Lesson Plan | Teachy Methodology | Polynomials: Properties

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to clearly present to students what is expected of them to learn and practice throughout the lesson. By defining these objectives, the teacher creates a central focus that guides both the structure of the lesson and the practical and digital activities that will be carried out. The main objectives are directly related to the academic content, while the secondary ones promote complementary skills important for the comprehensive development of students.

Main Objectives

1. Recognize and apply Girard's relations in polynomials.

2. Understand that the degree of the multiplication of two polynomials is the sum of the degrees of the individual polynomials.

Side Objectives

1. Understand the importance of polynomials in the context of real problems and technological applications.
2. Develop collaboration and communication skills while working on group projects.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to engage students from the beginning, encouraging them to use digital tools to explore the theme of the lesson. This not only motivates them but also helps them see the practical relevance of polynomials, establishing a solid foundation for the deepening of the following practical activities.

Warming Up

To begin the lesson on the properties of polynomials, the teacher should briefly introduce the topic, highlighting the importance of Girard's relations and how the degree of the multiplication of polynomials is the sum of the degrees. Then, ask students to use their cell phones to find an interesting or curious fact about polynomials in real applications, such as in engineering, physics, or even in modern technologies. This will allow them to connect with the topic in a contextualized and practical way.

Initial Reflections

1. What are polynomials and why are they important in mathematics?

2. What applications of polynomials did you find in your research?

3. How do Girard's relations apply to polynomials?

4. What is the importance of the degree in the multiplication of polynomials?

5. How can we see polynomials in our daily lives and in current technologies?

Development

Duration: 70 to 85 minutes

The purpose of this stage of the lesson plan is to provide students with the opportunity to apply their knowledge about the properties of polynomials in practical and interactive activities. By using modern technologies and playful contexts, students actively engage in the learning process, become protagonists of their own knowledge, and develop essential skills for the 21st century, such as collaboration, creativity, and problem-solving.

Activity Suggestions

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

Activity 1 - 🔍 Digital Detectives: Unraveling Polynomials

> Duration: 60 to 70 minutes

- Objective: Apply the properties of polynomials in a playful and interactive context, developing research and problem-solving skills.

- Description: Students take on the role of digital detectives to solve a mathematical mystery related to polynomials. Using digital devices, they must find clues on social media and educational websites, solve mathematical puzzles, and connect the properties of polynomials to uncover the final solution.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group should access a link sent by the teacher to a fictional website, where they will find initial information about the mystery.

• Students must follow clues involving solving polynomial problems using Girard's relations and the property of degree in polynomial multiplication.

• Groups must use cell phones to research more clues and information on social media, applying the studied properties to solve the puzzles.

• In the end, each group must present its solution and explain how they used the properties of polynomials to unravel the mystery.

Activity 2 - ⭐ Mathematical Influencers: Polynomials in Real Life

> Duration: 60 to 70 minutes

- Objective: Develop communication and creativity skills while teaching complex mathematical concepts in an accessible and engaging way.

- Description: In this activity, students become digital influencers who need to create educational content about polynomials. They will use short videos, Instagram stories, or TikTok posts to creatively and accessibly explain Girard's relations and the property of degree in the multiplication of polynomials.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group should choose a digital platform (Instagram, TikTok, YouTube) to create their content.

• Students must plan and execute content that explains the properties of polynomials using practical examples and real applications.

• Encourage students to be creative using visual effects, graphics, and animations to illustrate their explanations.

• In the end, each group must share its content with the class and explain its creative process.

Activity 3 - 🕹️ Gamification of Polynomials: Interactive Challenge

> Duration: 60 to 70 minutes

- Objective: Reinforce knowledge of the properties of polynomials in a dynamic and competitive way, promoting collaboration and quick reasoning.

- Description: Students will participate in an interactive game where they need to solve problems involving polynomials to progress in the game. Using an online quiz platform, such as Kahoot or Quizizz, they will be challenged to apply the properties of polynomials to accumulate points and compete between groups.

- Instructions:

• Divide students into groups of up to 5 people.

• Use an online quiz platform (Kahoot, Quizizz) to set up an interactive game with questions about the properties of polynomials.

• Each round of the game presents a problem or puzzle that students must solve using Girard's relations and the property of degree in polynomial multiplication.

• Groups must discuss among themselves and answer the questions within the stipulated time to earn points.

• At the end of the quiz, the results are presented, and the winning group receives a symbolic prize.

Feedback

Duration: 20 to 30 minutes

The purpose of this stage is to consolidate students' learning, allowing them to reflect on their experiences and share their conclusions. The group discussion and 360° feedback promote a collaborative learning environment, help develop communication skills and constructive criticism, and strengthen the understanding of mathematical concepts through the exchange of knowledge and perspectives.

Group Discussion

To start the group discussion, the teacher can use the following script: 'Now that all groups have completed their activities, I want you to share with the class what you learned and what were the most important conclusions you reached. Let's discuss the strategies you used and how the properties of polynomials were fundamental to solving the challenges. Who would like to start sharing?'

Reflections

1. What were the main challenges you encountered when applying Girard's relations and the property of degree in the multiplication of polynomials? 2. How did you connect the concepts of polynomials with practical and technological applications in the real world? 3. What did you learn about the importance of collaboration and teamwork when carrying out these activities?

360° Feedback

Instruct students to give constructive 360° feedback. Explain: 'Now we will conduct a 360° feedback session, where each student will receive feedback from their group peers about their performance in the activities. Please remember to be respectful and constructive. Talk about what your colleague did well and suggest something they can improve. Let's focus on skills such as communication, teamwork, and application of learned concepts.'

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to review and consolidate learning, highlighting the relevance of polynomials in the modern world. By connecting content with real and everyday applications, the importance of the studied theme is reinforced. Additionally, this stage promotes a motivational and engaging closing, encouraging students to continue exploring the mathematical universe.

Summary

🎉 Concluding the Journey of Polynomials! 🎉 In the blink of an eye, we navigated the magical world of polynomials. We learned about the mysterious Girard Relations 🕵️‍♂️, mastered the superpower of adding degrees in polynomial multiplication, and even became digital detectives and mathematical influencers! 🚀

World Connection

🌍 Polynomials in the Current World: The lesson showed that polynomials are where we least imagine: from robot engineering 🤖 to creating graphics in video games 🎮 and even in social media algorithms that we use daily. Connecting mathematics with modern technology made everything more exciting!

Practical Application

📚 Daily Applications: Polynomials are very important in areas such as engineering, physics, and computer science. Understanding their properties helps us solve complex problems and develop new technologies. They are the tools behind search engine optimization 🔍, financial modeling 💰, and even creating special effects in movies 🎥.