Lesson Plan | Teachy Methodology | Spatial Geometry: Dihedrals and Trihedrals
| Keywords | Spatial Geometry, Dihedrals, Trihedrals, Digital Methodology, Active Learning, 3D Modeling, Digital Games, Augmented Reality, Social Media, Critical Thinking, Problem Solving, Collaboration |
| Required Materials | Computers or tablets, Internet access, 3D modeling software (Tinkercad, SketchUp or similar), Cameras or cell phones for video recording, YouTube account or similar platform for video posting, Instagram account or Canva for creating posts, Augmented reality app or Google Earth, Projector or screen for presenting videos and posts, Material for note-taking and creating digital reports |
Objectives
Duration: 10 to 15 minutes
The purpose of this stage is to clearly establish the objectives of the lesson, preparing students for what will be addressed and ensuring that they understand the specific skills they need to acquire. This section also motivates students by connecting the content with their realities and showing the practical relevance of the concepts of dihedral and trihedral angles.
Main Objectives
1. Understand the concepts of dihedral and trihedral angles and how they are defined by planes.
2. Apply knowledge of dihedrals and trihedrals to solve geometric problems.
Side Objectives
- Connect the concepts of spatial geometry with everyday situations and the digital world.
- Develop critical thinking skills and collaborative problem-solving.
Introduction
Duration: 10 to 15 minutes
The purpose of this stage is to engage students from the start by connecting abstract mathematical concepts with their everyday and digital realities. By using mobile devices for quick research, students familiarize themselves with the topic dynamically, preparing for an initial debate that reinforces prior knowledge.
Warming Up
🟢 Introduction: Start the class by briefly explaining what dihedrals and trihedrals are. A dihedral angle is formed by two intersecting planes, while a trihedral angle is defined by three planes that meet at a common point. Ask students to use their cell phones to search for an interesting fact or curiosity about dihedrals and trihedrals. This quick research activity will help them connect with the topic in a personal and digital way.
Initial Reflections
1. 🔍 What differentiates a dihedral angle from a trihedral angle in geometric terms?
2. 🔍 How do you imagine that dihedrals and trihedrals are used in practical applications of everyday life?
3. 🔍 Did you find any interesting fact or unexpected application about dihedrals or trihedrals?
4. 🔍 Considering spatial geometry, what are the main difficulties you identify when working with dihedrals and trihedrals?
Development
Duration: 70 to 80 minutes
This stage aims to transform students' theoretical learning into applied practice, using digital tools and modern contexts. By promoting group activities, it is possible to encourage collaboration, creativity, and communication, which are essential for the holistic development of students.
Activity Suggestions
It is recommended that only one of the suggested activities be carried out
Activity 1 - Dihedrals and Trihedrals in the World of Games 🎮
> Duration: 60 to 70 minutes
- Objective: Apply concepts of spatial geometry using modern digital tools, fostering creativity and digital communication skills.
- Description: Students will create a scene in a 3D modeling software (like Tinkercad or SketchUp), where they will identify and build dihedrals and trihedrals present in the elements of the scene. Then, they will record an explanatory video for a fictional YouTube channel about how these concepts are applied in 3D modeling and their importance in digital games.
- Instructions:
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Form groups of up to 5 students.
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Use the chosen 3D modeling software to create a scene that includes dihedrals and trihedrals.
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Each group must find at least three dihedrals and two trihedrals in the created scene.
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Record a 5-minute video explaining the presence of the dihedrals and trihedrals, their characteristics, and relevance to the design of the scene.
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Post the video on the chosen video-sharing platform and share the link with the class.
Activity 2 - Math Digital Influencers 📱
> Duration: 60 to 70 minutes
- Objective: Develop communication and creativity skills using social networks as an educational tool, bringing mathematical concepts closer to students' everyday lives.
- Description: Students will create a series of Instagram posts, simulating the account of a digital influencer who teaches concepts of spatial geometry. The posts will include images, videos, and infographics about dihedrals and trihedrals, explaining their definitions and how to identify them in different contexts.
- Instructions:
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Form groups of up to 5 students.
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Create an Instagram account or a presentation on Canva to simulate the account of the digital influencer.
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Plan and create at least five posts that include: a definition of dihedrals and trihedrals, illustrated examples, practical applications, and an interactive activity for followers.
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Make sure to use relevant hashtags and appropriate language to engage the young audience.
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Present the posts to the class, explaining the reasoning behind each one and how they help to understand the concepts of spatial geometry.
Activity 3 - Virtual Treasure Hunt: Dihedrals and Trihedrals 🕵️
> Duration: 60 to 70 minutes
- Objective: Encourage critical thinking and problem-solving skills among students, as well as familiarizing them with augmented reality technologies for the learning of mathematical concepts.
- Description: Students will participate in a virtual treasure hunt where they must solve riddles and challenges related to dihedrals and trihedrals using augmented reality software or an interactive mapping app like Google Earth.
- Instructions:
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Form groups of up to 5 students.
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Use the chosen app to explore virtual environments in search of dihedrals and trihedrals.
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Each riddle or challenge encountered must be solved with a detailed explanation of the concept of dihedrals and trihedrals and their characteristics.
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Record the solution of each challenge with screenshots and explanatory notes.
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At the end, each group must present a digital report (in presentation or document format) with the challenges faced and the solutions found.
Feedback
Duration: 20 to 25 minutes
The purpose of this stage is to reflect on the learning process, sharing experiences and consolidating the knowledge acquired. The 360° feedback allows students to develop self-assessment and constructive communication skills, which are essential for academic and personal growth. The group discussion provides an opportunity for all students to benefit from the different perspectives and approaches used by their classmates.
Group Discussion
🗣️ Group Discussion: After all activities, gather students for a group discussion. Each group must share their experiences, challenges faced, solutions found, and what they learned during the execution of the activities. Follow a brief outline to introduce the discussion:
- Ask each group to present a summary of the activities carried out.
- Request that they share one positive aspect and one challenge they faced.
- Encourage students to ask each other questions about their findings.
- Conclude the discussion by highlighting the most important points that emerged from the groups' presentations.
Reflections
1. 📌 What were the main difficulties you encountered in identifying and constructing dihedrals and trihedrals during the activities? 2. 📌 How did digital tools facilitate or hinder the understanding of the concepts of dihedrals and trihedrals? 3. 📌 In what way do you think the knowledge of dihedrals and trihedrals can be applied in other subjects or in everyday life?
360° Feedback
🔄 360° Feedback: Instruct students to conduct a 360° feedback step, where each student must receive feedback from other group members. Guide the class to ensure that feedback is constructive and respectful, following these guidelines:
- Be Specific: Provide clear examples of what worked well and where there is room for improvement.
- Be Positive: Start with positive aspects before addressing points for improvement.
- Be Respectful: Use language that is encouraging and not offensive.
- Be Balanced: Try to provide a balanced number of positive feedbacks and suggestions for improvement.
Conclusion
Duration: 10 to 15 minutes
🎯 Purpose: This final stage concludes the lesson, helping students to consolidate the knowledge acquired in a fun and contextualized way. By summarizing and reflecting on the concepts learned and their practical applications, students are encouraged to see the relevance of the content beyond the classroom, motivating them to continue exploring and learning in an autonomous and engaged manner.
Summary
🔮 Fun Summary: Imagine you are inside an augmented reality game, where dihedrals and trihedrals are the keys to unlocking new levels! 🌟 During the class, we explored the concepts of dihedral angle (the intersection of two planes) and trihedral angle (the intersection of three planes) through 3D modeling, creating content for social media, and solving riddles in a virtual treasure hunt. Each activity was a piece of the puzzle to better understand spatial geometry! 🧩✨
World Connection
🌍 In the Current World: Spatial geometry is everywhere around us, from the architecture of cities to the graphics of the video games we love to play. With the advancements in digital technologies, such as augmented reality and 3D modeling, understanding concepts like dihedrals and trihedrals becomes increasingly relevant. They cease to be mere abstract figures from books to become essential tools in areas like design, engineering, and digital entertainment. 🎮🏙️
Practical Application
🔧 Applications in Daily Life: With the knowledge gained about dihedrals and trihedrals, students can see how these concepts are applied in constructing sturdy structures, creating visual effects in movies and games, and even solving complex design and engineering problems. This understanding opens doors to countless professional opportunities in technological and scientific fields. 🚀🏗️
