Objectives (5 minutes)

1. Understand the concept of compound interest: Students should be able to define what compound interest is and how it differs from simple interest. This includes understanding the compound interest formula and how it is applied.

2. Calculate compound interest: After understanding the concept, students should be able to calculate compound interest in different situations. This includes the ability to use the compound interest formula to determine the future value of an investment or loan.

3. Apply compound interest in real-world situations: In addition to calculating compound interest, students should be able to apply this knowledge in practical situations. This may include determining how much money they will have at the end of an investment period, or how much they will have to pay at the end of a loan period.

Secondary objectives:

• Develop problem-solving skills: Through the calculation of compound interest, students will have the opportunity to develop their mathematical problem-solving skills.

• Promote critical thinking: By applying the concept of compound interest to real-world situations, students will be challenged to think critically about how interest rates affect their personal finances.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by recalling the concepts of simple interest and capitalization, which were covered in previous lessons. This review is essential for students to clearly understand and compare the concept of compound interest. (3 - 5 minutes)

2. Presentation of problem situations: Next, the teacher can present two problem situations. The first could be: "If you invest R$ 100.00 in a savings account that pays 5% interest per year, how much money will you have at the end of 5 years?" The second problem situation could be: "If you take out a loan of R$ 500.00 with an interest rate of 10% per month, how much will you have to pay at the end of 6 months?" These situations will help spark students' interest and prepare them for the introduction of the concept of compound interest. (5 - 7 minutes)

3. Contextualization of the importance of the topic: The teacher should then explain that the concept of compound interest is fundamental to understanding how money can grow over time, either through investments or through debts. He can give concrete examples, such as the importance of starting to save early for retirement, or how high interest rates on loans can lead to unsustainable debts. (2 - 3 minutes)

4. Introduction of the topic: To introduce the topic of compound interest, the teacher can tell a brief story about the Italian mathematician Leonardo Fibonacci, who is famous for introducing the Fibonacci numbers, but also made significant contributions to the theory of compound interest. He can mention that Fibonacci was one of the first to realize the importance of compound interest and how it could be used to predict the growth of the rabbit population. This historical introduction can help capture students' attention and contextualize the relevance of the topic. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Theory of Compound Interest (10 - 12 minutes):

   1.1. Definition: The teacher should start by explaining the concept of compound interest, highlighting that it is different from simple interest, as in the case of compound interest, the interest is applied to the initial capital and the interest already accumulated.

   1.2. Formula: Next, the teacher should introduce the compound interest formula:

   - M = C * (1 + i)^n
   

   Where:

   • M is the amount (final value)
   • C is the initial capital
   • i is the interest rate (in decimal form)
   • n is the number of periods (months, years, etc.)

   1.3. Comparison with Simple Interest: The teacher should make a comparison between simple interest and compound interest, showing that, in the case of simple interest, the interest is applied only to the initial capital, while in compound interest, the interest is applied to the initial capital and the interest already accumulated.

   1.4. Explanation of the Concept: The teacher should explain the concept of "interest on interest," which is the main characteristic of compound interest. Practical examples can be used to illustrate the concept, such as the idea that if you invest R$ 100.00 at an interest rate of 10% per year, in the first year you will have R$ 110.00 (R$ 100.00 + R$ 10.00 of interest), but in the second year you will have R$ 121.00 (R$ 110.00 + R$ 11.00 of interest on the R$ 110.00).

2. Practical Examples (5 - 7 minutes):

   2.1. Investment: The teacher should present an example of how to calculate the future value of an investment with compound interest. For example, if you invest R$ 100.00 at an interest rate of 10% per year, how much money will you have at the end of 5 years?

   2.2. Loan: The teacher should present an example of how to calculate the amount to be paid at the end of a loan with compound interest. For example, if you take out a loan of R$ 500.00 at an interest rate of 10% per month, how much will you have to pay at the end of 6 months?

3. Exercise Resolution (5 - 6 minutes):

   3.1. The teacher should propose some exercises for students to practice solving problems involving compound interest. The exercises should vary in difficulty, starting with simple problems and gradually increasing in complexity. The teacher should provide immediate feedback and clarify any doubts that students may have.

   3.2. It is important for students to pay attention to the time unit (months, years, etc.) when solving problems, as this can affect the final result.

   3.3. The teacher should encourage students to share their problem-solving strategies and explain how they arrived at their answers. This not only helps reinforce the concept of compound interest but also promotes collaborative learning and critical thinking.

Return (5 - 7 minutes)

1. Group Discussion (2 - 3 minutes):

   1.1. The teacher should initiate a group discussion, asking students to share their answers or conclusions about the proposed exercises. This will allow students to see different ways of approaching a problem and help consolidate the concept of compound interest.

   1.2. The teacher can ask questions such as: "How would you apply the concept of compound interest in your daily lives?" or "Can you identify compound interest situations around you?".

   1.3. The teacher should encourage students to explain their answers and justify their conclusions. This will help develop their critical thinking and communication skills.

2. Connection with the Real World (2 - 3 minutes):

   2.1. The teacher should then make the connection between the learned theory and the real world. He can give examples of how compound interest is applied in various situations, such as in financial investments, bank loans, car and house financing, among others.

   2.2. The teacher can also talk about the importance of understanding compound interest to make conscious financial decisions. For example, by understanding how compound interest works, students can be more cautious when choosing a loan or more motivated to save and invest their money.

   2.3. The teacher can also ask students to think about situations in their daily lives where understanding compound interest could be useful. For example, when planning how much money they will have at the end of a certain savings period, or when calculating how much they will have to pay at the end of a loan.

3. Final Reflection (1 minute):

   3.1. To conclude, the teacher should ask students to reflect for a minute on what they learned in the lesson. He can ask questions such as: "What was the most important concept you learned today?" and "What questions remain unanswered?".

   3.2. The teacher should emphasize that it is normal to have doubts and that he will be available to clarify them in the next lesson. He can also encourage students to seek additional resources, such as math books or online tutorials, to reinforce what they have learned.

Conclusion (3 - 5 minutes)

1. Recap of Content (1 - 2 minutes):

   1.1. The teacher should recap the main points of the lesson, recalling the concepts of compound interest, the formula for calculating compound interest, and the difference between simple and compound interest.

   1.2. He can also give a brief summary of the exercises solved during the lesson and the practical examples presented.

2. Connection of Theory to Practice (1 - 2 minutes):

   2.1. The teacher should emphasize how the lesson connected the mathematical theory of compound interest to everyday practice.

   2.2. He can recall the problem situations presented at the beginning of the lesson and how the concepts of compound interest were used to solve them.

   2.3. He can also mention again the real-world examples given during the lesson, showing how understanding compound interest can be useful for making financial decisions.

3. Additional Materials (1 minute):

   3.1. The teacher should suggest some extra materials for students who want to deepen their knowledge of compound interest. This may include financial mathematics books, websites with exercises, and online tutorials.

   3.2. He can also suggest that students practice more compound interest exercises at home to reinforce what they learned in the lesson.

4. Importance of the Topic (1 minute):

   4.1. Finally, the teacher should emphasize the importance of compound interest for everyday life.

   4.2. He can give concrete examples, such as the importance of understanding compound interest when planning investments or choosing a loan.

   4.3. He can also mention how understanding compound interest can help students be more conscious in their personal finances, avoiding unsustainable debts and planning their financial future more securely.