Lesson Plan | Teachy Methodology | Function: Injective and Surjective

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to ensure that students have clarity about the main and secondary objectives of the lesson, establishing a solid foundation for the practical activities that will follow. By the end of this stage, students should be prepared to apply the concepts of surjective and injective functions in practical and digital contexts, making learning more meaningful and connected to their reality.

Main Objectives

1. Understand what a surjective function is, identifying that every image of the codomain is reached by at least one element of the domain.

2. Understand what an injective function is, recognizing that for distinct entries of the function, the outputs are also distinct.

Side Objectives

1. Relate the concepts of surjective and injective functions to practical situations in daily life and the digital world.
2. Encourage critical and analytical thinking through collaborative and technological activities.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to ensure that students have clarity about the main and secondary objectives of the lesson, establishing a solid foundation for the practical activities that will follow. By the end of this stage, students should be prepared to apply the concepts of surjective and injective functions in practical and digital contexts, making learning more meaningful and connected to their reality.

Warming Up

To start the lesson on injective and surjective functions, briefly explain that a surjective function is one where every image of the codomain is reached by at least one element of the domain, and that an injective function is one where distinct entries result in distinct outputs. Then, ask students to use their phones to search for an interesting fact or practical application of these topics on the internet. Encourage them to share what they found with the class.

Initial Reflections

1. What is the main difference between an injective function and a surjective function?

2. How can you identify an injective function by looking at its graph?

3. Did you find any practical application of injective or surjective functions during your research? Could you share?

4. Why is it important to understand the characteristics of injective and surjective functions in the context of mathematics and real life?

5. Are there situations in the digital world where these functions are applied? Which ones?

Development

Duration: 70-80 minutes

The purpose of this stage is to provide active and meaningful learning, where students apply the concepts of injective and surjective functions in practical and collaborative activities, using digital technologies as the main tool. This not only reinforces the content learned but also develops essential skills for the 21st century, such as critical thinking, teamwork, and creativity.

Activity Suggestions

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

Activity 1 - 🕵️‍♂️ Digital Treasure Hunt 🎲

> Duration: 60 - 70 minutes

- Objective: Stimulate the practical application of the concepts of injective and surjective functions through digital and collaborative activities, promoting learning in a playful and engaging way.

- Description: Students will participate in a digital treasure hunt using QR codes scattered throughout the classroom or school. Each QR code will lead to different problems related to injective and surjective functions, simulating situations from daily life or the digital world.

- Instructions:

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

• Distribute a map with locations where the QR codes are hidden.

• Each QR code reveals a problem or situation that students need to solve.

• The problems should address injective and surjective functions in practical contexts, such as social media algorithms, encryption, among others.

• Students should record their answers in an online form.

• The group that solves all problems correctly and the fastest wins the competition.

Activity 2 - 🎬 Mathematical Influencers 📲

> Duration: 60 - 70 minutes

- Objective: Promote understanding of the concepts of injective and surjective functions, encouraging creativity and practical application in the context of social media.

- Description: Students will create short videos in the style of social media explaining injective and surjective functions. The videos should be creative and use practical examples from everyday life or the digital world.

- Instructions:

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

• Each group must choose a theme related to injective and surjective functions to explain.

• Groups have access to cell phones and video editing applications.

• Videos should be short (1-2 minutes) and utilize practical examples like YouTube video recommendations or Instagram filters.

• Students must post the videos on a platform chosen by the teacher (e.g., Google Classroom or a closed YouTube group).

• All groups watch each other's videos and leave constructive comments.

Activity 3 - 🎮 Mathematical Gamification 🔢

> Duration: 60 - 70 minutes

- Objective: Use gamification to reinforce the concepts of injective and surjective functions, making learning interactive and engaging.

- Description: Students will participate in an online game, where each phase is a mathematical challenge related to injective and surjective functions. The game uses interactive platforms like Kahoot or Quizizz.

- Instructions:

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

• Explain the rules of the game and how the platforms work.

• Each phase of the game presents a challenge or problem to be solved about injective and surjective functions.

• Groups discuss and submit their answers through the platform.

• Scores are assigned based on the accuracy and speed of the answers.

• The group with the highest score at the end of the phases wins the competition.

Feedback

Duration: 15 - 20 minutes

The purpose of this stage is to consolidate learning through reflection and sharing experiences, as well as to promote communication and collaboration skills. Group discussions allow students to reinforce their knowledge by hearing different perspectives, while 360° feedback offers an opportunity for personal and academic development, encouraging a culture of respect and continuous improvement.

Group Discussion

Facilitate a group discussion with all students, where each group shares what they learned and their conclusions after completing the activities. Suggest that each group have a representative to present their main ideas. Use the following outline to guide the discussion:

1. Introduction: Ask students to briefly summarize the activities carried out.
2. Learning: Ask students what they learned about injective and surjective functions.
3. Challenges: Question if there were any specific challenges during the activities and how the group solved those challenges.
4. Practical Application: Encourage students to discuss how injective and surjective functions can be applied in real situations, both in daily life and in the digital world.

Reflections

1. What were the main differences you noticed between injective and surjective functions during the activities? 2. How did the use of digital tools help in the understanding of these mathematical concepts? 3. In what way can you apply what you learned today in other subjects or in your life outside school?

360° Feedback

Instruct the teacher to carry out a 360° feedback step where each student must receive feedback from the other group members. Guide the class to ensure that the feedback is constructive and respectful. Suggest they use the following format:

1. Positive Aspects: What did the colleague do well during the activity?
2. Areas for Improvement: Where could the colleague improve?
3. Practical Suggestions: What recommendations would you give to help the colleague improve?

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate learning in a light and fun way, reinforcing the connection between mathematical theory and its practical applications in the modern world. By summarizing the main points and relating them to real situations, the conclusion not only reinforces the content learned but also sparks continuous interest in the topic.

Summary

🎉 Fun Summary! 🎉 Imagine a deck of cards, where each unique card has its perfect pair. This is the Injective Function! Now, imagine that all the cards from the deck are on the table and each one corresponds exactly to a person. This is the Surjective Function! Today we explored these two incredible functions with activities that included a digital treasure hunt, TikTok-style video recording, and even an interactive quiz. A fun and interactive mathematical journey! 🚀

World Connection

🌐 In the Modern World 🌐 Injective and surjective functions are not just theoretical concepts; they are everywhere! From the algorithms that decide which videos appear on your YouTube feed to the encryption that protects your messages on WhatsApp. Understanding these functions helps decipher how the technologies around us work and interact with us in daily life.

Practical Application

📈 Applications 📈 Knowing injective and surjective functions is essential for understanding and developing digital technologies. They are used in programming, encryption, data analysis, and even engineering. Knowing how and when to apply these functions can open doors to various careers and opportunities in the digital future.