Objectives (5 - 7 minutes)

1. Understanding the Concept: The students will be able to define the term "Least Common Multiple (LCM)" and understand its significance in mathematics. They will learn that the LCM is the smallest positive integer that is divisible by two or more numbers.

2. Identifying the LCM: Students will be able to identify the Least Common Multiple of a set of numbers. They will comprehend the process of finding the LCM by listing the multiples and identifying the smallest common multiple.

3. Applying the Concept: Students will apply the concept of LCM to solve mathematical problems involving multiple numbers. This objective will enable them to use the LCM as a tool to simplify complex problems and calculations.

Secondary Objectives:

• Enhancing Problem-Solving Skills: In the process of learning about LCM, students will enhance their problem-solving skills. They will learn to approach mathematical problems systematically and logically.

• Developing Collaborative Skills: The flipped classroom approach will encourage students to work in groups, promoting collaborative learning. This will help them in developing team-building skills and learning from each other's perspectives.

• Promoting Self-Learning: The pre-class video assignment will promote self-learning and independent thinking among students. They will learn to take responsibility for their own learning, understand the importance of pre-class preparation, and actively participate in the in-class activities.

Introduction (7 - 10 minutes)

1. Recap of Multiples: The teacher begins the lesson by reminding students about the concept of multiples. Students have already been introduced to this concept in previous classes. The teacher can ask a few questions to refresh their memory, such as "What are multiples of 3?", "Can you list the first 5 multiples of 4?" This will help students connect the previous knowledge with the new concept of LCM.

2. Problem Situations: The teacher then presents two problem situations to the students:

   • "If a bakery sells donuts in packs of 6 and cookies in packs of 8, what is the minimum number of pastries the bakery can make packs of, so that no pastries are left out?"
   • "Amy wants to plant a row of flowers in her garden. The flowers bloom every 12 days, while the weeds need 8 days to grow. If Amy wants to see both flowers and weeds together, how often should she check her garden?"

3. Real-World Applications: The teacher then explains the importance of LCM in real life. For instance, in the first problem, the bakery needs to know the LCM of 6 and 8 to create packs without leftover pastries. Similarly, in the second problem, Amy needs to find the LCM of 12 and 8 to determine how often she should check her garden. This will help students understand that the concept they are about to learn has practical applications.

4. Topic Introduction: The teacher introduces the topic of "Least Common Multiple (LCM)" and its importance in mathematics. The teacher can say, "Today, we are going to learn about a special kind of multiple - the Least Common Multiple. It's a really useful concept that can help us solve many real-life problems, just like the ones we discussed earlier."

5. Engaging Curiosities: The teacher can make the introduction more interactive and engaging by sharing a few fun facts or curiosities related to LCM. For instance:

   • "Did you know that the concept of LCM can be traced back to ancient Egypt, where it was used to solve problems related to irrigation and building structures?"
   • "The concept of LCM is not just limited to mathematics. It also has applications in computer science, particularly in algorithms and cryptography."

By the end of the introduction, students should be familiar with the term "Least Common Multiple", understand its significance, and be curious to learn more about it.

Development

Pre-Class Activities (15 - 20 minutes)

1. Video Assignment: The teacher assigns a video tutorial to the students, explaining the concept of Least Common Multiple (LCM) and the method of finding the LCM of multiple numbers. The video should be engaging, visually appealing, and not more than 10 minutes long. It can be sourced from educational platforms like Khan Academy or YouTube. Students are to watch this video at home and take notes of important points.

2. Note-Taking: Students are asked to write a brief summary of the video in their own words and prepare a set of questions based on their understanding of the video. These questions can be about the concept itself, its applications, or any doubts they might have. The students will bring their notes and questions to the class the next day.

In-Class Activities (20 - 25 minutes)

Activity 1: LCM Scavenger Hunt

1. Introduction to the Activity: The teacher introduces the first in-class activity, the LCM Scavenger Hunt. The objective is to find the LCM of a set of numbers, leading to a discovery of a hidden treasure (a puzzle piece). The teacher explains that the treasure is divided into pieces based on the number of groups they will form.

2. Formation of Groups: The teacher divides the class into groups of four or five students each. The groups are then assigned a starting point, where they will find the first set of numbers.

3. Setting Up the Scavenger Hunt: The teacher has prepared a "scavenger hunt map" where each location corresponds to a number. Each group receives a copy of the map.

4. Play of the Activity: After receiving the starting point, the groups race to find the LCM of the numbers at their location using the method shown in the pre-class video. When a group finds the LCM, they move to the corresponding location on the map, where they will find a new set of numbers and repeat the process. The first team to reach the final location will get the first piece of the puzzle.

Activity 2: LCM Art Activity

1. Introduction to the Activity: The teacher introduces the second in-class activity, the LCM Art Activity. The objective is to create an artistic design using the LCM of two or more numbers.

2. Discussion about LCM: The teacher revisits the concept of LCM and its method of calculation, emphasizing its significance in finding a common point in the multiples of different numbers.

3. Art Materials: The teacher provides the art materials required for the activity, which includes colored paper, scissors, and glue.

4. Creation of Artwork: The groups use their understanding of LCM to decide the numbers for their artwork design. They then cut the colored paper into shapes representing the multiples of each number, and finally, assemble them to form a unique design.

5. Sharing of Artwork: Each group presents their artwork to the class, explaining the numbers they chose and how they applied the concept of LCM in their design.

Through these activities, students will be actively engaged in learning the concept of LCM, its method of calculation, and its application in a fun and creative way. The scavenger hunt will foster team spirit and promote healthy competition, while the art activity will encourage creativity and critical thinking.

Feedback (10 - 12 minutes)

1. Group Discussions: The teacher facilitates a group discussion among the students, where each group shares their solutions or conclusions from the in-class activities. This discussion should focus on the process of finding the LCM, the strategies used, and the challenges faced by the groups. Each group is given a maximum of 3 minutes to present their findings.

2. Connection to Theory: The teacher then guides the discussion towards connecting the practical activities with the theoretical concept of LCM. The teacher can ask questions like, "How did you use the concept of LCM in the scavenger hunt?" or "How did finding the LCM help you in creating your artwork?" This discussion will help students understand the relevance and application of the LCM concept in real-life scenarios.

3. Reflection: The teacher encourages the students to reflect on what they have learned in the lesson. The students are asked to think about questions such as:

   • "What was the most important concept you learned today?"
   • "Which part of the lesson was the most challenging for you, and how did you overcome it?"
   • "How can you apply the concept of LCM in solving other mathematical problems?"

4. Individual Feedback: The teacher provides individual feedback to each student based on their participation in the activities and the quality of their understanding demonstrated in the group discussions. This feedback can be in the form of praise for a job well done, suggestions for improvement, or further clarification on any doubts or misconceptions.

5. Closing Remarks: The teacher concludes the lesson by summarizing the main points learned about LCM and its application. The teacher also reminds the students of the importance of the concept in solving mathematical problems and encourages them to continue practicing and exploring the concept further.

In this feedback stage, the teacher assesses the students' learning outcomes and provides constructive feedback. The students also get a chance to reflect on their learning and consolidate their understanding of the LCM concept. This interactive feedback process promotes a deeper understanding of the concept and encourages students to take ownership of their learning.

Conclusion (5 - 7 minutes)

1. Recap of the Lesson: The teacher begins the conclusion by summarizing the main points of the lesson. The teacher reinforces the definition of the Least Common Multiple (LCM) as the smallest positive integer that is divisible by two or more numbers. The teacher also revisits the method of finding the LCM by listing the multiples and identifying the smallest common multiple.

2. Linking Theory, Practice, and Application: The teacher then explains how the lesson connected theory, practice, and applications. The teacher reminds the students of the pre-class video assignment, which provided them with the theoretical knowledge of LCM. The in-class activities, including the LCM Scavenger Hunt and the LCM Art Activity, allowed them to apply this theory in a practical and fun way. The teacher also highlights the real-world examples discussed in the lesson, which demonstrated the practical applications of LCM.

3. Additional Learning Resources: The teacher suggests a few additional resources for students who want to explore the concept of LCM further. This can include online games, interactive worksheets, and problem-solving videos. The teacher encourages students to use these resources to practice finding the LCM of different numbers and solve more complex problems involving LCM.

4. Importance of LCM in Everyday Life: The teacher concludes the lesson by reiterating the importance of the LCM concept in everyday life. The teacher can say, "Remember, the concept of LCM is not just about solving mathematical problems. It can be used in many real-life situations where we have to find a common point or a common multiple. For example, it can be useful in planning events, scheduling tasks, or even in understanding cycles in nature."

5. Final Remarks: The teacher ends the lesson by praising the students for their active participation and encouraging them to continue exploring and learning. The teacher can say, "I'm really impressed with the way you all engaged in today's lesson. Keep up the good work, and don't forget to apply what you've learned in your everyday life. See you in the next class!"

In this conclusion stage, the teacher reinforces the main points of the lesson, emphasizes the connection between theory and practice, and encourages further exploration and application of the LCM concept. The students are left with a clear understanding of the LCM concept, its importance, and its practical applications.