Lesson Plan | Teachy Methodology | Trigonometric Function: Graphs

Objectives

Duration: 10 to 15 minutes

The purpose of this stage of the lesson plan is to clearly define the main and secondary objectives that students should achieve by the end of the lesson, ensuring that the focus is on the essential skills of describing, drawing, and interpreting graphs of trigonometric functions. This stage also aligns expectations and prepares students to use digital tools and work collaboratively, providing an active learning environment that is contextualized with the digital reality of the students.

Main Objectives

1. Describe graphs of trigonometric functions, identifying characteristics such as amplitude, period, phase, and vertical shift.

2. Accurately draw graphs of basic trigonometric functions and their variations.

3. Extract key information from graphs of trigonometric functions, such as period and roots, to solve practical problems.

Side Objectives

1. Encourage the use of digital tools to explore and visualize graphs of trigonometric functions.
2. Promote collaboration among students to interpret and analyze information obtained from the graphs.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to spark students' interest in the topic through an active and participatory beginning. By using mobile devices to look for information and discussing in class, students contextualize their learning with their digital and everyday reality. Moreover, the key questions help activate the students’ prior knowledge, preparing them for the practical activities that will follow.

Warming Up

Start the class by introducing the topic of trigonometric functions and their graphs. Briefly explain that trigonometric functions, such as sine, cosine, and tangent, are fundamental in mathematics and have various practical applications, from engineering to music. Then, ask students to use their phones to find an interesting fact or a practical application of trigonometric functions in the real world. Encourage them to share their findings with the class.

Initial Reflections

1. What are the main characteristics of the graphs of sine, cosine, and tangent functions?

2. How can we identify the period of a trigonometric function from its graph?

3. What are the visual differences between the graphs of sine and cosine functions?

4. What types of real-world problems can be solved using graphs of trigonometric functions?

5. How do vertical and horizontal shifts affect the graph of a trigonometric function?

Development

Duration: 60 to 75 minutes

The purpose of this stage is to provide students with a practical and collaborative experience in exploring graphs of trigonometric functions. The proposed activities encourage the use of digital technologies and modern tools, contextualizing learning in an innovative and motivating way. Additionally, these activities aim to develop communication skills, problem-solving, and critical thinking, making learning more engaging and meaningful.

Activity Suggestions

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

Activity 1 - Drawing with Digital Influencers 

> Duration: 60 to 70 minutes

- Objective: Develop skills in creating and interpreting graphs of trigonometric functions, integrating them with digital and visual communication.

- Description: Students will create a post for a social media where they must explain and draw graphs of trigonometric functions. They will need to use image and video editing applications to create educational and visually appealing content, simulating being digital influencers teaching mathematics.

- Instructions:

• Form groups of up to 5 students.

• Ask them to choose a trigonometric function (sine, cosine, or tangent).

• Each group must create an explanatory post for a social media (Instagram, TikTok, or YouTube).

• Use image editing apps (such as Canva) and video editing apps (such as InShot) to create the content.

• Include in the post the description of the function, the graphs, and examples of practical applications.

• Post on a social media created specifically for the class or share in a private group.

• Each group should present the post to the class and explain the concepts addressed.

Activity 2 - Gamified Mission: Hacking the Graphs! 里

> Duration: 60 to 70 minutes

- Objective: Engage students in active and collaborative learning, developing problem-solving skills and the use of digital tools for trigonometric functions.

- Description: Students will be divided into groups and participate in a gamified challenge where they need to solve a series of riddles and tasks related to trigonometric functions. Each group will have a set of digital challenges to solve using specific math software, websites, and applications.

- Instructions:

• Form groups of up to 5 students.

• Distribute a set of digital mathematical riddles to each group (can be created on platforms like Google Forms, Kahoot, or Quizizz).

• The riddles should involve recognizing and drawing graphs of trigonometric functions, identifying characteristics such as period, amplitude, shifts, etc.

• Groups will use math software (such as GeoGebra or Desmos) to illustrate and solve the presented problems.

• Each time a riddle is solved, students receive a new clue for the next challenge.

• The group that completes all challenges first wins a digital certificate of 'Master of Trigonometric Graphs'!

Activity 3 - Mathematical Podcast: Exploring Trigonometric Waves ️

> Duration: 60 to 70 minutes

- Objective: Facilitate a deep understanding and communication of the characteristics of trigonometric functions and their graphs through an accessible and collaborative format.

- Description: Students will create and record a podcast episode where they discuss trigonometric functions, their graphs, and applications. They will explore how the graphs can be interpreted and used in various contexts, from music to engineering, providing an auditory and collaborative learning experience.

- Instructions:

• Form groups of up to 5 students.

• Each group should choose a type of trigonometric function to explore (sine, cosine, or tangent).

• Students should discuss and plan the content of the episode, including an introduction about the chosen function, explanations about its graphs, and at least two examples of practical application.

• Use audio recording apps (such as Anchor or Audacity) to record the episode.

• Include in the podcast fictional interviews with 'experts' (group members) or debates about the trigonometric functions.

• Each group can edit the audio adding effects and background music to make it more engaging.

• Episodes should be shared on a specific platform for the class or presented in class.

Feedback

Duration: 15 to 25 minutes

The purpose of this stage is to consolidate and reflect on the knowledge acquired during the lesson, promoting a deeper understanding through the sharing of experiences and constructive feedback. This final discussion allows students to value collaborative work and recognize the different perspectives and approaches used by their peers, as well as highlighting the importance of trigonometric functions in various practical contexts.

Group Discussion

Promote a group discussion with all students, where each group shares their experiences and conclusions while performing the activities. Use the following script to introduce the discussion:

1. Introduction: Remind the objectives of the lesson and what was accomplished in each activity.
2. Sharing: Invite each group to briefly present the content created (social media post, solved gamified challenges, podcast).
3. Reflection: Ask students what they liked most and what they found challenging in the activities.
4. Conclusion: Summarize the main learnings highlighting the importance of trigonometric functions in different contexts.

Reflections

1. What were the main difficulties encountered in creating and interpreting the graphs of trigonometric functions? 2. How did digital tools assist in understanding trigonometric functions? 3. In what way did the practical activities help strengthen the understanding of theoretical concepts?

360° Feedback

Instruct students to carry out a 360° feedback step, where each group member gives and receives feedback from other peers. Guide students to focus on constructive critiques and suggestions for improvement, using questions like:

1. What did I do well?
2. What could I have done better?
3. How can I improve in future activities?
4. Instruct students to be respectful and value the efforts of all members.

Conclusion

Duration: 10 to 15 minutes

 Purpose of the Conclusion 

The purpose of this stage is to summarize the main learnings in a fun and accessible way, reinforcing the practical relevance of the concepts covered. It is the moment to connect the dots, showing students how the knowledge acquired can be applied in their daily lives and future careers, encouraging continuous and contextualized learning.

Summary

 Lesson Summary: Roller Coaster of Trigonometric Functions! 

Today, students embarked on a mathematical adventure where they explored the ups and downs of trigonometric functions, such as the Sine and Cosine waves. The crew dove headfirst into graphs, drawing and interpreting each curve and wave. From mesmerizing social media posts, through digital riddle games, to creating mathematical podcasts, students became masters in the art of deciphering and creating graphs of trigonometric functions!

World Connection

 Connection to the Current World 

In this digital age, where everything is a click away, understanding the mathematics behind the graphs connects directly with various modern fields - from animations in video games to sound waves on music platforms, and even in the fluctuations of the financial market. Showing these practical applications helps make learning more tangible and relevant for students.

Practical Application

 Importance in Daily Life 

Trigonometric functions are not just abstract concepts; they are present in many aspects of everyday life. From civil engineering, which uses these graphs to plan bridges and buildings, to medicine, where they are applied in analyzing brain and heart waves, the ability to interpret and draw trigonometric graphs is a valuable skill applicable in many professions and personal projects.