Objectives (5 minutes)

The teacher will begin the lesson by stating and explaining the objectives:

1. Understand the concept of a function and how it is used in mathematics.
2. Identify and differentiate between the four types of functions: linear, quadratic, exponential, and trigonometric.
3. Apply knowledge of these functions to solve basic mathematical problems.

Secondary objectives:

1. Develop skills in critical thinking and problem-solving.
2. Foster an appreciation for the application of these mathematical functions in real-life situations.
3. Encourage collaborative learning through group activities and discussions.

At the end of this stage, the teacher will briefly recap these objectives to ensure the students understand what is expected of them by the end of the lesson.

Introduction (10 - 15 minutes)

• The teacher will start by refreshing the students' memory on the concept of a function, which they would have learned in their previous math classes. This can be done by giving simple examples like the relation between the number of hours worked and the amount of money earned, or the relation between the speed of a car and the distance it covers.

• To engage the students and pique their interest, the teacher will suggest two problem situations:

  1. A local bakery sells cupcakes and doughnuts. How can we represent the money earned by the bakery as a function of the number of cupcakes and doughnuts sold?
  2. A group of students is planning a charity run. They want to know how much money they can collect based on the number of participants. How can we represent this situation using a function?

• To further contextualize the importance of the subject, the teacher will mention real-world applications of functions. For instance, in Physics, the trajectory of a basketball shot can be modeled using a quadratic function, while in Economics, the growth of a company's profit over time can be represented using an exponential function.

• To introduce the topic and grab the students' attention, the teacher will share two interesting facts:

  1. The invention of functions dates back to the 17th century when mathematicians were trying to understand the motion of planets around the sun.
  2. The trigonometric functions we will learn, such as sine and cosine, are used in a variety of fields, including Engineering, Physics, and Computer Science, for analyzing periodic phenomena like sound and light waves.

• At the end of the introduction, the teacher should ensure that the students have a basic understanding of what a function is and how it is applied in various fields. The teacher will also clarify that they will be learning about different types of functions and how to use them to solve problems.

Development (15 - 20 minutes)

In this phase, students will explore the concept of the different types of functions through immersive and playful activities designed to enhance their understanding. These activities will allow students to apply their theoretical knowledge.

Activity 1 - Role-Play Game: "Acting Functions" (8 - 10 minutes)

The classroom will be divided into four groups with each representing a type of mathematical function (Linear, Quadratic, Exponential, and Trigometric). They are actors playing functions on a stage represented by an XY-plane on the classroom floor.

• Each group will be provided a set of ordered pairs (x, y) that represent their assigned function and will use these to understand the progression of their specific function type.
• Each group member will represent an instance (point) of the function on the provided XY-plane by standing at the proper coordinates. The rest of the class will visualize the function's graph.

Following the activity, the teacher will assist in drawing each of these graphs on the board to consolidate the learning and facilitate a discussion on the characteristics of each type of function: linear shows constant rate of change, quadratic forms a parabola, exponential grows rapidly, and trigonometric functions have a periodic nature.

Activity 2 - Card Sort Activity: "Sorting Functions" (7 - 10 minutes)

To further consolidate the understanding of function types, the teacher will provide each group with a deck of cards. Each card in the deck will have a graph of one of the function types, or a problem situation that can be modelled by one of the function types.

• Students, working cooperatively, are required to sort these cards into four piles corresponding to the function types.
• Once they complete sorting, they will be asked to discuss their reasons for each sorting choice.
• After the discussion, the teacher will help correct any misconceptions, explaining why each card belongs to its designated pile.

By performing these hands-on activities, students will visually and physically engage with the concepts of the four types of functions, reinforcing their understanding through active participation.

Wrap-up and Review (5 minutes)

For the final part of the lesson, the teacher will facilitate a whole-class discussion where each group shares their learning and observations from the activities. They will discuss the characteristic of each function type and real-life applications, highlighting again how mathematical functions are not abstract concepts but are integrated into daily life. The teacher concludes by highlighting the crucial role functions play in various scientific and engineering fields, thereby linking their mathematical learning with potential career paths.

These active learning methods aim to ensure that students acquire a robust understanding of mathematical functions, equipping them to understand more complex mathematical concepts and solve problems going forward.

Feedback (5 - 10 minutes)

• The teacher will begin by asking each group to share the solutions or conclusions they reached during the activities. This should be an open-ended discussion, encouraging all students to participate and voice their thoughts, fostering an environment of collaborative learning.
• The teacher will assist in connecting the practical hands-on activities with the theoretical knowledge the students have gained. They will facilitate a discussion on how the activities helped them understand the different types of functions and their characteristics.
• To further assess the students' understanding, the teacher will pose some questions. For instance, they could ask a group to explain why they classified a certain card under a specific function type during the card sort activity. This will help the teacher identify any lingering misconceptions and address them promptly.
• The teacher will encourage students to reflect on the day's lesson by asking them to write down the answer to three questions in their notebooks:
  1. What was the most important concept learned today?
  2. Which questions have not yet been answered?
  3. How would you explain the types of functions to a friend who missed today's class?
• After giving the students a few minutes to write, the teacher will ask for volunteers to share their answers. This will provide the teacher with valuable feedback on what the students have taken from the lesson and what areas may need more attention in future classes.
• To conclude, the teacher will summarize the key takeaways from the lesson and remind the students to review their notes at home. They will also remind the students that understanding functions is fundamental to higher-level math and encourage them to approach the teacher or their classmates if they have further questions as they review the material.
• Finally, the teacher will let the students know that they will be using their new knowledge about functions in future lessons and real-life applications, emphasizing the importance and relevance of the concepts covered in the class.

Conclusion (5 minutes)

• The teacher will commence the concluding part of the lesson by summarizing the main concepts presented throughout the class. They will remind the students of the basic concept of a function in mathematics and then recap each type of function (linear, quadratic, exponential, and trigonometric) with their unique characteristics. The teacher will use the graphs drawn on the board during the activities as visual aids for this recap.

• The teacher will explain how the lesson connected theory to practice by referring back to the activities conducted during the lesson. They will emphasize the role-play game and how it physically represented the progression of each function type on an XY-plane. They will also mention the card sorting activity, and how it helped students to identify and differentiate between the four types of functions.

• To further solidify the students' understanding of the topic, the teacher will suggest additional materials for self-study. They might recommend interactive online resources like Khan Academy and Desmos, where students can explore different types of functions interactively. They may also suggest relevant chapters from the student's textbook and other math resources for further reading and practice.

• Finally, the teacher will elaborate on how understanding functions is not just an academic exercise but a practical tool that is indispensable in everyday life. They will reiterate some of the real-life scenarios where functions apply, such as in physics to model the trajectory of a basketball shot, or in economics to represent the growth of a company's profit over time. The teacher will also mention how knowledge of functions opens up potential career paths in engineering, physics, computer science, and more.

• The teacher will conclude the lesson by encouraging the students to continue exploring the fascinating world of functions and reminding them that the doors of curiosity are always open for them to ask questions and learn more.