Lesson Plan | Teachy Methodology | Second Degree Function: Graph and Table

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to provide a clear and direct overview of the objectives that students should achieve by the end of the lesson. This will help focus and guide the practical activities and discussions that will occur, ensuring that all students are aware of the skills and knowledge they need to develop.

Main Objectives

1. Understand that it is possible to represent a quadratic function in graphs and tables.

2. Differentiate between the representation in graph form and table form.

3. Sketch a graph of a quadratic function.

Introduction

Duration: (15 - 20 minutes)

The purpose of this stage is to engage students from the start by connecting the lesson content to their daily lives and the use of digital technologies. This not only sparks interest but also provides a starting point for discussions and practical activities, laying the groundwork for a deeper exploration of the topic.

Warming Up

📱 Warm-up: Introduce the importance of quadratic functions, highlighting how they appear in different everyday contexts, such as in physics to describe parabolic movements or in economics to find maximum or minimum profit points. Ask students to use their cell phones to look up an interesting fact about the application of quadratic functions in real life. They should share their findings with the class, encouraging the use of social media as a learning tool.

Initial Reflections

1. 🔍 What did you discover about the application of quadratic functions in everyday life?

2. 🧮 How do you differentiate between the graphical and tabular representation of a quadratic function?

3. 📈 What do you think is the most challenging part of sketching a graph of a quadratic function?

4. ⚙️ What are the main components of a quadratic function that influence its graph?

5. 💡 How can technology and digital tools help in better understanding the graphs of quadratic functions?

Development

Duration: (75 - 85 minutes)

The purpose of this stage is to provide students with a practical and interactive experience where they can apply the concepts of quadratic functions in real or simulated situations. By using digital technologies and creative methods, students will collaborate, solve problems, and communicate their discoveries, thus consolidating their understanding in an engaging and contextualized manner.

Activity Suggestions

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

Activity 1 - 📊 Digital Influencer Challenge: Quadratic Function in Practice!

> Duration: 60 - 70 minutes

- Objective: Apply the theory of the quadratic function in real-life situations, using social networks as a communication and learning tool.

- Description: Students will be divided into groups, and each group will take on the role of a digital influencer who needs to explain to their followers how the quadratic function is applied in everyday situations. They will create a series of posts on a simulated social network, using graphs and tables to illustrate their points.

- Instructions:

• Divide students into groups of up to 5 members.

• Each group will choose a real context to apply the quadratic function (ex: trajectory of a ball launch, production cost and profit of a product, etc.).

• Using computers and cell phones, groups will research and create graphs and tables representing the quadratic function in the chosen context.

• Groups will create a sequence of posts (minimum of 5 posts) on a simulated social network (it can be on Instagram, Twitter, or another fictional platform).

• Each post must contain an image (graph or table) and a clear and concise explanation of how the quadratic function applies to that situation.

• Groups will share their posts with the class and answer questions from the 'followers' (other students).

• The teacher should monitor and assist the groups during the activity, ensuring that everyone understands and actively participates.

Activity 2 - 🎮 Gamified Mathematics: Graphs and Tables Competition!

> Duration: 60 - 70 minutes

- Objective: Promote understanding of quadratic functions through a healthy and engaging competition, encouraging collaborative use of digital technologies.

- Description: Students will participate in a gamified competition where they will need to solve problems involving quadratic functions and present their solution in the form of graphs and tables. Points will be awarded for accuracy, clarity, and creativity in their solutions.

- Instructions:

• Divide students into groups of up to 5 members.

• Present three problems involving quadratic functions. Each group will choose one problem to solve.

• Using computers and cell phones, groups will solve the problem and create graphs and tables representing the solution found.

• Groups will present their solutions to the class visually (using a projector or screen sharing).

• Each presentation will be evaluated by a committee composed of other students (non-participants from the group) and the teacher, using criteria such as accuracy, clarity, and creativity.

• The group with the highest score will win a symbolic prize, such as extra points or a digital certificate of proficiency in quadratic functions.

Activity 3 - 🛰️ Parabolic Mission: Exploring Trajectories with Digital Simulations!

> Duration: 60 - 70 minutes

- Objective: Facilitate understanding of the characteristics of the quadratic function through analysis of digital simulations, promoting practical application of mathematical concepts in physical situations.

- Description: Students will use a digital simulator to explore the parabolic trajectories represented by quadratic functions. They will analyze different situations and create explanatory reports based on the data generated by the simulator.

- Instructions:

• Divide students into groups of up to 5 members.

• Each group will use a digital simulator (such as PhET Interactive Simulations) to model different parabolic trajectories.

• Students will modify initial parameters (such as speed and launch angle) and observe how these changes affect the trajectory.

• Groups will record the data generated by the simulator in tables and create corresponding graphs.

• Based on the data and graphs, groups will develop an explanatory report detailing the behavior of the quadratic function in the different situations analyzed.

• The reports will be presented to the class, and there will be a Q&A session to deepen the understanding of the concepts.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to consolidate learning through collective reflection, allowing students to share their experiences and learn from each other. Additionally, the 360° feedback promotes the development of social and communication skills, which are fundamental for teamwork.

Group Discussion

🗣️ Group Discussion: Start the discussion by encouraging each group to share their experiences and conclusions with others. Use the following outline to guide the discussion: Ask each group to present a brief summary of their activities and the context they chose. Inquire about the challenges encountered during the creation of graphs and tables. Request that they share the main lessons learned and the digital tools they found most useful. Open the floor for questions and comments from other students, promoting a constructive exchange of ideas.

Reflections

1. ❓ How did the use of digital tools facilitate the understanding of the concepts of quadratic functions? 2. ❓ What difficulties did you encounter when representing the quadratic function in graphs and tables and how did you overcome them? 3. ❓ How did the activities help to connect theoretical content with practical applications in everyday life?

360° Feedback

🔄 360° Feedback: Instruct students to carry out a 360° feedback stage, where each participant must provide feedback to all members of their group. Guide students to be specific about what each colleague did well and what could be improved, using the formula: 'I liked.../I suggest...'. Emphasize the importance of being constructive and respectful so that everyone can learn and grow from the feedback received.

Conclusion

Duration: (10 - 15 minutes)

📝 Purpose: This stage aims to consolidate the knowledge acquired throughout the lesson, providing a fun and reflective summary of the content. Additionally, it connects theoretical learning to practical and modern applications, reinforcing the relevance of the topic in everyday life and the current digital world.

Summary

🎉 Fun Summary: Congratulations, digital mathematicians! Today, you have become masters of quadratic functions. We explored how these functions create amazing parabolic graphs and how these magical curves can be represented in tables. From ball trajectories to maximum profit points, you have shown that you understand mathematics in action! 📈📊

World Connection

🌍 In the Modern World: Today's lesson was not just about formulas and graphs; it was about connecting mathematics to real life and the digital world. By using social media, simulations, and digital tools, mathematics was brought into our modern age. This not only makes learning more relevant but also shows how mathematics is everywhere, from social media algorithms to business optimization.

Practical Application

🛠️ Everyday Applications: Understanding quadratic functions is crucial as they are present in areas ranging from physics to economics. Knowing how to sketch and analyze these functions allows predicting and optimizing practical situations, such as calculating the trajectories of objects and maximizing profits. In a world where data-driven decision-making is increasingly important, these skills are fundamental.