Objectives (5 - 7 minutes)

1. Understanding Scientific Notation: The teacher must ensure that students understand what scientific notation is, how it is used, and why it is useful. This can be done through a brief review of the topic and the presentation of practical examples of its use in various scientific disciplines.

2. Identification of Problems with Scientific Notation: The teacher should guide students to identify problems involving scientific notation, whether they are multiplication, division, addition, or subtraction. It is important for students to be able to recognize when scientific notation is appropriate and how to apply it correctly.

3. Solving Problems with Scientific Notation: Finally, the teacher should encourage students to solve problems involving scientific notation. This will allow students to apply what they have learned and develop their problem-solving skills.

Secondary Objectives:

• Development of Critical and Logical Thinking: Solving problems with scientific notation can help students develop critical and logical thinking skills as they learn to analyze and approach problems systematically.

• Practical Application of Knowledge: Through solving problems with scientific notation, students will have the opportunity to apply mathematical knowledge in practical situations, which can increase their engagement and understanding of the topic.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the lesson by reviewing the basic concepts of scientific notation, such as representing extremely large or small numbers using powers of 10. This can be done through a brief quiz or group discussion to assess students' prior knowledge.

2. Problem Situation 1: The teacher can present the following scenario: "Imagine you are a scientist and need to deal with extremely large or small numbers every day. How do you think scientific notation could help you in this work?" This question aims to arouse students' curiosity and demonstrate the practical relevance of the topic.

3. Contextualization of the Topic's Importance: The teacher can then explain that scientific notation is not only a useful tool for scientists but is also widely used in many other fields, such as economics, engineering, and computer science. Additionally, the teacher can highlight how the ability to work with scientific notation can facilitate the understanding and resolution of more complex mathematical problems.

4. Problem Situation 2: To illustrate the utility of scientific notation, the teacher can present the following problem: "Imagine you are studying the distances between stars. The star closest to Earth, Proxima Centauri, is about 4.22 x 10^13 kilometers away. Now, imagine you need to calculate the distance between Earth and the Andromeda galaxy, which is about 2.537 x 10^19 kilometers away. How could scientific notation help you solve this problem more efficiently?"

5. Introduction to the Topic: Finally, the teacher should introduce the lesson topic: problems with scientific notation. It is important to emphasize that during the lesson, students will learn to identify and solve problems involving scientific notation, which will help them develop their mathematical and problem-solving skills.

Development (20 - 25 minutes)

1. Theory Explanation (10 - 12 minutes):

   1.1. Review of Scientific Notation (3 - 4 minutes): The teacher should start the explanation by reviewing scientific notation, reminding students that it is used to represent extremely large or small numbers using powers of 10. The teacher can use practical examples, such as the distance between stars (from the problem presented in the Introduction), to illustrate the use of scientific notation.

   1.2. Multiplication and Division with Scientific Notation (3 - 4 minutes): The teacher should then explain how to perform multiplication and division operations with scientific notation. The teacher can start by showing how to multiply two numbers in scientific notation, emphasizing the importance of multiplying the bases and adding the exponents. Next, the teacher should show how to divide two numbers in scientific notation, emphasizing that it is necessary to divide the bases and subtract the exponents.

   1.3. Addition and Subtraction with Scientific Notation (3 - 4 minutes): After multiplication and division, the teacher should explain how to perform addition and subtraction operations with scientific notation. The teacher can start by showing how to add or subtract two numbers in scientific notation that have the same power of 10, highlighting that only the bases are added or subtracted. Next, the teacher should show how to add or subtract two numbers in scientific notation that have different powers of 10, emphasizing that it is necessary to adjust the powers of 10 to be equal before adding or subtracting the bases.

2. Guided Practice (5 - 7 minutes):

   2.1. Example Resolution (3 - 4 minutes): After the theory explanation, the teacher should guide students to solve practical examples of problems with scientific notation. The teacher should start with simple examples and gradually increase the difficulty. During this stage, the teacher should encourage active student participation, asking questions to check understanding and correcting errors as necessary.

   2.2. Discussion and Analysis of Results (2 - 3 minutes): After students have solved the examples, the teacher should lead a discussion about the results. The teacher should ask students how they arrived at their answers and if they noticed any patterns or useful strategies during problem-solving. The goal of this discussion is for students to reflect on the problem-solving process and identify the strategies that work best for them.

3. Independent Practice (5 - 6 minutes):

   3.1. Problem Solving (3 - 4 minutes): After guided practice, the teacher should provide students with some problems to solve individually. The problems should vary in difficulty and type, so that students have the opportunity to apply a variety of problem-solving strategies. The teacher should circulate around the room during this activity, offering help and feedback as needed.

   3.2. Review of Problems (2 - 3 minutes): After students have finished solving the problems, the teacher should review the answers with the class. During this review, the teacher should highlight effective problem-solving strategies and correct any common errors. The teacher should also take this opportunity to reinforce the scientific notation concepts and techniques that were discussed during the lesson.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should start the Return phase by promoting a group discussion about the problem-solving process. At this point, students will have the opportunity to share their solutions and strategies, and the teacher can ask questions to stimulate critical thinking and reflection. It is important for the teacher to encourage all students to participate in the discussion, ensuring that everyone feels comfortable sharing their ideas.

2. Connection with Theory (2 - 3 minutes): After the group discussion, the teacher should make the connection between practice and theory, highlighting how the problems solved during the lesson reflect the scientific notation concepts and techniques that were discussed. For example, the teacher may ask students to explain how they applied scientific notation to solve the problems and reinforce the importance of understanding theoretical concepts for practical problem-solving.

3. Individual Reflection (2 - 3 minutes): The teacher should then propose that students reflect individually on what they learned during the lesson. To do this, the teacher can ask questions such as:

   • "What was the most important concept you learned today?"
   • "What questions do you still have about scientific notation?"
   • "How can you apply what you learned today in other disciplines or real-life situations?"

   The teacher should give students a minute to think about the questions and then encourage them to share their answers. This reflection activity will allow students to consolidate what they have learned, identify areas they still do not fully understand, and realize the relevance of the topic to their learning and daily life.

4. Teacher Feedback (1 minute): Finally, the teacher should provide overall feedback to the class, praising students' efforts, highlighting strengths, and pointing out areas that need more practice or understanding. The teacher should also reinforce the importance of scientific notation and encourage students to continue practicing and exploring the topic on their own.

5. Lesson Closure (1 minute): To conclude the lesson, the teacher should summarize the main points discussed and tasks performed, reinforcing the importance of scientific notation and the ability to solve problems with it. The teacher should also announce the theme of the next lesson, preparing students for what is to come and encouraging them to continue studying and preparing.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by recapping the main points covered during the lesson. This includes a review of scientific notation, how to perform multiplication, division, addition, and subtraction operations with scientific notation, and the importance of solving problems with scientific notation. The teacher should ensure that all students have a clear understanding of these concepts before moving on.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes): The teacher should then explain how the lesson connected the theory, practice, and applications of scientific notation. This may include a discussion on how the problems solved during the lesson reflected theoretical concepts, and how scientific notation is applied in various scientific disciplines and everyday practices. The teacher should emphasize that the ability to work with scientific notation is a valuable skill that can be applied in many different contexts.

3. Suggestion of Supplementary Materials (1 - 2 minutes): To deepen students' understanding of scientific notation, the teacher can suggest some complementary study materials. This may include math books, educational websites, instructional videos, and software programs that allow students to practice solving problems with scientific notation. The teacher can also encourage students to look for additional scientific notation problems to solve on their own.

4. Importance of the Topic in Daily Life (1 minute): Finally, the teacher should highlight the importance of scientific notation in daily life. This may include a discussion on how scientific notation is used in fields such as science, technology, engineering, and mathematics, and how the ability to work with scientific notation can facilitate the understanding and resolution of problems in many other areas. The teacher should also emphasize that, in addition to being useful, scientific notation is a powerful and elegant tool that allows scientists and mathematicians to represent and manipulate numbers efficiently and effectively.