Lesson Plan | Teachy Methodology | Thales' Theorem

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to provide a clear understanding of the objectives to be achieved during the lesson, establishing a solid foundation for students to actively engage in the proposed activities. This will help guide learning and ensure that everyone is aligned with the expectations of knowledge and practical application of the Theorem of Thales.

Main Objectives

1. Understand that a set of parallel lines cut by two distinct transversals results in proportional segments.

2. Apply the Theorem of Thales in different contexts to solve problems involving proportionality.

3. Use digital tools to investigate and demonstrate the application of the Theorem of Thales.

Side Objectives

1. Develop collaboration skills through group activities.
2. Encourage critical thinking when analyzing examples of the Theorem of Thales in the real world.

Introduction

Duration: 15 - 20 minutes

The purpose of this stage is to engage students from the beginning and spark their curiosity about the topic. By searching for interesting facts on their own, students begin to take an active role in learning, sharing their discoveries and strengthening the collective understanding of the Theorem of Thales.

Warming Up

The Theorem of Thales is a powerful mathematical tool that relates proportions in triangles and other geometric figures, based on the idea that parallel lines cut proportional segments on two transversals. To start the lesson, ask students to use their mobile phones to search for an interesting fact about the Theorem of Thales. This could be the story of Thales of Miletus, examples of the theorem's use in engineering and architecture, or other practical applications of proportionality in different contexts.

Initial Reflections

1. What is the Theorem of Thales and how can it be applied to proportionality problems?

2. What are some real-world examples where the Theorem of Thales is used?

3. How would you explain the idea of proportional segments to someone who has never heard of it?

4. What did you find interesting during your research on the Theorem of Thales?

Development

Duration: 70 - 75 minutes

The purpose of this stage is to provide students with a practical and creative experience in applying the Theorem of Thales, using digital tools and modern technologies. This will enable students to understand the importance of the theorem in various everyday contexts, developing collaboration skills, critical thinking, and the use of digital technologies.

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: Apply the Theorem of Thales in everyday situations through a creative and visually appealing explanation.

- Description: Students will become digital influencers and create a 3-minute video for a social network explaining the Theorem of Thales through everyday examples, such as building construction or furniture design. They will need to use visual concepts and video editing apps to make the explanation clear and engaging.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group should choose an everyday example where the Theorem of Thales can be applied.

• Students will use their phones to record a video of up to 3 minutes explaining the Theorem of Thales and how it applies to the chosen example.

• Encourage students to use video editing apps to add graphics and text that facilitate understanding.

• The videos should be shared on a common platform so that everyone can watch.

Activity 2 - Geometric Detectives ️‍♂️

> Duration: 60 - 70 minutes

- Objective: Develop skills of analysis and application of the Theorem of Thales in investigative and practical scenarios.

- Description: Students will become geometric detectives and investigate a virtual crime scene. Using graphic design software or an online image editing tool, they will need to analyze images and diagrams to find evidence of proportional segments and apply the Theorem of Thales to solve the case.

- Instructions:

• Divide students into groups of up to 5 people.

• Each group will receive a set of images and diagrams of a virtual crime scene.

• Use graphic design software or an online image editing tool to analyze the images.

• Identify proportional segments using the Theorem of Thales.

• Present the group's conclusions to the class, explaining how they used the Theorem of Thales to solve the case.

Activity 3 - Architecture Adventures 

> Duration: 60 - 70 minutes

- Objective: Apply the Theorem of Thales in a 3D modeling project, contextualizing its importance in architecture.

- Description: Students will use an online 3D modeling program to design a small architectural structure, such as a bridge or a building. They will need to apply the Theorem of Thales to ensure all proportions and dimensions are correct and create a digital report explaining the proportions used.

- Instructions:

• Divide students into groups of up to 5 people.

• Choose an architectural structure to model (bridge, building, etc.).

• Use an online 3D modeling program to draw the structure.

• Apply the Theorem of Thales to ensure proportions are correct.

• Create a digital report with screenshots of the 3D model and explanations of the proportions used.

• Present the 3D model and report to the class.

Feedback

Duration: 15 - 20 minutes

 Purpose: The purpose of this stage is to consolidate learning through the exchange of ideas and experiences. Group discussion and 360° feedback allow students to reflect on what they learned, identify strengths and areas for improvement, and appreciate different perspectives on the practical application of the Theorem of Thales. This also promotes an environment of respect and collaboration, essential for students' academic and personal development.

Group Discussion

 Group Discussion: Start by recalling the activities carried out and emphasizing the importance of the Theorem of Thales in different contexts. Ask each group to share their findings and experiences. Here is a brief script that can be used:

1. Ask each group to present their video, report, or 3D model, highlighting the application of the Theorem of Thales.
2. Request students to explain how they chose their everyday examples and the challenges faced during the activity.
3. Encourage students to discuss how the use of digital tools helped or hindered their understanding of the theorem.
4. Open the floor for questions and general comments from the class regarding the presentations.

Reflections

1.  Reflection Questions:

1. How can the Theorem of Thales be observed in your everyday life beyond the chosen example?
2. In what way did the use of digital tools influence your understanding of the Theorem of Thales?
3. What were the biggest challenges faced in the group during the activity and how did you overcome them?

360° Feedback

 360° Feedback: Guide students on the importance of providing constructive and respectful feedback. Each student should receive feedback from other members of their group. Suggest that they comment on:

1. Strengths of each member's collaboration.
2. Areas where each member can improve.
3. How each contributed to solving the activity and effectively applying the Theorem of Thales.

Conclusion

Duration: 10 - 15 minutes

 Purpose: The purpose of this stage is to consolidate the concepts learned throughout the lesson, connecting the Theorem of Thales with practical and modern applications. By summarizing the main points and reflecting on the relevance of the theorem in our daily lives, students will be able to internalize the knowledge more effectively and recognize the importance of mathematics in their lives and future careers.

Summary

 Fun Summary: Let's imagine the Theorem of Thales is a mathematical superpower! It helps us understand that when we draw several parallel lines and cut them with some transversal lines, we form segments that are proportional.  In other words, it's like dividing a delicious cake into equal parts without messing up the measurements! This may seem simple, but it is a powerful concept that helps us in many fields, from art to engineering.

World Connection

 In Today's World: The Theorem of Thales has deep roots, but its applications are extremely modern. Think of architects using 3D modeling software to design skyscrapers, or engineers designing amazing bridges. They all use this principle to ensure that everything is perfect and proportional. So, what we saw today is not just theory but a constant practice in various professions and ambitious projects in the modern world.

Practical Application

 Daily Applications: The Theorem of Thales may seem distant, but it is present in many parts of our daily lives. Whether decorating a room and ensuring that all the frames are aligned, drawing graphs, or even understanding the perspective of photos, this mathematical principle helps us maintain proportion and symmetry, making our creations more harmonious and precise.