Lesson Plan | Teachy Methodology | Combinatorial Analysis: Number of Positive Integer Solutions

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to establish a clear understanding of what will be learned in the class and provide a solid foundation for students to apply their prior knowledge in solving practical problems of combinatorial analysis. This allows them to feel more confident and prepared for the subsequent practical activities.

Main Objectives

1. Understand the basic concepts of combinatorial analysis applied to positive integer solutions.

2. Solve practical problems using the technique of distributing objects with specific restrictions.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to establish a clear understanding of what will be learned in the class and provide a solid foundation for students to apply their prior knowledge in solving practical problems of combinatorial analysis. This allows them to feel more confident and prepared for the subsequent practical activities.

Warming Up

Start the class by presenting the topic Combinatorial Analysis: Number of Positive Integer Solutions to the students, briefly explaining that this branch of mathematics deals with counting distinct ways to distribute objects under certain conditions. Then, ask the students to use their cell phones to find an interesting fact about the topic within a maximum of 5 minutes. Encourage them to share these facts with the class, promoting an interactive environment from the beginning of the lesson.

Initial Reflections

1. What do you understand by positive integer solutions?

2. How can combinatorial analysis be applied in everyday situations?

3. What were the curiosities or interesting facts you found during your search?

4. Could someone provide a practical example of how to distribute objects, like oranges, among people so that everyone receives at least one unit?

Development

Duration: 75 - 85 minutes

The purpose of this stage is to provide students with a practical and contextualized way to apply the concepts of combinatorial analysis learned. Through creative and interactive activities, students are encouraged to solve real problems, using modern digital tools and collaborating in groups, enriching the learning experience and facilitating content assimilation.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 -  Digital Influencers Sharing  Oranges

> Duration: 60 - 70 minutes

- Objective: Apply concepts of combinatorial analysis in solving a practical problem, using social media as a context to contextualize learning.

- Description: In this activity, students will put themselves in the shoes of digital influencers who need to fairly share a batch of 10 oranges with their followers on three different social media platforms: Instagram, TikTok, and Twitter. Each social media platform must receive at least one orange.

- Instructions:

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

• Explain that they will be digital influencers and each group will have to decide how to distribute the 10 oranges among the three social media platforms (Instagram, TikTok, Twitter), ensuring that each receives at least one orange.

• Ask each group to use their cell phones to create a simulated post on the three social media platforms, explaining to followers how the distribution was made and the mathematical justification behind it.

• Students should use graphic design applications (like Canva) to create visual posts and a brief explanatory video, which can be recorded using their own cell phones.

• After creating the posts, each group should present their mathematical solutions and simulated posts to the class.

• At the end, open for a brief discussion about the different approaches and solutions found by the groups.

Activity 2 -  Gamification: Orange Rescue Mission

> Duration: 60 - 70 minutes

- Objective: Utilize gamification to engage students in applying mathematical concepts, making learning playful and interactive.

- Description: Students will participate in a gamified game in a virtual environment (such as Google Classroom or a gamification platform) where they need to solve combinatorial analysis problems to level up and eventually rescue oranges distributed in different places.

- Instructions:

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

• Ask the students to enter the previously prepared gamification platform and join the game 'Orange Rescue Mission'.

• Explain that the mission is to solve various challenges of combinatorial analysis to rescue 10 oranges distributed in three different chests, ensuring that each chest has at least one orange.

• The challenges will be presented in the form of questions and puzzles that students must solve in groups, using their cell phones and/or computers.

• Each time a group correctly solves a challenge, they level up and receive a hint about the location of the oranges.

• At the end, all groups should have correctly rescued the distributed oranges. Conduct a joint discussion about the different strategies and solutions adopted during the game.

Activity 3 -  Mathematical Storytelling: The Distribution of Oranges

> Duration: 60 - 70 minutes

- Objective: Develop communication and creativity skills while applying mathematical concepts, using digital narratives to explain complex mathematical processes.

- Description: Students will create a digital story using an online storytelling tool (like Storybird or Google Slides) in which they need to narrate the process of distributing 10 oranges among 3 characters, ensuring that each one receives at least one orange.

- Instructions:

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

• Explain that each group will create a digital story centered around the distribution of 10 oranges among 3 characters, each receiving at least one orange.

• Students must define the characters and the story's setting using an online storytelling tool.

• The story must include the mathematical explanation of the process of distributing the oranges so that readers understand how the solution was found.

• Groups should use visual and textual elements to make the story engaging and educational.

• Each group will present its story to the class, explaining the logic behind the distribution of oranges.

• Conclude with a debate about the creativity of the solutions and the clarity of the mathematical explanations in the presented stories.

Feedback

Duration: 20 - 30 minutes

The purpose of this stage is to provide an opportunity for students to reflect on what they learned, share their experiences, and receive constructive feedback from peers. Through discussion and feedback, students can identify areas for improvement, solidify their knowledge, and develop communication and collaboration skills that are essential for continuous learning and teamwork.

Group Discussion

Facilitate a group discussion with all students to share what they learned while performing the activities and their conclusions. Start the discussion by highlighting the importance of collaborative work and the practical application of mathematical concepts. Suggest the following outline to guide the conversation:

1. Ask students what were the biggest challenges they encountered during the activities and how they overcame them.
2. Request each group to share their solution strategies and the mathematical justifications used.
3. Ask students to discuss the different approaches and compare the solutions presented, highlighting the positives of each.
4. Encourage the class to reflect on how the use of digital tools influenced learning and problem-solving.

Reflections

1. What were the main challenges you encountered when trying to fairly distribute the oranges? 2. How did collaboration in groups help in solving the combinatorial analysis problems? 3. In what ways did the use of social media and digital tools influence how you thought about the problems?

360° Feedback

Conduct a 360° feedback stage, where each student should receive feedback from other group members. Explain to students the importance of providing constructive and respectful feedback. Suggestions to guide the feedback:

1. Each student should highlight one positive aspect of each colleague's participation in the group.
2. Each student should suggest an area for improvement or a tip for enhancing future collaborations.
3. Emphasize the importance of being specific and objective in feedback, avoiding personal criticisms, and focusing on observed behaviors and attitudes.

Conclusion

Duration: 10 - 15 minutes

 Purpose of the Conclusion 

The goal of this stage is to consolidate learning in a fun and engaging way, ensuring that students understand the relevance of what has been studied, both academically and in their everyday lives. By connecting the content to the current world and emphasizing its practical applications, the aim is to inspire continuous and meaningful learning.

Summary

 Playful Summary of the Class 

What an adventure, everyone! Today, we dove into the world of combinatorial analysis and unraveled the mystery of how to distribute 10 oranges among 3 people (or social media platforms!) in a way that everyone was happy with at least one orange. It was like a puzzle game where each piece (or orange) had to fit perfectly! 

World Connection

 Connection to the Current World 

In our hyper-connected world, combinatorial analysis is not just a mathematician's affair. It is present in how social media platforms distribute content, how algorithms select ads for different audiences, and even in how companies make decisions about the logistics of their products. Understanding these techniques makes us smarter and more prepared for the dynamics of the 21st century! 

Practical Application

 Importance in Daily Life 

Believe it or not, math can save you time and improve the efficiency of your choices! Whether planning an event, dividing tasks in a project, or even understanding how the apps we use daily work – combinatorial analysis is everywhere. Knowing how to distribute resources fairly and efficiently is a valuable skill in any area! ✅