Lesson Plan | Teachy Methodology | Trigonometry: Double/Triple Angle
| Keywords | Trigonometry, Double Angle, Triple Angle, Digital Methodology, Mathematics, High School, Practical Activities, Technology, Collaboration, Educational Videos, Escape Room, RPG, Digital Inclusion, Social Media, Active Learning |
| Required Materials | Phones, Computers, Internet Access, Escape Room Platform, Avatar Creation Tools (Bitmoji or similar), Digital Whiteboard, Projector/Media for displaying videos, Social Media Apps (fictional or real), Note-taking Materials (notebooks, pens) |
Objectives
Duration: 10 - 15 minutes
The purpose of this stage is to clearly present to students what will be covered in the lesson and what specific skills they will develop. This will help direct their expectations and mentally prepare them for the practical activities that will take place throughout the lesson.
Main Objectives
1. Understand and apply the double and triple angle formulas for angles.
2. Solve practical problems involving the calculation of sine, cosine, and tangent of double and triple angles.
Side Objectives
- Develop the ability to work collaboratively on mathematical problems.
- Encourage the use of digital resources and technological tools as support in learning trigonometry.
Introduction
Duration: 10 - 15 minutes
The purpose of this stage is to clearly present to students what will be covered in the lesson and what specific skills they will develop. This will help direct their expectations and mentally prepare them for the practical activities that will take place throughout the lesson.
Warming Up
To start the lesson, introduce the theme of trigonometry focusing on double and triple angles, highlighting their importance and practical applications, such as in engineering, physics, and other technological areas. Ask students to use their phones to look up an interesting fact about the topic. Encourage them to search for curiosities, modern applications, or even mathematical memes that involve trigonometry. This will help make the topic more accessible and relevant to their daily lives.
Initial Reflections
1. What are double and triple angles in trigonometry?
2. What is the importance of understanding the double and triple angle formulas?
3. Can you give examples of where these calculations are used in real situations?
4. What is the difference between the sine, cosine, and tangent functions when applied to double and triple angles?
Development
Duration: 70 - 75 minutes
The purpose of this stage is to allow students to deepen and apply the knowledge acquired about double and triple angles through practical and interactive activities. The proposed activities are designed to promote collaborative work, stimulate critical thinking, and connect mathematical learning to the students' everyday lives, using digital technologies as support tools.
Activity Suggestions
It is recommended that only one of the suggested activities be carried out
Activity 1 - Mathematical Influencers
> Duration: 60 - 70 minutes
- Objective: Explore the understanding of trigonometry applied to everyday life, developing communication and creativity skills through digital content creation.
- Description: Students will transform into digital influencers who need to explain to their followers the importance of double and triple angles in trigonometry. They will create a video or a series of posts on a fictional social media platform, using visual resources and detailed mathematical explanations.
- Instructions:
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Divide the class into groups of up to 5 students.
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Each group should choose a fictional social media platform (Instagram, TikTok, YouTube, etc.).
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Using their phones and/or computers, students should create a fictional mathematical influencer account.
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They should plan and create content, such as short videos, stories, and posts, explaining the concept of double and triple angles and demonstrating practical applications.
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Encourage the use of graphs, equations, and animations to make the posts visually appealing and informative.
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Groups should share their content on the fictional platform and comment on each other's posts, encouraging interaction and exchange of ideas.
Activity 2 - Mathematical Escape Room ️♂️
> Duration: 60 - 70 minutes
- Objective: Apply concepts of trigonometry in challenging situations, promoting teamwork and developing problem-solving skills.
- Description: Students will participate in a virtual Escape Room, where they need to solve a series of mathematical challenges related to double and triple angles to 'escape' from the room. They will use computers to access the Escape Room platform.
- Instructions:
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Divide the class into groups of up to 5 students.
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Each group should access the digital Escape Room platform (it can be a platform created by the teacher or adapted for the activity).
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The groups will face a series of mathematical challenges, including puzzles involving calculations of double and triple angles.
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For each challenge solved, students receive a hint to advance to the next level.
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The group that solves all the puzzles in the least amount of time will be the winner.
Activity 3 - The Sine Journey - RPG
> Duration: 60 - 70 minutes
- Objective: Engage students in a playful and interactive activity, encouraging the application of mathematical concepts through narrative and problem-solving.
- Description: Students will embark on an epic RPG (Role-Playing Game) journey, where they will need to solve mathematical puzzles related to double and triple angles to advance the story and earn rewards.
- Instructions:
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Divide the class into groups of up to 5 students.
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Each group should create a character using a digital avatar (can be done with tools like Bitmoji or other avatar creation apps).
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The teacher will act as the game master, narrating the story and presenting challenges to the groups.
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Groups must solve mathematical questions to advance the story, facing 'monsters' and overcoming obstacles related to double and triple angles.
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At the end of each challenge, groups earn 'experience points' and other digital items as rewards.
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At the end of the lesson, the group with the most experience points will receive a digital badge of 'Trigonometry Master'.
Feedback
Duration: 10 - 15 minutes
The purpose of this stage is to promote reflection and sharing of experiences lived during the practical activities. By discussing and evaluating in groups, students consolidate their learning, identify strengths and areas for improvement, and develop communication and constructive critique skills. The 360° feedback aims to encourage collaboration and mutual growth, providing an opportunity for each student to receive valuable insights about their performance.
Group Discussion
Promote a discussion with the entire class, where each group shares what they learned while performing the activities and their conclusions. Use the following script to introduce the discussion:
Introduction: Invite each group to briefly present the content they created and the main points they learned.
Highlights: Ask groups what were the most challenging and rewarding moments during content creation or puzzle solving.
Practical Applications: Encourage students to discuss how the concepts of double and triple angles can be applied in real-life situations outside the classroom and in future academic and professional activities.
Interactions: Ask students to comment on each other's work, highlighting strengths and providing constructive suggestions.
Reflections
1. What were the main challenges you encountered while working with double and triple angles? 2. How did the activity help consolidate mathematical knowledge and its practical application? 3. In what way did the use of digital and social platforms influence the way you learned the content?
360° Feedback
Conduct a 360° feedback step, where each student within their group should receive feedback from their peers. Instruct students to follow these guidelines for feedback:
Be Specific: Highlight specific actions and contributions that were positive during the activity.
Be Constructive: Offer improvement suggestions in a respectful and encouraging manner.
Be Balanced: Point out both strengths and areas that can be developed.
Explain the importance of constructive feedback for everyone's personal and academic growth.
Conclusion
Duration: 10 - 15 minutes
The purpose of this stage is to consolidate the knowledge presented during the lesson in a fun and engaging way, connecting mathematical concepts to the real world and highlighting their practical applications. This helps reinforce learning and shows students how trigonometry is relevant in their daily lives and future careers.
Summary
Super-Trigonometric Summary! Imagine that double and triple angles are superpowers that transform simple angles into mathematical heroes! We learned how to use these magical formulas to calculate the sine, cosine, and tangent of angles that are twice or three times larger. It's like multiplying adventures with a single click.
World Connection
Trigonometry in the Modern World In the digital era, where everything is just a click away, understanding double and triple angles can help from creating amazing graphics on social media to programming games and apps! Trigonometry is not just about math, it's about seeing the world from a new geometric and algebraic perspective.
Practical Application
Importance of Double and Triple Angles Knowing how to calculate double and triple angles is like having an extra tool in your mathematical survival kit. Whether for designing a bridge with more precision, adjusting sound wave frequencies, or even planning the perfect selfie angle, these formulas are essential!
