Lesson Plan | Technical Methodology | LCM

Objectives

Duration: 10 - 15 minutes

This stage aims to present the objectives of the lesson, highlighting the importance of developing practical skills and the connection to the job market. By clearly defining the objectives, students understand the relevance of the LCM in practical contexts, such as solving everyday problems and in future professional applications. This also motivates students to engage more deeply with the content, knowing that it has a direct and practical application in their lives and careers.

Main Objectives

1. Calculate the least common multiple (LCM) between two or more numbers.

2. Solve practical problems that involve calculating the LCM, such as determining equivalent fractions.

3. Apply the concept of LCM in real situations, such as determining when two people running on a track will meet again.

Side Objectives

1. Develop logical and mathematical reasoning skills.
2. Facilitate the understanding of other interrelated mathematical concepts, such as fractions and common divisors.

Introduction

Duration: (15 - 20 minutes)

The purpose of this stage is to introduce the lesson's theme in an engaging and relevant way, demonstrating to students the applicability of the LCM in real situations and in the job market. This helps to capture students' interest and curiosity from the start, preparing them for the practical and experimental learning that will follow.

Contextualization

The concept of Least Common Multiple (LCM) is an essential mathematical tool that we frequently encounter in everyday and professional situations. For example, when planning bus schedules that need to align at specific points or when synchronizing machine cycles on a production line. Understanding the LCM allows us to solve problems related to intervals and repetitions of events efficiently.

Curiosities and Market Connection

🔍 Curiosities and Connection to the Market:

Logistics: Transportation companies use the LCM to optimize routes and delivery times, ensuring that trucks leaving different locations meet at distribution points simultaneously. Engineering: In the industrial sector, the LCM is applied to synchronize machines operating on different cycles, avoiding stoppages and improving production efficiency. Technology: Programmers use the LCM to solve scheduling and synchronization problems in distributed systems, where multiple servers or processes need to coordinate their operations.

Initial Activity

🎬 Initial Activity:

Provocative Question: Ask students: "If two people start running at the same time on a circular track, one completing a lap every 4 minutes and the other every 6 minutes, after how long will they meet again at the starting point?" Short Video: Show a 3 to 4-minute video that playfully explains the concept of LCM and its importance in practical situations like organizing events or programming machines.

Development

Duration: 50 - 55 minutes

The purpose of this stage is to allow students to consolidate their understanding of calculating the LCM and its practical application through collaborative activities and fixation exercises. By applying knowledge to real situations and solving practical problems, students develop logical reasoning and mathematical skills, in addition to learning to work in teams and communicate their ideas clearly.

Covered Topics

1. Definition of Least Common Multiple (LCM)
2. Methods to find the LCM (factoring and listing multiples)
3. Application of the LCM in practical problems
4. Solving problems involving LCM

Reflections on the Theme

Guide students to reflect on how the LCM can be used to solve problems in different areas, such as synchronizing schedules in transportation companies or coordinating machine cycles in a factory. Encourage them to think of other everyday situations where this mathematical tool can be applied to facilitate organization and efficiency.

Mini Challenge

Building a Synchronized Schedule

Students will work in groups to create a synchronized schedule for a fictional company that has three activities that repeat at different intervals. The challenge is to find the shortest time in which all activities align again.

Instructions

1. Divide the class into groups of 4 to 5 students.
2. Distribute to each group three cards, each representing an activity with a different repetition interval (for example, 4 minutes, 6 minutes, and 8 minutes).
3. Ask the groups to calculate the LCM of these intervals to determine when all activities will align again.
4. After finding the LCM, groups should create a visual schedule on a poster or large paper, showing the moments when each activity will occur and when they will all align.
5. Encourage groups to present their solutions and explain the process used to find the LCM.

Objective: Apply the concept of LCM in a practical problem and develop teamwork and communication skills.

Duration: 30 - 35 minutes

Evaluation Exercises

1. Calculate the LCM of the numbers 10 and 15. Explain the process used.
2. Two traffic lights flash at intervals of 5 seconds and 8 seconds, respectively. If they flash together at a certain moment, after how long will they flash together again?
3. A factory has three machines that operate on cycles of 3, 4, and 5 minutes. After how long will all three machines be operating simultaneously again?
4. Find the LCM of the numbers 12, 18, and 24 and explain in what practical situations this calculation can be useful.

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate students' learning, ensuring they understand the relevance and applicability of LCM. By summarizing key points and promoting a reflective discussion, students can better internalize the content and see its practical importance. The lesson closing reinforces the connection between theory and practice, preparing students to apply the knowledge gained in real situations.

Discussion

💬 Discussion:

Promote a discussion with students about the concepts learned in the lesson, including the definition of LCM, the methods for finding it, and its practical applications. Ask students how they found the experience of working in groups during the mini challenge and how the activity helped them better understand the concept of LCM. Encourage them to share other everyday situations or job market scenarios where LCM could be useful.

Summary

📜 Summary:

Recap the main content presented during the lesson, emphasizing the definition of Least Common Multiple (LCM), the calculation methods (factoring and listing multiples), and the application of the LCM in practical problems. Remind students how these concepts were utilized in the practical activities and fixation exercises.

Closing

🔚 Lesson Closing:

Explain how the lesson connected theory, practice, and real applications, showing the relevance of LCM in solving everyday and professional problems. Highlight the importance of understanding LCM for optimizing processes, synchronizing cycles, and organizing events efficiently. Conclude by emphasizing that knowledge of LCM is a valuable tool both in academic life and in the job market.