Objectives (5 - 10 minutes)

1. Understand the concept of simple interest and its application in the financial context.

2. Understand how the change of values over time occurs, using simple interest as a reference.

3. Apply the concepts of simple interest and change of values over time in practical and real situations, such as the installment purchase of a product, taking out a loan, or making an investment.

   • Secondary Objective: Develop calculation skills and logical-mathematical reasoning.

The teacher should emphasize that the main objectives of the lesson are the understanding of the concept of simple interest and its application, as well as the understanding of the phenomenon of change of values over time. Students should be able to apply these concepts in practical and real situations, which implies the need to develop calculation skills and logical-mathematical reasoning.

Introduction (10 - 15 minutes)

1. Review of previous content: The teacher should start the lesson by briefly reviewing the concepts of percentage and proportion, which are fundamental for understanding simple interest. Additionally, it may be relevant to review the basic formula of simple interest: J = P * i * t, where J is the interest, P is the principal (or capital), i is the interest rate, and t is the time.

2. Problem-solving situations: The teacher can present two problem-solving situations to the students that will be solved throughout the lesson. The first one could be: 'João took out a loan of R$ 1,000.00 at an interest rate of 5% per month. How much will he have to pay at the end of 3 months?'. The second situation could be: 'Maria bought a TV for R$ 2,000.00 in 10 installments of R$ 250.00 each. What is the monthly interest rate she is paying?'.

3. Contextualization: The teacher should explain the importance of financial mathematics in our daily lives, showing that it is present in various situations, such as the installment purchase of products, taking out loans, and making investments. Additionally, it can be mentioned that knowledge about interest and change of values over time is essential for us to make more conscious and informed financial decisions.

4. Engaging students' attention: To spark students' interest, the teacher can share some curiosities or stories related to the lesson's theme. For example, they can tell the story of the Italian mathematician Leonardo Fibonacci, who lived in the 13th century and is famous for the Fibonacci sequence, which has various applications in financial mathematics. Another interesting curiosity is the origin of the term 'interest'. The word comes from the Latin 'usura', which means 'usurpation' or 'illicit gain', and was used to refer to the profit obtained by charging borrowed money.

5. Introduction of the topic: Finally, the teacher should introduce the topic of the lesson - simple interest and change of values over time - in a clear and objective manner, explaining that interest is the remuneration for the use of money and that the change of values over time is a phenomenon that occurs due to interest. It can also be mentioned that, although interest is often seen as something negative, it can also be positive, as in the case of investments.

Development (20 - 25 minutes)

1. Theory of Simple Interest (10 - 15 minutes)

   • Definition of Simple Interest: The teacher should start by explaining what simple interest is. They should emphasize that interest is the remuneration for the use of money and that there are two types: simple interest and compound interest. In the case of simple interest, the interest rate is applied only to the initial amount, not accruing on the accumulated interest.

   • Formula for Simple Interest: The teacher should present the basic formula for simple interest: J = P * i * t, where J is the interest, P is the principal (or capital), i is the interest rate, and t is the time. They should explain each of the variables and how they relate in the formula.

   • Application Examples: The teacher should give examples of how to calculate simple interest. For instance, they can show how to calculate the interest on a loan or the return on an investment. It should be emphasized that for the formula to be applied, it is important that the interest rate is in the same time unit as the term.

2. Change of Values over Time (5 - 10 minutes)

   • Definition of Change of Values over Time: The teacher should explain that the change of values over time is a phenomenon that occurs due to interest. They should show, through examples, how the value of money changes over time due to the application of interest.

   • Application Examples: The teacher should give examples of how the change of values over time can affect our financial decisions. For example, they can show how a small difference in the interest rate can result in a significant difference in the final value of a loan or an investment.

3. Practice of Concepts (5 - 10 minutes)

   • Resolution of Problem-Solving Situations: The teacher should revisit the problem-solving situations presented in the Introduction and, step by step, show how to solve each of them, applying the concepts of simple interest and change of values over time.

   • Questions and Answers: The teacher should encourage students to ask questions and clarify their doubts. They should also ask questions to assess students' understanding and to stimulate everyone's participation.

By the end of this stage, students should be able to understand the concept of simple interest, apply the formula for simple interest, and calculate simple interest in practical situations. Additionally, they should be able to understand the phenomenon of change of values over time and apply this knowledge in real situations.

Return (10 - 15 minutes)

1. Review of Concepts (5 - 7 minutes)

   • The teacher should start this stage by briefly reviewing the main concepts covered during the lesson. For example, they can ask students what they understand by simple interest and change of values over time, and ask them to explain the formula for simple interest. The teacher should then correct any misconceptions and clarify doubts that may still exist.

2. Connection with Theory (3 - 5 minutes)

   • The teacher should then explain how the practice carried out during the lesson connects with the theory. For instance, they can show how the calculations performed in the problem-solving situations are based on the formula for simple interest, and how these calculations allow understanding the phenomenon of change of values over time.

3. Practical Application of Content (2 - 3 minutes)

   • The teacher should then ask students to reflect on how the learned content can be applied in everyday situations. For example, they can ask students if they have ever had to calculate simple interest in a real situation, such as in the installment purchase of a product or when taking out a loan.

   • The teacher should also encourage students to think about other situations where the concepts of simple interest and change of values over time could be useful. For instance, they can ask students how they think these concepts could be applied in making financial decisions, such as choosing between different types of investments or evaluating loan proposals.

4. Final Reflection (1 - 2 minutes)

   • To conclude the lesson, the teacher should ask students to reflect for a minute on the following questions: 'What was the most important concept you learned today?' and 'What questions do you still have on the topic?'. The teacher should then ask some students to share their answers, and they should take this opportunity to clarify any remaining doubts.

By the end of this stage, students should be able to make a connection between theory and practice, understand the applicability of the learned concepts, and reflect on what they have learned. Additionally, the teacher should be able to identify the difficulties and doubts of the students and, thus, plan the next lessons according to their needs.

Conclusion (5 - 10 minutes)

1. Summary of Contents (2 - 3 minutes)

   • The teacher should summarize the main points covered during the lesson, recalling the concepts of simple interest and change of values over time, the formula for simple interest, and how to apply these concepts in practical situations.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes)

   • The teacher should emphasize how the lesson connected theory, practice, and applications. For example, they can mention that the theory was presented through the explanation of concepts and the formula for simple interest, the practice was carried out through the resolution of problem-solving situations, and the applications were discussed throughout the lesson with real and contextualized examples.

3. Extra Materials (1 - 2 minutes)

   • The teacher should suggest some extra materials for students who wish to deepen their knowledge on the topic. These materials may include books, websites, videos, and online exercises. For example, they can suggest reading a chapter from a financial mathematics book, consulting a website with explanations and examples of simple interest, watching an explanatory video on YouTube, and doing some practical exercises.

4. Importance of the Subject (1 - 2 minutes)

   • Finally, the teacher should emphasize the importance of the subject for students' daily lives. They can mention that knowledge about simple interest and change of values over time is essential for making more conscious and informed financial decisions, and that these concepts are present in various everyday situations, such as the installment purchase of products, taking out loans, and making investments.

   • The teacher should also emphasize that financial mathematics, besides being a curricular content, is a powerful tool that can help us better understand and deal with the financial world we live in.

By the end of this stage, students should be able to understand the importance of the learned content, identify the main points of the subject, and know where to seek more information if they desire. Additionally, the teacher should be confident that the students have understood the main concepts of the lesson and are prepared to move on to the next topics in financial mathematics.