbers.
   • They can emphasize that, although they may seem abstract, negative numbers are a powerful tool that allows us to describe and understand the world around us in ways that would not be possible with positive numbers alone.
   • The teacher can encourage students to continue practicing with negative numbers and to look for them in different contexts, so they can realize their presence and usefulness in everyday life.

The Conclusion is an essential part of the class, as it helps consolidate what has been learned, connect theory with practice, and motivate students to continue exploring the subject on their own. In addition, it provides the teacher with an opportunity to evaluate the effectiveness of the class and to make any necessary adjustments for future classes.