Lesson plan of LCM

Objectives (5 - 7 minutes)

Main Objectives:

1. Understand the concept of Least Common Multiple (LCM) and its importance in solving mathematical problems.
2. Develop skills to calculate the LCM of two or more numbers, using the prime factorization method.
3. Apply the LCM to solve practical problems, such as adding or subtracting fractions with different denominators.

Secondary Objectives:

1. Stimulate students' logical reasoning and problem-solving skills.
2. Encourage students' active participation in class, through discussions and group exercises.
3. Promote the understanding of the importance of mathematics in everyday life and in other areas of knowledge.

Introduction (10 - 15 minutes)

1. Review of Previous Content:

   • The teacher should start by reviewing the concepts of prime factors and Greatest Common Divisor (GCD), since these concepts are essential to understanding the LCM.
   • You can ask students quick questions to check if they remember these concepts, such as "What are prime factors?" or "How can we calculate the GCD of two numbers?"

2. Initial Problem Situations:

   • The teacher can present two problem situations to arouse students' curiosity and introduce the concept of LCM. For example, "If Mary has 3 shirts and 4 pants, how many different combinations of clothes can she make?" or "If John and Peter are assembling a puzzle, and John has 6 pieces and Peter has 8 pieces, how many pieces do they need to have to assemble a complete puzzle?"
   • The teacher should encourage students to discuss possible strategies for solving these problems with each other, but without providing an immediate solution.

3. Contextualization and Importance of the Subject:

   • The teacher should explain that the LCM is a concept widely used in various areas of mathematics, physics, and chemistry.
   • You can give examples of everyday situations that involve the use of the LCM, such as programming the watering time of a garden with different types of plants, or calculating the time it takes for two people, who walk at different paces, to meet at a specific point.
   • The teacher should emphasize that the LCM is a powerful tool for solving practical problems and that, therefore, it is important to understand this concept well.

4. Teaser for the Class:

   • To pique students' interest, the teacher can present curiosities or applications of the LCM in a more playful way. For example, "Did you know that the ancient Egyptians already knew the concept of LCM and used it to solve practical problems?" or "Have you ever thought about how engineers calculate the lifespan of a product that is subject to different rates of wear and tear?"
   • You can also present a more complex problem situation that involves calculating the LCM, such as, "If an orchestra has musicians who play at different tempos, and they want to play a song together, how can they calculate the start time for each musician, so that everyone finishes the song together?"

At the end of this Introduction, students should be motivated and prepared to delve deeper into the study of LCM. In addition, they should have a clear understanding of the importance and applicability of this concept.

Development (20 - 25 minutes)

1. LCM Theory (10 - 12 minutes):

   • The teacher should begin the theoretical part by explaining the concept of Least Common Multiple (LCM) of two or more numbers.
   • The LCM of two numbers is the least common multiple between them. That is, it is the smallest number that is a multiple of both numbers.
   • The teacher can use examples to illustrate this concept. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that is a multiple of both 4 and 6.
   • Next, the teacher should explain that the LCM of three or more numbers is calculated in the same way, but that it is necessary to find the least common multiple between all of them.
   • The teacher can use the example of the LCM of 3, 4, and 6, which is 12, to illustrate this concept.

2. Prime Factorization Decomposition Method (5 - 7 minutes):

   • The teacher should teach students the prime factorization method to calculate the LCM.
   • He should start by explaining what prime factors are. Prime factors are the prime numbers that multiplied together give the original number.
   • The teacher can use the example of the number 12. He should explain that the prime factors of 12 are 2 and 3, because 2 * 2 * 3 = 12.
   • Next, the teacher should explain that the LCM is calculated by multiplying all the prime factors with the highest exponent.
   • He can use the example of the LCM of 4 and 6, which is 12, to illustrate this method. He should show that the prime factors of 4 are 2 * 2 and the prime factors of 6 are 2 * 3. Then, he should multiply all the prime factors with the highest exponent, which in this case is 2 * 2 * 3 = 12.

3. Practical Exercises (5 - 6 minutes):

   • After the theoretical explanation, the teacher should propose practical exercises for students to solve in class. The exercises should involve calculating the LCM of two or more numbers, using the prime factorization method.
   • The teacher should circulate around the room, assisting students who are struggling and correcting the exercises as they are completed.
   • It is important that the teacher encourages students to discuss among themselves during the exercises, so that they can exchange ideas and learn from each other.
   • The teacher should remind students that the goal of the exercises is not only to find the correct answer, but to understand the step-by-step process of calculating the LCM.

At the end of this stage, students should have acquired a good understanding of the concept of LCM and the prime factorization method to calculate it. In addition, they should have had the opportunity to practice solving exercises, which will help to solidify the content.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):

   • The teacher should propose a group discussion, where each group of students will have the opportunity to present their solutions to the proposed exercises.
   • During the discussion, the teacher should encourage students to explain the reasoning they used to arrive at the solution, and to justify why they believe their answer is correct.
   • The teacher should also ask questions to the groups to check if they have understood the concept of LCM and the prime factorization method well.
   • It is important that the teacher creates an environment of respect and collaboration during the discussion, where all students feel comfortable participating and asking questions.

2. Connection with Theory (2 - 3 minutes):

   • After the discussion, the teacher should briefly recap the theory, highlighting the most important points that were discussed during the class.
   • The teacher should explain how the theory connects with practice, that is, how the concept of LCM and the prime factorization method are applied in solving practical problems.
   • The teacher should also clarify any doubts that students may have about the theory, and correct any misconceptions that may have arisen during the discussion.

3. Individual Reflection (2 - 3 minutes):

   • Finally, the teacher should propose that students reflect individually on what they learned in class.
   • The teacher can ask questions to guide students' reflection, such as, "What was the most important concept you learned today?" or "What questions have not yet been answered?"
   • The teacher should give students a minute to reflect and then ask some of them to share their answers with the class.
   • The teacher should listen carefully to the students' answers, and ask the necessary questions to clarify any doubts they may have.

At the end of this stage, students should have had the opportunity to reflect on what they have learned and to clarify any doubts they may have. In addition, they should have had the opportunity to practice the skill of explaining and justifying their solutions, which is an important skill for learning mathematics.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes):

   • The teacher should summarize the main points covered during the class, reiterating the definition and calculation of the Least Common Multiple (LCM) through the prime factorization method.
   • The importance of LCM in solving practical problems, such as adding or subtracting fractions with different denominators, should be emphasized.
   • The teacher should remind students that understanding and mastering LCM is fundamental for the study of other topics in mathematics.

2. Connection of Theory with Practice (1 - 2 minutes):

   • The teacher should reinforce how the theory presented connects with practice, explaining that the calculation of the LCM, although it may seem abstract, has very concrete applications in everyday life and in various areas of knowledge.
   • Examples of real-life situations that involve the calculation of LCM can be given, such as the programming of the watering time of a garden with different types of plants or the calculation of the time of encounter of two people who walk at different paces.

3. Extra Materials (1 - 2 minutes):

   • The teacher can suggest extra materials for students who want to deepen their knowledge of LCM. These materials may include books, websites, videos, and educational games.
   • The teacher should emphasize that practice is essential for mastering this topic, and that students should spend some time outside of class solving exercises and consolidating what they have learned.

4. Importance of LCM (1 minute):

   • Finally, the teacher should reinforce the importance of LCM in everyday life, explaining that the ability to calculate LCM can facilitate the solution of various practical problems, in addition to contributing to the development of logical reasoning and problem-solving skills.
   • The teacher can give examples of how the calculation of LCM is used in various areas, such as engineering, physics, chemistry, and economics.

At the end of this stage, students should have consolidated the knowledge acquired during the class and understood the relevance of LCM for their daily lives and for their future academic and professional careers.