Lesson Plan | Teachy Methodology | Geometric Progression: Terms

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to guide students towards the main objectives that will be achieved throughout the class. This initial moment provides clarity on the fundamental concepts of geometric progression, preparing them for subsequent practical activities and digital applications. The teacher must ensure that all students understand the importance of the topic, both in the academic context and in its application in modern and digital life.

Main Objectives

1. Recognize the concept of Geometric Progression (GP).

2. Calculate the nth term of a GP using appropriate formulas.

3. Apply GP knowledge in practical and digital contexts, such as exponential growth on social networks.

Side Objectives

1. Promote collaboration among students through group activities.
2. Encourage the use of digital tools for solving mathematical problems.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to engage students from the beginning, connecting the concept of Geometric Progression to practical and relevant examples in their digital lives. By seeking and sharing information, students activate prior knowledge and begin to see the applicability of what they have learned. This initial moment also serves to warm up the class for active participation in the following activities.

Warming Up

To start the lesson on Geometric Progression (GP), briefly explain that a GP is a numerical sequence where each term after the first is found by multiplying the previous term by a non-zero constant, called the ratio. Then, ask students to use their phones to research and share an interesting fact or practical application about geometric progressions in the digital world, such as the exponential growth of followers on social networks or the viral spread of content on the internet.

Initial Reflections

1. What is the definition of a Geometric Progression (GP)?

2. How do you think GP can be applied in the context of social networks?

3. Did you find any interesting examples of GP in your research? Share with the class.

4. What is the difference between a GP and an Arithmetic Progression (AP)?

5. How do you calculate the nth term of a GP?

Development

Duration: 70 - 85 minutes

The purpose of this stage is to provide a deep and engaging learning experience, allowing students to apply theoretical concepts of geometric progression in contexts that are relevant and motivating for them. Through the use of technologies and playful activities, the goal is to make mathematics more accessible and interesting, encouraging active participation and collaborative work.

Activity Suggestions

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

Activity 1 - The Journey of the Digital Influencer 📈

> Duration: 60 - 70 minutes

- Objective: Apply concepts of geometric progression in practical and familiar contexts, promoting understanding through a playful and digital approach.

- Description: Students will create a simulation of the growth of followers of a digital influencer using geometric progression. The activity involves creating a 'timeline' showing the exponential growth of followers over several weeks.

- Instructions:

• Divide students into groups of up to 5 people.

• Ask students to choose a fictitious 'digital influencer' who will be the protagonist of the activity.

• Each group must create a social media profile for the influencer using a digital tool, such as Canva or a fictitious Instagram.

• Students must determine a geometric progression formula to model the growth of followers. For example, if the ratio is 2, and the influencer starts with 10 followers, the sequence would be 10, 20, 40, 80, etc.

• Students must create a visual 'timeline' showing the growth of the influencer over the weeks, using graphics and digital presentations.

• Each group must present the 'timeline' and explain how they used geometric progression to calculate the growth of followers.

Activity 2 - Unraveling the World of Viral Videos 🎥

> Duration: 60 - 70 minutes

- Objective: Develop skills to calculate geometric progressions and apply this knowledge to real situations of exponential growth in the digital world.

- Description: Students will analyze the growth of views of a viral video on the internet, using geometric progression to predict the number of views over time.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group must choose a recent viral video (they can use their social networks or platforms like YouTube).

• Students must investigate initial view data and try to obtain a daily growth rate.

• Using the found ratio, students must calculate the predicted number of views for the next days, weeks, or months using the geometric progression formula.

• Groups must present their predictions in the form of graphs, tables, or digital presentations, explaining the calculations made and the logic behind the forecasts.

• Groups can compare their predictions with real data if available to check the accuracy of their calculations.

Activity 3 - Gamification: The Numbers Race 🚀

> Duration: 60 - 70 minutes

- Objective: Promote collaboration, healthy competition spirit, and practical application of geometric progression concepts through a gamified approach.

- Description: Students will participate in a gamified competition where they will solve challenges involving geometric progressions to advance in the game.

- Instructions:

• Divide students into groups of up to 5 people.

• Explain the rules of the game: each correctly solved challenge allows the group to advance one 'level' in the competition.

• Present a series of challenges involving geometric progressions, such as finding the nth term of a sequence or calculating the ratio of a given GP.

• Students must use their phones or computers to solve the challenges and submit their answers through a digital platform, such as Google Forms or Kahoot.

• At each level, the challenges become progressively more difficult, encouraging collaboration and critical thinking.

• At the end, the group that advances the most levels is declared the winner and may receive a symbolic prize.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to promote a deep reflection on the activities carried out, allowing students to consolidate their learning and benefit from a mutual exchange of perspectives. The group discussion and 360° feedback encourage critical analysis, collaboration, and the development of interpersonal skills, essential in both academic contexts and the digital world.

Group Discussion

Promote a group discussion with all students, where groups share what they learned while carrying out the activities and their conclusions. To introduce this discussion, follow a brief script:

1. Start: Begin by thanking everyone for participating in the activities and praise the effort of the groups.
2. Sharing: Ask each group to present a brief summary of their activities, highlighting the main challenges and learnings.
3. Interaction: Encourage students to ask each other questions, promoting an environment of idea exchange and reflections.
4. Conclusion: Finish by highlighting how the concepts of geometric progression can be applied in other contexts of digital life and encouraging students to continue exploring the topic.

Reflections

1. What were the biggest challenges you encountered when applying geometric progression in the proposed activities? 2. How can understanding Geometric Progression be useful in your daily activities, especially in the digital world? 3. Did you notice any difference between the predictions made and the real data? What may have caused these differences?

360° Feedback

Instruct the class to conduct a 360° feedback session, where each student should receive feedback from other members of their group. Guide students to follow these guidelines so that the feedback is constructive and respectful:

1. Respect: Remind students of the importance of maintaining respect throughout the feedback process.
2. Specificity: Ask students to be specific in their comments, pointing out both positive aspects and areas for improvement.
3. Constructiveness: Advise that feedback should be constructive, focusing on how peers can enhance their skills and future collaborations.
4. Reciprocity: Encourage everyone to participate actively and equally, promoting an environment of mutual growth.

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to synthesize the learning in an engaging and fun way, connecting it with the dynamics of the current world. This animated summary helps solidify the concepts, highlighting their practical importance and relevance in students' digital lives. With this, the aim is to motivate them to continue exploring mathematics with interest and curiosity. 🌟📚

Summary

🎉 Animated Summary! 🎉 Let's hop on the Geometric Progression Express! 🚂💨 We learned that a Geometric Progression (GP) is a numerical sequence where each term is found by multiplying the previous term by a constant known as the ratio. We saw magical formulas to calculate any term of the GP, like exponential growth (1, 2, 4, 8, ...), where each number is double the previous one! But we didn't stop there! We applied our knowledge to simulate the growth of followers of digital influencers, predict views of viral videos, and even played a gamified race solving GP problems! 🚀👾

World Connection

🌐 Connecting with the Modern World 🌐 This week's lesson showed how mathematics, especially Geometric Progression, is intertwined with today's digital world. From the explosive growth of followers on social networks to the viral dissemination of content on the internet, GPs are everywhere! This connection to modern reality makes studying not only relevant but also exciting and applicable to students' daily lives. 📱💻

Practical Application

🔧 Applications in Daily Life 🔧 Understanding Geometric Progression is essential for analyzing and predicting patterns of exponential growth. This is fundamental, for example, for anyone wanting to work with statistics, data analysis, digital marketing, or any field involving rapid growth and expansion. Knowing how numbers behave in a GP allows for more informed and strategic decision-making in various everyday situations. 📊✨