Lesson Plan | Active Learning | LCM Problems

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5-10 minutes)

The Objectives stage is fundamental to clearly establish what is expected for students to learn and be able to do by the end of the lesson. By defining the main objectives, the teacher guides both their planning and the students' focus on key points of the subject. This ensures that the lesson is focused and productive, maximizing the use of time in class for practical activities and in-depth discussions.

Main Objectives:

1. Empower students to calculate the least common multiple (LCM) of two or more numbers, essential for solving problems that involve fractions and practical situations such as the meeting of cyclists at a starting point.

2. Develop the ability to apply theoretical knowledge of LCM in practical contexts, using examples of real and simplified problems for complete understanding of the concept.

Side Objectives:

1. Encourage logical reasoning and the application of problem-solving strategies through the manipulation of numbers and fractions.

Introduction

Duration: (15-20 minutes)

The Introduction stage serves to engage students with the lesson's theme by using problem situations they may have encountered in their prior readings and contextualizing the practical importance of the LCM concept. This not only activates students' prior knowledge but also prepares them to apply what they have learned in new contexts, reinforcing the relevance of studying mathematics in real-life situations.

Problem-Based Situations

1. Imagine you are organizing a birthday party and need to divide the space for guests equally. You have 3 available rooms, but each one can hold a different number of people. Use LCM to find the maximum capacity of guests that can be accommodated equally in the 3 rooms.

2. Two friends, John and Mary, decide to run around a park of different sizes. John completes a lap around the park every 12 minutes, while Mary, who is faster, takes 8 minutes to complete a lap. Using LCM, determine how long it will be until they meet again at the starting point if both start running at the same time.

Contextualization

The concept of LCM is not just an abstract mathematical tool but has practical applications in everyday situations, such as organizing events and planning activities involving multiple people and times. Additionally, understanding LCM can help simplify and expedite calculation processes in areas such as engineering, economics, and computer science, demonstrating its relevance in various professions and real situations.

Development

Duration: (75-80 minutes)

The Development stage is designed to allow students to apply the theoretical knowledge of LCM in practical and challenging situations. By working in groups, students not only reinforce their understanding of the topic but also develop collaboration and communication skills. The activities are structured to be dynamic and engaging, encouraging students to think creatively and explore different methods of problem-solving.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - Math Party: Dividing the Cake

> Duration: (60-70 minutes)

- Objective: Apply LCM to fairly divide a resource (cake) into equal parts, developing calculation and teamwork skills.

- Description: Students will be challenged to organize a birthday party where they need to divide a cake into equal parts for a varying number of guests. The cake can be of different sizes, and the guests range from 5 to 50. Each group of students will receive a unique set of guest numbers and cake sizes to solve, using LCM to ensure that each piece of cake is equal for all guests.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute cards representing different cake sizes (for example, 1/2 cake, 1/3 of a cake, 1/4 of a cake, etc.) and cards with different guest numbers (from 5 to 50).

• Each group should calculate the LCM between the number of guests and the cake size to determine how much of each piece of cake is needed.

• Present their solutions and justify the use of LCM for this division.

• Discuss the different approaches and solutions found by the groups.

Activity 2 - Champions' Race: Meeting at the Podium

> Duration: (60-70 minutes)

- Objective: Use LCM to calculate the meeting of two runners in a race, applying mathematical knowledge in a real context.

- Description: In this activity, students will simulate a race among friends in a park, where each friend runs at a different pace. The challenge is to determine when they will meet again at the starting point. Using fictional data on speeds and sizes of parks, students will calculate the LCM of each runner's times to solve the problem.

- Instructions:

• Organize students into groups of up to 5.

• Provide each group with a sheet detailing the times two friends take to complete a lap in the park (for example, 12 minutes and 8 minutes) and the size of the park.

• Ask them to calculate the LCM of the times to determine when they will meet at the starting point.

• Each group should present their reasoning and solution to the class.

• Discuss the different calculation strategies and how LCM was essential to solve the problem.

Activity 3 - The Great Vacation Trip: Planning Routes

> Duration: (60-70 minutes)

- Objective: Apply LCM to solve a date synchronization problem in a travel planning context, promoting the understanding of LCM as a useful tool for solving practical problems.

- Description: Groups of students will be challenged to plan a vacation trip for a large family, where they need to calculate the LCM of the available vacation days for all family members, ensuring that everyone can travel together. Each family member has different vacation time availabilities, and the task is to synchronize the dates so that everyone can be present on the chosen dates.

- Instructions:

• Divide the class into groups of up to 5 students.

• Give each group sheets with the number of vacation days available for each family member.

• Students should calculate the LCM to determine how many vacation days are viable for all members.

• Each group will present their solution and discuss the difficulties they encountered.

• Reflect as a group on the importance of LCM in organizing events and family planning.

Feedback

Duration: (15-20 minutes)

The purpose of this lesson plan stage is to allow students to articulate and reflect on what they learned during practical activities. The group discussion helps consolidate knowledge, allowing students to articulate their thought processes and learn from their peers' experiences. Additionally, the key questions proposed aim to deepen students' understanding of the application of LCM in real contexts and its importance in everyday life.

Group Discussion

Start the group discussion by inviting each group to share their experiences and learnings. Suggest they begin by talking about the strategies they used to calculate LCM in each situation and discuss which were the most effective and why. Encourage students to reflect on the challenges faced and how they overcame them. This is a moment for students to learn from each other and for the teacher to assess understanding and the application of the LCM concept.

Key Questions

1. What were the main challenges faced when applying LCM in the proposed activities and how did you overcome them?

2. Was there any situation where different groups arrived at different solutions? How could this have occurred?

3. How can knowledge about LCM be applied in real-life situations outside the classroom?

Conclusion

Duration: (5-10 minutes)

The Conclusion stage serves to consolidate the learnings of the lesson, summarizing the main points addressed and reinforcing the connection between theory and practice. Additionally, it highlights the applicability of LCM in real situations, reinforcing the importance of mathematical study for solving everyday problems. This final reflection helps students recognize the value of what they learned and how they can apply this knowledge outside the school environment.

Summary

In this lesson, students explored the concept of Least Common Multiple (LCM), essential for solving division problems and periodic meetings, such as the meeting of cyclists or the division of resources into equal quantities. Students were able to apply LCM in different practical contexts, such as birthday parties, races, and vacation planning, reinforcing their understanding through playful and collaborative activities.

Theory Connection

Today's lesson connected the mathematical theory of LCM with practical applications, demonstrating how mathematical knowledge can be used to solve everyday problems. Through group activities, students were able to visualize and apply what they learned, consolidating theory through practice.

Closing

The importance of studying LCM goes beyond the classroom, being fundamental in real situations that require organization, planning, and efficiency, such as in the example of resource division in events or planning routes and timing in trips. Understanding and knowing how to apply LCM helps simplify these processes and make informed decisions, highlighting the relevance of mathematics in daily life.