Objectives (5 - 10 minutes)

1. Develop problem-solving skills with scientific notation: The primary objective of this lesson is for students to be able to understand and solve problems involving scientific notation. This includes being able to convert between decimal notation and scientific notation, as well as being able to perform mathematical operations (addition, subtraction, multiplication, and division) with numbers expressed in scientific notation.

2. Apply scientific notation to real-world situations: In addition to learning how to solve problems with scientific notation, students should also be able to apply this knowledge to real-world situations. For example, they should be able to use scientific notation to better understand science news articles or to solve science or engineering problems that involve very large or very small numbers.

3. Develop critical thinking and problem-solving skills: Throughout the process of learning about scientific notation, students should also be encouraged to develop their critical thinking and problem-solving skills. They should be encouraged to think about why scientific notation is useful and when it can be applied effectively.

Supporting Objectives:

• Facilitate group interaction: Through group activities, students should have the opportunity to interact, collaborate, and discuss concepts related to scientific notation.
• Spark interest in mathematics: By showing the practical application of scientific notation, teachers can help spark students’ interest in mathematics and show how it is relevant to the world around them.

The teacher should start the lesson by clearly defining these Objectives and briefly revisit them at the end of the lesson to reinforce what was learned.

Introduction (10 - 15 minutes)

1. Review of prior knowledge: The teacher should begin the lesson with a brief review of the concepts of exponents and decimal notation. This is essential so that students can properly understand the concept and application of scientific notation. The teacher can use practical examples and interactive questioning to engage students in the review and ensure that all students have a solid foundation before moving on.

2. Presentation of problem situations: The teacher should then present two problem situations that involve very large or very small numbers. For example, the teacher could ask students how many atoms are in a grain of sand or how many seconds are in a day. These questions should serve as a hook to introduce scientific notation as a useful tool for dealing with these types of problems.

3. Contextualization of the importance of scientific notation: Next, the teacher should explain the importance of scientific notation in various disciplines, including science, engineering, and economics. For example, scientific notation is used to express distances in the universe, sizes of subatomic particles, population growth rates, and extreme monetary values. The teacher can use real-world examples to illustrate these points and show students how being able to work with scientific notation can be useful in their everyday lives.

4. Introduction of the topic with curiosities: In order to pique students’ interest, the teacher can share some curiosities related to scientific notation. For example, the teacher could mention that scientific notation was first used by astronomers in Ancient Greece to represent the sizes of stars. Additionally, the teacher could mention that scientific notation is used in the gaming industry to represent the graphical quality of a game (e.g., 4k stands for 4,000 pixels). These curiosities can help make the topic more interesting and relevant to students.

Development (20 - 25 minutes)

1. Activity "Exploring Scientific Notation in the Universe" (10 - 12 minutes)

   • Description: The teacher divides the class into groups of up to 5 students. Each group is given a task to research and present on a magnitude in the universe that is expressed in scientific notation. Magnitudes could include, for example, the distance between planets, the size of stars, the energy released by explosions in space, etc.

   • Step by step: The teacher should provide tablets or computers for the groups to do their research. Students should then research their assigned magnitude, find its value in scientific notation, convert it to decimal notation and vice versa, and present their findings to the class.

   • Objective: This activity aims to help students understand scientific notation in a more concrete and applied way, as well as develop their research, communication, and teamwork skills.

2. Activity "The Scientific Notation Game" (10 - 12 minutes)

   • Description: Still in groups, students will participate in a board game created by the teacher. The game board will have different types of problems involving scientific notation, and students will have to solve the problems in order to advance in the game. Problems could involve converting between decimal notation and scientific notation, adding, subtracting, multiplying, and dividing numbers in scientific notation, among others.

   • Step by step: The teacher should organize the groups around the game boards and provide them with the necessary materials (dice, markers, etc.). Students should then play the game, solving the problems and advancing through the board. The teacher should circulate around the room, helping groups that are struggling and reinforcing concepts as needed.

   • Objective: This activity aims to reinforce the concepts of scientific notation in a fun and engaging way, as well as provide students with the opportunity to apply their knowledge in a practical context.

3. Activity "Scientific Notation Challenge" (5 - 10 minutes)

   • Description: To finalize the Development stage, the teacher proposes an individual challenge for students. They will be given a list of scientific notation problems to solve in a short amount of time. The challenge is to promote individual application of the knowledge acquired during the class.

   • Step by step: The teacher should distribute the list of problems to each student and provide a short amount of time for them to solve them. Students should work individually, applying what they have learned throughout the class.

   • Objective: This activity aims to assess students’ individual understanding of scientific notation and their ability to apply this knowledge to solve problems. Additionally, it also helps develop students’ quick-thinking and problem-solving skills.

Return (10 - 15 minutes)

1. Group discussion about the solutions found (5 - 7 minutes):

   • Description: The teacher should gather all students in a circle to share the solutions found by each group during the activities "Exploring Scientific Notation in the Universe" and "The Scientific Notation Game". Each group will have up to 3 minutes to present their findings and the challenges they faced. The teacher should encourage all students to participate, asking questions and expressing their opinions about the solutions presented.

   • Objective: This discussion aims to promote the exchange of ideas and collaborative learning. By sharing their solutions and challenges, students will have the opportunity to learn from each other and reflect on their own learning process.

2. Connection with the theory and reflection on the activities (3 - 5 minutes):

   • Description: After the group discussion, the teacher should revisit the theoretical concepts of scientific notation and connect them with the solutions found by the groups during the activities. The teacher should highlight how the theory applies in practice and vice versa. Students should then have a minute to silently reflect on what they have learned and what questions they still have.

   • Objective: This stage aims to reinforce learning by helping students make connections between theory and practice. Additionally, silent reflection allows students to process the information and identify possible gaps in understanding.

3. Learning check (2 - 3 minutes):

   • Description: The teacher should ask check-up questions to assess students’ learning. Questions should cover the main concepts learned during the class, including converting between decimal notation and scientific notation, performing mathematical operations with numbers in scientific notation, and applying scientific notation to real-world situations.

   • Objective: This stage aims to check whether students have achieved the Learning Objectives of the class. Check-up questions allow the teacher to identify areas that might need review or reinforcement in future classes.

4. Feedback and Conclusion (1 - 2 minutes):

   • Description: The teacher should conclude the class by providing feedback on the overall performance of the class, highlighting strengths and areas for improvement. The teacher should encourage students to continue practicing scientific notation at home and to seek additional help if needed. The teacher should also briefly summarize the main concepts learned during the class and how they apply in the real world.

   • Objective: This stage aims to effectively wrap up the class by encouraging students to continue learning and applying scientific notation. Additionally, it provides students with useful and constructive feedback about their performance, which can help them improve in future classes.

Conclusion (5 - 10 minutes)

1. Recap of the main points (2 - 3 minutes): The teacher should summarize the main points covered during the class, revisiting the fundamental concepts of scientific notation and how they were applied in the group activities. It is important that students have a clear and concise overview of these points in order to reinforce what was learned.

2. Connection between theory, practice, and applications (1 - 2 minutes): The teacher should emphasize the importance of connecting the theory, practice, and applications of scientific notation. This can be done by revisiting the activities that were done and how they reflect the real-world application of scientific notation. Additionally, the teacher can provide additional examples of how scientific notation is used in different fields, such as science, engineering, and economics.

3. Suggestion of extra materials (1 - 2 minutes): The teacher should suggest additional study materials for students who want to further their understanding of scientific notation. These materials could include textbooks, math websites, educational videos, and interactive games. For example, the teacher could recommend a mobile app that allows students to practice converting between decimal notation and scientific notation in a fun and interactive way.

4. Relevance of the subject to everyday life (1 - 2 minutes): Finally, the teacher should highlight the relevance of scientific notation to students’ everyday lives. This can be done by providing concrete examples of how scientific notation is used in everyday situations, such as in science news articles, in science or engineering problems, or even in technological applications that students use on a regular basis. The goal is to show students that scientific notation is not just an abstract concept, but a practical and useful tool that can make it easier to understand and solve complex problems.

5. Closing the class (1 minute): The teacher should close the class by thanking the students for their participation and effort. It is important to reinforce that scientific notation is a challenging topic, but with practice and dedication, all students are capable of mastering it. The teacher should also encourage students to continue studying and to seek additional help if needed.