Lesson Plan | Traditional Methodology | Percentage: Successive Percentages

Objectives

Duration: (5 - 10 minutes)

The purpose of this stage of the lesson plan is to present the main objectives of the topic of successive percentages to the students, preparing them for the content that will be covered. By clearly establishing what is expected for them to learn, students can focus their attention and efforts on the specific skills needed to solve problems involving sequential percentage calculations.

Main Objectives

1. Understand the concept of successive percentages and how they are applied.

2. Learn to solve problems involving successive discount calculations on the same amount.

3. Develop skills to interpret and solve practical daily life issues involving successive percentages.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to contextualize the topic of successive percentages, making it relevant and interesting for the students. By presenting a practical and everyday example, students can see the direct application of the content in their lives, which increases engagement and understanding. Additionally, curiosity about other practical applications reinforces the importance of the topic.

Context

To start the lesson on successive percentages, present students with a daily scenario: imagine they are buying clothes in a store that is offering different discounts on consecutive days. For example, a coat that costs R$200.00 has a 20% discount on Monday and, if it’s not sold, will have an additional 10% discount on Tuesday. How to calculate the final price of the coat after both discounts? This type of situation is common in sales and promotions, and understanding how to calculate these successive discounts is a valuable practical skill for everyday life.

Curiosities

It is interesting to note that successive percentages are not only used in discounts but also in areas such as economics, where compounded growth rates are calculated for investments and loans. For example, an investment that grows by 5% per year for three years does not result in a total growth of 15%, but rather in compounded growth, which is greater. This shows the importance of understanding how successive percentages work in the real world.

Development

Duration: (60 - 70 minutes)

The purpose of this stage of the lesson plan is to provide a detailed and clear explanation of the concept of successive percentages, using practical examples and mathematical formulas. By the end of this section, students should be able to apply the knowledge gained to solve problems involving sequential percentage calculations, both in sales discount contexts and in compound growth.

Covered Topics

1. Definition of Successive Percentages: Explain the concept of successive percentages, highlighting that it involves calculating percentages of a value that has already been altered by a previous percentage. 2. Basic Example: Present a simple example of calculating successive percentages, such as a 10% discount followed by an additional 20% discount on a product. 3. Mathematical Formula: Detail the mathematical formula for calculating successive percentages: If an initial value is 'P' and receives a discount of 'x%' followed by a discount of 'y%', the final value 'F' is given by: F = P * (1 - x/100) * (1 - y/100). 4. Successive Discounts in Sales: Show how to apply the formula to calculate final prices after multiple discounts using examples from sales and promotions. 5. Applications in Compound Growth: Explain how successive percentages are used in contexts of compound growth, such as investments, where the growth rate is applied to the accumulated value year after year.

Classroom Questions

1. A product costs R$250.00 and has two successive discounts of 15% and 10%. What is the final price of the product? 2. An initial investment of R$1,000.00 grows by 5% per year. What will the amount be after two years? 3. A store offers a 20% discount on an item costing R$500.00. If the item is unsold, the discount will increase to 30% the next day. What will the item's price be after both discounts?

Questions Discussion

Duration: (15 - 20 minutes)

The purpose of this stage of the lesson plan is to review and consolidate students' understanding of the concept of successive percentages, clarifying doubts and reinforcing learning through detailed discussion of the solved questions. This interaction promotes a deeper understanding and practical application of the content.

Discussion

• Question 1: A product costs R$250.00 and has two successive discounts of 15% and 10%. What is the final price of the product? Answer: First, calculate the price after the first 15% discount. This is done by multiplying R$250.00 by (1 - 0.15), resulting in R$212.50. Then, apply the second 10% discount on this new value by multiplying R$212.50 by (1 - 0.10), resulting in R$191.25. Therefore, the final price of the product is R$191.25. Detailed Steps: Calculate 15% of R$250.00: R$250.00 * 0.15 = R$37.50. Subtract the discount from the original value: R$250.00 - R$37.50 = R$212.50. Calculate 10% of R$212.50: R$212.50 * 0.10 = R$21.25. Subtract the discount from the new value: R$212.50 - R$21.25 = R$191.25.

• Question 2: An initial investment of R$1,000.00 grows by 5% per year. What will the amount be after two years? Answer: First, calculate the amount after the first year by multiplying R$1,000.00 by (1 + 0.05), resulting in R$1,050.00. Then, calculate the amount after the second year by multiplying R$1,050.00 by (1 + 0.05), resulting in R$1,102.50. Therefore, the value of the investment after two years will be R$1,102.50. Detailed Steps: Calculate 5% of R$1,000.00: R$1,000.00 * 0.05 = R$50.00. Add the growth to the original value: R$1,000.00 + R$50.00 = R$1,050.00. Calculate 5% of R$1,050.00: R$1,050.00 * 0.05 = R$52.50. Add the growth to the new value: R$1,050.00 + R$52.50 = R$1,102.50.

• Question 3: A store offers a 20% discount on an item that costs R$500.00. If the item remains unsold, the discount will increase to 30% the next day. What will the item's price be after both discounts? Answer: First, calculate the price after the first 20% discount. This is done by multiplying R$500.00 by (1 - 0.20), resulting in R$400.00. Then, apply the second 30% discount on this new value by multiplying R$400.00 by (1 - 0.30), resulting in R$280.00. Therefore, the final price of the item is R$280.00. Detailed Steps: Calculate 20% of R$500.00: R$500.00 * 0.20 = R$100.00. Subtract the discount from the original value: R$500.00 - R$100.00 = R$400.00. Calculate 30% of R$400.00: R$400.00 * 0.30 = R$120.00. Subtract the discount from the new value: R$400.00 - R$120.00 = R$280.00.

Student Engagement

1. 📊 Reflection: Ask students what everyday situations they can imagine where successive percentages would be useful. 2. 🛒 Discussion: Question students about other forms of discounts and promotions they have seen in stores and how they would calculate the final prices. 3. 💡 Curiosity: Request students to give examples of how understanding successive percentages can be useful in their future lives, such as in investments or loans. 4. ❓ Question: How does the order of discounts affect the final price? If we swapped the order of the discounts in Question 1, would the result be the same? 5. 📈 Analysis: Ask students to compare simple growth with compound growth and discuss the differences between them.

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to summarize the main points covered during the lesson, reinforce the connection between theory and practice, and highlight the importance of the content for the students' lives. This ensures that students leave the lesson with a clear and applicable understanding of the topic studied.

Summary

• Understanding successive percentages and their application in discounts and compound growth.
• Utilization of the mathematical formula to calculate final values after multiple percentages.
• Resolution of practical problems involving successive discounts and investment growth.
• Detailed discussion of practical examples, such as discounts on products and compound investment growth.

The lesson connected theory with practice by using everyday examples, such as store discounts and investment growth, to illustrate how successive percentages are applied in real life. This helped students see the relevance of the content learned and understand how to use it in practical situations.

Understanding successive percentages is fundamental for making informed financial decisions, such as calculating the final price of discounted products or predicting investment growth over time. These skills are essential not only for daily life but also for comprehending broader economic concepts and making efficient financial planning.