Lesson Plan | Teachy Methodology | Second Degree Function: Maximums and Minimums
| Keywords | Quadratic Function, Maxima and Minima, Mathematics, 1st Year of High School, Digital Methodology, Active Methodology, Collaborative Teaching, Practical Applications, Educational Technology, Gamification, Social Media, Educational Videos, Storytelling, Critical Thinking, Problem Solving |
| Required Materials | Cell phones with internet access, Computers with internet access, Video editing apps (e.g., InShot, Canva), Access to Instagram and TikTok, Access to the game developed on Scratch, Whiteboard and markers, Projector for video presentations, Instagram accounts for sharing Stories |
Objectives
Duration: 10 - 15 minutes
The purpose of this stage is to introduce students to the concept of maxima and minima of a quadratic function and prepare them to solve practical problems involving these calculations. By clearly establishing the objectives, students can understand what is expected of them and how the knowledge will be applied in real-world situations, making learning more meaningful and engaging.
Main Objectives
1. Understand the concept of maxima and minima of a quadratic function.
2. Solve practical problems involving the calculation of maxima and minima, such as calculating the maximum area of a rectangle with a perimeter of 36.
3. Analyze the application of quadratic functions in everyday and technological situations.
Side Objectives
- Develop critical thinking and problem-solving skills.
- Promote collaboration and teamwork through practical activities.
Introduction
Duration: 10 - 15 minutes
The purpose of this stage is to build a base of interest and student engagement with the topic that will be explored in depth during the lesson. By connecting mathematical concepts with real-world examples and allowing students to actively participate from the start, the lesson becomes more dynamic and relevant. The key questions will help initiate a debate and ensure that all students are on the same level of understanding before moving on to more practical activities.
Warming Up
To introduce the topic 'Quadratic Function: Maxima and Minima', briefly explain that the quadratic function is one of the most fundamental forms of quadratic functions in mathematics and has very relevant practical applications in various fields such as physics, economics, and engineering. Then, ask students to use their cell phones to search for and share an interesting fact or real application about the topic. This quick activity helps connect theory with everyday life, sparking students' initial interest.
Initial Reflections
1. What is a quadratic function?
2. How do you identify the maxima and minima in a quadratic function?
3. What are some practical applications of maximization and minimization in everyday life?
4. Who can share an interesting example of quadratic functions that they found in their quick research?
5. How can technology help us better understand quadratic functions?
Development
Duration: 70 - 80 minutes
The purpose of this stage is to provide students with an active and engaging learning experience, using digital technologies to solve practical problems related to the maxima and minima of quadratic functions. These activities aim to develop the ability to apply mathematical concepts in real contexts and foster creativity and collaboration among students.
Activity Suggestions
It is recommended that only one of the suggested activities be carried out
Activity 1 - 📱 Mathematical Digital Influencers 📊
> Duration: 60 - 70 minutes
- Objective: Stimulate students' creativity and practical application of mathematics in real-world situations, as well as develop effective communication skills and the use of digital technologies for learning.
- Description: Students will create a digital influencer campaign on Instagram or TikTok to explain the importance of the maxima and minima of a quadratic function. They should create short and creative videos using everyday situations where these mathematical functions are applied, such as calculating the maximum area of a rectangle given a perimeter or optimizing profits in a fictional company.
- Instructions:
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Divide students into groups of up to 5 people.
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Each group must choose an everyday situation where the maxima and minima of quadratic functions can be applied.
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Using cell phones, students should record a 1-2 minute video explaining the situation and solving the problem.
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The videos should be creatively edited using apps like InShot or Canva.
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Videos may include graphs, animations, and practical examples to make the explanation more engaging.
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At the end, each group must present their video to the class.
Activity 2 - 🎮 Function Game: Unraveling Maxima and Minima 🎲
> Duration: 60 - 70 minutes
- Objective: Encourage playful and collaborative learning through gamification, promoting the resolution of complex problems in a fun and intuitive way.
- Description: Students will participate in a digital game developed on Scratch where they will need to solve a series of problems involving maxima and minima of quadratic functions to advance levels. At the end, groups must discuss the strategies used and how the use of technology facilitated their understanding of the concepts.
- Instructions:
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Divide students into groups of up to 5 people.
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Provide access to the Scratch-developed game through computers or cell phones.
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Each group must complete all levels of the game, which present different problems involving maxima and minima of quadratic functions.
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The game levels may include challenges such as calculating the maximum area of geometric shapes, optimizing trajectories of objects, among others.
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After completing the game, groups should discuss their strategies and how the digital platform helped with understanding.
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Each group must present a brief summary of their strategies and learnings to the class.
Activity 3 - 🏞️ Mathematical Storytelling on Instagram 📷
> Duration: 60 - 70 minutes
- Objective: Develop students' ability to communicate complex mathematical concepts clearly and creatively, using digital tools and visual narratives.
- Description: Students will create a series of posts on Instagram, using Stories, to tell a story where the concepts of maxima and minima of quadratic functions are applied. They must use animations, graphs, and narratives to engage the audience and explain the concepts clearly and creatively.
- Instructions:
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Divide students into groups of up to 5 people.
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Each group must choose a theme or everyday situation where they will apply maxima and minima of quadratic functions.
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Using cell phones, students should create a series of 5 to 10 Stories on Instagram, narrating a story that involves solving a problem related to the chosen theme.
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The Stories should be creatively edited and presented using resources such as GIFs, stickers, and explanatory captions.
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Each group must share their Stories with the class and briefly explain the concept used.
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At the end, discuss with the class how technology and storytelling can be powerful tools for learning.
Feedback
Duration: 20 - 25 minutes
The purpose of this lesson plan stage is to provide a collective reflection on the learning acquired, allowing students to share their experiences and insights. Group discussion and 360° feedback encourage self-assessment and mutual evaluation, promoting a collaborative and constructive learning environment. This stage concludes the digital lesson, reinforcing the understanding of the concepts addressed and strengthening students' communication and teamwork skills.
Group Discussion
💬 Group Discussion: Hold a group discussion with all students where the groups share what they learned from the experience and their conclusions. Follow the script below to introduce and lead the discussion:
- Start by asking students what they thought of the activities and how they felt working with digital tools.
- Ask each group to briefly present their main discoveries and challenges faced during the production of the videos, playing the game on Scratch, or creating the Stories on Instagram.
- Encourage students to discuss how the activities helped in understanding the concepts of maxima and minima in quadratic functions.
- Urge the class to reflect on how digital learning can be applied in other academic and personal contexts.
Reflections
1. 📌 How did digital activities facilitate the understanding of the concepts of maxima and minima of quadratic functions? 2. 📌 What were the main challenges you faced when using digital tools to solve the proposed problems? 3. 📌 In what way did collaborative work influence the final result of the activities?
360° Feedback
🔄 360° Feedback: Conduct a 360° feedback session, where each student should receive feedback from the other members of the group they worked with during the activities. Instruct the class that feedback should be constructive and respectful. Explain that the goal is to help each member understand their strengths and areas for improvement.
- Each student should point out something positive they observed in a peer and a suggestion for improvement.
- Encourage groups to be specific and sincere in their comments, highlighting concrete examples of actions or behaviors of their peers.
Conclusion
Duration: 10 - 15 minutes
🔚 Purpose: This final stage concludes the lesson plan, providing a moment of reflection and synthesis of the learning acquired. The goal is to ensure that students understand the importance of the concepts addressed and how they apply to the real world, strengthening knowledge in a practical and meaningful way. 📚✏️
Summary
🎉 Lesson Summary: Imagine you are on a roller coaster! 🚀 At the highest point, you find the maximum, and at the lowest point, the minimum. Today, we explored how to find these points in quadratic functions, which are like our mathematical roller coasters. Through viral videos, games, and Instagram Stories, you learned to apply these concepts in real situations such as calculating the maximum area of a rectangle and optimizing profits in a fictional company. 📈📉
World Connection
🌍 In Today's World: In a world dominated by technology and digital, understanding how to optimize things is an essential skill. Technology companies, game designers, and even digital influencers use concepts of maxima and minima to create amazing products and make smarter decisions. Our lesson connected these mathematical concepts with modern digital tools, demonstrating how mathematics is present in almost everything around us. 💻📱
Practical Application
🔍 Applications in Everyday Life: Knowing how to calculate maxima and minima is crucial in various areas: from planning the efficient use of resources to optimizing trajectories in physics or seeking maximum profit in businesses. This knowledge not only helps solve practical problems but also develops logical reasoning and problem-solving skills, essential for any profession in the digital age. 💡
