Objectives (5 - 7 minutes)

1. Understand the concept of compound interest and its practical applicability, recognizing the difference between simple interest and compound interest.

2. Apply the compound interest formula to calculate the final amount of an investment or loan, taking into account the time and interest rate.

3. Solve practical problems involving compound interest, using problem-solving strategies and critical thinking skills.

Secondary Objectives:

• Develop the ability to work with complex mathematical formulas logically and systematically.

• Stimulate the ability to analyze and interpret numerical data in financial contexts.

• Promote understanding of the importance of compound interest in the financial world and how it affects investment and loan decisions.

Introduction (10 - 15 minutes)

1. The teacher starts the lesson by reviewing the concepts of simple interest, which were studied in the previous class. He may ask quick questions to verify if the students remember the fundamental concepts, such as the formula for calculating simple interest and how they are applied in practical situations. (2 - 3 minutes)

2. Next, the teacher proposes two problem situations to introduce the topic of compound interest. The first may involve an investment scenario, where the student needs to calculate the Return on an investment over several years. The second may be a loan scenario, where the student needs to calculate the final amount to be paid on a loan with interest. The teacher should not provide the formula to solve these situations, but rather allow the students to try to find a solution using their knowledge of simple interest. (5 - 7 minutes)

3. Next, the teacher introduces the need for a new concept - compound interest - to solve these situations more accurately. He can give a brief explanation of what compound interest is and how it differs from simple interest. The teacher can also mention that compound interest is widely used in real financial situations, such as bank loans, investments, and credit cards. (2 - 3 minutes)

4. To capture the students' attention, the teacher can share two curiosities about compound interest. The first is that Albert Einstein once stated that 'compound interest is the most powerful force in the universe' - a statement that emphasizes how significant and ubiquitous this concept is. The second curiosity is the story of the mathematician Leonardo Fibonacci, who supposedly invented the Fibonacci sequence to solve a problem related to compound interest. These stories can help illustrate the relevance and history of the topic. (1 - 2 minutes)

5. Finally, the teacher presents the Learning Objectives for the lesson and how they will be achieved. He should ensure that students understand the importance of mastering the concept of compound interest for their mathematical skills, as well as for their understanding of the financial world. (1 - 2 minutes)

Development (20 - 25 minutes)

Activity 1: The Compound Interest Game (10 - 15 minutes)

1. The teacher divides the class into groups of 3 to 4 students and gives each group a 'game kit' containing:

   • Cards with different compound interest scenarios (for example, a loan to buy a car, an investment in stocks, credit card debt, etc.). Each card has information such as the initial amount, the interest rate, and the time.

   • 'Money' chips representing the initial value of the scenario.

2. The students' task is to calculate the final amount after a certain period of time, using the compound interest formula. They should use the money chips to represent the calculated final amount.

3. The teacher explains the rules of the game:

   • Each group must choose a 'banker' who will be responsible for calculating compound interest and distributing the money chips.

   • The other group members are the 'investors' and must help the banker perform the calculations.

   • The goal of the game is to accumulate the highest final amount possible after the determined time (for example, 5 rounds of 1 minute each).

4. The teacher starts the game, setting a time for each round. During the game time, the teacher circulates around the room, observing the groups' interactions and providing assistance as needed.

5. After the determined time, the teacher stops the game and asks each group to count their money chips. The group with the highest final amount is declared the winner.

6. The teacher leads a post-game discussion, where students share their strategies, difficulties encountered, and insights gained. The teacher also takes the opportunity to reinforce the concepts of compound interest and clarify any misunderstandings.

Activity 2: Application of Compound Interest in the Real World (10 - 15 minutes)

1. After the game, the teacher proposes an activity applying compound interest in the real world. He presents students with a series of real financial scenarios (for example, a mortgage, a college savings plan, a retirement investment plan, etc.) and asks students to calculate the final amount in each scenario using the compound interest formula.

2. Students work in their groups to solve the problems. They can use calculators if necessary, but are encouraged to do the calculations manually to reinforce the understanding of the process.

3. After a set time, the teacher gathers the class and asks a representative from each group to share their solutions and strategies. The teacher provides feedback and clarifies any doubts.

4. To conclude the activity, the teacher asks students to reflect, in their groups, on the importance of compound interest in their daily lives and how they can apply what they have learned in their own financial decisions. Some examples of questions to guide the discussion could be: 'How do compound interest affect your savings?' and 'How can you use the concept of compound interest to make more informed financial decisions?'.

5. The teacher concludes the activity by highlighting the relevance and applicability of compound interest in the real world and reinforces the importance of mastering this concept for financial literacy.

Return (10 - 12 minutes)

1. The teacher begins the Return phase by asking students to share their solutions and conclusions from the activities. He can start by inviting a member of each group to briefly share the strategy used in the 'Compound Interest Game' and how they applied the compound interest formula to calculate the final amount. Then, the teacher asks students to reflect on the difficulties encountered and the strategies that were helpful in overcoming them. (3 - 4 minutes)

2. The teacher then gives a brief review of the key concepts covered in the lesson, highlighting the difference between simple interest and compound interest, the formula for calculating compound interest, and how to apply it to solve problems. He also reinforces the importance of understanding and being able to apply this concept in the real world, especially in financial situations. (2 - 3 minutes)

3. Next, the teacher proposes that students reflect individually on what they learned in the lesson. He can ask questions like: 'What was the most important concept you learned today?', 'What questions have not been answered yet?' and 'How do you plan to apply what you learned about compound interest in your daily life?'. Students have a minute to think about these questions. (1 - 2 minutes)

4. After individual reflection, the teacher asks students to share their answers with the class. He can choose some answers to discuss as a group, encouraging the participation of all students. During the discussion, the teacher can clarify any misunderstandings, provide additional feedback, and highlight the relevance of compound interest in daily life. (3 - 4 minutes)

5. Finally, the teacher concludes the lesson by summarizing the main points discussed and reinforcing the importance of practicing and reviewing the concept of compound interest. He may also suggest additional resources, such as websites, books, or videos, for students who wish to deepen their knowledge on the subject. (1 - 2 minutes)

Conclusion (3 - 5 minutes)

1. The teacher begins the Conclusion of the lesson by reinforcing the main concepts covered and the skills developed. He may recall the difference between simple interest and compound interest, the formula for calculating compound interest, and how to apply it in practical situations. Additionally, the teacher highlights the critical thinking and problem-solving skills that students exercised throughout the lesson. (1 - 2 minutes)

2. Next, the teacher connects theory with practice, highlighting how the activities carried out in the lesson illustrated the application of compound interest in the real world. He may emphasize the impact of these concepts on everyday financial decisions, such as loans, investments, and savings. The teacher may also underscore the relevance of compound interest in the global financial system. (1 - 2 minutes)

3. To conclude, the teacher suggests additional materials for students who wish to deepen their knowledge of compound interest. This may include books, websites, videos, or educational games related to the topic. The teacher may also suggest additional compound interest exercises for practice at home. He should emphasize the importance of regular review and practice to ensure understanding and retention of the content. (1 - 2 minutes)

4. The teacher concludes the lesson by reinforcing the importance of compound interest in the real world and encouraging students to apply what they have learned in their daily lives. He may mention specific examples of how understanding compound interest can benefit students, such as making informed financial decisions, effective money management, and building wealth over time. (1 - 2 minutes)