Lesson Plan | Traditional Methodology | Operations: Problems with Rational Operations

Objectives

Duration: (10 - 15 minutes)

This stage aims to provide a clear and objective overview of what will be learned during the lesson and which skills students should develop. Defining objectives helps guide both the teacher and the students, establishing clear expectations and focusing on the essential aspects of the content to be addressed.

Main Objectives

1. Teach students to solve problems involving basic operations with rational numbers (addition, subtraction, multiplication, and division).

2. Demonstrate the practical application of operations with rational numbers in everyday situations, such as calculating expenses in a supermarket or filling up the fuel tank.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to capture students' attention by contextualizing the lesson's theme with relevant day-to-day examples. This helps to demonstrate the practical importance of the content to be learned, making the lesson more interesting and engaging.

Context

To start the lesson, present students with a practical, everyday situation: imagine you are in a supermarket with your family and need to calculate the total value of the groceries. Each product has a different price and often the prices include cents. Additionally, you may find promotions like 'buy 3, pay for 2', which require performing mathematical operations to know the exact amount to be paid. Another example is when we need to calculate the total cost of filling the car's tank, considering the price of fuel per liter and the amount needed to fill the tank.

Curiosities

Did you know that operations with rational numbers are widely used in various professions? For example, engineers calculate materials and costs, economists evaluate expenses and revenues, and even chefs adjust recipes to serve different numbers of people. Understanding how to manipulate these numbers is crucial for success in many areas of life.

Development

Duration: (60 - 65 minutes)

The purpose of this stage is to detail and explain operations with rational numbers, providing a solid theoretical foundation and practical examples so that students fully understand how to perform these operations. Additionally, solving practical problems helps to solidify knowledge and demonstrates the utility of rational operations in everyday situations. This stage is crucial to ensure that students are capable of applying what they have learned in various contexts.

Covered Topics

1. Introduction to Rational Numbers: Explain what rational numbers are, including fractions, decimals, and integers. Detail that rational numbers are those that can be written as a fraction of two integers, where the denominator is not zero. 2. Addition and Subtraction of Rational Numbers: Demonstrate how to perform addition and subtraction of fractions with like and unlike denominators. Show practical examples to illustrate the process of finding a common denominator and adjusting fractions before adding or subtracting. 3. Multiplication of Rational Numbers: Explain the process of multiplying fractions, emphasizing that you simply multiply the numerator by the numerator and the denominator by the denominator. Present examples to reinforce understanding. 4. Division of Rational Numbers: Detail the process of dividing fractions, which involves multiplying by the inverse fraction. Provide clear examples to demonstrate this operation. 5. Practical Application in Everyday Problems: Show how to apply these operations in real problems, such as calculating the total spent on groceries or the cost of filling up the fuel tank. Present detailed problem situations and guide step-by-step resolution.

Classroom Questions

1. 1. João bought 3.5 kg of fruit for R$ 12.75 and 2.25 kg of vegetables for R$ 8.50. How much did he spend in total? 2. 2. Maria has 1.75 liters of juice and wants to divide it equally among 5 friends. How many liters of juice will each friend receive? 3. 3. A fuel tank has a capacity of 45.5 liters. If the price per liter of fuel is R$ 4.30, how much does it cost to fill the tank completely?

Questions Discussion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the knowledge acquired, allowing students to reflect on what they have learned and discuss their answers. This provides immediate feedback and helps clarify any remaining questions, ensuring a complete understanding of the content.

Discussion

• Question 1: João bought 3.5 kg of fruit for R$ 12.75 and 2.25 kg of vegetables for R$ 8.50. How much did he spend in total?

Solution: First, we add the amounts: R$ 12.75 + R$ 8.50 = R$ 21.25. Therefore, João spent R$ 21.25 in total.

• Question 2: Maria has 1.75 liters of juice and wants to divide it equally among 5 friends. How many liters of juice will each friend receive?

Solution: We divide the total amount of juice by the number of friends: 1.75 / 5. To make it easier, we can convert 1.75 to a fraction: 1.75 = 7/4. So, 7/4 ÷ 5 = 7/4 * 1/5 = 7/20. Converting back to decimal: 7/20 = 0.35 liters. Therefore, each friend will receive 0.35 liters of juice.

• Question 3: A fuel tank has a capacity of 45.5 liters. If the price per liter of fuel is R$ 4.30, how much does it cost to fill the tank completely?

Solution: We multiply the tank's capacity by the price per liter of fuel: 45.5 * 4.30. To make it easier, we can break down the multiplication: 45.5 = 45 + 0.5. So, 45 * 4.30 + 0.5 * 4.30 = 193.5 + 2.15 = 195.65. Therefore, it costs R$ 195.65 to fill the tank completely.

Student Engagement

1. 1. Why is it important to know how to perform operations with rational numbers in everyday situations? 2. 2. How can you apply what you learned today in other areas of your life? 3. 3. What other everyday situations might require the use of operations with rational numbers? 4. 4. Did you encounter any difficulties when solving the problems? If so, which ones? 5. 5. How can understanding rational operations help in your future professional career?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to reinforce and consolidate the knowledge acquired during the lesson, providing a review of the main points covered. This helps to solidify the content and ensure that students understand the importance and practical application of operations with rational numbers.

Summary

• Introduction to rational numbers, including fractions, decimals, and integers.
• Addition and subtraction of rational numbers with like and unlike denominators.
• Multiplication of rational numbers by multiplying numerators and denominators.
• Division of rational numbers by multiplying by the inverse fraction.
• Practical application of operations with rational numbers in everyday problems.

The lesson connected theory with practice by demonstrating how operations with rational numbers are used in everyday situations, such as calculating the total value of groceries in the supermarket or the cost to fill the fuel tank. Practical problems were presented and step-by-step resolution was guided, facilitating students' understanding of the applicability of the content learned.

Understanding operations with rational numbers is fundamental for daily life, as these operations are present in various everyday activities, such as calculating expenses, dividing food among people, or even adjusting recipes in the kitchen. Additionally, these skills are essential in various professions, from engineering to economics, making this knowledge valuable and practical.