Lesson plan of LCM

Objectives (5 - 7 minutes)

1. Understand the concept of the Least Common Multiple (LCM):

   • Students should be able to define LCM and understand its importance in solving mathematical problems.
   • They should be able to recognize the different methods for finding the LCM, such as prime factorization and the product method.

2. Apply the LCM in problem situations:

   • Students should be able to use the concept of LCM to solve practical problems, such as calculating the LCM of two or more numbers.
   • They should be able to apply the LCM to simplify fractions or solve divisibility problems.

3. Develop critical thinking and problem-solving skills:

   • Students should be able to analyze a problem, identify the best way to solve it using the LCM, and implement that solving strategy.
   • They should be able to evaluate the accuracy of their answer and make adjustments if necessary.

Secondary objectives:

• Promote active learning and group participation:

  • Students should be encouraged to work in groups to solve problems, fostering collaboration and exchange of ideas.
  • They should be encouraged to ask questions, clarify doubts, and discuss different approaches to problem solving.

• Stimulate curiosity and interest in mathematics:

  • The teacher should seek to relate the concept of LCM to the students' daily experiences, making the subject more relevant and interesting.
  • Students' curiosity should be aroused by presenting them with challenging problems that require the use of the LCM for their solution.

Introduction (10 - 15 minutes)

1. Review of Related Content:

   • The teacher should begin the lesson by recalling mathematical concepts that are fundamental to understanding the LCM, such as division, multiples, and factors. This can be done through a quick quiz or group discussion. (3 - 5 minutes)

2. Problem Situations:

   • Next, the teacher should present two problem situations that involve the concept of LCM. For example:
     1. "If a bus passes a bus stop every 20 minutes and another bus passes the same stop every 30 minutes, in how much time will the two buses pass by the same stop again together?"
     2. "A farmer needs to plant seedlings of two species of trees. The first needs to be replanted every 18 days and the second every 24 days. In how many days will the two species of trees need to be replanted again on the same day?" (5 - 7 minutes)

3. Contextualization of the Subject:

   • The teacher should then explain the importance of LCM in everyday life, showing how it can be used to solve practical problems, such as those presented earlier. He may mention, for example, that the LCM is useful for calculating the time it will take for two events to repeat themselves at the same moment, or for planning actions that depend on cycles of different durations. (2 - 3 minutes)

4. Gaining the Attention of the Students:

   • To pique the interest of the students, the teacher can share some curiosities about the LCM. For example:
     1. "Did you know that the LCM is used to calculate the repeating period of a decimal number in a fraction? For example, the number 1/3 in decimal repeats infinitely, but if you calculate the LCM of 3 and 10, which is the denominator, you will find that the repeating period is only 3 digits long, which is quite useful in some applications, such as division of complex numbers."
     2. "Another curiosity is that the LCM is also used in music! In musical theory, the LCM is used to calculate the LCM (Least Common Multiple, that is, LCM in English) of the beats of the notes, which helps to determine the rhythm of a song." (3 - 5 minutes)

The teacher should ensure that the students understand the relevance of the LCM, both in mathematics and in other areas of knowledge and everyday life. He should also encourage students' curiosity, showing that mathematics, although it can be challenging, can also be fascinating and useful.

Development (20 - 25 minutes)

1. Practical Activity - "LCM Battle" (10 - 12 minutes):

   • The teacher divides the class into groups of 4 to 5 students. Each group receives a large sheet of paper, pencils, and an eraser.
   • The teacher lists 5 pairs of numbers on the board and asks each group to find the LCM of each pair. The pairs of numbers vary in difficulty, allowing groups of different skill levels to be challenged.
   • The students in each group discuss among themselves the best strategy to find the LCM of each pair of numbers and then solve the problem on the sheet of paper.
   • When all groups are finished, the teacher calls one group at a time to present how they found the LCM of each pair of numbers. The other groups can ask questions or make comments.
   • The teacher reinforces the effective strategies used by the groups and corrects any errors. He also highlights the importance of the LCM in solving the problems and how it can be applied in different contexts.

2. Discussion Activity - "LCM in Everyday Life" (5 - 7 minutes):

   • After the practical activity, the teacher leads a group discussion on how the LCM is applied in everyday life.
   • The teacher proposes some hypothetical situations, challenges or real-life problems that can be solved using the LCM. For example:
     1. "If you have two alarms on your cell phone, one that rings every 15 minutes and another that rings every 20 minutes, in how much time will they ring together again?"
     2. "If you are organizing a party and need the music, lighting and food service to repeat themselves at different intervals, how can you use the LCM to plan this efficiently?"
   • Students are encouraged to actively participate in the discussion, sharing their ideas, strategies, and solutions. The teacher acts as a mediator, guiding the discussion, asking questions to stimulate critical thinking and clarifying concepts if necessary.

3. Fun Activity - "LCM Game" (5 - 6 minutes):

   • To conclude the Development stage, the teacher proposes a card game called "LCM Game". Each group receives a deck of cards, where each card has a number. The objective of the game is for each group to find the largest number of pairs of cards whose LCM is equal to a number that the teacher determines.
   • The teacher explains the rules of the game and how the LCM is used to earn points. For example, if the number given is 30, the group that finds the LCM of each pair of cards and has the largest number of pairs with LCM equal to 30 wins the game.
   • The teacher monitors the game, clarifies doubts, provides guidance, and encourages cooperation and communication among group members. He also emphasizes the importance of logical reasoning, strategy, and persistence - skills that are essential for mathematics and for life.

The teacher should ensure that all activities are carried out in a playful way, promoting interaction and collaboration among the students. He should also be attentive to identify and correct possible conceptual errors or difficulties that the students may have during the activities.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):

   • The teacher gathers all the students and starts a group discussion about the solutions or conclusions found by each team during the previous practical activities and discussions.
   • He can start by asking each group what strategies they used to find the LCM and how they applied them to the proposed problems.
   • The teacher should promote an environment of respect and active listening, where all students feel comfortable sharing their ideas and opinions, and where differences in thinking are valued.
   • During the discussion, the teacher should ask questions that lead the students to reflect on the problem-solving process, the importance of LCM, and how it can be applied in different situations.

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

   • Next, the teacher should help students make the connection between the practical activities, the discussions, and the theory presented at the beginning of the lesson.
   • He can, for example, ask the students how they used the concept of LCM to solve the problems in the practical activity and how this relates to the definition and calculation methods of the LCM that were presented.
   • The teacher can also ask students to reflect on how the problem-solving strategies they used in class can be applied to other contexts or disciplines.

3. Individual Reflection (2 - 3 minutes):

   • To conclude the lesson, the teacher suggests that the students make a brief individual reflection on what they have learned. He can guide the reflection with questions such as:
     1. "What was the most important concept you learned today?"
     2. "What questions have not yet been answered?"
   • Students are encouraged to write down their answers in a notebook or on a sheet of paper, which can be useful for reviewing the lesson content later or for preparing for the next lesson.
   • The teacher should respect the students' reflection time and not pressure them to share their answers if they do not feel comfortable. However, he should be available to answer any questions or clarify any doubts that students may have.

4. Teacher's Feedback (1 minute):

   • At the end of the lesson, the teacher should provide general feedback on the class's performance, highlighting the positive points and the areas that need to be improved.
   • He should praise the students' effort and participation, emphasizing the importance of teamwork, effective communication and critical thinking.
   • The teacher should also reinforce the relevance of the LCM, showing how it can be applied in different everyday situations and in other disciplines.

The objective of this Return stage is to consolidate learning, promote reflection and self-assessment, and provide constructive feedback for students. This helps ensure that students have acquired the skills and knowledge proposed for the lesson and that they are prepared for the next step in the learning process.

Conclusion (5 - 7 minutes)

1. Summary of Main Points (2 - 3 minutes):

   • The teacher should begin the Conclusion of the lesson by recapitulating the main concepts and procedures covered. He can do this through a brief review, highlighting the definition of the Least Common Multiple (LCM) and the different methods for calculating it, such as prime factorization and the product method.
   • The teacher can also recall the problem-solving strategies that were discussed and practiced during the lesson, reinforcing the importance of critical thinking and analysis of situations.
   • He should emphasize how the LCM can be applied in different contexts, both in mathematics and in everyday life, to solve divisibility problems, simplify fractions, calculate repetition times and plan cyclic events.

2. Connection between Theory, Practice and Applications (1 - 2 minutes):

   • The teacher should explain how the lesson connected the theory, practice and applications of the LCM. He can highlight how the theory was presented at the beginning of the lesson, followed by practical activities that allowed students to apply and deepen their understanding of the concept, and finally by discussions and examples that demonstrated the relevance and usefulness of the LCM in real situations.
   • He should emphasize that mathematics, although it may seem abstract at times, has practical and concrete applications that are relevant to various areas of knowledge and everyday life.

3. Supplementary Materials (1 minute):

   • The teacher should suggest supplementary materials for students who wish to deepen their understanding of the LCM. These materials may include math books, educational websites, instructional videos, online games, and math problem-solving apps.
   • He may also indicate extra exercises to be done at home in order to consolidate the knowledge acquired in the lesson.

4. Relevance of the Subject (1 - 2 minutes):

   • Finally, the teacher should summarize the importance of the LCM, reinforcing that the concept is a fundamental tool for solving mathematical problems and for the development of logical and critical thinking.
   • He can also highlight that, although mathematics can be challenging, mastering concepts such as the LCM can bring not only personal satisfaction, but also practical benefits, such as the ability to solve complex problems, make informed decisions and efficiently plan time and resources.

The Conclusion is a crucial part of the lesson, as it allows students to consolidate what they have learned, reflect on the relevance and application of the concepts presented, and prepare for the next step in the learning process. The teacher should ensure that the Conclusion is clear, concise, and engaging, and that students leave the lesson with a solid and confident understanding of the LCM.