Learning Objectives (5 - 7 minutes)

1. Understanding the Decimal System: The main objective is for students to understand what the decimal system is, how it works, and why it is widely used. They should be able to explain that the decimal system is based on units of ten, with each position to the right of a number being ten times smaller than the position to its left.

2. Converting Between Units in the Decimal System: Students should be able to convert between different units in the decimal system, including larger and smaller units. For example, they should understand how to convert 100 centimeters to 1 meter or 1000 meters to 1 kilometer.

3. Applying the Decimal System to Practical Problems: Finally, students should be able to apply their knowledge of the decimal system to solve practical problems. This could involve converting units of measure in real-world problems, or performing mathematical operations with decimal numbers.

Secondary objectives include:

• Developing Critical Thinking and Problem-Solving Skills: When solving problems involving the decimal system, students should be able to develop their critical thinking and problem-solving skills. They should be encouraged to think independently and experiment with different approaches to problem-solving.

• Promoting Self-Directed Learning: Through the use of online resources and the flipped classroom methodology, students should be encouraged to take ownership of their own learning. This includes preparing for class, reviewing content after class, and seeking clarification when needed.

Introduction (10 - 15 minutes)

1. Review of Prior Knowledge: The teacher begins the lesson by reminding students about basic numeration concepts and the importance of the base 10 (decimal) system in our daily lives. They may do this through quick and interactive questions, asking students to count out loud from 1 to 100, for example, or asking them to identify the value of different places in a three-digit number.

2. Problem-Based Scenarios: Next, the teacher presents two problem-based scenarios that involve the decimal system. For example, they could ask students how to convert 250 centimeters to meters, or how much it would cost to buy 2.5 kg of bananas if the price per kilogram is $3.50. These problem-based scenarios serve to pique students' interest and show the relevance of the decimal system to everyday situations.

3. Contextualization of the Topic: The teacher then contextualizes the importance of the decimal system, explaining that it is widely used in various fields, such as science, engineering, economics, and even everyday activities like shopping for groceries, measuring a recipe, or calculating the speed of a car.

4. Grabbing Students' Attention: To capture students' attention, the teacher could share some fun facts about the decimal system. For example, they could mention that the decimal system was introduced by the Indians between the 1st and 4th centuries AD, and that before that, most civilizations used different numeration systems, such as the Roman numeral system (which used Roman numerals) and the Babylonian system (which used base 60).

5. Introduction of the Topic: Finally, the teacher introduces the topic of the lesson - the Decimal System - explaining that in this lesson, students will learn how to convert between units in the decimal system and apply this knowledge to solve practical problems. They could share that although it may seem complicated at first, the decimal system is actually quite simple and logical, and that students will master it quickly if they pay attention and practice.

Development (20 - 25 minutes)

1. "Decimals in Action" Activity: (10 - 12 minutes)

   • The teacher divides the class into groups of 4 or 5 students.
   • Each group receives a set of cards, with each card representing a different unit of measurement (meter, centimeter, kilogram, gram, etc.).
   • The teacher then presents a series of everyday scenarios that involve conversions between units in the decimal system (for example, "If you have 2 meters of fabric, how many centimeters do you have?").
   • The groups should discuss the scenario, choose the appropriate unit cards, and use those cards to perform the conversion. They should then present their answer to the class.
   • The teacher should circulate around the room, observing the group discussions and providing guidance when needed.
   • This activity allows students to practice converting between units in the decimal system in a fun and contextualized way, reinforcing their understanding of the concept.

2. "The Lost Treasure" Activity: (10 - 13 minutes)

   • The teacher introduces the scenario: "You are a team of archaeologists who have just discovered an ancient treasure map, but the coordinates are in an unknown numeration system. You need to decipher the coordinates to find the treasure!"
   • The teacher then distributes to each group a set of cards with decimal numbers (e.g., 0.1; 0.01; 0.001; etc.) and a set of cards with the decimal place values (ones, tenths, hundredths, thousandths, etc.).
   • The groups should work together to match the decimal number cards with the place value cards, forming the correct decimal numbers that represent the coordinates of the treasure.
   • The teacher should circulate around the room, assisting the groups in understanding the logic of the decimal system and performing the conversions correctly.
   • This activity provides students with an opportunity to physically manipulate decimal numbers and decimal place values, reinforcing their understanding of the concept and developing critical thinking and problem-solving skills.

3. "Decimals in Practice" Activity: (5 - 8 minutes)

   • The teacher asks students, in their groups, to choose an everyday object or situation (e.g., the height of a student, the length of a song, the amount of water in a glass, etc.).
   • They should then measure or estimate the value of that quantity in different units in the decimal system (e.g., meters and centimeters, minutes and seconds, liters and milliliters, etc.).
   • The groups should record their observations and conclusions on a piece of paper, which will be shared with the class at the end of the activity.
   • This activity allows students to apply what they have learned about the decimal system to solve real-world problems and see the relevance of the topic to their everyday lives.

Debrief (8 - 10 minutes)

1. Group Discussion: (3 - 4 minutes)

   • The teacher brings the whole class together and facilitates a group discussion. Each group has up to 2 minutes to share the solutions or conclusions they came up with during the activities.
   • During the presentations, the teacher should encourage students to explain how they applied the decimal system to solve the problems given, what strategies they used, and what difficulties they encountered.
   • The teacher should ask questions to stimulate students' thinking and deepen their understanding of the content. For example, they could ask, "Why did you choose to convert the measurement from centimeters to meters, and not the other way around?" or "How did you know that the decimal place value corresponded to the desired unit of measurement?".

2. Connecting to Theory: (2 - 3 minutes)

   • After the presentations, the teacher connects the hands-on activities to the theory of the decimal system. They should reinforce the concepts that have been learned, emphasizing the importance of understanding the relationship between the places of decimal numbers and the units in the decimal system, and how this makes it easy to convert between different units.
   • The teacher should also review the main points of the lesson, reminding students about what the decimal system is, how it works, and why it is important. They can do this interactively, by asking students to summarize what they have learned in their own words, or to give examples of situations where we use the decimal system.

3. Final Reflection: (2 - 3 minutes)

   • To wrap up the lesson, the teacher asks students to take a minute to reflect on the following questions:
     1. What was the most important concept you learned today?
     2. What questions do you still have?
   • After the reflection, the teacher asks a few students to share their answers with the class. This allows the teacher to assess students' understanding and identify any potential gaps in knowledge that can be addressed in future lessons.
   • The teacher should encourage students to write down their questions and difficulties to review at home, and to continue practicing converting between units in the decimal system in their free time.

Conclusion (5 - 7 minutes)

1. Content Summary: The teacher begins the Conclusion by summarizing the main content covered in the lesson. They reiterate the concept of the decimal system, explaining how the base 10 system works and the relationship between the places of the digits. They also reinforce the importance of the decimal system in our everyday lives, especially in situations involving measurements and quantities. (2 - 3 minutes)

2. Connection between Theory, Practice, and Applications: The teacher highlights how the lesson connected theory (with the explanation of the decimal system), practice (with the activities on converting between units and deciphering coordinates), and applications (with the discussion on the relevance of the decimal system in everyday situations). They emphasize that theoretical understanding is essential for practical application, and that solving real-world problems helps solidify theoretical knowledge. (1 - 2 minutes)

3. Supplemental Materials: The teacher suggests some supplemental materials for students to further their studies on the decimal system. This could include math textbooks, educational websites, explanatory videos, online games, and so on. For example, they could recommend using Khan Academy, which offers a range of interactive and educational resources on mathematics. (1 minute)

4. Relevance of the Topic: Finally, the teacher reinforces the importance of the decimal system to students' lives. They emphasize that the decimal system is not only an essential part of mathematics but also a crucial tool for understanding and navigating the world around us. They can give examples of how we use the decimal system in everyday situations, such as when shopping, measuring things, calculating time and distance, and so on. The teacher encourages students to continue practicing converting between units in the decimal system and to look for more examples of how the decimal system is used in everyday life. (1 minute)