Lesson Plan | Teachy Methodology | Function: Even or Odd

Objectives

Duration: 10 - 15 minutes

This stage aims to present the fundamental concepts of even and odd functions clearly and objectively, emphasizing the importance of correctly identifying these types of functions for solving mathematical problems. This understanding will serve as a foundation for practical and dynamic activities throughout the lesson.

Main Objectives

1. Understand what an even function is (f(x)=f(-x))

2. Understand what an odd function is (f(x)=-f(-x))

3. Check if a given function is even, odd, or neither

Side Objectives

Introduction

Duration: 10 - 15 minutes

This stage aims to activate students' prior knowledge and engage them from the beginning of the class. By searching for interesting facts about even and odd functions, students connect the studied concepts with reality and perceive the relevance of the topic. Furthermore, the initial debate with key questions establishes a common knowledge base and prepares students for the subsequent practical activities.

Warming Up

To start the class, explain to students that even and odd functions are essential mathematical concepts found in various contexts, from graph analysis to solving equations. Ask students to use their phones to search for an interesting fact about even or odd functions, such as a practical application of these concepts in the real world or a curiosity related to them. Encourage students to share what they found with the class.

Initial Reflections

1. What distinguishes an even function from an odd function?

2. How can we identify an even function just by looking at its graph?

3. Why is it important to distinguish between even and odd functions?

4. What are some examples of even and odd functions that you have seen before?

5. Is there any practical application of these functions that you found during your research?

Development

Duration: 70 - 80 minutes

This stage aims to lead students to apply the theoretical concepts of even and odd functions practically and contextually, using modern technologies and dynamics to make learning interactive and engaging. The proposed activities aim to develop collaboration, creativity, and problem-solving skills while deepening students' mathematical knowledge.

Activity Suggestions

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

Activity 1 - Digital Influencers of Functions

> Duration: 60 - 70 minutes

- Objective: Apply mathematical concepts in a practical and contextualized way, using popular digital platforms to engage and educate.

- Description: Students become mathematical digital influencers. In groups of up to 5 people, they will create and post a short video on TikTok or Instagram Reels explaining and demonstrating an even function and an odd function. The goal is to make the content accessible, interesting, and viral. The videos should use visual examples, graphs, and practical explanations to engage the audience.

- Instructions:

• Form groups of up to 5 students.

• Choose a social media platform (TikTok or Instagram Reels).

• Assign roles within the group (e.g., presenter, editor, researcher).

• Create a script explaining the concepts of even and odd functions.

• Film and edit the video using editing tools available on phones or computers.

• Incorporate graphs, visual examples, and animations to illustrate the concepts.

• Post the video using relevant hashtags and tag the school.

• Monitor engagement and comments, ready to respond to audience questions.

Activity 2 - Programming Challenge: Even or Odd?

> Duration: 60 - 70 minutes

- Objective: Develop programming skills and practical application of mathematical concepts, promoting logical thinking and teamwork.

- Description: Students will use an online programming platform (like Scratch, Repl.it, or any other accessible programming tool) to create a program or game that identifies functions as even or odd. In groups of up to 5 people, they will develop the code and test the program to ensure it works correctly.

- Instructions:

• Form groups of up to 5 students.

• Choose the online programming platform to be used.

• Assign roles within the group (e.g., developer, tester, documenter).

• Develop the algorithm that checks if a function is even, odd, or neither.

• Code the algorithm in the chosen platform.

• Test the program with different functions and adjust as necessary.

• Document the process and the results of the program.

• Present the completed program to the class, explaining its functioning and the results obtained.

Activity 3 - Graphic Adventure: Exploring Functions

> Duration: 60 - 70 minutes

- Objective: Integrate mathematics with creative narrative and game design, promoting understanding of concepts through gamification.

- Description: Students will create an interactive graphic adventure using tools like Twine or Google Slides. The story will involve exploring a world where characters encounter different obstacles representing even and odd functions. Players will need to solve mathematical puzzles to progress in the story.

- Instructions:

• Form groups of up to 5 students.

• Choose the tool to create the graphic adventure (Twine, Google Slides, etc.).

• Assign roles within the group (e.g., writer, graphic designer, programmer).

• Develop the narrative of the story, including obstacles that represent even and odd functions.

• Create graphs and visual elements to make the story interactive and engaging.

• Program the mathematical puzzles that need to be solved to advance in the story.

• Test the graphic adventure ensuring all elements work correctly.

• Present the graphic adventure to the class, explaining the concept of each encountered mathematical obstacle.

Feedback

Duration: 20 - 25 minutes

The purpose of this stage is to consolidate learning through sharing experiences and reflections, as well as to promote personal and collective growth through constructive feedback. This process helps students recognize their strengths and areas for improvement, encouraging a culture of collaboration and mutual respect.

Group Discussion

Promote a group discussion with all students. Encourage each group to share what they learned during the activities, highlighting challenges faced, discoveries made, and the application of the concepts of even and odd functions. A brief script to introduce the discussion can be: 'Now that we have completed the practical activities, let's share our experiences. Each group, please talk about what you learned, the challenges you faced, and how you applied the concepts of even and odd functions. How did these activities help you better understand the topic?'

Reflections

1. What were the greatest difficulties encountered during the activities? How did you overcome them? 2. How did the digital methodology used in the activities help in understanding the concepts of even and odd functions? 3. Did you find any connection between the activities carried out and real-world situations?

360° Feedback

Conduct a 360° feedback phase. Ask each student to receive feedback from their group peers on their participation. Guide them to ensure that the feedback is constructive and respectful. Some points to consider are: collaboration, creativity, contribution to the group, and application of mathematical concepts. Introduce the phase with something like: 'Now let's carry out a 360° feedback stage. Each of you will receive feedback from your group peers on your participation in the activities. Remember to be constructive and respectful in your comments. Think about aspects like collaboration, creativity, and application of mathematical concepts.'

Conclusion

Duration: 10 - 15 minutes

The purpose of this stage is to consolidate learning in a playful and memorable way, connecting mathematical concepts with the technological and everyday reality of students. This reinforces the importance of what has been studied, motivating students to apply the knowledge acquired in their daily lives and future careers.

Summary

Let's transform our understanding of even and odd functions into a mathematical adventure!  Imagine that functions are our superheroes: even functions have the ability to mirror perfectly, while odd functions possess the power of a mirrored and inverted transformation!  We showed how to identify these mathematical heroes by observing their graphs and formulas.

World Connection

In the digital age, understanding even and odd functions is more relevant than ever. Social networks, recommendation algorithms, and even data analysis use mathematical concepts to operate efficiently. Understanding these concepts helps to navigate and make better use of the technologies around us. 

Practical Application

By mastering even and odd functions, students gain essential tools for problem-solving in various fields such as engineering, computer science, and economics. These concepts are fundamental for symmetry analysis in graphs and process optimization. 