Lesson Plan | Teachy Methodology | Determinant: 3x3

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to establish specific learning objectives for the lesson, ensuring that both the teacher and students have clarity on what will be achieved. This aims to direct the focus of practical and digital activities, increasing the effectiveness of learning about determinants of 3x3 matrices using the Sarrus rule.

Main Objectives

1. Understand the concept of determinant for 3x3 matrices.

2. Apply the Sarrus rule to calculate determinants of 3x3 matrices.

3. Solve mathematical problems involving the determination of determinants of 3x3 matrices.

Side Objectives

1. Encourage students' ability to work collaboratively.
2. Encourage the use of digital and technological resources as learning tools.

Introduction

Duration: 15 to 20 minutes

The purpose of this stage is to connect the students with the topic in an engaging and practical way, using digital resources that are part of their daily lives. This warm-up also allows students to share what they discovered, promoting a collaborative environment and sparking curiosity about the topic. Through the key questions, it seeks to encourage debate and review previously studied concepts, preparing students for the practical activities of the lesson.

Warming Up

🌟 To introduce the topic 'Determinant: 3x3', explain that this is a crucial mathematical tool for solving systems of linear equations and other applications in linear algebra. Then, ask the students to use their cell phones to search for an interesting fact about matrix determinants or the Sarrus rule. For example, they may discover that determinants are used in computer graphics to transform images and 3D games.

Initial Reflections

1. 🔍 What exactly is a determinant and where is it used in the real world?

2. 🤔 Why is the Sarrus rule an efficient tool for calculating determinants of 3x3 matrices?

3. 📊 How do you think determinants can be applied in other disciplines, such as physics or economics?

4. 🧮 Did anyone find an interesting example of the application of determinants in their research?

5. 📚 Let's discuss: What is the difference between calculating determinants of 2x2 and 3x3 matrices?

Development

Duration: 70 to 80 minutes

This stage aims to provide students with the opportunity to apply the knowledge gained about 3x3 matrix determinants in a practical and contextualized manner. Using modern digital technologies, students engage in collaborative and playful activities, reinforcing learning through real-life situations and digital tools that are part of their reality. This increases student engagement and motivation, making the learning process more dynamic and effective.

Activity Suggestions

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

Activity 1 - 🔍 Social Media Detectives: Decoding Matrices 🕵️‍♀️🕵️‍♂️

> Duration: 60 to 70 minutes

- Objective: Apply the Sarrus rule in a practical and contextualized way, developing problem-solving skills in teams and using digital resources common to students' daily lives.

- Description: In this activity, students will become 'Social Media Detectives'. Using their mathematical skills, they will need to solve puzzles that involve calculating 3x3 determinants to uncover a series of clues scattered across different fictional social media profiles created for the activity.

- Instructions:

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

• Provide each group with a set of fictional social media profiles, where each post contains a riddle or problem requiring the calculation of the determinant of a 3x3 matrix using the Sarrus rule.

• Each profile has coded information and clues that can only be unlocked by correctly solving the calculations presented.

• Groups need to use their cell phones or computers to decode the clues and follow the trail of information to solve the final riddle.

• At the end of the activity, each group should present how they arrived at the solution to the riddle and discuss the practical applications of determinants in the proposed scenario.

Activity 2 - 🎮 Gamification: Mathematical Adventure in the Digital World 🕹️

> Duration: 60 to 70 minutes

- Objective: Promote engagement through gamification, allowing students to apply the Sarrus rule in a fun and interactive way, reinforcing learning through collaborative play.

- Description: In this activity, students will participate in a digital game created on a gamification platform like Kahoot or Quizizz. They will face mathematical challenges involving the calculation of determinants of 3x3 matrices. Each correct answer will allow them to advance through different levels of the game, with the final mission of 'saving' a character trapped in a mathematical riddle.

- Instructions:

• Form groups of up to 5 students and provide each group access to the digital game on the chosen platform.

• Explain that each level of the game contains a mathematical challenge that requires calculating the determinant of a 3x3 matrix.

• Groups must solve the problems using the Sarrus rule and input their answers into the platform to advance to the next level.

• As groups progress, the challenges become more complex, requiring collaborative strategies and quick decision-making.

• At the end, groups that complete all levels should discuss the stages they found most challenging and how they overcame those difficulties.

Activity 3 - 📱 Mathematically Correct Digital Influencers 🌟

> Duration: 60 to 70 minutes

- Objective: Develop students' ability to communicate complex mathematical concepts in a creative and accessible way, using social networks and digital creation tools as support.

- Description: Students will turn into digital influencers who need to create explanatory content for their 'audiences' on how to calculate determinants of 3x3 matrices using the Sarrus rule. They should use video creation tools like TikTok or Instagram Reels to produce and share their material.

- Instructions:

• Form groups of up to 5 students and choose the social network and video creation tool to be used.

• Each group must create a script that clearly and creatively explains how to calculate the determinants of a 3x3 matrix using the Sarrus rule.

• Use audiovisual resources, such as graphics and animations, to make the content more accessible and interesting.

• Record and edit the videos, ensuring that all group members participate in some way.

• Share the videos with the class and discuss the different approaches and explanations presented.

Feedback

Duration: 20 to 25 minutes

The purpose of this stage is to promote reflection and consolidation of knowledge acquired during the lesson. Through group discussion, reflective questions, and constructive feedback, students have the opportunity to analyze their experiences, share learnings, and identify areas for improvement. This process not only reinforces learning but also develops communication, collaboration, and self-assessment skills.

Group Discussion

🌟 Group Discussion: 🌟 Start the discussion by asking each group to share a summary of the activity they performed, the challenges faced, and how they were overcome. Suggest that each group highlight a main learning takeaway and a practical application of the determinant of a 3x3 matrix that they discovered during the activity. Ask which digital tools were most useful and how collaboration contributed to problem-solving.

Reflections

1. 🔍 How did the digital methodology help in understanding the calculation of 3x3 determinants? 2. 🤔 What were the main challenges encountered and how did you overcome them? 3. 📊 How did teamwork and the use of digital resources influence learning?

360° Feedback

🗣️ 360° Feedback: Instruct students to gather in their groups and provide feedback to each other on their participation in the activities. Guide them to be constructive and respectful, using the formula: What was good? What can be improved? Encourage students to thank those who provided feedback and reflect on how they can apply the suggestions in the future to improve teamwork and individual performance.

Conclusion

Duration: 10 to 15 minutes

📝 Purpose of this Stage: 📝 The conclusion aims to review the main content in a light and engaging way, connecting learning with the students' daily reality and highlighting the practical importance of the topic. This moment serves to consolidate knowledge and ensure that students leave the lesson with a clear and applicable understanding of the concepts studied.

Summary

🌟 Fun Mathematical Summary: 🌟 Imagine you are a digital adventurer unraveling mathematical mysteries! Today we explored calculating determinants of 3x3 matrices using the Sarrus Rule. We traversed through riddles on social media, played an electrifying virtual game, and even became digital influencers explaining complex concepts in a fun and accessible way. Now, we are true masters of determinants! 🎓

World Connection

🌐 In Today's World: 🌐 In the modern digital world, concepts like determinants of matrices are not just theory; they are essential tools in areas ranging from computer graphics to understanding complex systems in economics. Today's lesson showed us that learning mathematics can be dynamic and integrative, directly connecting to the digital technologies and platforms we use daily.

Practical Application

📈 Applications in Daily Life: 📈 Understanding determinants of 3x3 matrices is crucial for solving systems of equations, which appear in various fields such as engineering, physics, and data science. Furthermore, these skills are applicable in analyzing transformations in game graphics, modeling economic scenarios, and much more.