Objectives (5 - 7 minutes)

• The teacher will define the concept of the Least Common Multiple (LCM) as the smallest multiple that two or more numbers have in common.
• The teacher will explain that the LCM is used to find a common denominator when adding or subtracting fractions with different denominators, and to simplify fraction operations.
• The teacher will outline the lesson plan, informing students that they will be learning about the LCM through interactive problem-solving activities.

Secondary Objectives:

• The teacher will emphasize the importance of the LCM in various real-world applications, such as time management, scheduling, and finding the next occurrence of an event.
• The teacher will encourage students to actively participate in the lesson, asking and answering questions, and engaging in hands-on activities to reinforce their understanding of the LCM.
• The teacher will provide a brief overview of the key terms and concepts that will be covered in the lesson, such as multiples, common multiples, factors, and prime numbers, to ensure that all students have the necessary background knowledge to understand the LCM.

Introduction (10 - 12 minutes)

• The teacher begins the lesson by reminding students of the previous topics related to the current lesson. They could briefly touch upon the concept of multiples, factors, and prime numbers, ensuring that students remember these foundational concepts.

• The teacher then presents two problem situations to the students:

  1. The teacher asks, "If a school has math class every 2 days and science class every 3 days, when will both classes be on the same day again?"
  2. The teacher presents a second problem, "If a music chord is played every 4 seconds and a drum beat is played every 6 seconds, when will the two sounds coincide again?"

• The teacher contextualizes the importance of the Least Common Multiple (LCM) by explaining its real-world applications. For example, they could mention that the LCM is used in time management and scheduling to determine when multiple events will occur at the same time. They could also highlight its use in simplifying fractions, an essential skill in various fields such as cooking, engineering, and architecture.

• To grab the students' attention, the teacher could share interesting facts or stories related to the LCM. For instance:

  1. The teacher could tell a story about how ancient civilizations used the concept of LCM (unbeknownst to them) in their calendars to predict astronomical events and plan their agricultural activities.
  2. The teacher could share a fun fact that the LCM of the numbers 1 to 10 is 2520, a number that is divisible by all the numbers from 1 to 10.

• The teacher concludes the introduction by stating that by the end of the lesson, students will be able to solve the problems presented at the beginning and understand the significance and applications of the LCM.

Development (20 - 25 minutes)

1. Defining the Concept and Basic Rules of Least Common Multiple (6 - 8 minutes)

   • The teacher reintroduces the concept of multiples and factors and explains how these concepts are fundamental to understanding the LCM.
   • They then define the LCM as the smallest multiple that two or more numbers have in common. They illustrate this concept with a few simple examples.
   • The teacher writes down the mathematical notation for LCM (e.g., LCM(6, 8)) and explains that the numbers inside the parentheses are the numbers whose LCM is being found.
   • They show how to find the LCM of two numbers using a method called the cake method or the ladder method. They explain that this method involves writing down the multiples of each number until a common multiple is found.
   • The teacher demonstrates this method with a couple of examples on the board, showing how to find the LCM of numbers like 6 and 8, or 12 and 15.

2. Finding the LCM of More Than Two Numbers (6 - 8 minutes)

   • The teacher explains that the process of finding the LCM of more than two numbers is similar to finding the LCM of two numbers. However, instead of stopping when a common multiple is found, the process continues until the multiples of all the numbers overlap.
   • They use the same method as before but with more numbers for the next example. For instance, they might find the LCM of 3, 4, and 5.
   • They provide step-by-step instructions to the students and encourage them to follow along, asking questions if they are unsure about any step.

3. Using LCM to Add and Subtract Fractions (5 - 7 minutes)

   • The teacher explains how the LCM is used to add and subtract fractions with different denominators, which is a fundamental application of the LCM.
   • They write down two fractions on the board with different denominators and explain that before adding or subtracting them, we must first find a common denominator.
   • The teacher demonstrates this process with an example, showing how the LCM of the denominators is used as the common denominator.
   • They then show how to convert the fractions into their equivalent fractions with the common denominator and perform the addition or subtraction.
   • The teacher emphasizes the importance of simplifying the results using the LCM, if possible.

4. Practical Applications and Real-World Examples (3 - 4 minutes)

   • The teacher revisits the initial problem situations presented in the introduction and demonstrates how to solve them using the LCM.
   • They provide additional real-world examples where the LCM is used, such as finding the best time to meet with friends who have different schedules, or determining when two buses will arrive at the same time if they have different intervals.
   • The teacher encourages students to participate in the discussion, asking them to propose their own problems that can be solved using the LCM.

Throughout this development stage, the teacher should engage the students by asking them questions, encouraging them to solve problems on their own, and clarifying any doubts they may have. They should also provide ample opportunities for students to practice finding the LCM and using it in different contexts. This active engagement will help solidify the students' understanding of the concept and its applications.

Feedback (8 - 10 minutes)

• Assessing Understanding (4 - 5 minutes)

  • The teacher begins the feedback stage by conducting a quick review of the main points discussed during the lesson. They ask a few students to recap the definition of the LCM and the process of finding the LCM of two or more numbers, as well as how to use the LCM to add or subtract fractions.
  • The teacher checks for understanding by asking the students to solve a couple of problems on the board, one involving finding the LCM of two numbers, and another requiring the students to use the LCM to add or subtract fractions.
  • They observe the students' problem-solving techniques, correct any misconceptions, and provide additional guidance as needed.
  • The teacher assesses the students' understanding based on their ability to correctly apply the concepts and procedures they have learned. They also pay attention to the students' participation in the activities, their engagement in the discussions, and their responses to the questions.

• Reflecting on Learning (4 - 5 minutes)

  • The teacher then encourages the students to reflect on what they have learned in the lesson. They ask the students to consider the following questions:
    1. What was the most important concept you learned today?
    2. What questions do you still have about the LCM?
  • The teacher gives the students a minute to think and then asks a few volunteers to share their thoughts with the class. They listen to the students' responses, address any remaining questions or misconceptions, and provide additional explanations or examples as needed.
  • The teacher emphasizes the practical applications of the LCM and how it can be used in various real-world situations. They also remind the students that the LCM is not just a mathematical concept but a tool that can help them in their everyday life.

• Providing Homework Assignment (1 minute)

  • The teacher concludes the lesson by assigning homework that reinforces the concepts learned in the class. The assignment could include problems that require the students to find the LCM of different numbers and to use the LCM to add or subtract fractions. The teacher reminds the students to show their work and to write down any questions or difficulties they encountered while doing the assignment.
  • The teacher also encourages the students to explore more about the LCM on their own time, suggesting resources such as online tutorials, math games, and practice worksheets.

• Closing the Lesson (1 minute)

  • The teacher thanks the students for their active participation and enthusiasm during the lesson, and encourages them to continue practicing the concepts they have learned. They remind the students that understanding the LCM is a building block for more advanced math concepts and encourage them to keep up the good work. They also remind the students of the next lesson's topic and any materials they will need to bring for the class.
  • The teacher dismisses the students, reminding them to complete their homework and to review the concepts learned in the class. They wish the students a good day and look forward to seeing them in the next class.