Objectives (5 - 7 minutes)

1. Understand the concept of Real Number: The teacher must ensure that students understand what real numbers are and how they fit into the number system. This includes the idea that real numbers are a combination of rational numbers (numbers that can be expressed as a fraction) and irrational numbers (numbers that cannot be expressed as a fraction).

2. Know the Operations with Real Numbers: Students should be able to identify and perform the four basic operations (addition, subtraction, multiplication, and division) with real numbers. Additionally, they should understand the rules of precedence, how to perform operations with parentheses, and the use of commutative and associative properties.

3. Apply the Operations with Real Numbers in Problem Situations: Students should be able to apply what they have learned to solve real-world problems involving real numbers. This includes the ability to interpret the problem, determine the appropriate operation, and execute the operation correctly and efficiently.

   Secondary Objectives:

   • Promote students' critical thinking skills when dealing with real numbers and their operations.
   • Foster the ability to solve complex problems systematically and logically.
   • Develop students' confidence in their ability to handle challenging mathematical concepts.

Introduction (10 - 15 minutes)

1. Review of Previous Content (3 - 5 minutes): The teacher should start the lesson by briefly reviewing the number system (natural, integer, rational) and the basic operations (addition, subtraction, multiplication, and division). This review will help establish a solid foundation for the introduction of real numbers and their operations.

2. Problem Situations (5 - 7 minutes): The teacher should present two problem situations involving real numbers. One of them could be a budget problem, where students need to add and subtract real numbers to determine the total cost of various items. The other could be a scale problem, where students need to multiply and divide real numbers to determine the ratio of one object to another.

3. Contextualization (2 - 3 minutes): The teacher should explain the importance of real numbers and their operations in the real world. This may include examples of how real numbers are used in various disciplines such as science, engineering, finance, and arts. The teacher may also share stories of how a lack of understanding of real numbers and their operations can lead to errors and misunderstandings.

4. Engage Students' Attention (2 - 3 minutes): To spark students' interest, the teacher can share fun facts about real numbers. For example, the teacher may mention that although it seems like there are infinite real numbers between 0 and 1, in fact, there are more real numbers than there are points on a straight line. Additionally, the teacher may mention that the existence of irrational numbers, such as π and √2, was a revolutionary concept in the history of mathematics.

Development (20 - 25 minutes)

1. Data Modeling Activity (10 - 12 minutes)

   • Scenario: The teacher should present a scenario in which students are employees of a delivery company. They have received a list of orders to deliver to different locations in the city. Each order has a weight ranging from 0 to 10 kg.
   • Task: Students must add up the weight of all orders to determine the total weight of the cargo to be delivered. Then, they must calculate the average weight of the orders.
   • Materials: The teacher should provide students with order cards with different weights.
   • Discussion: After students complete the calculations, the teacher should lead a discussion on how this activity relates to real numbers and their operations. He should emphasize that the weight of the orders is a real number and that the sum and average of the weights are operations with real numbers.

2. Problem-Solving Activity (10 - 12 minutes)

   • Scenario: The teacher should present a scenario in which students are engineers from a construction company. They are working on a project to build a building with 10 floors. Each floor will have a height of 3.5 meters.
   • Task: Students must calculate the total height of the building. Then, they must determine how many additional floors could be built if they had 15 meters of total height available.
   • Materials: The teacher should provide students with building blocks representing the floors of the building.
   • Discussion: After students complete the calculations, the teacher should lead a discussion on how this activity relates to real numbers and their operations. He should emphasize that the height of the building is a real number and that the sum and multiplication of real numbers are essential operations to solve this construction problem.

3. Game Activity (5 - 7 minutes)

   • Scenario: The teacher should present a scenario in which students are players in a mathematical board game. They advance on the board by adding, subtracting, multiplying, and dividing real numbers.
   • Task: Students, in small groups, must play the game, advancing on the board and performing operations with real numbers as needed.
   • Materials: The teacher should provide a mathematical board game involving operations with real numbers.
   • Discussion: After the game ends, the teacher should lead a discussion on how this activity helped reinforce the concepts of real numbers and their operations. He should emphasize the importance of being able to apply these concepts quickly and accurately, a skill that is promoted by the game.

Feedback (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should gather all students and facilitate a group discussion. Each group should share the solutions or conclusions they reached during the activities. This will allow students to learn from each other, see different approaches to the same problems, and develop communication and argumentation skills.

2. Connection to Theory (2 - 3 minutes): The teacher should then make a connection between the activities carried out and the theory presented at the beginning of the lesson. He should highlight how the operations with real numbers were applied in the problem situations and how students were able to solve these problems. This step is crucial to consolidate the acquired knowledge and for students to realize the relevance and applicability of mathematical concepts.

3. Individual Reflection (2 - 3 minutes): The teacher should propose that students reflect individually on the lesson. This can be done through 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 everyday situations or in other disciplines? These questions will help students process what they have learned and identify any gaps in their understanding. Additionally, they will allow the teacher to receive valuable feedback on the effectiveness of the lesson and possible modifications that can be made in future classes.

4. Sharing Reflections (1 - 2 minutes): Finally, the teacher should suggest that some students share their reflections with the class. This can be done voluntarily or through random selection. The goal is to encourage students to express their ideas and listen to others' ideas, thus promoting a greater understanding and respect for individual and collective thinking.

Conclusion (5 - 7 minutes)

1. Lesson Summary (2 - 3 minutes): The teacher should recap the main points covered during the lesson. He should review the concepts of real numbers, their operations, and the application of these operations in real-world situations. The teacher should emphasize the importance of understanding and being able to perform operations with real numbers, not only in mathematics but also in various other disciplines and daily life.

2. Theory-Practice Connection (1 - 2 minutes): The teacher should highlight how the lesson managed to connect mathematical theory with practice. He can refer to the activities carried out during the lesson, explaining how they allowed students to apply the theoretical concepts of real numbers and their operations in a practical and meaningful way.

3. Extra Materials (1 - 2 minutes): The teacher should suggest extra materials for students who wish to deepen their understanding of the lesson topic. This may include reference books, interactive math websites, educational videos, and math apps. For example, the teacher may suggest an online math game involving operations with real numbers as a fun and engaging way to practice what was learned.

4. Subject Relevance (1 minute): Finally, the teacher should emphasize the importance of the lesson topic for everyday life. He can share examples of how operations with real numbers are used outside the classroom, such as in personal finance, science, engineering, and arts. The teacher can encourage students to observe and reflect on these examples in their daily lives, thus reinforcing the relevance and applicability of what was learned.