Objectives (5 - 7 minutes)

The teacher will:

1. Introduce the concept of Mathematical Finance as a discipline that applies mathematical models and methods to financial markets and decision-making.
2. Outline the main goals of the lesson, which are to understand the basic concepts of Mathematical Finance, such as interest, principal, and time, and to apply these concepts in simple financial calculations.
3. Briefly explain the flipped classroom methodology, where students will first study the subject at home using provided online resources, and then apply their knowledge in class through interactive activities.

Secondary objectives:

• Encourage students to develop critical thinking skills by applying mathematical concepts to real-world financial situations.
• Promote collaborative learning by engaging students in group activities during the class.

Introduction (10 - 12 minutes)

The teacher will:

1. Remind students of the concept of interest and compound interest, which they have previously learned in their Mathematics classes. The teacher will use this opportunity to emphasize the importance of these concepts in real-world financial situations. (2 minutes)
2. Present two problem situations to the students:
   • Scenario 1: "Jackie wants to save money to buy a new smartphone. She has $500 and can save $50 per month. If the smartphone costs $800, how long will it take her to save enough money?"
   • Scenario 2: "Michael wants to start a small business. He needs to borrow $1000, and the interest rate is 10% per year. If he pays back the loan in one year, how much will he have to repay, and how much will he save if he pays it back in six months?" (5 minutes)
3. Contextualize the importance of Mathematical Finance by discussing its real-world applications. The teacher can mention how financial institutions, investment firms, and even individuals use mathematical models to make informed financial decisions. (2 minutes)
4. Introduce the topic of the lesson by posing two intriguing questions:
   • "Have you ever wondered how banks decide how much interest to pay on your savings account?"
   • "Do you know why sometimes it's better to pay for something in installments instead of all at once?" (2 minutes)
5. Grab the students' attention by sharing two interesting facts related to Mathematical Finance:
   • Fact 1: "Did you know that the concept of compound interest, which is a fundamental principle in Mathematical Finance, is often attributed to Albert Einstein, who called it 'the most powerful force in the universe'?"
   • Fact 2: "In the world of investing, there's a strategy called dollar-cost averaging, which is a form of Mathematical Finance. It's when an investor buys a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. This strategy can help investors avoid making bad investment decisions based on short-term market fluctuations." (1 minute)

Development

Pre-Class Activities (15 - 20 minutes)

Students will:

1. Watch an engaging educational video on the basics of Mathematical Finance, such as the Khan Academy's "Introduction to Interest" or "Introduction to Compound Interest" (5 - 7 minutes).

2. Read a simplified guide on the concept of interest, principal, time, and their mathematical relationship. The teacher can provide a short article or a chapter from a basic economics textbook (5 - 7 minutes).

3. Take an online quiz to assess their understanding of the pre-class activities. The quiz should include simple questions on interest, compound interest, principal, and time. The teacher can use platforms like Google Forms or Quizizz to create and share the quiz with the students (5 - 6 minutes).

In-Class Activities (20 - 25 minutes)

The teacher will:

Activity 1: "Financial Decision-Making Game" (10 - 12 minutes)

1. Divide students into groups of 4 or 5, ensuring each group has a mix of abilities and skills.

2. The teacher gives each group a hypothetical financial situation (e.g., saving for a car, paying off a loan, planning for a trip), along with the necessary data (initial amount, monthly savings, interest rate if applicable, and the final goal).

3. The teams must use the concepts of interest, principal, and time to determine how long it will take to reach their financial goal. If applicable, they should also calculate the amount they will need to pay back if there is an interest rate involved.

4. Each group presents their solution to the class, explaining their thought process and the calculations they made.

Activity 2: "Financial Story Problems" (10 - 13 minutes)

1. The teacher provides each group with a different financial story problem that requires the application of the learned concepts (e.g. buying a car on installments, saving for college, investing in stocks).

2. Each group discusses the problem, identifies the relevant data, and applies the concepts of interest, principal, and time to solve it.

3. After finding a solution, the groups create a short presentation explaining the problem, their solution, and how they arrived at it.

4. The groups present their problems and solutions to the class, fostering a discussion on different ways to apply Mathematical Finance in different scenarios.

Feedback (8 - 10 minutes)

The teacher will:

1. Facilitate a group discussion where each group shares their solutions or conclusions from the activities. (3 - 4 minutes)

2. Connect the solutions presented by the students with the theoretical concepts of Mathematical Finance, highlighting how the students applied these concepts in their calculations. The teacher should also point out any common errors or misconceptions, and correct them. (3 - 4 minutes)

3. Ask each group to reflect on the most important concept they learned during the lesson and share it with the class. This can help consolidate the learning and provide an opportunity for the teacher to address any remaining questions or concerns. (2 minutes)

The teacher will then:

4. Summarize the key points of the lesson, emphasizing the importance of understanding the concepts of interest, principal, and time in making informed financial decisions. (1 minute)

5. Assign homework that reinforces the concepts learned in class, such as solving more complex financial problems or researching real-world examples of the application of Mathematical Finance. The teacher can provide a list of online resources or a textbook chapter for the students to use. (1 minute)

6. Conclude the lesson by reminding the students that Mathematical Finance is a powerful tool that can help them make informed financial decisions throughout their lives. (1 minute)

This feedback stage is essential for the students to consolidate their learning, understand their mistakes, and reinforce the correct application of Mathematical Finance concepts. It also provides the teacher with valuable insights into the students' understanding, which can guide future instruction.

Conclusion (5 - 7 minutes)

The teacher will:

1. Summarize the main points of the lesson, recapping the basic concepts of interest, principal, and time, and their relationship in Mathematical Finance. The teacher will also reiterate the importance of these concepts in real-world financial decision-making. (2 minutes)

2. Explain how the lesson connected theory, practice, and real-world applications. The teacher will highlight how the pre-class activities introduced the theory, the in-class activities allowed for the practical application of the concepts, and the discussion of real-world financial situations linked the concepts with their practical use. (2 minutes)

3. Suggest additional materials for students who wish to further explore the topic. This could include more advanced videos, articles, books, or online courses on Mathematical Finance. The teacher can also recommend financial planning tools or apps that students can use to apply the concepts in a practical way. (1 minute)

4. Finally, the teacher will remind students of the importance of Mathematical Finance in their everyday lives. They will emphasize how understanding these concepts can help students make better financial decisions, whether it's saving for a purchase, planning for college, or investing in their future. The teacher will also stress that the skills they learned in this lesson are not just for the classroom but are applicable throughout their lives. (2 minutes)

This conclusion stage is crucial for reinforcing the learning objectives, highlighting the connections between theory and practice, and promoting further exploration of the topic. It also helps students understand the relevance of Mathematical Finance in their lives, motivating them to continue learning and applying these concepts.