Objectives (5 - 7 minutes)

1. Understanding the decimal system: Students should be able to understand how the decimal system works, recognizing that it is a positional numbering system where each position to the left is ten times greater than the position to its right.

2. Identification of positional values: Students should be able to identify the positional value of each digit in a decimal number. This includes recognizing that the rightmost digit represents units, the second digit from the right represents tens, the third digit from the right represents hundreds, and so on.

3. Performing basic operations: Students should be able to perform basic operations (addition and subtraction) with decimal numbers, following the rules of the decimal system. This includes aligning the digits correctly when performing the operation.

Secondary Objectives:

• Development of critical thinking: By working with the decimal system, students will have the opportunity to develop their critical thinking skills, as they will need to analyze, compare, and manipulate numbers logically.

• Application of knowledge: Students will be encouraged to apply the knowledge acquired in everyday situations, such as when shopping, calculating bills and coins, among others.

Introduction (10 - 12 minutes)

1. Review of previous content: The teacher should start the lesson by quickly reviewing the basic concepts of numeration and positional value that were learned in previous classes. This can be done through targeted questions to the students, such as "What is positional value?" or "How does the numbering system we use every day work?" (2 - 3 minutes)

2. Problem situations: Next, the teacher should present two problem situations to arouse the students' interest and prepare them for the new content. For example:

   • "If I had 10 reais and spent 5, how many reais would I have left?"
   • "If I had 100 reais and spent 50, how many reais would I have left?" These questions serve to give students a clue about the importance of the decimal system in everyday situations. (3 - 4 minutes)

3. Contextualization: The teacher should then explain the importance of the decimal system, demonstrating how it is applied in various everyday situations, such as in shopping, accounting, measurements, among others. This will help motivate the students by showing the relevance of what they are about to learn. (2 - 3 minutes)

4. Introduction of the topic: Finally, the teacher should introduce the topic of the lesson. This can be done by telling a brief story about the origin of the decimal system, mentioning that it was developed by Hindus and Arabs between the 1st and 9th centuries. Additionally, the teacher can explain that the decimal system is widely used worldwide for being intuitive and efficient. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Theory and fundamental concepts (10 - 12 minutes):

   • Introduction to the Decimal System (3 - 4 minutes): The teacher should start by explaining that the decimal system is a positional numbering system, in which each position to the left is ten times greater than the position to its right. They can reinforce this idea by showing the representation of the numbers 10, 100, and 1000 and highlighting that the "1" in each number represents the quantity of tens, hundreds, and thousands, respectively.
   • Positional value (3 - 4 minutes): The teacher should then explain the concept of positional value, explaining that the digit in each position of a decimal number has a different value, depending on its position. They can demonstrate this using examples, such as the number 123. In this example, the "3" represents units, the "2" represents tens, and the "1" represents hundreds.
   • Basic operations (4 - 5 minutes): The teacher should then introduce the concept of basic operations with decimal numbers. They can start with addition, explaining that to add decimal numbers, it is necessary to align the decimal points and then add the digits in the same positions. The process is similar for subtraction, but instead of adding, you subtract. The teacher should demonstrate this using simple examples, such as 1.2 + 0.3 and 1.2 - 0.3.

2. Practice and Application (10 - 13 minutes):

   • Practical exercises (5 - 7 minutes): After the theoretical explanation, the teacher should provide students with the opportunity to apply what they have learned through practical exercises. They can start with simple exercises on identifying positional value, such as "In the number 753, what is the positional value of 7?". Then, the teacher can move on to exercises on addition and subtraction of decimal numbers, such as "Calculate 1.2 + 0.3" and "Calculate 1.2 - 0.3". The teacher should move around the classroom, assisting students as needed.
   • Fun activities (3 - 4 minutes): To make the practice more fun and engaging, the teacher can introduce some fun activities. For example, they can divide the class into groups and hold a competition to see who can solve more exercises correctly in a set time. Or they can propose a card game where students must add or subtract decimal numbers on the cards.

3. Theory reinforcement (5 - 6 minutes):

   • Group discussion (2 - 3 minutes): After the practice, the teacher should facilitate a group discussion to reinforce the concepts learned. They can ask questions like "What is the positional value of the digit 2 in the number 123?" or "How did you solve the exercise on adding decimal numbers?". This will help students consolidate their learning and clarify any doubts they may have.
   • Connection to the real world (2 - 3 minutes): Finally, the teacher should connect theory with practice, explaining how the concepts learned are applied in the real world. For example, they can show how the decimal system is used in everyday situations, such as in shopping, accounting, and measurements. Additionally, the teacher can ask students to think of other situations where the decimal system can be applied. This will help students realize the relevance of what they are learning and motivate them to continue studying.

Return (8 - 10 minutes)

1. Review and Conclusion (3 - 4 minutes): The teacher should start this stage by reviewing the main points covered in the lesson. They can ask students to summarize what they have learned, highlighting the importance of the decimal system, the positional value of digits, and the basic operations with decimal numbers. The teacher should clarify any doubts that may have arisen and reinforce the more complex concepts.

2. Connection of theory, practice, and applications (2 - 3 minutes): Next, the teacher should emphasize how the lesson connected theory, practice, and applications. They can explain that through the theoretical discussion, students acquired the necessary knowledge to perform basic operations with decimal numbers. Then, through practice, they had the opportunity to apply this knowledge in real situations. Finally, the teacher should reinforce the relevance of what was learned, showing how the decimal system is used in daily life, in various situations.

3. Reflection on learning (2 - 3 minutes): The teacher should then propose that students reflect on what they have learned. They can ask questions like:

   • "What was the most important concept you learned today?"
   • "What questions have not been answered yet?"
   • "How can you apply what you learned in class in everyday situations?"

   Students should have a minute to think about their answers. Then, the teacher can ask some students to share their reflections with the class. This will help consolidate learning and identify any areas that may need review or reinforcement.

4. Feedback and future tasks (1 - 2 minutes): Finally, the teacher should provide feedback to students on their performance in the lesson. They can praise strengths, such as active participation and critical thinking, and suggest areas that may need more practice or study. Additionally, the teacher can propose some homework tasks for students to practice what they have learned. For example, they can ask students to solve some exercises on adding and subtracting decimal numbers, or to identify the positional value of digits in decimal numbers. The teacher should make it clear that they are available to clarify any doubts that may arise and that they will review the tasks in the next lesson.

Conclusion (5 - 7 minutes)

1. Summary of contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered in the lesson. They can reinforce the definition of the decimal system as a positional numbering system, where each position to the left is ten times greater than the position to its right. Additionally, they should remind students of the importance of understanding the positional value of digits in a decimal number and how to perform basic operations (addition and subtraction) following the rules of the decimal system. The teacher can use examples to illustrate each point and ensure that students have understood the concepts.

2. Connection between theory, practice, and applications (1 - 2 minutes): Next, the teacher should reinforce the connection between the theory presented, the practice carried out, and the applications in the real world. They can mention how the theoretical explanation prepared students for the practice of basic operations with decimal numbers, and how these skills can be applied in everyday situations, such as in shopping, accounting, and measurements. The teacher should emphasize that the knowledge acquired in the lesson is relevant and useful, and that students can continue to improve these skills through practice and application.

3. Complementary materials (1 - 2 minutes): The teacher should then suggest some complementary study materials for students. This may include textbooks, math websites, educational videos, and online games related to the decimal system. The teacher should encourage students to explore these resources at their own pace, to consolidate and expand their understanding of the decimal system.

4. Importance of the decimal system (1 - 2 minutes): Finally, the teacher should emphasize the importance of the decimal system. They can explain that although the decimal system is just one of many numbering systems, it is widely used worldwide for being intuitive and efficient. The teacher can mention how the decimal system simplifies our daily life, making it easier to count, calculate, and measure. They can give examples of how the decimal system is used in different contexts, from counting objects to measuring time and space. The teacher should end the lesson by reinforcing the relevance of the decimal system, encouraging students to value what they have learned and to apply this knowledge in their daily lives.