Lesson Plan | Teachy Methodology | Relationships and equations of magnitudes

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to ensure that students understand the main concepts that will be addressed during the lesson, contextualizing them in a way that they feel prepared to apply this knowledge in practical activities. This initial preparation is essential to facilitate the understanding of proportionality relationships and the graphical and algebraic representation of these relationships, promoting a solid foundation for the development of proposed mathematical skills.

Main Objectives

1. Identify relationships between directly and inversely proportional quantities.

2. Express proportionality relations through algebraic sentences.

3. Associate first-degree linear equations with two unknowns to lines on the Cartesian plane.

Side Objectives

1. Encourage the use of digital tools for the visualization and analysis of graphs.
2. Develop collaborative problem-solving skills in mathematics.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to ensure that students understand the main concepts that will be addressed during the lesson, contextualizing them in a way that they feel prepared to apply this knowledge in practical activities. This initial preparation is essential to facilitate the understanding of proportionality relationships and the graphical and algebraic representation of these relationships, promoting a solid foundation for the development of proposed mathematical skills.

Warming Up

To begin the study of relationships and equations of quantities, briefly explain that this topic involves understanding how two variables can be related in a proportional manner and how this relationship can be mathematically represented by algebraic sentences and graphically on the Cartesian plane. Then, ask students to use their phones to find an interesting fact about the topic. This may include examples of direct and inverse proportionality in real life, such as the speed of a car and travel time, or fuel consumption and distance traveled.

Initial Reflections

1. What are some examples of directly proportional quantities you found?

2. And what about inversely proportional quantities? Any interesting examples?

3. How can we mathematically represent these relationships?

4. In what ways can social media or other digital tools help us visualize these relationships?

5. What is the importance of understanding these relationships in our daily lives?

Development

Duration: 70 to 80 minutes

The purpose of this stage is to provide students with applied and contextualized learning, allowing them to explore mathematical concepts of direct and inverse proportionality through practical and collaborative activities. By using digital tools, students not only reinforce their theoretical understanding, but also develop analysis and communication skills, essential for the modern world.

Activity Suggestions

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

Activity 1 - 🔢 Mathematical Digital Influencers

> Duration: 60 to 70 minutes

- Objective: Apply the concepts of direct and inverse proportionality in a realistic and modern context, using digital tools to represent and analyze data.

- Description: Students will be challenged to create an advertising campaign for a fictional brand, using concepts of direct and inverse proportionality. They will need to calculate and graphically represent how different variables affect the results of the campaign.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group should choose a fictional brand and define two parameters that will be directly and inversely proportional. For example, for a digital marketing campaign, they might choose the number of posts and audience engagement (directly proportional) and the cost of posts and financial return (inversely proportional).

• Using spreadsheet software (Google Sheets), students must insert fictional data for their variables and create graphs that represent these relationships.

• Each group should create a slide presentation (Google Slides) to explain their findings, including the graphs and the algebraic sentences that represent these relationships.

• Finally, each group presents its campaign to the class, explaining how the concepts of proportionality influenced their decisions.

Activity 2 - 📊 Gamification: The Proportions Game

> Duration: 60 to 70 minutes

- Objective: Strengthen students' understanding of proportions and equations through a playful and interactive approach, encouraging collaboration and active learning.

- Description: Students will be divided into teams to participate in an online interactive game that challenges their knowledge of direct and inverse proportionality. They will need to solve problems and earn points as they advance through the game’s stages.

- Instructions:

• Divide students into groups of up to 5 people.

• Use a gamification platform like Kahoot or Quizizz to create an interactive game with questions about direct and inverse proportionality.

• Each team should access the game using their phones or computers.

• The game problems should involve identifying proportional relationships and formulating algebraic sentences for these relationships.

• The more advanced questions should ask students to graphically represent the proportional relationships using their devices.

• At the end of the game, the teams with the highest scores are recognized and receive a symbolic prize, such as digital certificates of 'Masters of Proportion'.

Activity 3 - 📐 Storytelling with Social Media: The Journey of Proportions

> Duration: 60 to 70 minutes

- Objective: Incorporate mathematics into the context of social media, allowing students to practice mathematical communication through visual and graphic narratives.

- Description: Students will create a series of posts for a fictional social media platform, telling a story that involves using direct and inverse proportions to solve everyday problems. The posts should include graphs and mathematical explanations.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group should choose a daily scenario where they can identify relationships of direct and inverse proportionality, such as preparing a culinary recipe or managing a household budget.

• Using a graphic design tool like Canva, students should create a series of posts that tell the story of the chosen scenario, highlighting the calculations and graphs of the proportional relationships.

• Each group should create at least five posts, including an introduction, three that develop the problems and solutions in the proportional relationships, and a conclusion.

• Finally, the groups present their stories to the class, explaining how they applied the concepts of proportionality.

Feedback

Duration: 25 to 30 minutes

The purpose of this stage is to consolidate learning through socialization and collective reflection, providing students the opportunity to critically evaluate their practices, share knowledge, and receive constructive feedback. This process of reflection and idea exchange reinforces the concepts learned and promotes a collaborative and engaging learning environment.

Group Discussion

💬 Group Discussion: After completing the activities, gather students in a circle or use a video conferencing tool to promote a group discussion. Use the following outline to guide the discussion:

1. General Introduction: 'Now that we have completed our activities, let's share our discoveries and experiences. Each group will have a few minutes to present their conclusions.'

2. Group Presentations: Allow each group to briefly share the results of their activities, highlighting the graphs, algebraic sentences, and identified proportional relationships.

3. Debate: Encourage students to ask questions and provide constructive feedback to peers about their presentations. Ask groups what their main challenges were and how they overcame them.

4. Final Reflection: Ask students to reflect on how using digital tools influenced their learning and how this approach might be applied in other subjects.

Reflections

1. 📊 Reflection Questions:

1. 'What did you find most challenging when trying to graphically represent proportional relationships?'

2. 'How did the use of digital tools, such as spreadsheets and graphic design software, facilitate or complicate the learning process?'

3. 'How do you imagine that the knowledge of direct and inverse proportionality can be useful in everyday life and in future careers?'

360° Feedback

🔄 360° Feedback: After the group discussion, instruct students to conduct a round of 360° feedback within their groups. Each student should prepare constructive feedback for other group members, highlighting strengths and suggesting areas for improvement. Guide the class to ensure that feedback is respectful and positive, using sentences like 'I liked that...' and 'I suggest that...'. This helps build a collaborative and supportive learning environment.

Conclusion

Duration: 10 to 15 minutes

🎯 Purpose 🎯: This stage serves to consolidate and reflect on learning, showing how the mathematical concepts discussed are relevant in various contexts of the modern world. The fun summary reinforces students' memory, while the discussion on practical applications keeps learning relevant and engaging.

Summary

🎉 Summary 🎉: Let's think of the lesson as a digital party! We reviewed the relationships between directly and inversely proportional quantities, expressed these relationships with algebraic sentences, and even drew lines on the Cartesian plane. We used digital tools to be the trendiest mathematical influencers and ventured into interactive games to reinforce our knowledge. In the end, each group shared their campaigns and stories in an authentic presentation marathon! 🚀📊

World Connection

🌐 In the World 🌐: The lesson connected with the current world by using modern contexts such as advertising campaigns and social media, where proportionality is present. Digital tools are essential today, whether for creating cool graphs or developing analytical skills that are valued in any future career.

Practical Application

🔍 Applications 🔍: Knowing how to identify and represent proportional relationships is vital, whether to calculate travel time, adjust culinary recipes, or even manage a budget! Understanding how two variables relate helps us make more informed and effective decisions in our daily lives.