Lesson Plan | Teachy Methodology | Polynomials: Numerical Values

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to clarify to students the main objectives of the lesson, guiding them on what is expected to be learned and developed throughout the session. This provides a clear and targeted focus for the study of polynomials and the practice of numerical value calculations, essential for the practical application of acquired knowledge.

Main Objectives

1. Understand the definition of polynomials and their structure.

2. Calculate the numerical values of a polynomial by substituting the variable x with specific numbers.

Side Objectives

1. Encourage the use of digital tools in solving mathematical problems.
2. Promote collaborative work among students, creating an active and engaging learning environment.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to establish an initial knowledge base about polynomials, engaging students from the beginning of the lesson. The personal research activity using phones connects prior learning with practical, everyday examples, while the key questions foster an enriching debate that reinforces understanding and relevance of the topic.

Warming Up

To start the lesson on polynomials and numerical values, briefly explain that polynomials are algebraic expressions made up of constant terms and variables raised to different powers. Then, ask students to use their phones to look for an interesting or curious fact about polynomials in everyday life, such as applications in engineering, economics, or computer science. This reinforces the relevance of the topic and provides a connection to the real world.

Initial Reflections

1. What is a polynomial?

2. How are polynomials used in everyday life?

3. What is the importance of understanding the numerical value of a polynomial?

4. Did you find any interesting examples of polynomial applications in your research? Share with the class.

5. How did you feel about studying polynomials before this class?

Development

Duration: 70 - 85 minutes

The purpose of this stage is to provide students with an immersive and practical experience, where they can apply the knowledge acquired about polynomials in real and modern contexts. The activities are designed to promote creativity, collaboration, and strategic use of digital technologies, ensuring meaningful and engaging learning.

Activity Suggestions

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

Activity 1 - Mission Influencer: Unraveling Polynomials!

> Duration: 60 - 70 minutes

- Objective: Engage students in creating educational content, promoting the understanding of polynomials in a fun and modern way through the use of social media.

- Description: Students will take on the role of digital influencers and create a video explaining the concept of polynomials and how to calculate numerical values, using practical and everyday examples. They should use platforms like Instagram, TikTok, or YouTube to share the video.

- Instructions:

• Divide students into groups of no more than 5 people.

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

• Students must create a script explaining the concept of polynomials, their importance, and how to calculate their numerical value.

• Encourage the use of humor, creativity, and attractive visual elements to make the video more engaging.

• Groups should film and edit the video using their phones or computers.

• Publish the video on the chosen platform and share the link with the class.

• At the end, each group should watch their peers' videos and provide constructive feedback.

Activity 2 - Digital Escape Room: The Polynomial Adventure!

> Duration: 60 - 70 minutes

- Objective: Stimulate teamwork and logical reasoning among students, using gamification to make the learning of polynomials more dynamic and interactive.

- Description: Students will participate in an online 'Escape Room' game where they need to solve puzzles involving calculations of numerical values of polynomials to advance to the next level and eventually escape.

- Instructions:

• Divide students into groups of no more than 5 people.

• Each group should access a link to a digital 'Escape Room' platform created for the activity.

• Students will find various challenges and mathematical puzzles based on polynomials that need to be solved to advance.

• By solving each puzzle correctly, the group will receive a clue for the next challenge.

• The platform will record the time each group took to complete, encouraging healthy competition among teams.

• At the end, all groups should meet to discuss the strategies used and reflect on the learning obtained.

Activity 3 - Polynomials in Economics: Data Analysis!

> Duration: 60 - 70 minutes

- Objective: Apply the concept of polynomials in real-world situations, developing skills in data analysis and presentation, as well as understanding the usefulness of polynomials in economics.

- Description: Students will use digital spreadsheets to analyze economic data, applying polynomials to model trends and make forecasts. They must present their analyses and conclusions in a digital presentation.

- Instructions:

• Divide students into groups of no more than 5 people.

• Provide each group with a set of real economic data (e.g., stock prices over time).

• Students must use digital spreadsheets (such as Google Sheets or Excel) to input the data and create graphs.

• Teach students how to fit a polynomial to the data using the regression tool of the spreadsheets.

• Each group should analyze the trend represented by the polynomial and make forecasts based on the mathematical model.

• Students must prepare a digital presentation (such as Slides or PowerPoint) to showcase their analyses and conclusions.

• Present their findings to the class, discussing the implications and accuracy of the forecasts made.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate the students' learning by providing an opportunity for reflection and sharing experiences. Through group discussion and 360° feedback, students can improve their communication skills, collaborate more effectively, and develop a deeper understanding of polynomials and their practical applications.

Group Discussion

🤝 Group Discussion: Promote a group discussion where students will have the opportunity to share what they learned during the activities. Suggest the following outline to guide the discussion: Start the discussion by asking groups to present a summary of the activities they performed, highlighting the main learning points; Request each group share the challenges they faced and how they overcame them; Ask students to reflect on how the use of digital tools helped in understanding polynomials and discussions of numerical values.

Reflections

1. 📊 How did creating digital content (video/presentation) help you understand polynomials? 2. 🧠 What was the biggest challenge you encountered when calculating the numerical values of polynomials? 3. 🔍 How did analyzing economic data using polynomials broaden your understanding of the practical application of this concept?

360° Feedback

📣 360° Feedback: Instruct students to participate in a 360° feedback stage, where each will receive feedback from group members about their contribution. Guide the class on the importance of keeping the feedback constructive and respectful. Suggest that each student highlight at least one positive point and one area for improvement for each peer.

Conclusion

Duration: 10 - 15 minutes

📚 Purpose: This stage aims to consolidate the knowledge acquired by students, reinforcing the importance of the studied content and its practical applications. The conclusion provides an integrative view, showing how polynomials, while appearing abstract, are closely linked to the dynamics of the modern world and are fundamental tools in various areas of knowledge and technology.

Summary

🚀 Quick Summary of Polynomials: Polynomials are those powerful mathematical expressions, where we have variables (the famous x) raised to different powers, added to constants. Today, we discovered how we can substitute these variables with specific numbers to obtain numerical values. It’s like taking a cake recipe and swapping ingredients for real measurements to see the final result! 🍰

World Connection

🌍 Connection with Today's World: In today's digital world, understanding polynomials goes beyond the classroom! They are behind many technologies we use. Whether in social network analysis, data modeling for predicting economic trends, or even in optimizing artificial intelligence algorithms, polynomials are present, helping shape our interactions and daily decisions.

Practical Application

🔧 Practical Applications: Knowing how to calculate numerical values of polynomials is a useful skill not only for solving mathematical problems but also for understanding and analyzing real phenomena. For example, forecasting economic growth, analyzing scientific data, or even creating attractive graphs for presentations using digital tools. With polynomials, we can model and predict the behavior of various variables in our daily life.