Lesson Plan | Teachy Methodology | Triangle Existence Condition

Objectives

Duration: 15 - 20 minutes

This stage aims to introduce and contextualize students regarding the main objectives of the lesson, ensuring they understand the importance of recognizing the metric conditions for constructing a triangle. In addition, it establishes learning expectations and prepares students for the practical activities that will follow.

Main Objectives

1. Recognize and understand the metric conditions necessary for the formation of a triangle.

2. Apply the concept of side sums in practical problems and everyday examples.

Side Objectives

1. Develop teamwork and collaboration skills.
2. Encourage logical reasoning and problem-solving abilities.

Introduction

Duration: 15 - 20 minutes

This stage aims to introduce and contextualize students regarding the main objectives of the lesson, ensuring they understand the importance of recognizing the metric conditions for constructing a triangle. In addition, it establishes learning expectations and prepares students for the practical activities that will follow.

Warming Up

To introduce the topic Triangle Existence Condition, briefly explain that a triangle is a fundamental geometric figure with three sides and three angles, and that there are certain requirements that must be fulfilled in order to construct it. Then, ask students to use their phones to research an interesting fact about triangles or their conditions of existence. This fact can be a mathematical curiosity, an application in engineering or architecture, or even a reference in their social media. Encourage them to share what they found with the class.

Initial Reflections

1. What do you understand about the conditions necessary for the existence of a triangle?

2. Did you find any interesting applications of triangles in the real world during your research?

3. Why do you think the sum of the lengths of two sides of a triangle needs to be greater than the length of the third side?

4. Has anyone used this concept in everyday situations? If so, how was it?

Development

Duration: 70 - 75 minutes

The purpose of this stage is to engage students through practical and creative activities that utilize technology, allowing them to apply the theoretical knowledge acquired in a contextualized and collaborative manner. These activities aim not only to reinforce content but also to make learning more meaningful and fun.

Activity Suggestions

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

Activity 1 - Triangle Influencer

> Duration: 60 - 70 minutes

- Objective: Make students explain, practically and creatively, the concept of the conditions for the existence of a triangle, using communication, video editing, and collaboration skills.

- Description: In this activity, students will become digital math influencers and create a short video in the style of a TikTok 'challenge' explaining the conditions for the existence of a triangle.

- Instructions:

• Divide the class into groups of up to 5 students.

• Explain that each group will need to create a video of up to 2 minutes where they creatively explain how the sum of the lengths of two sides of a triangle must be greater than the third side.

• Videos should be made using students' cell phones and may include elements such as graphics, skits, animations, or any other tool they find interesting.

• Groups should use free video editing apps suggested by the teacher, such as InShot or Kinemaster, to edit their video.

• After creation, the videos will be shared in a private class group on a communication platform (WhatsApp, Google Classroom, etc.) so that everyone can watch.

• Students watch their peers' videos and vote on the most creative ones. A Google form can be used for voting.

Activity 2 - Geometric Detectives

> Duration: 60 - 70 minutes

- Objective: Use digital simulations to explore and understand the necessary conditions for the existence of triangles, developing investigation, data recording, and teamwork skills.

- Description: Students will become math detectives and use an online triangle construction simulator to solve a mystery involving the creation of a valid triangle.

- Instructions:

• Divide the class into groups of up to 5 students.

• Provide a riddle in which the detectives need to find out which combinations of side lengths can form valid triangles.

• Each group should access an online triangle construction simulator, like GeoGebra, to test their hypotheses.

• Students should record their findings and explanations in a shared document (Google Docs).

• Ask groups to prepare a final report detailing the investigation process and the conclusions they reached.

• Groups present their reports to the class, explaining how they solved the mystery and the combinations of measures tested.

Activity 3 - Triangle Escape Room

> Duration: 60 - 70 minutes

- Objective: Promote the practical application of the conditions for the existence of triangles through a playful and collaborative activity, developing problem-solving and teamwork skills.

- Description: Students will participate in a themed virtual Escape Room, where they must solve a series of mathematical puzzles involving the conditions of existence of a triangle to 'escape' the room.

- Instructions:

• Divide the class into groups of up to 5 students.

• Explain that each group will participate in a virtual Escape Room created in Google Forms or another quiz platform.

• The puzzles include mathematical problems that students must solve to discover codes that will allow them to advance to the next room.

• Each group will need to collaborate and apply their knowledge about the conditions for the existence of triangles to solve the challenges within a set time (approximately 50 minutes).

• The groups that solve all the puzzles in the shortest time will be the winners.

• Conclude the activity by discussing the challenges faced and the strategies used to solve the problems.

Feedback

Duration: 20 - 25 minutes

This stage aims to consolidate learning through reflections and constructive feedback, promoting self-assessment and the development of critical and social skills. Group discussion and 360° feedback are essential for students to recognize their achievements as well as identify areas where they can improve, thus strengthening collaborative learning and mutual respect.

Group Discussion

Promote a group discussion with all students, where groups share what they learned from the experience and their conclusions. Suggest a brief script that the teacher can use to introduce this discussion:

1. Start by thanking all students for their engagement and collaboration in the activities.
2. Ask students how they felt during the activities and what was the most challenging and enjoyable part for them.
3. Ask each group to share an interesting discovery or insight gained during the activities.
4. Encourage students to reflect on how the use of technology facilitated or hindered their understanding of the topic.
5. Conclude by highlighting the importance of collaboration and the use of digital tools for future learning.

Reflections

1. What did you find most surprising or interesting about the conditions for the existence of a triangle? 2. How did the use of digital simulators and video editing apps help in understanding the topic? 3. What skills beyond mathematical knowledge did you develop during the activities? How can this be useful in your everyday life?

360° Feedback

Conduct a 360° feedback stage where each student should receive feedback from the other students in their group during the activity. Guide the class to ensure that the feedback is constructive and respectful. Open the discussion with the importance of feedback for personal and professional growth, and suggest that they follow the format of 'Strengths' and 'Areas for Improvement.' Provide examples to help guide the feedback, such as: 'You explained the concepts very well during the video' or 'I thought you could have been more involved in the video editing.'

Conclusion

Duration: 10 - 15 minutes

🔍 Purpose: This stage aims to consolidate learning through a fun and contextualized review, highlighting the relevance of the content to the contemporary world and its practical applications. It is a crucial moment to reinforce the importance of the learned concept and engage students in its application to real situations.

Summary

🎯 Summary: Let's remember that the condition for the existence of a triangle depends on the rule that the sum of the lengths of two sides must be greater than the length of the third side. Imagine that this rule is like a secret password that the triangle needs to enter correctly to exist in the geometric world! 🌟

World Connection

🌍 In the World: Today, we learned how mathematics is present in our lives, whether in building bridges, in futuristic architectural designs, or even in games and animations. The conditions for the existence of the triangle ensure that these structures are safe and stable. By understanding this rule, we are more connected to the modern digital world and its endless possibilities for application!

Practical Application

✨ Applications: Understanding the conditions for the existence of triangles is essential for various fields such as architecture, engineering, and design. It helps ensure that structures are safe and functional, as well as allowing the creation of innovative and efficient shapes in everyday projects.