Lesson Plan | Teachy Methodology | Exponential Function: Inputs and Outputs

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to contextualize and clearly establish the learning objectives for the students, allowing them to understand what is expected of them by the end of the lesson. By defining the objectives, it ensures that both the teacher and the students are aligned regarding the focus and desired outcomes, promoting a more organized and directed teaching environment.

Main Objectives

1. Identify inputs (x) and outputs (y) of exponential functions in different contexts.

2. Solve applied problems involving calculations of inputs and outputs in exponential functions.

Side Objectives

1. Develop critical thinking skills when analyzing graphs and tables of exponential functions.
2. Use digital tools to visualize and understand the dynamics of exponential functions.

Introduction

Duration: 10 - 15 minutes

The purpose of this stage is to warm up the students to the lesson's theme, creating a sense of relevance and connection to the real world. By using information research on their phones, autonomy and curiosity are promoted. The key questions serve to initiate an initial debate, activating the students' prior knowledge and preparing them for the practical activities that will follow.

Warming Up

To introduce the topic of exponential functions, explain to the students that this function is widely used in various fields such as economics, biology, and computer science. Ask the students to use their mobile phones to find an interesting fact or a real example of the application of exponential functions. Give them a few minutes to research and then ask some students to share what they found with the class.

Initial Reflections

1. What is an exponential function?

2. Where can we find exponential functions in real life?

3. What is the importance of exponential functions in different areas of knowledge?

4. What are the characteristics of an exponential function?

5. How can we identify the inputs (x) and outputs (y) in an exponential function?

Development

Duration: 70 - 80 minutes

The purpose of this stage is to provide students with a practical, playful, and contextualized experience using digital technologies, allowing them to apply and deepen their knowledge of exponential functions. The activities aim to promote engagement, collaboration, and the development of relevant digital skills in the modern world.

Activity Suggestions

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

Activity 1 - Digital Influencers and Exponential Growth 📈

> Duration: 60 - 70 minutes

- Objective: Understand the concept of exponential function through a practical and current context, using digital tools and data analysis.

- Description: Students will divide into groups to analyze the exponential growth of a fictional digital influencer's followers over six months. Each group will use graphs and tables, as well as simulate posts and digital marketing strategies that will impact follower growth or decline. They will use digital tools like Google Sheets to plot data and identify growth patterns.

- Instructions:

• Divide the class into groups of up to five people.

• Each group will receive a fictional profile of a digital influencer with initial follower data.

• Students should use their phones or computers to search for digital marketing strategies that affect follower growth.

• Use Google Sheets to create a table and a graph showing follower growth over time.

• Simulate posts and actions on social media that may impact the number of followers and record this data in Google Sheets.

• Analyze the resulting graphs to identify patterns of exponential growth.

• At the end, each group prepares a brief presentation on their conclusions and strategies used.

Activity 2 - Hacker Challenge of Exponential Growth 🖥️

> Duration: 60 - 70 minutes

- Objective: Apply the concept of exponential function in a digital security context, using simulations with technological tools.

- Description: Students will be challenged to solve a digital security problem where they must find the exponential formula that represents the growth of a digital threat over time. Using simulations and specific software, they will identify patterns and propose solutions to mitigate the problem.

- Instructions:

• Divide the class into groups of up to five people.

• Each group will receive a fictional scenario about a digital threat (such as the spread of a computer virus).

• Students should use their devices to research the exponential growth of digital threats and security software.

• Create a simulation on the computer using an online platform (like Graphing Calculator) to track the growth of the threat over time.

• Determine the exponential formula that accurately represents the growth of the threat.

• Propose strategies to mitigate the exponential growth of the threat and discuss in the group.

• Each group should share their findings and strategies in a brief presentation.

Activity 3 - Gamifying Exponential Growth 🕹️

> Duration: 60 - 70 minutes

- Objective: Reinforce the understanding of exponential functions through a playful and interactive approach, dynamically utilizing gamification.

- Description: Students will participate in an educational game where they will be challenged to complete missions involving calculations of exponential functions. Using gamification applications and online platforms, they will solve problems, unlock levels, and earn virtual rewards while reinforcing their knowledge of exponential functions.

- Instructions:

• Divide the class into groups of up to five people.

• Each group will use an educational gamification app or platform, such as Kahoot! or Quizizz, to participate in the game.

• Students should create an account on the chosen platform and access the game prepared on exponential functions.

• Solve the missions and challenges, which will include calculations of inputs (x) and outputs (y) of exponential functions.

• Upon completing each mission, they unlock new levels and receive virtual rewards.

• Monitor the progress of each group and assist with tips and additional explanations as needed.

• At the end of the game, each group should reflect on their learning and share their strategies for solving the challenges.

Feedback

Duration: (20 - 25 minutes)

The purpose of this stage is to consolidate learning, promote critical reflection, and foster the development of social and communicative skills. Through group discussion and 360° feedback, students will have the opportunity to evaluate their own contributions and learn from their peers' experiences, making the learning process more collaborative and enriching.

Group Discussion

Facilitate a group discussion with all students, encouraging each group to share what they learned during the practical activities and their conclusions. Use the following outline to guide the discussion:

1. Introduction: Briefly remind the objectives of the lesson and the activities carried out.
2. Sharing: Ask each group to present their main discoveries and strategies used in the activities.
3. Critical Analysis: Request that the other groups ask questions and comment on the presentations, promoting constructive debate.
4. Conclusion: Summarize the main points discussed, highlighting best practices and lessons learned.

Reflections

1. How did data analysis help you understand exponential growth? 2. What were the biggest challenges while performing the activities and how did you overcome them? 3. How can you apply knowledge about exponential functions to other situations in daily life?

360° Feedback

Instruct the students to carry out a 360° feedback, where each student must give and receive feedback from their group peers about collaboration and participation in the activities. Guide them to ensure the feedback is constructive and respectful, using phrases like 'I liked when you...' or 'You could improve on...'. Highlight the importance of recognizing the efforts and contributions of all group members.

Conclusion

Duration: (10 - 15 minutes)

✒️ Purpose: The purpose of this stage is to provide a cohesive and reflective closure to the lesson content, connecting theoretical concepts to the students' reality. By summarizing the main points in a fun way and relating them to the current world, the goal is to reinforce learning and spark continuous interest in the topic. This conclusion aims to consolidate knowledge, showing its practical relevance and applicability in daily life, encouraging students to see mathematics as a powerful tool present in modern dynamics.

Summary

🎲 Fun Summary: Imagine you are playing a super exciting board game! Every time you roll the dice, the number of followers of a digital influencer, or the spread of a computer virus, magically doubles! This is how exponential functions work! They take a small number and, with each step, make it grow rapidly, like a magician pulling rabbits out of a hat! 🐰✨

World Connection

🌐 In Today's World: Today's lesson showed how the concepts of exponential functions are everywhere! From viral videos on TikTok and Instagram to the spread of information (good and bad) on the internet. Understanding how something can grow exponentially helps decode the success of trends on social media and the importance of digital strategies in the modern era. 📱💡

Practical Application

🔧 Applications: Exponential functions are not just abstract formulas on paper; they are present in population growth, economics, computer science, and even the spread of epidemics. Understanding these concepts can help solve everyday problems, such as planning business growth or understanding the impact of a marketing campaign.